This post is devoted to a few memories of Boris Tsirelson who passed away at the end of January. I would like to mention that a few days ago graph theorist Robin Thomas passed away after long battle with ALS. I hope to tell about Robin’s stunning mathematics in a future post.

Boris Tsirelson (1950 – 2020); Boris’ home-page, and Wikipedia. (More links, below.)

The title of the post is taken from the title of a very interesting 1999 paper by Boris Tsirelson and Oded Schramm: Trees, not cubes: hypercontractivity, cosiness, and noise stability

I was very sad and shocked to hear that Boris Tsirelson had passed away. Boris was one of the greatest Israeli mathematicians, and since 1997 or so we established mathematical connections surrounding several matters of common interest. Here are a few memories.

### Love for coding

1) One thing that Boris told me was that he loves to code. Being a “refusnik”, he could not get into Academia and (luckily) he could work as a programmer. And he told me that afterwards deciding what he liked more – programming or doing mathematical research – was no longer a trivial question for him. Boris chose to go back to mathematical research, but he continued to enjoy programming, and when he needed it in his mathematical research, he could easily program.

### Love for quantum

2) Another thing that Boris loved is “quantum”, the mathematics and physics of quantum mechanics and various connections to mathematics. Early on he proved his famous Tsirelson’s bound related to Bell’s inequalities, and later he was enthusiastic about the area of quantum computing. (And he learned it quickly, taught a course about it in 1997, and his 1997 lecture notes are still considered very useful.)

### Black Noise and noise sensitivity

3) Perhaps the most significant mathematical connection between us was in the late 90s, and was centered around the theory of noise stability and noise sensitivity by Benjamini, Schramm and myself, which was closely related to a theory initiated by Boris Tsirelson and Anatoly Vershik. The translation between the different languages that we used and that Boris used was awkward, since the analog of Boolean functions that we studied was the “noise” that Boris studied, and the analog of noise sensitive Boolean functions in our language was “black noise” in Boris’s language. In any case, we had email discussions and we also met a few times with Itai and Oded regarding this connection.

### Black Noise and noise sensitivity II

4) Boris developed a very rich theory of black noise with relations to various areas of probability theory and operator algebras. He also found hypercontractivity that we used in our work quite useful to his applications, and also in this theory, he considered both classical and quantum aspects. I know only a little about Boris Tsirelson’s theory and its applications, but as far as tangent points with our Boolean interests are concerned, I can mention that Boris was enthusiastic by the result of Schramm and Stas Smirnov that percolation is a “black noise” and also that, in 1999, Boris and Oded Schramm wrote a paper whose title started with “Trees not cubes!”, presenting a different angle on this theory.

Tsirelson saw white noise (what we call noise stability) as manifesting “linearity” while “black noise” (what we call noise sensitivity) as manifesting “non-linearity”. Over the years, I often asked him to explain this to me.

### Tsireslon’s Banach spaces

5) Geometry of Banach spaces is a very strong area in Israel so naturally I heard as a graduate student about “Tsirelson’s space” from 1974 and some subsequent developments in the 80s. Boris Tsirelson constructed a Banach space that does not contain an imbedding of or .

### Bible codes

6) My first personal connection with Boris was related to claims regarding a hidden Bible Code, and a 1994 paper claiming a statistical proof of the existence of these Bible codes. For many years my attitude was that these claims should be ignored, but around 1997, I changed my mind and did some work to see what was going on. Now, Boris kept a site linked in his homepage devoted to developments regarding the Bible Code claims. In this site Boris kindly reported about my first 1997 paper on the topic, my observation that the proximity of two reported p-values for the two Bible code experiments was “too good to be true”, and my interpretation that this suggests that the claimed results manifest naïve statistical expectations rather than scientific reality. A few weeks later, Boris reported about a much stronger evidence (by McKay and Bar Nathan) against the Bible Code claims (they demonstrated codes of similar quality in Tolstoy’s “War and Peace”) and subsequently after some time he lost interest in this topic.

### Quantum computing skepticism

6) In 2005 we had some correspondence and meetings regarding my quantum computing skepticism. In his first email he told me that my reference to “decoherence” seemed strange and I realized that I consistently referred to “entanglement” as “decoherence” and to “decoherence” as “entanglement”.

7) In his 1997 lecture notes on quantum computing (that I cannot find on the web, so I count on my memory), Boris addressed the concerns of early quantum computers skeptics like Rolf Landauer. He did not accept the analogy between quantum computing and analog computation, but he also regarded the analogy with digital computation as problematic. Rather, he regarded quantum information based on qubits as something (at least a priori) different from both these examples. (Update: I found one non-broken link to the lecture notes; indeed the subtitle of Chapter 9 is “neither analog nor digital”.)

A joke that I heard from Boris at that time

8) I remember that once when I asked him about some aspects of quantum fault tolerance he told me the following joke: A student is entitled to a special exam, he arrives at the professor’s office, is given three questions to answer and he fails to do so. He request and is granted a make-up exam two weeks later. When the student shows up at the office two weeks later the professor, who forgot all about it, gave him the same three questions. “This is extremely unfair”, said the student “you ask me questions that you already know that I cannot answer.”

### Noise sensitivity and high energy physics

9) In 2006 I came up with the idea that noise sensitivity might be a great idea for physics. Knowing very little physics, I wrote a little manifesto with this idea and tried it, among other people, on Boris. As it turned out, Boris had the idea that noise sensitivity could add a useful modeling power to physics (especially high energy physics) well before that time. (And by 2006 he was already a bit skeptical regarding his own idea.) He also told me that one of the motivations of his 1998 paper with Tolya Vershik came from some mathematical ideas related to physics of the big bang. When I asked him if this was written somewhere in the paper itself, he answered: “Of course, not!”

### Boris Tsirelson’s lecture at Oded’s memorial school

10) in 2009 we organized a meeting in memory of Oded Schramm and Boris gave a lecture related to the Schramm-Smirnov “percolation is black noise” result with a single theorem. And what was remarkable about it that it was that he presented a classical theorem with a quantum proof. You can find the videotaped lecture here (And here are the slides. Boris never wrote up this result.) Following this lecture we had a short correspondence with Scott A. and Greg K. about quantum proofs to classical theorems. (Namely theorems that do not mention quantum in the statement).

### Tsirelson’s problem

11) Our last correspondence in 2019 was about Thomas Vidick’s Notices AMS article about Tsirelson’s problem. (This was a couple of months before the announcement of the solution.) Boris was pleased to hear about these developments, as he was regarding earlier developments in this area. He humorously refers to the history of his problem on his homepage and this interview.

12) People who knew Boris regarded him as a genius from a very early age, and former students have fond memories of his classes.

### More resources:

Boris’s home page contains “Museum to my courses” with many useful lecture notes; link to a small page on quantum computation with a link to Boris’ 1997 lecture notes on quantum computing. Links to comments on some of Tsirelson’s famous papers. Tsirelson’s 1980 bound. Boris published papers, and his “self-published” papers.

Boris was a devoted Wikipedian and his Wikipidea user page is now devoted to his memory; Here is a great interview with Boris; A very nice memorial post on Freeman Dyson and Boris Tsirelson on the Shtetl Optimized; Tim Gowers explains some ideas behind Tsirelson’s space over Twitter; and here in Polymath2.

Below the fold some emails of interest from Boris, mainly where he explained to me various mathematics. (More can be found in this page.)