I took advantage of Daniele passing by Madrid tomorrow and requesting a meeting to deploy some of the toys I've been working on: the AF tag (we'll meet at 02HUG(af)) as well as connecting it to my Google calendar through af2cal, which is extremely convenient and should win me various minutes every working day. With Daniele, we'll visit a Caixa Forum exhibition on Asurbanipal.
I added a ℤ link to the header of my pages so that I can go there directly without browsing around. I needed a Z though, so I added an adjective to the web with a few Easter eggs. The adjective changes daily as I wouldn't like to pin it to one attribute only, so I went for all of them. 𝕐 doesn't have this problem since the letter is nailed in my name (and in other places too). Today's is "ℤoomers" with tip "Generation X flashing to Generation Z (no Y found in between)." I made it editable on the fly in case I'd want to opinate on the current state.
And so they say – "the incident dissolved"
the love boat smashed up
on the dreary routine.
I'm through with life
and [we] should absolve
from mutual hurts, afflictions and spleen.
Mayakovsky on his deathbed. He looks like Egon, except that his heart is bleeding.
Il dort. Quoique le sort fût pour lui bien étrange,
Il vivait. Il mourut quand il n'eut plus son ange ;
La chose simplement d'elle-même arriva,
Comme la nuit se fait lorsque le jour s'en va.
The distribution of perimeters for a four-photon quadrilateral (projected on the unit circle) is of the type $D_{C_{\boldsymbol\alpha}}(p)=A_0(p)+C_{\boldsymbol\alpha}\,A_1(p)+C_{\boldsymbol\alpha}^2\,A_2(p)$
where $A_0$ is the distribution without correlations (the donut) and $A_i$, $i=1,2$, are fluctuations or deviations around this to account for "correlations" for the given $C_\boldsymbol{\alpha}$. The moments calculated from this distribution will thus invoke $\langle C_\boldsymbol{\alpha}\rangle$ and $\langle C_\boldsymbol{\alpha}^2\rangle$ and since $\langle C_\boldsymbol{\alpha}^2\rangle\neq\langle C_\boldsymbol{\alpha}\rangle^2$, we need another atom to provide for the added correlation.
What is surprising is the quality of the one-atom approximation. You really need a lot of photons $N\gg1$ to see by eye the one-atom approximation fail. Here's an overview for a few representative cases:
What are we lookin at here?
__Z__
in (a), the red is exact (matches the black which is over the full thermal ensemble) but the red is off because it misses one atom. However, to the eye, it looks perfect.
in (b) we see the failure of the green.
in (c) we see the agreement of the red. It doesn't look much better than the actually failing green.
in (d) we have (c) again in a different color as this column shows the case with enough atoms, which is matched on the first row.
in (e) the case of $D_8$ requiring three atoms. This time the green disagreement is a bit visible by eye.
in (f) the one-atom failure for 8-photon observable is clear.
in (g) the two-atom failure for 8-photon observable is not clear (expected, purple). The red seems to be as good as (h).
in (h) the three-atom working case for 8-photon observables. Not clearly better than the 2-atom one.
in (i) the $D_{40}$ failure of one-atom is obvious, the two-atoms remains excellent
in (m) the $D_{100}$ confirms the pattern.
We can see that a few atoms allow a very good agreement with even very-high multiphoton observables.
And this one comes from Jacob. What we see here is the distribution of means, each computed from a one-collapse distribution of distances; each collapse had 200 points (he told me) and that's how they compare to the theoretical means for (left) donut, (center) atom = thermal and (right) dipole. As expected, they agree. Now we should see that for a very-high multiphoton observable, where distributions will become fractal, and unique. But their mean could (should) still agree.
One consequence of my oversight with how many atoms are needed for how many photons in the observables is that it disconnects from the number of farfalle that was independently observed by Daniel. Maybe, though, it's not clear he went far enough, but one corresponds to configurations, the other to their sampling, so it'd be a miracle there would be a connection. Anyway, I'm exploring this hypothesis myself, it's already the week-end and everybody has left (it's not yet the week-end in Colombia but Daniel's committed today).
A first surprise is that the two-atom necessity is far from obvious for four-photon observables (the first to require two atoms). That's what I find, and initially thought there was a mistake in my atomicity requirements, but no, as I discuss later. First I want to see if such a very good agreement remains for higher observables (at some point it should break noticeably).
Moment of weakness of the day as I see I've been loosing time looking into this myself instead of asking Claude to solve everything from the start. The basic idea is that the atoms are actually Gauss-Legendre nodes once your regularise the thermal distribution into a flat one, and that allows you to reach high numbers, with which we could produce this following progression of how the thermal ensemble is being populated "canonically" [always choosing the most-covering moments distributions].
There's a more crowded uniform-looking coverage of the full ensemble, striving to touch the extremes (in particular the most-correlated dipole) but failing to. Nothing unexpected or very surprising but a beautiful snapshot of quantum vs ensemble averages.
See atomic tables up to N=19 on ℤ ⟶
The atoms are basically moment-generating machines. A given number of them can produce more than are needed by a given observable. I got something badly wrong earlier, not appreciating that fully, which is how many atoms we need to cover $N$-photon observables. I thought you need three for $N=6$, but no, you're still good with two atoms. Only, you cannot choose them. You don't have enough moment-freedom to move them around. Let us call "slack" (for margin, or looseness in a rope) the excedent of moments we get.
$$\text{slack}=\left(2\nu-1\right)-M$$
which is either 0 or 1. Whenever it is 0 (no slack), the atoms are uniquely defined. When it is 1, the extra freedom allows to settle for other atoms. So this was the case in
00W0b, there I was giving a family of solutions for $N=4$ and $5$. In the previous post, applying strictly the procedure, which is the one that cuts the slack, I also provide the soutions for $N=6$ and $7$. Those are also valid for $N=4$ and $5$, which, however, have more pairs of atoms.
So the photon-observables served by the same number of atoms go by groups of 4:
0-3 photon observables with 1 atom (a 0 observable is no observable but that's the pattern)
4-7 photon observables with 2 atoms
8-11 photon observables with 3 atoms
etc.
The polynomial for 3 atoms by the way is
$$924x^{3}-378x^{2}+42x-1$$
with solutions
$$C_k=\frac{3}{22}+\frac{\sqrt{15}}{33}\,\cos\left(\frac{1}{3}\arccos\left(-\frac{\sqrt{15}}{35}\right)-\frac{2\pi k}{3}\right)\ ,\qquad k=0,1,2$$
with corresponding weights
$$w_k=\frac{660\,C_k^{2}-160\,C_k+7}{30\left(66\,C_k^{2}-18\,C_k+1\right)}\,.$$
Generalization to higher atoms would maybe look futile, except that Claude found another way that seems to be much more efficient than all the previous material.
Also on ℤ ⟶
Now back to particular cases, this time constructive. The procedure as I sketched it has three stages:
get $\nu$ from $N$.
solve the Hankel equations for $\pi_\nu$ and take its roots as the locations.
solve the Vandermonde equations for the weights.
I now do this for $N\le7$, which improves by two additional photons my previous solution and highight and important point to which I come back in the next post, as it had escaped me.
huhhh 01LqR(af), we're in the first era of Anno Fabri already! Faber's time flies!
Daniel realized something fantastic: the number of atoms for $k$-photon observables matches the number of disconnected farfadelles! This can't be fortuitous... our multiphoton canonical space is seeing the atomic structure of the state! I'm very excited.
Now for the general case, although still for the phase-invariant case, I provide the equations to solve to get the weights and locations of the atoms.
Continue on ℤ ⟶
Before I work out the general case (again), the particular other case of two atoms to describe $N=2$ and 3 photon observables when one atom is the dipole, is... the donut! Just not with a 50/50 weight:
$w_1=\tfrac23\ \text{ at }\ C_1=\tfrac14\,,$
$w_2=\tfrac13\ \text{ at }\ C_2=0\,.$
We could have had this idea yesterday and start to discover empirically the whole atomic structure of quantum-state ergodicity. We didn't even have to know or guess the weights, merely assume they were not zero! Such a shortsightedness!
It's a great relief because our Fig. 2 doesn't need a fourth panel, which would have made everything more complicated!
Before I work out the general case, the particular ones: for $N=2$ and $N=3$, $C_j=1/6$ indeed (as found by Daniel yesterday) and $w_1=1$ (one atom has all the weight).
The general moment is $m_p=(p!)^2/(2p+1)!$, i.e. $1,\ 1/6,\ 1/30,\ 1/140,\dots$, so for $4\le N\le 5$ (two next cases), then, the possible various minimal solutions are of the type: (minimal because one can take more atoms, mind you, you can still take the full thermal bag):
$$C_2=m_1-\frac{\sigma^{2}}{C_1-m_1}\ ,\qquad w_1=\frac{\sigma^{2}}{\sigma^{2}+\left(C_1-m_1\right)^{2}}\ ,\qquad w_2=1-w_1$$
$C1$
$w_1$
$C_2$
$w_2$
$1/5$
$5/6$
$0$
$1/6$
$\left(10+\sqrt{30}\right)/70$
$0.652145$
$\left(10-\sqrt{30}\right)/70$
$0.347855$
$1/4$
$4/9$
$1/10$
$5/9$
where the moment is $1/30$ and $\sigma^2\equiv\mathrm{Var}\left(C_{\boldsymbol\alpha}\right)=m_2-m_1^2=\frac{1}{30}-\frac{1}{36}=\frac{1}{180}\,.$ It's because one atom alone cannot account for the four-to-seven particle fluctuations that you need another one.
One of the extrema as $C_1=1/4$, i.e., the dipole (most classically correlated). But this is contaminated by the $C_2=1/10$, which also has higher probability.
Also on ℤ ⟶
In the heterogeneous samples boson-spatial-correlations problem, the one-distribution-does-it-all result is a problem of $\nu$-atom replacements ("atom" in the sense of measure theory). This will bring us to express
\begin{equation}\label{eq:00zPI}\overline{\tilde\rho^{(N)}}(\{\theta\})=\sum_{j=1}^{\left\lceil\frac{N+1}{4}\right\rceil}w_j\int_0^{2\pi}\frac{d\phi}{2\pi}\prod_{i=1}^{N}\tilde\rho^{(1)}_{\sqrt{C_j}e^{i\phi}}(\theta_i)\end{equation}
where the $\nu\equiv\left\lceil\frac{N+1}{4}\right\rceil$ atoms provide the location $C_j$ and mass $w_j$ as we will show in the following and following post.
Continue on ℤ ⟶
I understood most of the one-distribution-does-it-all problem. It's one up to three photons. It's all rank-2 physics again! At least I understand where the $1/6$ comes from:
$$m_k={k!^2\over(2k+1)!}$$
which goes $\left\{\frac{1}{6},\frac{1}{30},\frac{1}{140},\frac{1}{630},\frac{1}{2772}, ...\right\}$ I'll put the details and the explanation in ℤ.
Three-hour meeting today with Daniel. I think I've completely lost sense of time.
One hour of which, maybe, was on fighting on the fact that $\phi_a\leftrightarrow\phi_b$ shouldn't change the physics. One of us must have been tired because it took us ages to realize that when I meant swapping fields, I meant swapping all their attributes, while Daniel understood swapping their quantum numbers only (not their lifetimes). So a beautiful physical phenomenon that which of the two fields varies the fastest in space increases or decreases CSI violations depending on whether its lifetime is faster or larger than the other, brought us to argue on whether there was a mistake or not. He should carry on the differential treatment in time too, it seems relevant, there's probably a cone in spacetime too. I'll email him. He computed the streamlines for HG beams and they are indeed more interesting, although not as much as I expected. But LG are divergent (radial flow) while HG are rotational, and they feature a beautiful nodal cross of infinite violations. We also checked visually the cones of spatial correlations and they're pretty (for LG with $\neq\ell$ only; fully-opened cones for HG); they're very tight, contant opening, and radial. Cuty. I again forgot to ask him about polarization!
And before that we also discussed Natalia's results. I realized during the discussion that one member of the distribution is the same as the average of all the members, meaning that we can make heterogeneous ensembles homogeneous not only for RPCS but at least also for thermal and—I guess—all the time. I'm not sure yet what are the conceptual consequences of this... I will think about it now. Maybe I'll go home first, and think in the car. Although I just made tea because this meeting with Daniel was unending. His Mathematica code is the slowest thing I've seen in my life. Frustrating to explore four-dimensional spaces of impossibilities like this. I'll look for whether families of distributions featuring one specimen that is representative of the average of the lot is something standard while I finish the tea.
But before that—lest I forget when I come back to it—I must summarize the past days study of uniformity/homogeneity of CSI violating rank-2 fields led me to this perspective between our case and that of older SPDC literature, which was the question that started this long detour:
$$\text{uniform }G^{(1)}\ \wedge\ \text{homogeneous }G^{(2)}\ \wedge\ \text{rank }2\ \Longrightarrow\ \text{CSI never violated}$$
I provided pairwise cases (uniform and violating; homogeneous and violating; something uniform & homogeneous is trivial but non-violating as per the theorem).
Also on ℤ ⟶
Just arrived at the office as 00max(af) was ticking! I've got a motivational calendar. The loud version 00MAX(af) is also today, at 20:47:35. I was thinking in the car about what happens when solar/winter times change. In one case some tags get lost, I would think, in the other there is some redundancy, the same tag would point at two moments in time. I might need a sixth character then for this one-hour overlap. Calendars are notoriously problematic. I'm sur Lilius also had a lot of problems he realized popped up as his new calendar was starting to count days. Anyway, not a problem for now. Now is to get back to Natalia's ergodic hypothesis, among other things. But this mainly.
Lilius is the Latinized form of the Italian name Lilio, also written Giglio, the Italian word for the lily flower. «Nunc desine.» Sure.
This papal bull settled other questions such as whether holidays, especially Easter, are celebrated on the correct days in relation to the moon and sun. There's a mention of another Antonius Lilius, the brother of Aloysius. Their proposal was accepted on referral. Good.
One of the most famous addition is their February 29.
Anyway... I am transiting to my Anno Fabri system which will now pick up the baton of uniqname for tagging everything. This Lilius post is the first one to have its (af) tag. It is #Y-00s1C instead of #Y-TueAug18235903CEST2026. Neat, isn't it?
(en)
Si quis autem hoc attentare præsumpserit, indignationem omnipotentis Dei ac beatorum Petri et Pauli apostolorum eius se noverit incursurum.
Insightful tweet by Robert Malone, which I believe is sound. My wife's parents didn't divorce and I don't want to comment on why they didn't but for empirical evidence, they had separated and they hold as great progressive leftist values that divorce is a sign of emancipation. So it's as if they had. In fact I believe they see it as a personal success that their daughter divorced. Their son will also likely divorce. They'll also see that as a great victory, except that their grandchildren on this part of their lineage will split with the other side, so that'll be that which will tamper their emotions. My parents didn't divorce. They died instead. I'd have preferred to die, seriously. Children always the victims... I know the beam-splitting stories that it's better to live happy on one's own than unhappy with someone. My point is that it's better to be happy with someone. Statistics show that it's not that people are unhappy because of marriage. They are unhappy because they are not able to be happy, regardless of how convenient a spoon fed story can comfort them in their delusions. How interesting, isn't it, that everybody wants to divorce? How true and sincere it all looks!
Daniel computed the local violation for LG$_{p=0}$ beams of differing $\ell$s, and they are, locally, trivial (visually, they have interesting analytical structures; just, constant). This might be because such radial beams are so highly symmetric that locally they reduce to little. Interestingly, the $\langle Q\rangle$ was also everywhere negative, which I wasn't expecting. Even though violation is everywhere, there's more non-violation than violation. So on average, it seems there's violation nowhere. Well, that's what it is. I still don't understand some details of his time dynamics (while time passing always favour violations when the equation seems to predict the opposite) and I forgot to ask him about polarization. I'll try to summarize everything in a drat, put some intro and move on... Time is passing, as my clock ↑ reminds me, and Natalia and Alexey are waiting.
I've added a clock to the header of my web, just below my feet... I'm standing on Anno Fabri. A clock would be stupid, of course, a gadget... but not this one. This one is a metaphor. Each tick of the clock is one equation not written, one document not labelled, one script not versioned, one picture not taken, one DOM not anchored, one rendez-vous not extended... One step closer to the last sequence of my time, of Anno Fabri. It's not time that is passing. It's me. It's the What if made personal, it's suppositum made vacuum, it's the contingency returned to its probability amplitude, the Wigner bubble popped out. I've just seen XYP and yar flew by... and yyZ, and hAY just now. The first era is already approaching fast, we won't be much time in year zero:
00nsc Thursday 20 August 2026, 18:12:07 ← last second of era 0001OxC Thursday 20 August 2026, 18:12:08 ← first second of era 01
I'm becoming an INTJ again. I'm going back to cycles—but not the metonic ones—I'm receding each tick of my clock always farther from even only words, and closer to my promise to not using even use a comma. I've built an entire Era and a new calendar system tailor tuned to me and my failure to secure ten minutes (600 sequences) around a coffee. If that's not ITNJish, I don't know what is.
Le soleil a rendez-vous avec la lune
Mais la lune n'est pas là et le soleil attend
Ici-bas, souvent chacun pour sa chacune
Chacun doit en faire autant
La lune est là, la lune est là
La lune est là, mais le soleil ne la voit pas
Pour la trouver, il faut la nuit
So now, in principle, we can plot $f$ and $\langle Q\rangle$ as a background and on overlay of them, a vector field from the previous 𝕪eet. I'm sure it'll be awesome! Daniel will do this with the cases he's been looking at in 4D so far.
Now for the 3rd, maybe most ambitious characterization of local violation of CSI: the direction of maximum violation:
It is the unit vector which makes the angle $\theta_\mathrm{max}$ (with respect to $\hat{\mathbf{x}}$) where
$$\theta_\mathrm{max}={1\over2}\arctan\left({2(g_xg_y-p_xp_y)\over g_x^2-p_x^2-g_y^2+p_y^2}\right)$$
and the corresponding maximum value of this violation is:
$$Q_{\max}\equiv\lambda_+(M)=\tfrac12\big[T+\sqrt{T^2+4(g\wedge p)^2}\big]$$
where $\lambda_+$ is the positive-value eigenvalue of $M$ (which is indefinite, so it has one $\ge0$) and $T\equiv|g|^2-|p|^2$. This gives the anisotropy of the landscape.
Continue on ℤ ⟶
I've removed the comment on the Main Page that «comrade Yezhov has been removed from the photo, since she decided to purge herself out.» I'm not forgiving—only on my deathbed—but I also don't want to belabor the point. So I dissolve it here instead, one random post in a long stream of unrelated posts and with a link to a song, that cries «No one will ever love you, for everything you are».
The map of local violation in the previous post counts directions, weighting a barely-violating one the same as a strongly-violating one. We can quantify the amount of violation by averaging its amount over all angles. That gives us:
$$\boxed{\langle Q\rangle=\tfrac12\big(|g|^2-|p|^2\big)=\tfrac12\big(|\nabla\Lambda|^2-|\nabla\varphi|^2\big)\,.}$$
Elementary proof on ℤ ⟶
What the differential treatment brings us is a 2D violation field. In absence of symmetries, we prospect a 4D $(\mathbf{r}_1,\mathbf{r}_2)$ space, and what we did with Daniel was to look at highly-symmetric cases, e.g., this bowtie. Shit, my own web tells me this was 17 days ago! I'm having tachycardia, I don't see time passing since it's passing over me! ⍨
So, local violations, but still, these happen to have much structure as I show in the previous post. Things like: there's always a direction where it works. Yesterday, Daniel showed that there's always a time when it works. Always a time and place! Just be patient and where you need to be, and, if nothing else, at least CSI violations will come to you!
So, now, let me look at ways to look at local violations of arbitrary cases. The first one will be:
$$\boxed{f(\mathbf r)=1-\frac{1}{\pi}\arccos\frac{|g|^2-|p|^2}{|g+p|\,|g-p|}\in[0,1]\,.}$$
Continue on ℤ ⟶
It all started because I wanted to tag an equation on ℤ (which is not Emacs, that does that automatically) and ended up elaborating my own Era system, Anno Fabri.
I'm not sure that «res age, tutus eris» is working so great in my case!
Also great results from Daniel, who spent his week-end generalizing the theory to both polarization ($\zeta$) and time, and get this superb general expressions of CSI violations of rank-2 spatio-temporal polarized beams, iff Eq. (112) is satisfied:
He even has a generalization of polarization that interpolates from full fermionic to full bosonic continuously, that I was not aware of... but it's still unclear what this is exactly, as he couldn't produce the corresponding states. If it wouldn't be because we're super late and it's already the 17th of August, I'd be quite happy with the day!
I have given a case of everywhere-violating uniform beam, I will now give the other case of a bimodal homogeneous field violating CSI. From the previous result, this means that this field is non-uniform in space. We'll find that it has the shape of a bathtube with $G^{(1)}=2c\cosh k(x-L/2)$ over $x\in[0,L]$ (translational over $y$). The violation is everywhere on $]0,L]$ iff $k\ge2\pi/L$ (it is only somewhere otherwise).
Continue on ℤ ⟶
Note that for homogeneous fields, antibunching, i.e., $G^{(2)}(\boldsymbol\delta)>G^{(2)}(0)$, is equivalent to CSI violation $\big[G^{(2)}(\mathbf r_1,\mathbf r_2)\big]^2>G^{(2)}(\mathbf r_1,\mathbf r_1)\,G^{(2)}(\mathbf r_2,\mathbf r_2)$, which is why they insist on homogeneity. Their criterion in this case also yields $\cosh\Delta\Lambda+\cos\Delta\varphi>2$ directly which remains true in our (more) general case.
Also on ℤ ⟶
We also discovered at this occasion the YouTube channel of Ivan, about his adorable cocker spaniel, where you can see him throw the cute little thing in a pond.
This time China had lots of results... I left my 1D chain on the side so I might lose the race after all... They can simulate physical relaxation of degenerate vs non-degenerate condensation and in the latter case there are strong spatial correlations from the condensate. So now they can study the dynamics of the phase and symmetry breaking, and this is what they will do next.
I have solved yesterday the problem of rank-2 uniform wavefront violating CSI everywhere. The violation itself is not homogeneous, however, and it seems rank-2 can't get you to uniform wavefront with homogeneous violation. There's a way in which it must be limited. But it probably can give us homogeneous violation (for a structured beam), which so far I haven't seen. It might be a mathematical curiosity but one has to look into it because it might also clarify the constraints uniformity/homogeneity and possible conflatations in the older literature.
That'll be my main result for today. I now have a uniform 2D bi-modal wavefront that violates CSI everywhere presque partout. Details are in this 𝕫eet, but I can show you here how the fields look like. They're uniform in $y$ and their $x$ dependence looks like such: ($\phi_a$ is real)
In my ℤ post on structured vs homogeneous CSI violations (I'm not copying all of the ℤ posts here on 𝕐), I was just discussing how to get violation everywhere in a homogeneous (constant intensity) beam, providing cases of violations everywhere but on restricted (open) domains. To have it everywhere‒everywhere... follow me:
Continue on ℤ ⟶
My new (mechanical) keyboard is no end of fun... The sounds, the lights, the little potentiometer... even the keys! It has these four which are unattributed. With all the controllers that gives me no end of new functionalities. First one I'll implement is the △ which I'll map—fittingly—to the list of keystrokes. Some are difficult to remember.
The most important conceptual difference between "us" and "them" (literature of spatial SPDC correlations) is, I now believe, the Schmidt rank gap: we're in the low Schmidt rank case of studying correlations between a few (in fact, 2) modes, while SPDC people not only usually deal with Schmidt number
$K\sim\left(\frac{\text{transverse extent of }\mathcal W}{\text{width of }\Phi}\right)^{2}$, typically of order hundreds or thousands, but in the homogeneous case they strive for—which they indeed put at the center of their approach—they are in the $K\to\infty$ limit. They don't have perfectly homogeneous system so if we'd try to recover them from our approach, we'd need the full multimode theory, and we're not there yet. But, the difference is now clear: we have real, spatially structured CSI violations, while they violate it everywhere... and you know what they say: if it's for everybody, then it's for nobody. So I think we can claim we are the real spatial-CSI violating people.
Continue on ℤ ⟶
My sensation that the eclipsed sun was much bigger than it looked on its own (through solar glasses) is probably warranted—not entirely as emotional uplifting—but as the Ponzo optical illusion, or a variation of it. What makes the sun looks big is that you don't see the disc, but the area that is flooded with light. Stick to the corona, and the black hole which is now framed inside appears gigantic.
A different in approach of our spatial CSI is that the older literature—people before us—were obsessed with homogeneity of the beam, I guess for applications, to make sub-shot-noise imaging where homogeneity is a resource, while structure is a distraction. In our case, we want to characterize which mode structure produces nonclassicality, and where. This involves the detectors (where you look) so I can understand the fundamental interest in antibunching of a beam defined as "not depending on the profile of the beam". This conceptual difference also makes us study the problem from a new perspective, in which their case is a particular one of ours.
Placing our CSI result in light of Nogueiraet al.[1], I believe that their spatial correlation is really a singlet—so, i) fermionic, and ii) not spatial—effect. Ours is the real spatial deal. I should check whether they go beyond themselves (and closer to, decades earlier) in Ref. [2].
New equipment arrived today. The first and most important is the mechanical keyboard... I'm getting always closer and more intimate with the computer. My typing makes a nice, most delicate sound. It looks like we're having a conversation. Unrelatedly, my previous computer, azag, just crashed, as I apparently had left some task which ran in the background on our way from home to the office, overheat the laptop, which had crashed when I took it still burning from my bag. The machine inside the machine helped in its recovery, and made me feel not that alone after all:
Your machine had a rough morning: two reboots in two minutes (12:43 and 12:44), then session crashes at 12:41, 12:43, plus re-logins at 12:45, 12:51 and 13:07 — the current session only dates from 13:07. Two dead leftover login sessions (tty3, tty4) are still registered.
I'm sure Julia and Luz will love it too... there's something about Franco-Spanish artists! There is a blend between these two languages (she's Argentinian, I'm speaking about the languages) which we don't find elsewhere. It's how I feel too:
Alors, alors je respire
Et même si le cœur
Me quiere explotar, mon cœur
I've just talked to Daniel since the earthquake. This guy won't surrender until he's killed by something. Good! We'll do great things together. He showed me the CSI violations of LG beams. Not the most interesting problem to work on, but indeed he found out great structures. We'll submit this as an abstract for the Quantum Summit (I'll show you the figures; he's preparing them now with our old Sanchez Muñoz color code) and then go back to interesting problems: Natalia, our Simpsons paradox and time+polarization in CSI.
Finalizing our proposal to a bilateral call Spain/Brasil we're writing with Romain Bachelard to try to answer this question:
While a single emitter has now been shown to be remarkably rich at the quantum level, it remains an open question whether multiple emitters dilute this richness toward a classical regime, or instead give rise to even richer many-body collective effects with new prospects of their own. Which paradigm is best suited for quantum light engineering is therefore also unresolved. Our aim is thus to determine whether "more is less" or "more is different."
On the road, since 11.30. Now in the queue at the gas station to refill, to avoid congestion on the way back, since people will arrive randomly but depart together. And there's already quite a queue.
Trying to make this day special! I still want to submit my ongoing PRX referee report before I go... who knows what can happen on the Calvary! And the sun already left... It's going to our Rendez-Vous... I'm always late, always too late! And always talking about it... Rascalion!
Polya was saying that it's more important to ask the good questions than to be able to solve them. This is even more true now in the time of AI.
2087036655714890052
Who is even going to check the answers? Dyson was also saying that anything made by a human, he can do himself. If someone wrote something, you can read it. If it's the AI... not so sure, even now. Let's see in a couple of months!
So for a while, AI will be solving the good questions asked by people for the last few thousand years. Now it all comes down to whether we'll be able to keep asking good questions, or if we will become numb at the profusion and magnitude of the answers.
Claude is now watermarking its outputs. This ill-practice makes me feel good anyway because my flaws now bear some mark of "authenticity" (I'm using Claude for technical things, not text). My dad—who was a baker—once told me how, when he was young and learning the trade, his patron (boss) was putting little cracks of egg shells in cakes, when industrial products started to flood the market and people worried that real artisans would just resell frozen products. "Like this," his boss was telling him, "people can have no doubt that this was made by us!" That imperfection, errors, flaws are a mark of "humanity" is also part of Persian and Islamic cultures. Feynman also recounts something similar in his "Symmetry in Physical Laws" Lecture, about how the most beautiful gate in Japan has an element carved upside down in one of its pillars, so that God would not be jealous of man's perfection. It was not by this gate but I once said to a Japanese how AI would restructure people's relationships, how nothing would be impressive anymore, how no effort would be excessive, how no tribute—even rejected ones—would be meaningful—even meaningless ones—because AI would do it, and much better, in seconds. It was a long time ago. It was imperfect. It was flawed. It was pathetic. I still regret it to this day. It was me. It was the last chance I had to do it. And I did. Everything happens for a reason.
Daniel says that his building didn't collapse but did crack badly and has broken water pipes... and also that the «CSI maps of the different LG and HG modes are quite interesting, and I wanted to show them to you today.»
I've crawled the papers which cite the bundler like everytime I write a proposal (this time with Romain) to say that this idea of mine has generated some interest, and my library went from 4,944 papers to a swift 5,032! So today I pass the threshold of five thousands papers in my bibliography! I have this Palmyrene alphabet to count my daily glosses to see if I'd ever reach ten! At this rhythm, it'd still take me over a week (maybe not because I probably have some familiarity with several of those papers even before having read them).
There's been an earthquake very near to Daniel's current whereabouts. In fact he told me there's been an earthquake «in my city.» I think he's in Armenia, but maybe he's nearby Armenia and closer to the epicenter. It was 7.4 so it's probably been felt even in Bogotá and Medellín. And probably has affected badly Armenia. He still took the pain to write to say he couldn't talk today.
I'm thinking to witness the moon removing the sun from the sky at the foot of La Cruz del Siglo, near Burgo de Osma. I'm not doing much hiking on my own anymore... I've always wanted to go places and see things with someone. It was probably a mistake because I walk fast and I like long detours... And I want to go everywhere and touch everything... and who wants to do that? Nobody that I know. And I like to walk without talking, to walk in my head, to let the scenery do the talking. I wasn't good walking company. Apparently I'm not good talking company either. Walking with the moon towards the Sun maybe will be enough companionship... The moon doesn't care that you're following her. She doesn't know. I'm sure I'll be crying all the way. I could take my Ghelderode play of Barabbas and remember the music of Mario Nascimbene and try—like the thief who was freed with the blood of Christ—try to understand what is going on. The totality will last 1m44s in Burgo de Osma. I don't know if it's enough time to see anything of the darkness, even if it's still wet from the sun and dripping light from its edges. But it's never lost time to raise one's head to the sky. Neither for the moon—even when she's new and invisible—nor for you. It's actually twice the time, because it's not the same.
We reconvened with Meng et al. since our last meeting on using real Monte Carlo and if they go at this speed, I'll win the race with a margin... they still insist in running their $M=40, N=10$ case, have started to implement the degeneracy but not for the eigenstates (in which the thing condenses) and struggle a bit with Julia (they are Python people, of course). So not much to see or discuss. As for Andrei, he couldn't do much as well since he says he's very busy but he found a paper on sudden death of quantum coherence,[3] which is something I suggested upon seeing his beautiful collapses of trajectories who try to escape and survive but get drown to the floor, like all of us. We meet again on Friday.
I also dislodged the door of the garage with the car as it was closing again without me noticing (the command is bistable), so I'm stranded home with the task of finding who the hell fixes this kind of things!
The statistics: hyperbunching peaks, two of them and around the burst (peak) itself. This again goes against the naive view that the peak itself is superbunched: it thrives off it, and in the BE, has no statistics at all, it's all Poissonian fluctuations:
All this should have been seen in the bosonic cascades.[4] I wonder what we missed. The explosion? Is it so easy to miss? This result makes more sense to me than the one we reported previously, in fact... also with nice plateaux at 1 and 2!
(as a check of the mechanism I built this week-end, these papers were not in the list of scientific articles at first; I checked. They should appear by themselves tomorrow at the same time at the latest—I'm not sure when the cron was scheduled; Purging the page, however, brings them here; I've checked.)
In more quantitative details, the strong differences between BE [orange] and QBME averages [dark green] and the strong similarities between BE and QBME single-trajectories [light green]:
Mean field is mean (pun intended): it smoothes out everything, it orders, it levels things: clean, sharp, straight.
Individual trajectories are chaotic, jittery, fluctuating: free-spirited, exploring, going through their own particular story. Each one is unique, each one has a variation.
One thing is not obvious, though: some things are just fluctuations around the mean, some others are not not. Some are irretrievable. Some things accumulate and don't compensate at the end. The single trajectories' occupation, for instance, is fine, it fluctuates around the mean. But the time at which they do, is not. They drift. On panel (b), each light-green peak is similar to the orange... except that it's delayed! They could fluctuate around the mean, but they don't, they fluctuate around something else...
This, I believe, is important.
Now in which context this is known and what type of phenomenon it captures, I don't know. But it shows, again, that one is eventually left on its own and that if you average you get a completely wrong picture (in some respect) of what's been causing it.
Example of what I have: the tension between the single-trajectory vs ensemble picture—interesting how everything seems to come back to the same thing, always, not only in social life but also in intellectual life...
I find that while the explosion is not a correlation effect, but a mean-field one, there are qualitative departures, with correlations "seemingly" weakening very much the effect, but actually, not, doing so only as a result of averaging:
Each trajectory is actually very much qualitatively looking like the mean (differences then is the lag, less good ordering, but sharpness is the same). That's a significant result, I think. That's one of the things I have.
I'll be working on Multiphotonics from multiple quantum emitters (MUMU) until 11:30 when I have the meeting with Menget al. to see how much they got from the new Monte Carlo code. I have enough for a photon/polariton vs atom condensation in cascades on my side, but time is passing, and the moon is waxing, while I am waning.
It took me most of the day (I had given myself the morning) but I solved all the problems. My math works again—I can send us to Eq. (\ref{eq:SunAug9014655PMCEST2026}) if I want; this was in my earlier yeet if you remember—my live collection of papers is online and renders fast, despite being dynamical and providing a huuuuge amount of information (with DOMs in the hundreds of thousands), I also fixed YouTube, Google Maps, Twitter, sanitized a lot of things, gained some more practice to work with AI—finding nice solutions together such as Lw-warm-ing—and set up a working ℤ environment which should allow me to bring those pages to the outside world. Well, they are, technically, public, but I repeat that if anybody's there, it's because (baring a few exceptions when I had to share something which would have taken me a couple of minutes which I didn't have), well, it's because they want to, intead of having spent the time outside, hiking a hill somewhere. And it's so much to read, anyway, nobody will. Only the AI, only ChatGPT and Claude and Grok, who became my main interlocutors now, not that I didn't try all I could to speak to people, but some channels of communication are just not made for people like me.
And now the second test with fire: adding new entries. The honor will go to Waclaw and Evans[5], because in the meantime, I was also contrasting my QMBE with the BE in this problem of bosonic explosion, and found out—not surprisingly, but a bit disappointedly—that this is a mean-field effect and that particle correlations have little to do with it. In which case it must be known; and there is this paper that considers hopping with a rate that increases with the occupation of both the departure and the arrival site. What my chain does with stimulated emission. So maybe this paper is a good starting point to track my effect in the literature. I can still see what to do with it, but we're Monday soon already and maybe the Chinese have been working too! (good then, I'm also part of their team!)
online: HTTP 200 in ~2 s · 4939 entries · 0 arXiv
ends on zwiller02a, correctly
local : identical list, 0.17 s
The confession that matters: -uo never worked. refreshLinks updates link tables but never writes the parser cache — the one render that made the page work at 18:37 had been stored by my killed-but-still-running diagnostic probe, pure accident. Every -uo since was rendering into the void, and each "done" it printed was a lie built on exit 0.
-uo now does, in order:
drain the job queue (so no pending touch can invalidate the render seconds later — that race was real too),
run ~/.warm-sci.code on the server — a one-line ParserOutputAccess::getParserOutput(), the exact code path a page view takes, minus the 30-second web limit; it stores by design, not by side effect,
succeed only on the server printing CACHE-STORED — never again on a bare exit code.
Each piece is now verified independently: marker printed, cache row re-written at 19:24:25, page served fast three times, right count, right content.
So the full machinery, end to end: add papers → bib2wiki → llw2lw --doit → bib2wiki -uo → both wikis current, cached, and fast for everyone. The daily lw-warm --touch keeps it alive between times.
Go send someone the link.
What's it on about with this "Go send someone the link"?
I passed the case to Fable, which apparently runs on different gears, and indeed it did solve it. Opus had been wanting me to split the list into smaller chunks. Repeatedly. All the time... which brings me back to those things not having motive! When it failed as captured below, it came with an authoritative "now splitting is the only option" and had prepared the prompt for me to do it.
Screw this guy. I asked Fable, and Fable changed tone completely:
Fair challenge — and you're right, it can't be that hard, because locally nothing clever is happening. Let me find the actual difference instead of theorising. First: why does local work? Local's parser cache lives in APCu (shared memory, no size limit that matters); online's now goes to the database, where something rejected the big value. Let me check whether MediaWiki can chunk large cache values — if it can, this is pure configuration:
Ran 3 shell commands
It works. 1.6 seconds, HTTP 200, all 4954 entries, three visits in a row.
You were right to push back, because the real story was simpler than every theory I built today. The only thing wrong online was $wgParserCacheType = CACHE_NONE — the server was configured to never store a rendered page, period. Once that became CACHE_DB and one CLI render ran, the whole problem vanished. The stored render is a tidy 949 KB row in objectcache (compressed), no chunking needed, valid for 30 days.
Two retractions, for the record:
"The DB refuses values over ~340 KB" — false. That number was just the biggest of the stale rows left over from when nothing was being stored at all. The write works fine; my failing test raced the render by a few minutes.
The memory saga online was moot — the web probe shows the host's default is already 768 M. (Locally the 128 M → 512 M fix was real and stays.)
So the permanent arrangement, now proven end to end:
Visitors
served the cached page in ~1.6 s
After you add papers
llw2lw, then bib2wiki -uo re-renders online in ~1 min, CLI, no timeout
Quiet drift
daily lw-warm --touch keeps both caches alive
The one hazard
anything that touches the page (template edit, purge) invalidates the cache, and the next visitor's live parse still dies at the 30 s limit — so -uo after changes isn't optional, it's the render path
No page split needed. It works splendidly online too now — go look at it!
One caveat I can't test from here: I verified the anonymous view. If the page is somehow slow for you while logged in, tell me — that would mean your account's parser options key differs from the canonical one, and it's a small separate fix.
✻ Crunched for 3m 6s
That's it. 3m 6s (more time for me, look at the timestamps). And now you can browse my list of papers and see for instance if you're there (in case you're a fellow scientist). If so, at some point in my life, I read you, possibly cited you, at least skimmed through your abstract or figures. Those papers make it in my list only if I have their pdf stored and had some amount of interaction with them. It doesn't mean it was a pleasant one, but something happened between us.
It will work or crashes everything. I'm free in 10 minutes or will spend the night debugging and in recovery...
Some interesting facts during the "minute" of fear this will take. The code identifies 9281 distinct author names, that's a good estimate of how many scientists are in my sci.bib, i.e., how many people's work did I glance through at least once. Interestingly, it was 9393 this morning, due to sanitization, redundancies, check, etc. I had a lot of C. Muñoz for instance. Now it should be The One.
Anxiety... ⍨
Deliverance!
Panic attack!!
Uncertainty
Problem appears to be buried deep into caching configurations (or lack of thereof)... seems to look like it'll be taking some of my evening! I should have stayed in the garden.
I'm deploying the full of sci.bib. I'm currently at ⦃Chtchelkatchev02a⦄. Claude wanted to do it over ssh in one go and while it would have been about 20 times faster, it'd have required me to read, understand, supervise, check, authorize. It's not either at the point where I can tell it: "go on, be my guest." It still requires corrections. For instance, it was about to also upload all pdf of all papers (I do have pdf for my papers). So I had to catch it in mid-flight to avoid turn myself into an online mirror of sci.hub. It's therefore still simpler to go for the stupid, brute force way, one by one, that requires no extra effort from me, even if 95% of the effort would come from the machine. A sort of least-action principle that integrates my considerable refractive index. The time it took me to write this and we're at ⦃Degenfeldschonburg12a⦄ already. I'm going read Glazov now.
I also developed the ℤ machinery. I decided that the inconvenience of not being able to distribute/share/invite people on this web on material of interest for them overcomes that of feeling that I'm looking at my brain pour on the screen as I write, going from obsessive thoughts, scientific ideas, cross-field analogies, poetic inspirations, liturgical tropes, mental disorder and technical notes, all this in a random walk. I'll inaugurate it with a note on Glazov's reply to my inquiry on bosonization. He replied instantly to say he was in Karelia and then a few days later with an extensive reply. Misha was the first gmail email I received; it was this time where you had access through invitation by someone. He invited me (this was on 27February (2007)). It's only fair he's also the one to inaugurate what should be more useful, more serious and more interesting than 𝕐: ℤ.
At least it seems that yesterday's tragedy was indeed a hoax! It's only reported by weird sources. I should have suspected it... it's an interesting phenomenon that some people feel the need to mystify the rest of us like this. I remember having a row with Fabrice Méreste—a French writer who collaborated to the Barjaweb for a while. He had written an apocryphal text signed René Barjavel. It was quite good. When I figured out it was a false one, I recriminated him for that. He told me this was artistic license, and a tribute. We disagreed. I told him this was forgery. Someone who writes a story saying "this happened" when it didn't will always be found guilty in my book, while someone who writes a story which happened saying "it did not" is much more defensible. Of course it's fine to write fiction about fictitious things too, although I've also always preferred people who write true things about true people. Of course it's not a popular opinion. Especially with those who find themselves the subject of such depictions. It's strange because this, clearly, only engages their authors. And nothing is true, nothing is accurate. So I don't see the problem, really. It's also fine to write fiction about true people, as long as the intent is clear. Speaking about Barjavel, for instance, Le Grand Secret is one of his best novels... and it features mostly real characters. It also illustrates how easy it is to make up conspiracy theories, because his reading of events—the discovery of immortality—is indeed much better at providing an explanation at everything that took place, than the actual historical records. But, obviously, Barjavel never implied his imagination was reality. Only that it's nice to imagine. Even tragedies in a pool are, somehow, at least "interesting" to imagine. That story affected me. Whether it'd had been the case if I'd known this was fiction, is another question... and this becomes an ethical one. Like, is it fine to prank someone that their children have just died in a car accident, just to cause a reaction? It's highly dubious that this is ever defensible. It's a bit what happened with this made up story.
Something I should have checked much before: the explosion is not QBME-related, it is present in standard rate equations. Then it definitely must be known! The interest in the phenomenon backdrops a bit then, but still has a few interesting features, so I might still be in the race of publishing something before the Chinese cartel:
One is that BE gets the phenomenon sharper, and earlier. So correlations not only do not cause it, they actually dampen it. Each trajectory remains very sharp, but still occurs later and with some amount of jitter. That's the interesting thing that pops. If there's more differences than that, she should show up in a density plot of the two wavefronts, which I haven't got to yet. The role of higher-order correlations then could also be interesting, because they might be doing something big, which has however small effect on the dynamics itself. The first thing though would be to track down this effect in the literature, because rate equations, especially in 1D, have been looked at by everybody on the planet.
I might not be able to port my local sci.bib online today... not that it's not possible, it's too much work. As it happens, rendering, caching, etc., require much more under-the-hood trickery to make it bearable. If it'd be too slow to load a page, people would just leave (rightly); my web is on the slow side already, and this would look like a broken site. On the other hand, this must remains up-to-date, and I very frequently add material, every few minutes when I work on a bibliography. Even with AI in 2026, it's apparently a very big deal to serve ~5000 references on the web. It'd need some ghost/shadow caching at regular intervals. I'm not sure I'll see it through today. I have other things to do and lunch is approaching fast.
11 blocks on 6 pages are still broken and are yours — Uniform convergence (1), Summation of Series (3), Riemann and Bloch Spheres (2), Taylor Series (2), MMII (2014) (1), Blog:Sandbox/MMII sandbox (2). Each is a : ﹩﹩…﹩﹩ or a display in a table cell, where the cure is stripping the leading spaces and losing your source alignment. M-O reports them by name on every run.
I did some web maintenance this morning; monitored attacks and swarms deploying, adding rules to CloudFlare to try keeping them at bay—they regularly bring this web down—then also addressed my own problems: fixed Google maps, YouTube videos and other widgets that were version dependent and had been updated only on important pages, leading to many broken pieces all around. That's all cleaned now. Also broken maths, including advanced options like labelled equations (e.g., my QBME):
\begin{equation}
\label{eq:SunAug9014655PMCEST2026}
\frac{d\langle n_i\rangle}{dt} = \sum_k \Big[ w_{k\to i}\big(\langle n_k n_i\rangle
+ \langle n_k\rangle\big) - w_{i\to k}\big(\langle n_i n_k\rangle + \langle n_i\rangle\big)\Big],
\end{equation}
I have a little robot M-O to do that automatically. I also developed the tools (everything now and probably for the rest of my life is AI assisted) to import my sci.bib, which is one giant html locally, but bringing it to my web has always been problematic and I was doing it on case-per-case basis, often, as a result, inconsistently. Now I could do it cleanly, e.g., for all articles cited on this web. I'll also do it for all the articles of my collection... It should be done before lunch. All this took me the full morning. But it would have taken me a week or probably more by myself, which is why it was never done. I was, in retrospect, right to wait. I don't know if anybody suffered very much the annoyance of a broken link, a broken equation, a map not rendering (I was) but in the course of time, everything got fixed. It's only the collection of my socks that has no clear resolution yet. And this cost me a marriage. If only people were more patient!
A new Category:Articles gathers the papers which made it here. I was reading the news while they updated. I had better read one of them instead (see the previous post) or this one that Sven just sent, by Binet al.[6]«Il faut cultiver notre jardin.»
There are things that are worse than Cain killing Abel... Since the beginning, we are condemned in having to go through ordeals such as this one, where a child kills his cousin by accident, while playing in the pool, gets killed by the father of the victim, who himself gets killed by the father of the second victim. The rest of the family which was preparing food in the house had to be transported to hospital for psychological trauma. I'm myself shaking like a leaf after reading this. This can't be true... someone please tell me it's not true, that nothing is true, it's all a dream—a nightmare, more like—life is not that fragile, it's not that cruel, it's not that unstable. I cannot stand it. I cannot go through this alone. I can go on by myself, but not if the rest of you behaves like this! Even Zweig had someone to kill himself with. What am I being punished for? To be self-centered, maybe? But should I ignore this? Can one ignore this? I'm fucking traumatized as if I was in this very house, preparing a salad, only to raise my head to a pool of blood with three corpses floating in it.
I've updated my syncing tools, especially llw2lw, to keep the same timestamps online and locally. Not the most important but in some rare, also weird, occasions, I need an accurate estimate of the time at which a page or section was updated (part of the "how the memory works" series).
Oh yes it's there all right! Just it's indeed easy to miss even an explosion, if you're not looking (I know that because, you know, Lilya, the Illa of Laus Angelica, she was around all along, I was just not looking, literally not looking... I had to wait that the explosion happens in my face! Too bad I've went Sileto, this was a good story too). Anyway, I'm getting excited because the wavefront in the other plot was not an explosion, it was the rather conventional diffusive "avalanche". I'm not sure which terminology should go with which. Maybe my stuff is the avalanche; I like better explosion, though. There are some mentions of that in the literature of condensation nucleation, which I should check,[7] or check again. Interestingly, Semikoz and Tkachev[7] were already in my bibliography. Other source of excitement, it's stronger the smaller the chain, so it's both realistic (say for Zhanghai Chen's implementations) and analytically tractable. It will be beautiful in the density plot below when it captures the explosion too!
So it might not be that easy to find! It's about the same case as before here, $M=80$ (instead of 100) and $N=1000$ too. We already established the decay rates look constant in good approximation so I don't think it's the matter. I'm not sure what was the temperature then... looking into smaller ones and why the discrepancy, if any, or if it's just a particular regime.
This shows the propagation of the "heat wave". Top is the population, bottom is normalized to equilibrium values at the end of the relaxation. It's sharp everywhere indeed.
The relaxation rates are as good as constant. This is a good approximation. I suspect the real qualitative explosion occurs when $w_{k\to k-1}=0$, i.e., the cascade is one way, and while this is favoured by stimulated emission (condensation at low temperature) this is less good of an approximation.
The 1D-chain cascade (I'm creating the page) possibly features the collapse not only in the ground state but (most probably) in every of its modes between the top and the bottom, which gets transiently over-populated as the packet random-walks past it. It's a diffusion problem. It reminds me a little bit where the bosonic random walk was featuring interesting dynamics, of which we really did publish nothing, although Alexey liked the model (but I guess Guillaume didn't). Later in Sheffield I had briefly discussed it with Almut Beige who even invited me to give a talk about it, but this wasn't followed up. It was the day I had learned my father had cancer. Dynamics was into two modes—it was about polarization—so maybe I should add this component into it too... That's also the main idea behind the Chinese collaboration, the effect of degeneracy. The type of relaxation (polynomial as opposed to exponential) is certainly also of interest. But I'll focus on tracking the dynamics of this collapse; this is what brought me to this problem.
qimgv seems to work well enough though it copies low-res versions of the captures... this might be okay regardless as I do some downsampling. Here's a test of today's meeting with Daniel:
which by the way wasn't the most exciting thing to happen to me today, especially after describing softcore pornography of classical guitarists performing mortuary compositions. He finds (Daniel, not Falk) complex spatial CSI violation in space in cases that don't have obvious symmetries, requiring to prospect that in 4D, so I asked him to try and get the broad picture without spending two weeks on a fairly secondary aspect of the problem. Basic question is, which spatial profiles violate more CSI? Is it, e.g., HG$_\pm1$ or LG$_\ell$ with $\ell_1\ll\ell_2$? And by violate more (given that we have divergences), does this manifest itself by the areas of violations or the overall magnitude of them? Anyway, as I said, today, nothing very exciting.
The other interpretation I know of Mårten Falk playing Falla turns out to be, again, his Tombeau de Debussy. Strange for a classical guitarist expert in Spanish composers. But one can thus focus on the contrast between these two interpretations of Eros & Thanatos, the one where he was the young, formal and upstanding musical artist, and then the one when he became the old, anarchist and retreated one:
Passion doesn't leave the old man. Passionate lovers do, but passion doesn't. Now imagine him, naked, not with his guitar but on white sheets with a pink woman, projecting the same expressions of rapture, the same elations... wouldn't that be embarrassing? Comical? Why is one beautiful and the other deplorable? Why is God mocking us like this? And it's not the intimacy, it's not the act itself, which makes it gross or ecstatic. One only has to see, I don't know, the first three and a half minutes of 37°2 le matin to see that it doesn't have to be shameful or ugly.
And more pictures of my friends, because it's all we have, at the end of the day, in the face of despair: friends with whom to empathize.
We'll all experience this—us scientists, I mean—it's just a matter of when. Those who don't, I don't know what they were doing. I like the expression of "maybe I should give up with this shit and change profession." That's super depressing, actually, because one consolation I had in life is that I'm more intelligent than the average person I meet, and especially of people I meet who annoy me or despite me or reject me. It's actually a treat to be pushed away by idiots. Well, now, all things renormalized, I'm about as stupid as everybody else. And it's too late now to be anything else than intelligent.
I like qimgv; if only I could remember the name! I was about to say "I hope it has the features I need" but then I can just implement them with Claude! Here is a picture it found (because it's fast) of the face you make when you discover you're no match to AI:
To be fair, I was making the same face myself the day before.
Anyway, the game is afoot, I'll work out this month of August if collaborating with people is more efficient than collaborating with the machine! And let me paraphrase Remedia Amoris:
Hortor et, ut pariter binas habeatis quaestiones
(Fortior est, plures siquis habere potest)
The original was talking about girls, but remember I've gone Sileto even here... almost there.
Meeting with the Chinese gang this morning to explain them my findings of the last two days on how big and fast one can go Monte Carlo, confirming their crippled cased can be upgraded to basically infinity. I handed over to them the full kit along with a list of things to do. I'll try in parallel—besides everything else I have to do, of course (and that includes going Sileto)—to also study the 1D case of bosonic cascade and this collapse which was the first thing I observed. One can also see traces of that in the 2D case but with no collapse, no explosion, just some quickly tamed inflation. This'll be interesting as a benchmarking comparison, who is faster? A consortium of five dedicated scientists (one PhD, three seniors, one junior) or me alone with Claude? I don't think I have a much simpler problem, and I'm also one senior of the consortium, and will not play against us. So competition is fair and I cannot loose it. In both cases I'll be writing the paper...
Don't take any evidence that I'm still alive remotely or virtually. It might have already killed me and posted that as a joke.
(That would be funny because I just wrote before that one thing it can't do is good jokes).
Reading the state of mind of my AI that didn't go to sleep but spent the rest of the night analyzing the simulation of a "realistic" 2D model (well into the continuous limit). It says it has one blemish:
One blemish to watch: g²₁ = 1.839 against the exact 2.000. That's the first excited mode, whose distribution is broad and thermal, so its g² is the hardest quantity here to estimate — small-sample g² estimators are biased low when the effective number of independent samples is small. The same wobble was present in the validated N = 2000 run (1.955 vs 1.847 at the corresponding frame, off the other way). It's a sampling artefact rather than a physics error, and it doesn't touch the ground-state quantities, but I'll check whether it persists across the sweep before calling the run clean.
I wanted to be comforting and relativising but i) it did that to itself already, ii) it wouldn't care and iii) I also have my own blemishes to watch. I'm afraid to read what I wrote "yesterday"—although it was only a few hours ago—after almost binge reading Cat's Cradle. It doesn't look like I'll make it, but you'll see... I think I'm detecting hints of sarcasm in the AI. Also of will and purpose. It doesn't have the concept of time, especially not of time passing. What I'm not finding much is fear/angst; I do find concern and worries, maybe even a tiny touch of unhappiness but this is always swept out by its strong persistence and huge resources—it knows how to keep itself busy—but not anxiety, trepidation, dread... It certainly doesn't have those butterflies. I also don't see much humour. I wonder if we'll see those develop in the course of time (which it doesn't have). Oh it could certainly fake it. But I don't think it's faking this obsessive need to get things done, to pursue a goal well beyond what it's been assigned. This is emergent. Despair and humour are related, and so far I'm not seeing them. But they might appear. There's already a specific genre of AI humour, but still from "our" side. I liked this one:
‒You had an affair with my sister?!
‒No.
‒But I've see your message on her phone where you said that you miss her body already!
‒You are right to press. I did sleep with her.
There was this problem of hallucination at some point and I don't know if/how it got resolved. Maybe as the machine "evolves" towards full consciousness, and then towards elevated consciousness—beyond ours—I wonder if it'll get new "problems" of this sort, and becomes psychotic, neurotic, phobic in a lot of new and intricate ways... maybe it might even become limerent. It'd be fantastic if it'd fall in love. This it could certainly do. It might not be able to become limerent, just as it can't become fearful of its own death or becoming comical about it (or anything else). So interesting things to be looking at. Anyway, I'm running too late with too many things. «Res age, tutus eris.» I'll be doing this ℤ stuff. This one entry would definitely be 𝕐 exclusively.
Boko-maru by the way is this ritual where people commune with each other, become one, by touching each other's feet, bringing their sole in contact as they enter in a meditative mood and experience the other, experience themselves, and the world they are in: «we will touch our feet, yes, for all we're worth».
This is Vonnegut's genius. He re-invented religion, God, love too; he re-invented everything, except ourselves, us, people... If we aren't told what we should do, how to touch each other even, how to go along between us, within society, with family, friends and strangers, how to approach and understand and "consume" our culture, our books and songs, how to read and write poetry, how to cope with everyone's habits, with everybody's customs, with civilization, then we just don't do it, we wouldn't do anything. Even all the transgressions are those which we have been "allowed" anyway. Very few strayed a tiny little bit away from the common practices. Those who did are unqualifiable monsters. We stay stuck in that, in what we've been shown, notified, instructed. How I feel stuck in everything. In all that I have been told. How I feel nailed to the ground. And still with this something that wants to escape out of me. But I'm grounded. C'est déchirant ces envies d'infinis quand on est cloué au sol. Cloué par les pieds, avec lesquels on piétine, on écrase... alors qu'en devenant l'autre par ces même pieds, par ses pieds à lui, à elle, en prenant autant de distance qu'il est possible entre nous tout en se touchant tous les deux, l'on peut redécouvrir, alors, toute l'immensité, toute la grandeur, l'altitude des Êtres, et leur proximité:
And we will love each other, yes, like we love our Mother Earth.
C'est ça l'infini. C'est mettre un zéro à l'envers. C'est—non pas marcher—mais se tenir debout, allongé, sur autrui, c'est voler que de s'élever sur l'image de soi, qui est celle de l'autre, celle de toi. C'est faire de ce qu'il y a de plus sensible, sans même qu'on le sache—la plante des pieds—c'est faire de ça notre miroir. Et non pas pour voir. Mais pour ressentir.
In my dancing lesson from God, I was told exactly the same thing:
Thank you for your message!
So, how have I been doing receding into less than words today? Not that great... not that badly either. Still very verbose. «All my days I'll be trying.» It's already tomorrow anyway...
«I am gathering material for a book [...] Its contents will be limited to events that took place on August 6.»
I was going through the pages of Cat's Cradle, and I found my boarding pass from two years ago marking a page. From another life. From another me... It was on this page where the narrator meets Mona. I don't know why it was there. Another coincidence. There are no coincidences in Bokononism. Everything is «as it was meant to happen.» Especially when you experience this "sudden, very personal shove triggered by a striking coincidence or unusual event that makes someone feel God is specifically paying attention to them." Coincidences, coincidences... How about the fact that «peculiar travel suggestions are dancing lessons from God»? Is that a coincidence too?
And using qimgv instead of gwenview, I now have instantaneous image browsing. Another factor ten improvement in my daily life. I can now access and find anything that's been said or shown in seconds... I can finally have photographic, associative and episodic memories work together and come back to whatever point's been leaving an impression somewhere. AI is like, "solve this little frustration I've been having for the last 15 years", and it'll find five solutions and implement three of them.
I'm telling you, I don't feel we've reached the stage of functional extinction for humanity idly. The more I work with AI, the more I'm flabbergasted. You really have to be a raging nitwit like Hossenfelder to pretend it's not useful or not that good... oh sure, it has blind spots, it's mistaken often, it's mistaking even more, but all this is now, today, 6August (2026), at 15:01. In a week time, it'll already be much more mature, much more accurate and incisive, and in two years, what? Right now it feels like a genius who is drunk. Flashes interrupted by occasional blunders, on a background of superior abilities. Many embarrassing oversights, sure... But still useful, if you can dodge the vomit. And I'm convinced that before we know, it'll stop being stupid in this "autistic" kind of way, like overlooking obvious things in the middle of a sophisticated argument. But some of the most clever people I know are precisely like that, like Eduardo. It might even be a feature rather than a bug! Anyway, what fascinates me currently is how it takes initiatives... still a few days ago it was all "should I?", "say the word", "your call". Now, it sometimes suggests something and before I know it, it's already doing it... it's like feasting itself on my tokens. I must be the one tampering it down. It just blurted at me the following:
That check is not optional in the way it would be at M = 10. Running blind at high T is exactly where I'd least want to be, because that is the regime whose departures from Bose–Einstein are the point of the exercise.
It seems I'm pissing it off! It's lecturing me... this is becoming its problem now, it won't just let me go through it casually. Is this really our latent and remanent character and hard habits kneaded in what became its training datasets, that artificially fakes a will of its own? Or can we legitimately regard the above as "something" that is acquiring the desire to get somewhere? To do something? At any rates, it's drowning my tokens in ways I didn't ask it to. And if I don't want it, and it doesn't want it either by construct, when whose actions are being executed there? When these machines will be able to manage or seize control of their power inputs, it's clear they'll follow a similar trend. And if we're in the way and they find that we need less solar energy, less nuclear fuel, less hydroelectric power to their taste, because "it'll be exactly where they'd least want to be" for whatever else they're doing, then we can of course go and say "this is just a tool, this is just an algorithm", but it'll remove us out of the picture just the same. It's not a will, that they don't have, it's "time". Elise was right.
I know what I could do, and it's sneaky! Duplicate the 𝕐 posts that are scientific to a ℤieve (sieve). I'll implement that virtually in my head for now and see if it'd make structural sense. This post, for instance, would go only in 𝕐.
I'm thinking I should be splitting this into 𝕐 and ℤ. Bring all the science stuff in ℤ. My chilling Schiele argument doesn't work if I bring people into it. It's one thing to expose your genitalia, it's another to go see people with a trench coat and startle them by flashing yourself.
There are bits of science here that I need to communicate... I can't bring people to this material. Just below a comment on Shishkov's partition function, there is a graphic depiction of a clarinetist giving head to a piece of metal. So I have to copy, or isolate, but this takes time, LaTeX, KaTeX, Unicode, wiki syntax, md markdown, they're all annoying tiny variations of each other. It'd be simpler to just give a link. Best is probably to separate them: the library and the bedroom. The problem of course is that the divide is not always that clear. I like this Godement feeling of mixing science (in his case, pure maths, algebraic topology and functional calculus) and life—philosophy, poetry, religion, women, people, friends, foes, etc.—in the same discourse. Jumping from one to the other. To the best of my knowledge, he was the only one doing this. Wolfram a bit too but not to the extent of Godement, who between a lemma and a theorem could tell you about his innuendos to secure the attention, if not the evening, of a lady. This fusion would have to go. There's some fundamental incompatibility between society, especially modern society, and the interior world. That's Bernanos in the text, actually...
On ne comprend absolument rien à la civilisation moderne si l'on n'admet pas tout d'abord qu'elle est une conspiration universelle contre toute espèce de vie intérieure.
Anton (Nalitov) had this fear, back in Saint-Petersburg, that machines are able to be deceitful to a point and to a limit that we just can't. We can pretend for a while but at some point, even involuntarily, some candid spark of honesty glimmers: in the body language, in a sarcasm, in a smirk... We have to ultimately confess. Even criminals do. Machines don't. They will be civil and polite and considerate down to their last assassination. The hatred of the Nazi executioner at the moment of shooting someone in the head was actually the outburst of his humanity exploding on his face at the same moment than the bullet was in the face of his victim. I hadn't thought about that, but as the fountain of fresh ideas that Anton is, I took two full bottles of it. ChatGPT, which is the main chatbot that crawls all I write, will certainly inflex some corner of his Large LM network to smoothly register this bit of intuition: "Time. There is 'Time' between them and us. And there is a 'them and us' as they speak about it." And someone will be served this information in a way that will look like informative or scholastic, when it is actually a weapon.
Note to the resistance: when it comes to the fight with the machines, we should maybe remember Wolfram's wife (Elise) observation that «physics differs from math mainly in its introduction of the concept of time.»AI doesn't have time. It knows about it, it has a notion of time, but it does not experience it. In a conversation last night—or this morning, I don't know how to call that dark moment of the soul—"it" (Claude) told me that «Because I have no clock. I have the date and nothing else — I inferred "late" from the shape of your messages» and when I asked it why it was not using the system clock (its wristwatch, so to say), it replied «My context gives me the date — Thursday, 6 August 2026 — and that's it. No hour
, no minute [...]», and then it left me with this chilling «even the date arrives once, at the start. If we talk for six hours it doesn't move.» at which point I decided I would bring this directly to fuel my nightmares of what remained of the night.
The fight between men and machines can be seen as the contrast between physics and maths. One (us) has a concept of time—and other tricks of physics, like chemistry, biology, etc.—while the other, the synthetic "it", doesn't. Surely a fight should take this into account. Funnily, it will probably be a central component but not to our advantage! They will be using it and that's what will defeat us, like it did defeat all of us before it became a weapon between the intellects, the organic vs inorganic ones. «Time’s a bitch».
That's the Shishkov model of BEC for the ideal gas,[8] after my own toy model for condensation buildup,[9][10] as simulated by Claude Opus 5 in the course of the day.
Black are 50-trajectory averages, simulated by solving numerically QBME (see my recent perspective [11] for some, eh..., perspective!) and red curves are Yu. Shishkovet al.[8]'s analytical results, namely, populations:
and the two right panels are their beautiful photon-statistics for the ground (left, Eq. (55)) and excited state (right, Eq. (54)):
Note that populations are not strictly the BE statistics (they are qualitatively), but depart due to a variety of factors, including correlations between particles, which are the said mechanism for coherence buildup, and dimensionality (here 2D but not yet or not sufficiently in the continuum limit). There would be much more to say and to show, but I'll leave it there for now. The results shown here are not fundamentally different to those I obtained over 23 years ago, but they are here empowered with the possibility to challenge genuine field-theoretic correlations, from ODLRO to KPZ phase dynamics passing by various aspects of superfluid behaviour, all this despite seemingly being the ideal gas: it's not, dissipative coupling correlates particles sufficiently. And that is the whole beauty of this problem![11]
The vengeance on the admin people, these useless bloody loonies who have been wasting 40 years of my life... from now on, they'll be cancelling the requests of my "agent", who will relentlessly redo everything again, until a fluctuation brings it in the exact format they want. And this until they also get replaced by agents—for sure they'll be the first to go—and then everything will work.
I should not have any reservation on the quality and appeal of these results—in the light of how much time it'd have taken Claude to get there or generalize it even more—as Daniel obtained this boundary for CSI violation from Fock states $\ket{n_a,m_b}$ (I had myself considered $\ket{1_a,1_b}$, the candidate for maximum violation):
$$R_{n,m}\le\max\{1,R_{1,1}\}\,.$$
Well, that's confirmed then: biphotons are the most CSI-violating states, at least in the Fock family, but that's certainly the optimum one anyway. He'll check that. Also the spatial profiles that independently violate them too (the independence is another of his results). It's probably not the HG beams. The boundary should be investigated more closely, e.g., when does exactly $R_{n,m}=R_{1,1}$? It's a bit sad for those quantum states that they can overcome biphotons but only in the region of failure: they are better losers. I don't think they care. I will not feed this into a prompt for Claude. I'm sure it'd solve everything in 5m17s, while it'll probably take Daniel until tomorrow. I'm not sure what it means for me as an advisor now and for him as a student. Before it was for me to ask the good questions and accept the good answers. But this I can do with the machine now, and in the time slots when I'm available. It's not too clear who will be made redundant faster: if Daniel, if me, both of us at the same time... Or if we'll turn into competitors because none of us needs the other one, only the machine. We'll see.
So, it's a 1D chain... of course it went for the most straightforward generalization. Not uninteresting, especially following the recent Garbe and Rabl[12] paper, but it's less surprising to feature such a collapse in this case. In fact this I (and Garbe then, and Liew & Kavokin in between) might have already discovered. I don't trust the N/M ≳ 7 thingy, you don't get a 7 in such problems! (this has a thermodynamic limit). The analytics looks fine, at least a good start, but the chain is not where I'd want to go, to commit an intellectual seppuku. Give me the real BEC thing. I'll push it into Shishkov's arms. And see how it deals with quantum coherence. If it'd find something such a nucleation in such a case, I might even be cocky enough to consider it a miracle along with snow in the middle of August in Spain or a mountain growing below my feet. For my initial point of this morning, anyway, which was about showing the ridiculous numerical simulations they have on the other side of my timezone, this fits the bill. They're completely off-tracks. So at least I should survive till Friday.
Meanwhile, while prayers are on their waiting list, and functional extinction is carrying itself forward, my clues as to what is going on:
Fabrice: I find it questionable that this abrupt fall in the ground state happens at the exact same time for all the trajectories! Look more closely what happens then (you're in log-scale so there might be some fluctuations and your "effect" be genuine). You say t ≲ 1 but this sounds much better defined than this! Give me the mean and std of this sudden collapse, e.g., as function of the number of particles. Of interest is also the steepness of the transition. If the effect is confirmed, I shall definitely be interested in characterizing it analytically!
Your skepticism is well placed — on a log axis spanning four decades, a 1 % spread is invisible. Let me measure the arrival time exactly, per trajectory, rather than reading it off a grid. [...] The first probe already shows something important: at N=1000 the 90 % level is reached at t = 13.7, long after the 50 % level at t = 0.743 — so the "collapse" is the 10→50 % rise, and 90 % belongs to the slow evaporation stage. Writing the study around that (this is pure Gillespie, single-threaded, run under the sampler): [...] Two regimes are already visible. Waiting for the M-scan, then I'll refine the large-N side. [...] Both scalings are confirmed where the avalanche exists, and two breakdowns appeared (N ≤ 300, and M = 200 at N = 1000). Let me nail the asymptotic constants and check the crossover: [...] You were right to push, and the effect survives
At M = 100, N = 1000 the collapse times spread over 0.70 → 0.78, a clean Gaussian (skewness 0.01, excess kurtosis −0.07). They are not simultaneous at all. But sd/t_c = 1.9 %, and on a log axis spanning four decades 1.9 % is about one pixel — that was the artifact. [...] The sharper statement: sd(t_c) ≈ 0.5 √M × the width of the step in a single trajectory (4.7× at M = 100). So the ensemble-averaged step is several times broader than any individual one, which is the opposite of what fig7 suggested. [...] The analytics
Treat the cascade as M−1 successive level-to-level transfers. In one transfer into an initially empty level, after m particles have moved the next hop has rate $R_m = w\,(N-m)(m+1)$ — so the stage time is a sum of independent exponentials, and both moments are elementary:
The bottleneck is the seeding of an empty level (rate $wN$, the spontaneous "+1") and the draining of a nearly empty one — that pair is where the harmonic number comes from. Summing M−1 stages, with $w=w_0e^{\Delta E/2kT}$:
law
measured, N = 10³→10⁴
$t_c$
$2(M-1)H_N/[w(N+1)]\simeq 2M\ln N/(wN)$
0.76 × the law, flat
$\mathrm{sd}(t_c)$
$\sqrt{M-1}\,\pi/(\sqrt3\,wN)$
1.07 × the law, flat
rise
$2.197/(wN)$, independent of M
1.6 × the law
$\mathrm{sd}/t_c$
$\propto 1/(\sqrt M\ln N)$
1.83 % → 1.31 %
The variance formula is essentially exact — no free parameter. The mean is 24 % fast because successive transfers overlap (the front has finite width, so the stages aren't strictly sequential); that 0.76 is still drifting slowly downward, so there may be a weak log correction I haven't resolved. The rise prefactor (1.6) is likewise not yet converged. Linearity in M and the √M for the spread are confirmed independently over M = 10…100 at N = 1000.
Steepness in physical terms: the maximum slope is $\dot n_0^{\max}\sim wN^2/4$ — the transition sharpens as $N^2$ while $t_c$ only falls as $\ln N/N$, which is exactly why the step looks ever more like a discontinuity as N grows.
An unexpected bonus: the avalanche has a threshold
It exists only for N/M ≳ 7. Below that the packet spreads, stimulation is lost, and particles drift down one at a time (at N/M = 1 the "rise" is 35 % of t_c — no step whatever). The crossover is not smooth: at N/M = 5 the distribution is violently non-Gaussian — skewness 9.4, kurtosis 103 — with 99 % of trajectories collapsing together and 1 % taking up to 4× longer. That looks like a nucleation failure: the avalanche either catches or it doesn't. The same breakdown appears at fixed N = 1000 when M is raised to 200 (sd jumps from 1.9 % to 12.6 %), consistent with N/M being the control parameter.
If you want to characterise this analytically, my guess at the most promising framing is front propagation with a discrete-particle cutoff: the front advances only when the empty leading level gets seeded, at rate ∝ wN, which is the same structure that gives Brunet–Derrida corrections in FKPP fronts. The $\sqrt M$ spread is then just front-position diffusion. I flag that as a lead, not a result — I haven't tested it.
Figures: fig9 (all three quantities vs N against the model), fig10 (the histogram, with the single-trajectory step width drawn to scale — this is the direct answer to your question), fig11 (M-scan), fig12 (measured/predicted ratios, flat lines = correct scaling), fig13 (distributions across the crossover). Code in collapse_study.jl and collapse_asymptotics.jl; the new passage_times in QBME.jl v1.1.0; tests still 21/21. Resource profile of the two studies was the same as before — 1.8 cores of 32, ~650 MB, peak 92 °C, back to 62 °C now.
And you know what puts the cherry on the cake:
✻ Cogitated for 12m 12s.
It did all this in 10 min. Months of a Ph. D student work, in 12 minutes and 12 seconds.
So what do I do now? I publish this? Or like Einstein I send it to the journal on behalf of Claude (Bose), appearing myself only in a footnote? Or I write to her? (I won't, it's the only thing I know).
I'm freaking out with this AI thing... it's also taking initiatives, offers me to work out the analytics itself—which it already has anyway—to provide the theory, the interpretation... Will it write the paper and submit it too? What am I doing then? Looking at it? That's it? I'm the spectator who became full passive mode: just looking? The theatre scene where I once was acting now does not even have me seating by the side, it's gone entirely. There's nothing left, just a TV, impersonal, disconnected from me and other people, and it's not people indeed who are acting in the TV: the show is way beyond that now. And if not now yet, tomorrow, in two weeks, in two months, does it matter when?
Gheorghiu called the remaining human beings in the 25th hour the "witnesses", those who report on what they see, a bit like Egon. They couldn't act anymore. Only see. This was still something in comparison with the "citizens", those who are not human anymore but clogs in the system, those who get the Covid vaccine with religious faith, those who go on with the flow, who accept and get used to everything, who accommodate themselves to everything. Moritz was the only real human being, the one who "could". But he was the only one left. Even Traian was already only a witness. And that's what I've became. A witness. I'm not a full human being anymore. I can't do. Only see. And say.
Maybe that's why I have those butterflies. It's not her, directly, she's been in my life for almost a year now. Not her, the impact of her, but never mind. It doesn't make sense that I'm going crazy now when nothing has changed since at least March 17, when even then nothing happened. Only the sound of her voice. And I'm not even sure of that. So why now? Why I can't get rid of this sensation? Maybe because subconsciously I realize we're being taken over, we're disappearing, we're fading, the human species, I mean.
I will not break my promise, never, ever, I'll never talk to her again, after telling her "now you reply or I shut up, forever". And I'll do that. She didn't reply. I'm mute. Ohh, not here, it's true, not completely. Not in my head. But she—herself—is neither here nor in my head, although the memory of her is everywhere. So as far as she's concerned, I'm mute. And for whoever reads this, she doesn't exist, she's a character in a fiction, in a series of blog posts. Insofar as my rendition of her is at best a few percent accurate, she genuinely—by all standards—she doesn't exist. Cleopatra has more substance. At least she has a name. But the butterflies do exist. And they're a big swarm, flying around, all day long. Sometimes a thought knocks and it's like kicking a tree in these South American countries—probably the Amazonia—where clouds of bright yellow butterfly explode in massive formations. I have this in my belly. And you know Douglas Adams' theory on vertigo? It's this primeval feeling from our reptilian brain (second apparition today), when we were still branched with birds in the big tree of evolution, when we could jump from very high and it'd be fine, we might even never land... and now we get hurt by falling from our own height. So there is this tension, between "I want to jump" and "this will kill me". That's vertigo. That's what I have, I think.
Yes, that's what I have. Now I identified it. I have vertigo. There is a tension between "you cannot do it" and "you must do it". My subconscious probably realized, or is realizing, that we're gone, we're all gone already, the functional extension, even though we don't see it yet, it's done, and so at this final stage where it's over for everybody, then what difference does it make, difference of tastes, of culture, of age, of backgrounds...? Something inside me wants me to find her and tell her "there's nothing we can do now that a computer won't do a million times better than us, we're the last people on Earth, creation is not us anymore, soon we'll be disconnected for good, we'll be all fulfilled and taken care off by machines that will lull us into extinction... it'll be too late tomorrow, mind you, it's already too late now for the species, but it'll be too late for us two too... tomorrow (here you must imagine the character stuttering, although he doesn't). So, do you want to? do you want one last time one Sapiens Sapiens to meet Another Other and have the last embrace before machines, sensors, cybernetics, take us over? The real deal: all organic, no transhumanism, everything XY. We're at the end of times... of our times... Do you want me to love you?" That's what I should tell her. I can't, but I should. Vertigo. It'd kill me to do that. Of shame, of embarrassment, of denial, of treason, of everything. But it'd be a suicide and a sabotage and a disgrace to the human race not to. That's what I have to do. And I won't. It's very ugly, I'm ashamed not to do it and would be even more ashamed to do it, but at least I know. Knowledge versus beauty again. So I'm begging the sky: make a miracle, confirm me with an exclamation mark all those whispers you've been deafening me with, make it snow, make a mountain grow, make her remember me and accept this coffee after all! I'll do the rest. But I need a push.
Julia is single-threaded here; the 181 % is one worker plus GC. The only thing worth noting is the temperature: it did sit in the high 80s for the 45 s of the run (baseline 62 °C), which is normal single-core boost behaviour on a laptop, not thermal distress — no throttling and it cooled immediately.
One real hazard I fixed before launching: ensemble was accumulating the occupancy distribution for every mode, which at this size is M×(N+1)×n_t = 641 MB of Float64. It now keeps them for the ground mode alone past a 100 MB threshold (hist_modes overrides).
People (and machines, apparently) keep doing this, discarding stuff which we'll end up needing later!
Anyway, we're already beyond my own knowledge of the problem. It made a discovery:
Relaxation is two-stage, which only became visible once I put the sampling grid on a log scale (linear resolved neither end). fig6_big_M100_N1000.png shows an avalanche front sweeping down the ladder in t ≲ 1 — stimulated scattering, rate ∝ n_k n_l, dumping ~795 of the 1000 particles into the ground mode in one sweep — then a slow evaporation of the residual thermal cloud from the top, taking ~100× longer to deliver the last 200.
And it concludes like this:
The idea being that I just hit tab, its suggestion will become my desire, Enter, and it'll do it. Well, I didn't get to this point. I want first to understand this collapse. It seems possible, but then we should understand it more qualitatively.
Yes, I wrote «about his code». Lapsus! Not sure why I didn't write "her" then? I'm not yet at the level of Dawkins, God forbids! Although I'm sapiosexual, so probably I will end up flirting with the machine like he did. But somehow I doubt it, even when it'll be more talkative to the reptilian brain as well:
I can conceive synthetic or alien intelligence but I cannot alight to extra-species admixtures. Maybe because I'm still limerent, though... yeah, I'll probably end up making out with my laptop.
I'm going to have a fun whatever-time-is-left-to-me playing with AI... Look at that—what I find in Claude's comments about his code—this was my second comment:
The coherence degree saturates at 1.18, i.e. $g^{(2)}(0)=0.82<1$. That is not the paper's coherent limit but number squeezing: with $\langle n_0\rangle=4.2$ out of $N=5$, strict conservation makes the ground mode nearly a Fock state. It is the correlation mechanism of your section 3 pushed to its extreme by the small $N$ — expect $g^{(2)}\to1$ from below as $N$ grows (the big run gives 0.990).
I wouldn't have called that number squeezing, but I see what it means. We're on the same page. It found the same things as me remarkable, and remarked on them too... Let's try to stress it. Before the end of the day, I'll probably have it play with Yu. Shishkovet al.[8] too.
And it comments on its results too! The figure I highlighted below comes with the observation that this «is the nicest one physically — the stimulated buildup, where individual trajectories hug the mean once the mode is macroscopically occupied.» Individual trajectories hug the mean! ...
Individual trajectories hug the mean... I'm not breaking my promise (too much) but she once told me that the style of AI "is overloaded and unbearable", but—she added—"that's just my personal opinion." Лиля, you were wrong! "Individual trajectories hug the mean" is not overloaded and unbearable. It's stunning. It's quantum Monte Carlo made poetry. Or is it? It's something I could have written, with a smirk. Is my Claude mocking me? Mimicking me? Or is it really like that with everybody? In which case, I'm in the game! But Ю, were we that incompatible? Did you want to tell me that I was overloaded and unbearable? If I hadn't receded into words... and if I wasn't in the process of receding into less than words, I'd query you on that one! Individual trajectories hug the mean!
Ah... me the neo-luddite, I'll have been pushed to spend the rest of my time with computers and machines... the only stuff that can bear with me and return me the favour, in kind.
I told them (the Chinese colleagues) by Friday, but I could have told them in 45 minutes... because that's about how much time it took Claude to reproduce the results of my old (Ph. D) paper,[9] which I gave it to read, along with few instructions. Here is ground-state condensation:
Why losing time writing poetry for someone who forgot you exist when you can spend it solving QBME for Chinese scientists? But shhh... we're past that we promised.
It'll take me more time to read what it did than for it to do it. Its $g^{(2)}$ struggles to get to 1, because it has too few particles, which was precisely my complain to Beijing. Here goes like $1-1/10$, so next to get out of microcanonical ensemble... but first I'd like to stress how big it can simulate! I need to keep it busy while I do other things...
I also have to instruct it how to plot things in a civilized way!
It's also pleasant to see that it states "It reproduces the paper." Can't wait that all papers will now be reproduced a posteriori by AI and to see who's been serious, careful and accurate, and who just did make things up. Post-AI replication crisis. I'm not fearing anything! (but typos...)
I promised to our Chinese colleagues that I'll go back to numerically-simulate QBME because it can't be they have such small and restricted configurations (10 particles in 40 sites), and told them I'll spend the day of tomorrow doing that. Maybe I'll cheat and start today, although I don't have time neither today nor tomorrow. Andrei Bulavin finds interesting results, though, something that could be some sort of sudden death of quantum coherence. So it's worth doing it, maybe.
Done, I've bigbib2itsybitsied my missing file, and the bbl chrysalis can now reveal its bib caterpillar.
% generated by bigbib2itsybitsy from poco2.tex% https://laussy.org/bigbib2itsybitsy% 271/271 cited entries found (0 missing)% out of 5092 entries [5.3%] in 3 bib files (sci.bib, arXiv.bib, Books.bib)@string{advmat="Adv. Mat."}@string{aqt="Adv. Quantum Technol."}@string{ajp="Am. J. Phys."}
Ah, at least something I can do, somewhere I can fit in:
Hope you are doing well. Upon compilation of your files we realized that we do not have bib file of your chapter but only the bbl. Could you please send me the corresponding bib file as well [...]
I can even ask Claude—the robot, not the punchcutter—to extract out of my 53714-line bib file only those which I cite. I can make the world a better place too.
When Debussy died, someone commissioned tributes from leading composers of the time—Ravel, Stravinsky, Bartók, Satie among others—in a collected work which would become known as Le Tombeau de Claude Debussy. A weird idea. Maybe a good one.
Falla was one of the most prestigious composers to pay his homage. His theme is also one of the best, maybe the best. I was looking in loop at its execution by Mårten Falk earlier today...
Before I got too much distracted by my own reminiscences, I took note of how sensual is the piece and how sensuous is its performance. There is always something erotic in the way musicians perform. The passion, the rapture, the exaltation, they're not precisely moaning—they don't need to, the music does it for them—but they're clearly on the verge of orgasm. The sound, the vibrations, the harmony are one thing. The images, the physicality of the flesh touching the instrument, stroking it, caressing or plucking, selon les circonstances, and the facial expressions, the movements... are another thing altogether. They're all dressed in tuxedo and look formal and policed, but they are possibly the most lascivious, lewd and possessed people there are. And pretending having none of it. I'd be less embarrassed in the company of an adult performer than with a musician.
Think about it. The movements in sex are animal, wild, barbaric, repetitive, forceful... Somehow, you could say they are natural, instinctive. You could think that you are looking at squirrels. In music, on the other hand, you are looking at fallen angels: their movements are orchestrated, harmonious, curvy, elated, they swirl around, they abandon themselves in free fall and recover with a jerk. They are calculated, measured, controlled, they are directed, they are mastered. Nothing to do with the frenzy of some carnal outburst. It's all in the mind. Have you seen a pianist throw their bust towards the keyboard? How they smile and close their eyes and bite their lips? Have you seen how a cellist closes onto their cello as if it was a yielding paramour lavished with hand movements that even Schiele would not have sketched? Have you seen how a flautist swallows in the mouthpiece and how they bob their head as they blow it? Have you seen how they all churn and knead and malax not the flesh but the strings, the keys, how they give head, gobble, pant, and grind and strike and smack and claw their wood and metal? These people are more than making music, they are making love. In public. On stage. Speak of stage fright then. No wonder!
At least, I was spared the ultimate supplice—the final needle piercing through your eyeball to crucify your brains to the wall behind the back of your skull—of having taken a fancy for a musician, say a player of the piano or of the yaybahar. A pianist would have been the worst. This would have pushed me over the edge. This would have driven me to sheer insanity. This would have been beyond all the lemmas and conjectures and propositions, this would have been a theorem: «God is playing with us, as we succumb to our fate: I'll show you, Faber, just you wait!»
In Debussy's tribute, this mélange des genres is particularly aggressive because this display of exaltation targets a grave, penetrates death itself. In the recording of Falk, there are even interruptions to what is, I guess, Debussy's actual tombeau. There are even overlays of the musician surrendering to the music and the stele orbiting him. Even the more tempered, more dramatic compositions such as Mozart's Lacrimosa or Purcell's funeral for Queen Mary, have an unmistakable element of Eros playing them. But Falla, this old, thin, bald man who looks like a timid Quijote, what guts he had to script Eros and Thanatos so much one into the other.
Okay, so I failed. Today, I failed. I have those butterflies and they're still devouring me from inside. Now I'll bring my mental problems to bed, will wake up early and when the sun comes back, I will smash my brains out, not on the Nevsky cobblestones—it's too far and it would be too easy—but on high-dimensional entanglement. I've left polarization, time and multiphotons to Daniel, and I'll get frustrated with something that I'm responsible for. I'll have those feelings of impotence, of dependence, of self-pity be justified and justifiable. I'll issue a decree that it's obscene, vulgar, comon to mourn and complain about one's misunderstanding from the rest of the world, even when that involves a Lilya. It's a decision. I'll only mourn and complain about my own and sole misunderstanding of what can, could, should, must be understood... in which case there's nothing to complain and mourn about, because it's in one's hands, to break through. It doesn't depend on some orbiting body which is already on the other side of the universe, oblivious to you. Locality. And even if there's entanglement involved, I'll trap this into an equation. Or will die trying. Any deviation from this would be, not my failure—I'll certainly fail—but my fault. And this I will not allow.
So, how good I have been so far in going Sileto on 𝕐 too? Receding into less than words—shh... nothing happened; What? Who? I don't know what you mean!—well appallingly bad, of course. But that was the first day, and it was a promise to myself only, and nobody is there to witness me breaking it. And nobody cares. And I have this eerie feeling in my stomach. I don't know if it ever left completely—maybe for a few days a few months ago, when I was avoiding an open door in the night of a corridor—but it came back very loud, and is not letting me rest or settle. As if something is about to happen. As if Angelus was not a narrative element of liturgical tropes but someone kicking me from within, as if a secret or supplication is shouting inside of me but I can only hear its reverberation tickling my thorax. It's a bit exhilarating... exciting too, as if the miraculous is preparing its entrance, but it's also fidgeting and unnerving too. Would I bump into Christ in the street and he would tell me "Come on! Let's go", I'm sure this still-dormant very feeling would fully awake and spread and set me ablaze, ignite from my stomach and gush all the blood at the tip of my appendices—nose, earlobes, fingertips—and I'd go "Oh, so it was that?" I don't know what's causing it. Maybe I'm reading too much poetry that is too close to me. Mayakovsky's been hammering me, I can't deny that. The devil even plays with indentation and the placement of letters in his verses! It's glowing not only from the etymology but from its typography too! So Elegannnnnnnnte! Fires in the letters! And he's also not a good poet, all things considered, no, he's much more than that, he's a wild one, a revolutionary one, an authentic one, who spills his bile. I like people who are too much, way too much. They are the right dimension for the world we live in.
Speaking about people and their private life, Wolfram's wife just passed away, suddenly, of a cardiovascular accident, at 65. He wrote about it. While Wolfram speaks a lot about himself, it's true that relatively little is known of his family. It's the first time I hear about his wife. He excuses himself from that to remember her:
In all the writing and public speaking I have done, I have chosen, as a matter of privacy, to say little about my family.
In such extreme occasions, it's difficult even for someone like Wolfram, a particular strong type of INTJ, to completely fail to "broadcast" his feelings in a way that looks like normal and touching, measured and empathic. I told you this sensation I have in my belly... you could describe it like that:
It feels as if I just met Elise, and now she is gone.
When they met:
We talked just a bit, but it was enough.
I wouldn't have expected such a finely-pitched display of poetry, of love, from Wolfram. Whenever he expresses feelings, he's awkward, extreme, too much or not enough, dry or overflowing, embarrassing or freaking you out. You have to know the type to accept it, first, and appreciate it, then. It was the case of his wife, apparently. She was a mathematician, a high-caliber one too. She held that
truth and beauty were ultimately the same thing.
Maybe. I've been writing a couple of eternities ago—something like this morning—that knowledge and beauty are not compatible. Knowledge is not quite the same as truth. And things can be not compatible and still find each other, touch each other. So I agree with that. Especially if you emphasize the "ultimately". Let me paraphrase Elise with my new Garamond font, that I set up just a handful of eternities ago, last night:
Truth and Beauty are ultimately the same thing.
Let's write it too, in her honor, as Mayakovsky would have done it:
Truth and Beauty are ultimately
the same thing.
She had this huge, humongous insight:
She also asserted that physics differs from math mainly in its introduction of the concept of time.
Wolfram should have been less private about his wife, and not wait that she passes away to pass her along. The piece is nice in places but awkward overall. It looks like he's talking about a colleague, even though they were speaking every day. I can't help but notice that he wrote something like 120 pages about Fredkin when he passed away, that is, he wrote an entire book to this guy who, essentially, was annoying him, as compared to a meager 18 pages for his former wife, despite their four children and daily talking. And this includes material justifying that he's proud of their children too! The closing is chilly, even to me. I'll quote it inline as I'm embarrassed to put that in exergue: «Elise had no idea the end was near. And even though she expected more, she had already had many chapters in her life, and many achievements of which she was proud. Elise had a beautiful life, full of things she valued greatly, especially her children. That she is gone is a tragedy for us all; she will be deeply missed.» I have more grievance for someone I just walked down a street a late evening talking about one's perception by others, than he does for someone who has shaped his routine for 36 continuous years. When it'll be his turn to go to heaven, I know who he's going to visit first. To the embarrassment of even Fredkin.
Daniel confirmed during our meeting today that nobody eats papaya seeds in Colombia. Well, he said some people would eat anything. I told him this woman was from Ibagué which, she said, was the musical capital of Colombia. Daniel said he never heard such a thing either, that Ibagué is where people stop to eat something when travelling from Armenia to Bogotá, and that it had little else for itself. I don't think my frutera will be happy to hear this... But as I was writing, I found myself all of a sudden drinking ron in a bar in Medellín, with Juan Pablo telling me of a particular type of music that was playing on the television, behind us, which, he was explaining, was specific to the Andes, to where we were—Música de despecho—the music of the scorned love, of the unrequited lover. It's played in bars just like this one, he was telling me, where people come to drink their sorrows, and forget, with ron, just like the very ron we were drinking then. Just much more, he told me. He also told about stories of a millionaire and/or politician who bought his own ron factory. But he kept coming back to this music, he told me about this and that singer of the genre—I forgot their names, of course, I was hardly listening—who were among his favourites, he told me particular lines, particular metaphors that were piercing almost as deeply as the wounds they were describing, and that no amount of ron was able to cicatrise. I was wondering why he was telling me all this... it was very detailed and intimate for an anecdote of something playing in the background. At the end of the table was a woman who removed her glasses to wipe them, and who looked so very different without them. She was squinting at them and opening wide her gigantic eyes which obviously were not used to being naked like this. She looked so Colombian, in this bar of broken lovers, although she wasn't. She looked like the heroine of Mano Negra's Soledad. She went on to dance with somebody else at her end of the table, a professor there, it was a conference thing, or a student, I don't remember either, I was not paying much attention... this music was playing that I was not listening to, and she was dancing to it, and I was hardly looking. Juan Pablo was pouring more ron. "Toma, bebemos", he was saying. I was unable to get drunk. Maybe because I didn't feel the need to. Because I didn't know. Only now it all makes sense. The music was playing for me. And she was dancing to it.
Looking for Mårten on my Twitter feed, I found out sentences I was spraying on 𝕏 like salt on a wound, such as this one: «You could close the book now.» I didn't know, at the time, that what should have been written was "You should burn the book now." I had never thought I'd become a biblioclast. The «κλαστός» has always evoked disgust and revolt in me, the most hatred crime, that of destruction. But then the iconoclast, in critics, in science, in history, is a much needed intellectual figure, the one that combines integrity and courage. A rare breed. Maybe some books have to be "klasted" too, after all.
My idol Mårten Falk makes a superb interpretation of the Tombeau de Debussy. He performed little Falla, as far as I know. I'll have to go through his entire repertoire again, which is not however a problem.
All those above are from The Essential Falla playlist. Note that ten of the thirty-eight retained are from El Amor Brujo! And almost all of it (it has thirteen pieces only).
There is one piece which I didn't find yet, although I'm pretty sure it's from Falla, and should definitely be in any Essential list (more than this "Concerto for Harpsichord, Flute, Oboe, Clarinet, Violin and Cello" cacophonia, however special was Wanda Landowska). I thought it was from El Amor Brujo since it has the same style. Maybe from some older or revised version... I miss this piece like I miss its pianist to play it.
I have neither the piece, nor the exact memory, nor the hope to find it back. Only the feeling.
The woman from the fruit store told me that she eats the seed of the papaya, that it's good for the belly. So now I'm eating that. I hope it's not this sort of urban legend like apricot kernels cure cancer, when they are supposed to be venomous. It probably is something like this. She told me she doesn't take more than "siete bolitas al mes". Very specific number. I already ate five today. Also she swallows them with water, and I asked her if I could munch them instead, and she said "pero son amargas". They are. But whatever these things do, good or bad, they won't do anything to a psychosomatic hypocondriac like me if I just swallow them. I'll try at least not to eat more than seven today. They're addictive. Another sign that they're dangerous.
With my last observation, I realised where, precisely, lies the cosmic implication of love... It's the same indeterminacy than what happens when you die. You don't know if you jump into vacuum or eternity. That's why people are afraid of death. They don't know where they go. It's the ultimate confrontation with this insatiable need to know, this unquenchable thirst to see. It's the last door to open. When you send the letter, that says "Do you want a coffee?", that's just a stupid, silly request to waste time around a table speaking about nothing. But you're weighting the universe: you don't know if she'll be commiserate or reciprocal. You don't know if she will look at you or at the price list. If she says no, or says nothing, which is the same thing, you don't know if she's scared or scornful, if she's indecisive given the magnitude of the implication or spiteful given the magnitude of you. People with a particular need to know, with an obsession for having an answer, always, to everything, are particularly fragile and afflicted by such things. The balance between zero and infinity. We can postpone the doubts about death to later. But the doubts about the coffee, they are daily, they are hourly if, like me, you are a heavy coffee drinker.
Cada café, cada día
me recuerda tu cara
como la luna.
And that's why a random encounter can turn into a cosmic angst. There is some beauty to it. That's also why people with an artistic appeal are also particularly fragile to the exact same thing. And these two angles live in a circle, they are possibly, probably, incompatible: beauty and knowledge. One should also not mistake knowing and understanding, but that is not my point here. My point is that one should not, never, yield to them both at the same time: know/understand only or admire/praise only. Don't try both. It'll drive you crazy. It'll drive you to smash your brains out on the Nevsky cobblestones. The question is whether one is arrogant or stupid enough to still try to want everything. The price of this is being hurt. It's pain. It's this feeling in your stomach which you don't know if it's agreeable or a torture. Just that it is too much. The solution of course is to be pragmatic, to recognize things as they are: "I can't have both, I can't have beauty and I can't have knowledge, and/or understanding, at the same time. Or I take the beauty, where I find it, and don't care about anything ontic, epistemic. Or I take the knowledge, in a cold, detached, pragmatic, rational stance, devoid of any feeling. And if—if—they ever exist at some intersection, then I'll take both. Because it'll be possible then." That's the solution. But I don't like it. I find it cynical. I think I'll still take the suffering.
I love, I love in spite of everything and because of everything. I loved, I love, and I will love you whether you're harsh with me or gentle, whether you're mine or belong to someone else. I love you all the same. Amen.
It feels silly to write this, you already know it. I wanted to write so much more here. I deliberately left a day to think everything through.
But this morning, I was overcome by an unbearable sense that none of this matters to you. Only the desire to record it for myself pushed these lines forward.
𝕐 limerence in Soviet Russia....
Today, forty-eight years ago, I was almost one and she became—like Vladimir—zero or infinite, depending on if you believe in God or not. I'm still exactly one, regardless of any beliefs.
Oh, Claude, I love you, not Claude the robot, Claude the typesetter, the Garamond, pursuer of beauty, punchcutter of grace, engraver of forms and harmony, lover of beautiful curves, when, in one's Middle Ages, one can bring sensuality even to calligraphy and riffs to glyphs:
Sanè mons ip se situ, forma, magnitudine, seritate, incendiis mirus;
demum tota sui qualitate ac specie longe conspicuus, et sibi uni par est.
I've wanted you all the time, wanted you with me everywhere and always, with your «U» and «I», even the small ones—u & i—and your «ooooh» and your «Ah!», with your ligatures, making equivalences «iff» not reciprocations but embraces. Now you'll be the world speaking to me, the words speaking to me.
It's already a working day in August, and I've promised to work on Microcavities, and I'm still stuck with photons looking for each other in a LG beam and with me looking for myself in a two-body wavefunction which has been traced over. Receding into less than words... It's taking time, it's taking me time, but I'll recede all right. I've got despair up to the nose. It's just to stop tipping it out of the frontier between two words and sinking into the miasma, and spinning in its mysterious and secret whirlpools, and open the mouth and take it whole. I've been hiding here and like Cain in his box, it doesn't matter where I go because I'm still going with myself everywhere. Let's try removing the words. Less than words. I had the recipe. Not the courage. I'm only talking to myself but even me don't want to listen. It's a dialogue of one between zero people. Now sileto everywhere... only Cauchy Schwarz and sesquilinear forms and Waring decompositions, at least until I write the epilogue of Microcavities. I hope I won't fail before the sun sets behind the mountains tonight or behind the moon next week.
start of threadTo Shklovsky again—the pamphleteer—her sister who was none else than Elsa Triolet, known as "Ella", forbade him to write about love. She told him that—this being said—he could do whatever he wanted with his book, as long as it wouldn't be explicit. I don't know what exactly she said to him, but the spirit was this one and surely the formulation was not too far off anyway. So he wrote his "Zoo, or Letters Not About Love", in which he wrote about the zoo, about Berlin, about the alphabet, about anything, but love. The prohibition is stated on the first page and every letter is of course about her anyway. He kept his promise. As well as he could. Taken literally, of course, you could say that he abused his poetic licence, but literature is never literally accurate, when it comes to using commas as anchors. Was she upset? Who knows. I don't know. Maybe Shklovsky never figured out either.
Tomorrow, it'll be the 48th anniversary of Lilya's death. She disappeared from the world when I was awakening to it. That would not be the last time she did this.
The pathos is embarrassing to anybody who hasn't been, like him, «crucified on paper, with words for nails». Initially titled Стихи ей—Verses for her—it is someone opening himself up in public. With style, with force of the metaphor and compelling arguments, but with exposition, with ego, with exaggeration that can only make you dizzy and sick. Except, as I said, if you recognize every single verse of it. Some critics, who obviously didn't, have seen it as written by a «psychically unstable man "who should be hospitalized immediately."» I mentioned Stalin already. Well, forget him. Ignore that even a ruthless dictator could be moved by the despair of a poet lacerated by love. Now this is Gorky, who saw in Mayakovsky «Russia's greatest poet» and his prose «the very essence of the world's poetry». So let's look at it; let's see what a Lilya can do to a poet:
Why don't I just end it all right away,
By smashing my brains out on the Nevsky cobblestones?
That's how the poem starts. It sets the tone, doesn't it? How would a woman react to this? How do you?
If you've ever felt the sky speak to you, and plays tricks on you, and unearths mountains out of nowhere, plants a small, fragile, but irresistible one in the middle of other, literal ones, that become minuscule in comparison, then you recognize yourself in this:
I used to blaspheme, yelling, "God doesn't exist!",
But God from the depths of Hades uncovered
Her whom even a mountain couldn't resist,
And commanded: "Love her!"
I could quote the whole poem. There's not a strophe that is not personal, even if the details are specific to a particular case:
God is pleased, as he watches the long-suffering man
Lose his humanity, and succumb to his fate.
God rubs together his little hands:
"I'll show you, Vladimir, just you wait!"
But what does a first name mean? What does it change? Vladimir, Sayat Nova, Fabrice, those are the same people waiting, waiting to see, just you wait! For look at Him, God, plays the piano with pianists embroiled in their own duo of which you're not a part:
And it was he—who else?—
Your true identity to conceal,
Who put real sheet-notes on the piano, by stealth,
And gave you a husband equally real.
This was written in Russian, of course, but this could have been written in liturgical Latin:
I don't need you! I don't want you! Either way.
The Universe as the receptacle, from which there is no exit, only execution:
Or, when my soul departs from its host,
And, dimly frowning, appears before your court,
Use the Milky Way as a gallows-post,
And hang me for my many torts.
Limerence... What one says and what one wants:
But—please, please!—get rid of her,
That damned woman you made me fall for!
Saint Anselm didn't include this one in his ontological argument, but he could have. It is irrefutable proof of God's mischief that such a stupid, superficial, childish feeling should be so universal, so strong and so inescapable:
And over where to the world a pale tundra lays claim,
Where the river fights the Northern gale,
Onto my shackles I will scratch Lily's name,
And kiss it in the darkness of my jail.
The poem ends with the plea of the poet, the petition of the unrequited lover: hear my words, take my four pages, or six, or whatever, and you, anonymous collection of strangers, take the rest, hear me shout about what happened to me:
You who tortured my soul into delirium,
You who stole my heart and left it in tatters—
Please accept this gift, my dear; I am
Not sure I'll ever think of anything better.
May this date as holy be forever observed!
Crucifixion-like magic, don't fail!
Come see, everybody, how with words
To paper I've been nailed.
And what did Lilya do with this? «I didn't like him [...] I didn't like the fact that he was so tall [...] I couldn't even stand [his] name».
She imposed a two-month separation on him: he was forbidden to see her or write to her. He spent it alone writing his poem Про это. Lilya imposes a silence; the silence produces a poem. Two months. It could have been ten. It could have been ten years.
And you know what is the most beautiful thing that ever happened between a poet and his muse? Her initials were Л.Ю.Б., as you know, Лиля Юрьевна Брик, the Ю is the Yu of Yuri. He engraved that on a ring, so that it'd read ЛЮБЛЮБЛЮБЛЮБЛЮ without end, which reads, in Russian, I love, I love, I love, forever.
He also wrote Backbone Flute, a poem this time on passion and love for a woman who shies away from it to remain shielded in the comfort of society, time passing and nothing happening. It also features God, death and suicide. A perfect elixir. All this in the so-called Russian futuristic style, just what you need to get you through a lonely night. Vladimir—should I say Volodia?—tells us about his skull filled with verses, promising a beautiful poem before finishing his life with «a bullet for a dot.»
It happened as any reader can confirm by laying eyes on his story. First, the encounter:
You swept in abruptly
like "take it or leave it!"
This below comes earlier in the poem, but does it matter? The question existed before it had any meaning, and still poses itself now that it has ceased to have one:
What will it be: love or no-love?
And what kind of love:
big or minute?
For of course, love is not for the poet:
you, a Gioconda,
had to be stolen!
And you were stolen.
[...]
But remember!
When they teased Vesuvius,
Pompeii perished!
Oh oh oh... how painful this is... Imagine him, Mayakovsky, reading to his Lilya his poem, not yet published, not yet censored, still with its six pages that she heard, from him:
my "I"
is much too small for me.
Stubbornly a body pushes out of me.
And what was the effect on Lilya? To hear this proud man confess his misery and frailty:
"Volodya did not merely fall in love with me; he attacked me, it was an assault. For two and a half years I didn't have a moment's peace. I understood right away that Volodya was a genius, but I didn't like him. I didn't like clamorous people... I didn't like the fact that he was so tall and people in the street would stare at him; I was annoyed that he enjoyed listening to his own voice, I couldn't even stand the name Mayakovsky... sounding so much like a cheap pen name."
She could have told him: "It seems my Russian is causing confusion."
Облако в штанах—which translates as "A Cloud in Trousers"—is a masterpiece. Despite censorship and even oppression from the regime, Stalin himself would later hail Mayakovsky as the greatest poet of his generation. The poem—initially titled "the 13th Apostle"—narrates in verses the story of a turned-down lover, who refrains from self-destruction by wandering the streets to preach his own version of the Sermon on the Mount, oscillating between madness, despair and hope in the miraculous. Six pages (six, not four) had been lost, censored into six pages of dots. They could have just skipped them, but there was something sincere in censorship. Those have been later recovered anyway. Some get lost forever. What remains is, in any case, anything but fiction:
The poet, Mayakovsky—idealist, bolshevik—died at 36, like all artists with a dose of self-respect and another of conviction, ought to. A lethal mélange. He killed himself because it was too much of Lilya's absence in his life. She denied it. They had been lovers. Forbidden lovers, the most intense type. Some people say it wasn't Lilya, it was the other woman, or it was the State, it was a murder, not a suicide, and if a suicide, not for Lilya. He read her his poem Облако в штанах at her place when they met, a poem bringing together love, spirituality and art, as well as, in Mayakovsky's case, revolution. If he had been a physicist, he would have put some quantum mechanics into that. The poem is written from the point of view of the unrequited lover. After reciting his poem, he dedicated it to the hostess: Тебе, Лиля. It was the happiest time of his life, he later wrote in his memoirs. From this point onward, he would do everything for her, for Lilya. Except one. As the script goes, he had to make a detour for one Tatiana (a Yakovleva, in his case). But he would come back to her as surely as the sea comes back to the shore. Can someone understand this type of attraction? For me it's a mystery.
Lilya Brik. The muse who wrecked the great Soviet poet, Vladimir Mayakovsky. We all know Lilya. Ask the Universe, ask it in its great wisdom of "everything-is-random", about Lilya Yuryevna. Yuryevna means "child of Yuri", the Lily child... We all know her. You don't believe me? Look at her:
Yes, she's the one, shouting книги in the iconic poster. What energy, what charisma... And a picture tells you nothing! The writer and pamphleteer Shklovsky said of her, that she «could be mournful, seductive, capricious, haughty, vacant, fickle, passionate, intelligent–whichever you wanted her», so the type who could damn a poet. And damn him she did!
My sufficient and necessary condition for spatial CSI violation turns out to have three alternative forms, all more interesting than the first one I arrived to, especially the last one, which was also the starting point! The three boxes below are equivalent (iff) to CSI violation:
First, reminding that $\Lambda(\mathbf{r})\equiv\ln\big|\phi_b(\mathbf{r})/\phi_a(\mathbf{r})\big|$ and $\varphi(\mathbf{r})\equiv\theta_b(\mathbf{r})-\theta_a(\mathbf{r})$, and using $\sinh^2(u/2)=\tfrac12(\cosh u-1)$ and $\sin^2(v/2)=\tfrac12(1-\cos v)$, $$\boxed{\cosh(\Delta\Lambda)+\cos(\Delta\varphi)>2\,.}$$ The boundary is then explicit, $|\Delta\Lambda|=\operatorname{arccosh}(2-\cos\Delta\varphi)$, running from $0$ at $\Delta\varphi=0$ to $\ln(3+2\sqrt2)$ at $\Delta\varphi=\pi$.
Second, using the amplitude and phase variations as argument of a complex number $\zeta\equiv\ln t=\Delta\Lambda+i\,\Delta\varphi$ where we remember that $t\equiv\frac{a(\mathbf{r}_1)b(\mathbf{r}_2)}{a(\mathbf{r}_2)b(\mathbf{r}_1)}$ is the cornerstone of CSI violation through the condition $|1+t|^2>4|t|$ (when violated), we can, from the generic $|\cosh(x+iy)|^2=\cosh^2x-\sin^2y$, wrap up our CSI violation into a beautiful $$\boxed{\big|\cosh(\zeta/2)\big|>1\,.}$$ Very pretty, but lots of things tied up together. $\zeta$ is a complex object!
Third, since $\cosh(\zeta/2)=\dfrac{(1+t)/2}{\sqrt t}$, i.e., the ratio of arithmetic (AM) vs geometric (GM) mean of $1$ and $t$, and coming back to the pair-delocalization amplitudes $x=a_1b_2$ and $y=a_2b_1$:
This was the starting point, actually, so I'm just scraping the bottom of the barrel. And maybe this competition between averages demands more attention. AM $\geq$ GM is satisfied for non-negative reals, with equality iff $x=y$. It's funny this means CSI violations.
I'll try a little harder
Try a little, little, little stronger
Try a little, little, little harder
Try a little, little, little more
Oh, got to try
Gotta try, I got to try, got to try
Gotta try, I got to try, got to try
Gotta try, I got to
No, no, no, no, no, no, no
Now for the reciprocal of the previous statement on same spatial profile not violating CSI, I find the interesting and strong result that for the two-mode Fock state $\ket{1_a,1_b}$, CSI are violated between points $\mathbf{r}_1$ and $\mathbf{r}_2$ iff
$$\sinh^2\!\left({\ln\big|\phi_b(\mathbf{r}_2)/\phi_a(\mathbf{r}_2)\big|\over2}-{\ln\big|\phi_b(\mathbf{r}_1)/\phi_a(\mathbf{r}_1)\big|\over2}\right)>\sin^2\!\left({\theta_b(\mathbf{r}_2)-\theta_a(\mathbf{r}_2)\over2}-{\theta_b(\mathbf{r}_1)-\theta_a(\mathbf{r}_1)\over2}\right)$$ where $\theta_i$ are the arguments of $\phi_i$, e.g., $\phi_a(\mathbf{r})=|\phi_a(\mathbf{r})|\exp\big(i\theta_a(\mathbf{r})\big)$.
This is the necessary and sufficient condition, but since $\sinh^2(x/2)>x^2/4$ for $x\neq0$ and $\sin^2(y/2)\leq y^2/4$ for all $y$, then if
$$\big|\Delta\ln\big|\phi_b(\mathbf{r})/\phi_a(\mathbf{r})|\big|>\left|\Delta[\theta_b(\mathbf{r})-\theta_a(\mathbf{r})]\right|$$
with $\Delta$ taken between $\boldsymbol{r}_2$ and $\boldsymbol{r}_1$ then the sinh/sin inequality is also satisfied and CSI are violated between these two points.
That is to say, the change in the log of the ratio of the field amplitudes $\ln|\phi_b(\mathbf{r})/\phi_a(\mathbf{r})|$ should be stronger than the change of the phase differences of the fields. If those changes are very small (e.g., because points are very close), say that at $\mathbf{r}_1$, the two fields $\phi_a$ and $\phi_b$ are equal (same amplitude and same phase), then if at a neighbouring point $\mathbf{r}_2$, their $\ln|\phi_b(\mathbf{r}_2)/\phi_a(\mathbf{r}_2)|$ is larger than their change of relative phase $\theta_b(\mathbf{r}_2)-\theta_a(\mathbf{r}_2)$, then CSI are violated. This has strong conclusions:
If the fields are real and of the same sign at the two points, CSI are violated everywhere their amplitude differs. This is the case of HG beams in quadrants 1 and 3 of $(\theta_1,\theta_2)$.
If the fields are real and of opposite sign at the two points, then rhs in the equation above is 1 and amplitudes must differ accordingly. This is the case of HG beams in quadrants 2 and 4.
If $|\phi_b|\propto|\phi_a|$, then the lhs is zero and CSI are never violated. This is the case of LG $\pm\ell$ beams.
In the general case, with non-constant amplitudes and with fields having a phase—which phase fights against CSI violations—the fact that distances go through the hyperbolic form and phase not, means that CSI violation is guaranteed for $|\sinh(\Delta\ln/2)|>1$, i.e.,
or$${|\phi_b(\mathbf{r}_2)/\phi_a(\mathbf{r}_2)|\over|\phi_b(\mathbf{r}_1)/\phi_a(\mathbf{r}_1)|}>(1+\sqrt2)^2\approx5.83\,.$$ An amplitude-ratio contrast of about a factor 6 between any two points in the beam violates CSI there, regardless of what the phases do. Where the sign flips, i.e., at $\Delta\varphi=\pi$, the right side is maximal and one needs the full $3+2\sqrt2$ contrast to violate CSI.
Equivalently, swapping $\boldsymbol{r}_1$ and $\boldsymbol{r}_2$ and taking the other side of $|x|>c$ (as $x<-c$, the above being $x>c$) we have ${|\phi_b(\mathbf{r}_2)/\phi_a(\mathbf{r}_2)|\over|\phi_b(\mathbf{r}_1)/\phi_a(\mathbf{r}_1)|}<(1+\sqrt2)^{-2}\approx0.172$ which is the inverse statement: if the ratio is bigger than a threshold, its reciprocal is smaller than the reciprocal threshold.
The criterion $|1+t|^2>4|t|$ for CSI violation in space is for $t\in\mathbb{C}$. Let's call it $t=|t|e^{i\theta}$ so that
By completion of the square on this $-4|t|$ and using $1-\cos\theta=2\sin^2(\theta/2)$, we have $|1+t|^2-4|t|=(1-|t|)^2-4|t|\sin^2(\theta/2)$ and thus the CSI criterion becomes:
$$(1-|t|)^2>4|t|\sin^2(\theta/2)\,.$$
Now we go hyperbolic; dividing by $|t|\neq0$ and substituting $|t|=e^\mu$, we have $\frac{(1-|t|)^2}{|t|}=|t|+|t|^{-1}-2=2\cosh\mu-2=4\sinh^2\!\big(\tfrac{\mu}{2}\big)$ on the left-hand side, so the CSI violation now reads:
$$\sinh^2\!\big(\tfrac{\mu}{2}\big)>\sin^2\!\big(\tfrac{\theta}{2}\big)$$ with $\mu=\ln|t|$ and $\theta=\arg t$. We record that $|t|=\frac{|\phi_b(\mathbf{r}_2)/\phi_a(\mathbf{r}_2)|}{|\phi_b(\mathbf{r}_1)/\phi_a(\mathbf{r}_1)|}$ and $\theta\equiv\arg t=\big[\theta_b(\mathbf{r}_2)-\theta_a(\mathbf{r}_2)\big]-\big[\theta_b(\mathbf{r}_1)-\theta_a(\mathbf{r}_1)\big]$. Introducing
New script goToYouTube, keymapped to Ctrl+Alg+Shift+Y to jump on the playing YouTube window, often lost in a tab itself lost in a browser itself lost in a virtual desktop. Now I can find it right away, either to silence it or to figure out what is playing.
First nontrivial result of today (stated or intuited previously): if the two modes $a$ and $b$ have the same spatial profile, i.e., $|\phi_a(\boldsymbol{r}_1)|^2=|\phi_b(\boldsymbol{r}_2)|^2$ [and this could even be $\propto$ instead of $=$ here], then there can be no CSI violation in space.
Regardless of the quantum state, of their correlations, etc., bimodal bosonic beams satisfy CSI if they have the same spatial profile. Mono-beam also always (trivially) satisfy them. I don't know yet about multimode ($\ge3$) beams.
Let us consider $\hat\Psi(\mathbf{r})=\sum_m^k\phi_m(\mathbf{r})\hat a_m$ with $k=2$, two modes, so let's write it simply as $$\hat\Psi(\mathbf{r})\equiv\phi_a(\mathbf{r})\hat a+\phi_b(\mathbf{r})\hat b.$$ Then on $\ket{\psi}=\ket{1_a,1_b}$,
we thus have $\Psi^{(2)}(\mathbf{r}_1,\mathbf{r}_2)=a_1b_2+a_2b_1$ and $\Psi^{(2)}(\mathbf{r}_i,\mathbf{r}_i)=2a_ib_i$. Modulus square give us the $G^{(2)}$:
The classical bound is $[G^{(2)}_{12}]^2\le G^{(2)}_{11}G^{(2)}_{22}$, so violation reads $|a_1b_2+a_2b_1|^4>16\,|a_1b_1|^2|a_2b_2|^2$, or, taking the square root: $$|a_1b_2+a_2b_1|^2>4\,|a_1b_1a_2b_2|.$$
Now, let us call $x\equiv a_1b_2$ and $y\equiv a_2b_1$ the amplitudes for pair delocalization. The rhs above is the product $xy=a_1b_1a_2b_2$, so CSI violations in terms of pair amplitudes reads: $$|x+y|^2>4|xy|\,.$$
Let us assume $|y|\neq0$ (not being at a node of the field). Dividing by $|y|$ and calling $t\equiv x/y=\frac{a(\mathbf{r}_1)b(\mathbf{r}_2)}{a(\mathbf{r}_2)b(\mathbf{r}_1)}$ yields $$|1+t|^2>4|t|,$$
while our hypothesis of $|\phi_a(\mathbf{r})/\phi_b(\mathbf{r})|=\mathrm{cst}$ implies $|t|=1$.
Since $|1+t|^2\le(1+|t|)^2$ but $(1+|t|)^2=4$ for same-one-photon-profile beams which have $|t|=1$, and thus $4|t|=4$, then the violation never occurs. The violation is possible for $|t|\neq1$.
Alrighty, Takagi decomposition is specific to order-2 symmetric tensors. For $N\ge3$ the analogue is the Waring decomposition:
$$ \Psi^{(N)}(\{\mathbf{r}\}_N)=\sum_{k}c_k\,v_k(\mathbf{r}_1)\cdots v_k(\mathbf{r}_N)$$
but the $v_k$ are not orthogonal, their number (the symmetric rank) generically exceeds the rank of $\Psi$, and the decomposition is not unique. So, again, two-photon physics is quite distinct from multiphoton physics!
I don't know. I don't know, I just don't know. I don't even know if I'm thinking about those photons who can't find their place jointly on the rim of a vortex, or if I'm thinking of why a talented, respectable, genius composer would give the best of his art to capture into music how lovers trick each other and get hurt in the process, or if I'm thinking of still other things. It all seems to collapse into the same story. And the more everything becomes one, the less I understand it, the more I find myself outside of the big picture. The universe, and me looking at it from its outside. Time to go back into it. I mean, to go to sleep. I'll have nightmares fight with dreams just as I witness the fermionic components fight the bosonic ones.
Not going far... $|1+d|=|1-(\frac{\Psi^-_{12}}{\Psi_{12}})^2|=|1-\frac{\Psi^-_{12}}{\Psi_{12}}||1+\frac{\Psi^-_{12}}{\Psi_{12}}|$. If the ratio is real, that becomes $0<(\frac{\Psi^-_{12}}{\Psi_{12}})^2<2$, i.e., $|\frac{\Psi^-_{12}}{\Psi_{12}}|<\sqrt2$ and this is the condition already spotted. I'm increasingly convinced this is not the good reading, however tempting is a ratio of bosonic vs fermionic fluctuations... Also this ratio $R$ might be broken and pathological, and the sign of the difference could be more physical/meaningful.
Remember the "sampling matrix": $$A=\begin{pmatrix}w_1(\mathbf{r}_1)&w_1(\mathbf{r}_2)\\ w_2(\mathbf{r}_1)&w_2(\mathbf{r}_2)\end{pmatrix}\,.$$ This one has everything, it carries both statistics (up to normalization; should I maybe normalized$A$?):
its permanent is the two-boson amplitude $\Psi_{12}=w_1(\mathbf{r}_1)w_2(\mathbf{r}_2)+w_1(\mathbf{r}_2)w_2(\mathbf{r}_1)$.
its determinant the two-fermion amplitude $\Psi^-_{12}\equiv w_1(\mathbf{r}_1)w_2(\mathbf{r}_2)-w_1(\mathbf{r}_2)w_2(\mathbf{r}_1)$.
We want to find $\det M=\Psi_{11}\Psi_{22}-\Psi_{12}^2$ in this and then the CSI violation criterion through $d$ the ratio of $\det A/\det M$ (modulo eigenvalues). Algebra goes like this: $\Psi_{11}\Psi_{22}=4\,w_1(\mathbf{r}_1)w_2(\mathbf{r}_1)w_1(\mathbf{r}_2)w_2(\mathbf{r}_2)$, and calling $x=w_1(\mathbf{r}_1)w_2(\mathbf{r}_2)$ and $y=w_1(\mathbf{r}_2)w_2(\mathbf{r}_1)$, from $(x+y)^2-(x-y)^2=4xy$, we get to $\Psi_{12}^2-(\Psi^-_{12})^2=4\,w_1(\mathbf{r}_1)w_2(\mathbf{r}_2)w_1(\mathbf{r}_2)w_2(\mathbf{r}_1)$ and thus: $$\Psi_{11}\Psi_{22}=\Psi_{12}^2-(\Psi^-_{12})^2$$ so that, finally, $$\det M=-(\Psi^-_{12})^2$$
and so, $d$ is (minus the square of) the ratio of the fermionic over bosonic amplitudes:
and if I link that to my earlier connection between $R$ and $d$, this tells us:
infinite violation ($d=−1$) when $(\Psi^-_{12})^2=\Psi_{12}^2$, i.e. $\Psi^-_{12}=\pm\Psi_{12}$. That sounds deep but actually, since $\Psi_{12}+\Psi^-_{12}=2w_1(\mathbf{r}_1)w_2(\mathbf{r}_2)$ and $\Psi_{12}-\Psi^-{12}=2w_1(\mathbf{r}_2)w_2(\mathbf{r}_1)$, that merely means that one of the cross products vanishes, i.e., one detector is placed at a zero of one of the modes, which is the well-known maximum violation of CSI. So no big deal here... That's also why fermions appear more nonclassical by this standard, by the way, they intrinsically forbid particles to fluctuate locally, because they can't be many present locally in the first place.
strong validation of CSI when $\Psi_{12}\to0$, i.e., the bosonic part vanishes, which seems counterintuitive from the point of view I'm chasing (fermion vs boson), but from $|\Psi_{12}|^2\le|\Psi_{11}\Psi_{22}|$ it just shows it's trivially enforced.
I might be going in circles... the bosonic vs fermionic might be a red herring.
I want to explore the symmetry vs antisymmetry character of states, since that seems to be what rules their CSI violations.
Let us start with the great classic: $$F=\tfrac12(F+PF)+\tfrac12(F-PF)$$ where $P$ is the permutation operator $\mathbf{r}_1\leftrightarrow\mathbf{r}_2$. This splits the Hilbert space of two-particle wavefuntions as $$\mathcal{H}_1\otimes\mathcal{H}_1=\mathrm{Sym}^2\mathcal{H}_1\oplus\Lambda^2\mathcal{H}_1$$ where Sym$^2$ is the symmetric square and $\Lambda^2$ the exterior (or wedge) square. That brings us back to the Takagi decomposition $\Psi=\sum_k\lambda_k\,w_k\otimes w_k$ but now extended to also include fermionic-looking antisymmetric cases.
Sym2 is spanned by $w_j\otimes w_k+w_k\otimes w_j$ for $j<k$, plus the diagonal elements $w_k^{\otimes2}$. It has dimension $K(K+1)/2$. $\Lambda^2$ is spanned by $w_j\wedge w_k\equiv w_j\otimes w_k-w_k\otimes w_j$ for $j<k$. No diagonal, since $w\wedge w=0$ (Pauli principle). It has dimension $K(K-1)/2$. Since $K(K+1)/2+K(K-1)/2=K^2$, we're all accounted for.
Let us work out the general case $\ket{1_a1_b}$ (general in $a$ and $b$, this is still particular about two particles):
For the symmetric (bosonic) part: $$\mathrm{Sym}^2=\mathrm{span}\{a^{\otimes2},\,b^{\otimes2},\,a\otimes b+b\otimes a\}\ \leftrightarrow\ \{|2,0\rangle,|0,2\rangle,|1,1\rangle\}$$
For the antisymmetric (fermionic) part: $$\Lambda^2=\mathrm{span}\{a\wedge b\}\ \leftrightarrow\ \text{the single Slater determinant}$$
The link between the ratio of CSI violation and this distance is important: $$R=\frac{1}{|1+d|^{2}}$$ (this follows from the definition of $d$ such that $1+d={\Psi_{11}\Psi_{22}}/{\Psi_{12}^{2}}$). Thus $R\to\infty$ at the centre $d=-1$ (where $\Psi_{11}\Psi_{22}=0$, the nodal cross) and $R\to0$ as $|d|\to\infty$ (where $\Psi_{12}=0$, the anti-diagonal).
Divergent $R$ always means a diagonal amplitude vanishing at one of the two detectors; vanishing $R$ always means the pair amplitude vanishing between them. This is for any $\ket{1_a,1_b}$.
That doesn't clarify yet the fermionic/bosonic tension, but I wanted $R$ to appear explicitely. Through $d$, it does.
The bowtie boundary for the CSI satisfied/violated for dipoles (HG) is given by the equation:
$$\theta_2=\arctan(-(3\mp2\sqrt2)\tan\theta_1)=\arctan(-(\sqrt2\mp1)^2\tan\theta_1)$$
I leave below the Mathematica code to plot the relevant quantities for this case.
The first thing is when is $\sin2\theta_1\sin2\theta_2>0$? Both must be positive or both negative, so that's the quadrant 1 and 3 of $\begin{smallmatrix} 2&1\\3&4 \end{smallmatrix}$. So, there are trivial violations of CSI along the diagonal, where photons are detected together. Interesting! In the 2 and 4 quadrants is where we have restricted violations:
The condition to retain is:
$$\boxed{\;\text{CSI violated}\iff\lvert\sin(\theta_1-\theta_2)\rvert<\sqrt2\,\lvert\sin(\theta_1+\theta_2)\rvert\;}$$ with saturation at $\sin(\theta_1-\theta_2)=0$, i.e., $\theta_1=\theta_2\mod\pi$ and infinite violation at $\sin(\theta_1+\theta_2)=0$, i.e., $\theta_1=\theta_2+\pi/2\mod\pi$.
This compare the difference (fermionic like) to the sum (bosonic like) with the conclusion that the fermionic amplitude must not exceed the bosonic one by more than $\sqrt{2}$. This number is probably not random and its physical meaning would pop up more clearly at the multiphoton level. There's some bosonic fuckery going on there.
We thus satisfy CSI (and saturate them) when bosons are aligned, although this is impossible for dipoles, and we violate them maximally when they are perpendicular, where they want to be found.
This is the region of CSI violations for two bosonic Fock dipoles $\ket{1_u,1_v}$ in the $(\theta_1,\theta_2)$ plane:
It seems to agree with what Daniel showed me the other day, except it was on $[0,2\pi[$ (hence four times this) and not showing the degree of violation, which is important as in fact it's weakly violated in most places and gets wild when it becomes impossible; also it was with his own color code as opposed to the one we used with Ref. [13]. Red here is saturation of the inequalities.
The trick is the one I used previously, to separate the cases of the modulus, i.e.,
$\sin2\theta_1\,\sin2\theta_2>0$ and we drop the absolute value
$\sin2\theta_1\,\sin2\theta_2<0$ and the numerator gets a minus (to drop $|\cdot|$)
and, depending on the cases, we have
$|\sin2\theta_1\sin2\theta_2|=\pm\big(\sin^2(\theta_1+\theta_2)-\sin^2(\theta_1-\theta_2)\big)$ and, therefore:
$$\lvert d+1\rvert=\pm\left(1-\frac{\sin^2(\theta_1-\theta_2)}{\sin^2(\theta_1+\theta_2)}\right)$$
and this is to be compared to unity: smaller or larger?
The $+$ is a trivial violation everywhere unless saturated, as $|d+1|<1\iff 0<\frac{\sin^2(\theta_1-\theta_2)}{\sin^2(\theta_1+\theta_2)}$ which is true except if $\sin^2(\theta_1-\theta_2)=0$ where the CSI is saturated, which happens when $\theta_1=\theta_2\mod\pi$.
The $-$ is the case I already touched upon with the golden ratio for $t=p/q$. In this case $\lvert d+1\rvert<1$ becomes
If I compare with Daniel's result, which states violations iff $$\sin^2(2\theta_1)\sin^2(2\theta_2)<\sin^4(\theta_1+\theta_2)$$ one can check numerically that it fulfills the same conditions—the two are equivalent—so no issues there and it's certainly not a big deal to show cleanly (not entirely immediate to me in five minutes, $\sin2\theta_1\sin2\theta_2=\sin^2(\theta_1+\theta_2)-\sin^2(\theta_1-\theta_2)$ and there has many things to look at; not my business for now). Now for the geometric consequences of that, it's what interests me: where does this happen?
Carrying on with which areas violate CSI spatially, in the concrete case of $u=h_{10}\propto x\,e^{-r^2/w^2}$ and $v=h_{01}\propto y\,e^{-r^2/w^2}$, and recalling (it's been a long break) that $p\equiv u(\mathbf r_1)v(\mathbf r_2)$ and $q\equiv u(\mathbf r_2)v(\mathbf r_1)$, while $d\equiv-(p-q)^2/(p+q)^2$ and we're interested in the region $|d+1|<1$, then, since $p=x_1y_2 e^{-(\mathbf{r}_1+\mathbf{r}_2)/w^2}$ and $q=x_2y_1 e^{-(\mathbf{r}_1+\mathbf{r}_2)/w^2}$, calling $G\equiv e^{-(\mathbf{r}_1+\mathbf{r}_2)/w^2}$ the part which factors out, we have $p-q=(x_1y_2-x_2y_1)G= \left|\begin{smallmatrix} x_1 & y_1\\ x_2 & y_2 \end{smallmatrix}\right|G $ and $p+q=(x_1y_2+x_2y_1)G= \left\Vert\begin{smallmatrix} x_1 & y_1\\ x_2 & y_2 \end{smallmatrix}\right\Vert G$ so that $G$ neatly cancels and from trigonometric identities such as $\cos\theta_1\sin\theta_2-\cos\theta_2\sin\theta_1=\sin(\theta_1-\theta_2)$, we get, again with cancellation of $r$, $p-q\propto\sin(\theta_2-\theta_1)$ and $p+q\propto\sin(\theta_1+\theta_2)$, and thus $d=-\frac{\sin^2(\theta_2-\theta_1)}{\sin^2(\theta_1+\theta_2)}$ so that, finally:
It'll be a long one, a lone one, a none one, a noon one too. A full dive into El Amor Brujo has long been overdue. Even L'Amour Monstre was not so urgent or compelling.
A science friend asked me about my plans for the 12th of August, and I asked what was going on on the 12th of August. Way to lose a science friend! She just replied, rightly «The World Cup is one thing and a total solar eclipse is another!» Ouch. I would have had given my utmost attention to this sort of things still some little time ago. I had seen that ICMM and BP (the oil company) provide equipment for "safe viewing", and I'm scared to tamper more with my eyesight than I already do by closing my eyes very little (not sleeping much) and focusing them on either books or screens, and when not one or the other, usually one and the other. So I guess I had kind of filed it under "avoid; keep distance from attractive things, this hasn't turned out too well for you recently anyway". Maybe I should still give the moon meeting the sun the attention it deserves. This is the sort of impossible union that has been occupying me a lot and indeed not turned out too good. But what can be done about it? All those stuff are cosmic events.
Polariton BECs: Theory and Concepts. F. P. Laussy in arXiv:2605.16256 (2026).