# Amy Triumphs* at the Shtetl

It was not until the 144th comment by a participants named Amy on Scott’s Aaronson recent Shtetl-optimized** post devoted to a certain case of sexual harassment at M. I. T. that the discussion turned into something quite special. Amy’s great comment respectfully disagreeing with the original post and most of the 100+ earlier comments gave a wide while personal feminist perspective on women in STEM (STEM stands for science, technology,  engineering, mathematics). This followed by a moving comment  #171 by Scott describing a decade of suffering from his early teens. Scott, while largely sympathetic with the feminist cause, sees certain aspects of modern feminism as  major contributors to his ordeal.

Then came a few hundred comments by quite a few participants on a large number of issues including romantic/sexual relations in universities, rape, prostitution, poverty, gaps between individuals’ morality and actions, and much more. Many of the comments argued with Amy and a few even attacked her.  Some comments supported Amy and some proposed their own views. Many of the comments were good and thoughtful and many gave interesting food for thought. Some people described interesting personal matters. As both Scott and Amy left school early to study in the university, I also contributed my own personal story about it (and Scott even criticized my teenage approach to life! :) ). Amy, over 80+ thoughtful comments, responded in detail, and her (moderate) feminist attitude (as well as Amy herself) stood out as realistic, humane, and terribly smart.

* The word triumph is used here in a soft (non-macho) way characteristic to the successes of feminism. Voting rights for women did not exclude voting rights for men, and Amy’s triumph does not mean a defeat for  any others; on the contrary.

** “Shtetl-optimized” is the name of Scott Aaronson’s blog.

# Test your Intuition/Knowledge: What was Lord Kelvin’s Main Mistake?

### The age of the earth

(Thanks to Yeshu Kolodny) We now know that the age of the earth is 4.54±1% Billion years.

From Wikipedea: In 1862, the physicist William Thomson (who later became Lord Kelvin) of Glasgow published calculations that fixed the age of Earth at between 20 million and 400 million years. He assumed that Earth had formed as a completely molten object, and determined the amount of time it would take for the near-surface to cool to its present temperature. His calculations did not account for heat produced via radioactive decay (a process then unknown to science) or convection inside the Earth, which allows more heat to escape from the interior to warm rocks near the surface.

What was the main reason for Lord Kelvin’s wrong estimation

a) Radioactivity – Heat produced by radioactive decay; this was a process unknown to science for decades to come.

b) Convection – The transfer of heat not through radiation or heat-conduction but through the movement of hot parts to the surface; this is a process familiar in home cooking.

# My Quantum Debate with Aram III

This is the third and last post giving a timeline and some non technical highlights from my debate with Aram Harrow.

### Where were we

After Aram Harrow and I got in touch in June 2011, and decided to have a blog debate towards the end of 2011, the first post in our debate describing my point of view was launched on January, 2012 and was followed by three posts by Aram. The discussion was intensive and interesting.  Here is a link to my 2011 paper that initiated the debate and to a recent post-debate presentation at MIT.

## Back to the debate: Conjecture C is shot down!

In addition to his three posts, Aram and Steve Flammia wrote a paper refuting one of my Conjectures (Conjecture C).  We decided to devote a post to this conjecture.

# Quantum refutations and reproofs

### Post 5, May 12, 2012. One of Gil Kalai’s conjectures refuted but refurbished

Niels Henrik Abel was the patron saint this time

The first version of the post started with this heartbreaking eulogy for Conjecture C. At the end most of it was cut away. But the part about Aram’s grandchildren was left in the post.

## Eulogy for Conjecture C

(Gil; old version:) When Aram wrote to me, inn June 2011, and expressed willingness to publicly discuss my paper, my first reaction was to decline and propose having just private discussions. Even without knowing Aram’s superb track record in debates, I knew that I put my beloved conjectures on the line. Some of them, perhaps even all of them, will not last. Later, last December, I changed my mind and Aram and I started planning our debate. My conjectures and I were fully aware of the risks. And it was Conjecture C that did not make it.

### A few words about Conjecture C

Conjecture C, while rooted in quantum computers skepticism, was a uniter and not a divider! It expressed our united aim to find a dividing line between the pre- and post- universal quantum computer eras.

### Aram’s grandchildren and the world before quantum computers

When Aram’s grandchildren will ask him: “
Grandpa, how was the world before quantum computers?” he could have replied: “I hardly remember, but thanks to Gil we have some conjectures recording the old days, and then he will state to the grandchildren Conjectures 1-4 and the clear dividing line in terms of Conjecture C, and the grandchildren will burst in laughter about the old days of difficult entanglements.” Continue reading

# My Quantum Debate with Aram II

This is the second of three posts giving few of the non-technical highlights of my debate with Aram Harrow. (part I)

After Aram Harrow and I got in touch in June 2011, and decided to have a blog debate about quantum fault-tolerance towards the end of 2011, the first post in our debate was launched on January 30, 2012.  The first post mainly presented my point of view and it led to lovely intensive discussions. It was time for Aram’s reply and some people started to lose their patience.

(rrtucky) Is Aram, the other “debater”, writing a dissertation in Greek, as a reply?

# Flying machines of the 21st century

### Post II, February 6, 2011. First of three responses by Aram Harrow

Dave Bacon was the patron saint for Aram’s first post.

(Aram) There are many reasons why quantum computers may never be built…  The one thing I am confident of is that we are unlikely to find any obstacle in principle to building a quantum computer.

(Aram) If you want to prove that 3-SAT requires exponential time, then you need an argument that somehow doesn’t apply to 2-SAT or XOR-SAT. If you want to prove that the permanent requires super-polynomial circuits, you need an argument that doesn’t apply to the determinant. And if you want to disprove fault-tolerant quantum computing, you need an argument that doesn’t also refute fault-tolerant classical computing.

## From the discussion

### Why not yet? Boaz set a deadline

(Boaz Barak could [you] explain a bit about the reasons why people haven’t been able to build quantum computers with more than a handful of qubits yet? Continue reading

# My Quantum Debate with Aram Harrow: Timeline, Non-technical Highlights, and Flashbacks I

## How the debate came about

(Email from Aram Harrow, June 4,  2011) Dear Gil Kalai, I am a quantum computing researcher, and was wondering about a few points in your paper

(Aram’s email was detailed and thoughtful and at the end he proposed to continue the discussion privately or as part of a public discussion.)

(Gil to Aram) Thank you for your email and interest. Let me try to answer the points you raised. …   (I gave a detailed answer.) …  Right now, I don’t plan on initiating a public discussion. How useful such public discussions are (and how to make them useful) is also an interesting issue. Still they were useful for me, as two of my conjectures were raised first in a discussion on Dave Bacon’s blog and another one is partially motivated by a little discussion with Peter Shor on my blog. Continue reading

# Meeting with Aram Harrow, and my Lecture on Why Quantum Computers Cannot Work.

Last Friday, I gave a lecture at the quantum information seminar at MIT entitled “Why quantum computers cannot work and how.” It was a nice event with lovely participation during the talk, and a continued discussion after it. Many very interesting and useful remarks were made. Here are the slides. (The abstract can be found on this page.)

After having an almost a year-long debate with Aram Harrow, I finally met Aram in person, and we had nice time together during my visit.

Aram is so nice that had it been up to me I would certainly make quantum computers possible :) (But this is not up to us and all we can do is to try to explore if QC are possible or not.)

We talked about quite a few topics starting with various exotic models of noise that treat differently classic and quantum information, the relevance of locally correctable codes and their quantum counterparts, the sum of Squares/Lasserre hierarchy, unique games and hypercontractivity, my smoothed Lindblad evolutions , NMR and spin-echo, quantum annealing and stoquasicity, and works by Mossbüer, Rekha Thomas, and Monique Laurent were mentioned.

### More

I just returned yesterday night from Yale after a very fruitful visit.  Here is a picture of a snowcar decorated with car mirrors from the great blizzard.

# The Quantum Debate is Over! (and other Updates)

### Quid est noster computationis mundus?

Nine months after is started, (much longer than expected,) and after eight posts on GLL, (much more than planned,)  and almost a thousand comments of overall good quality,   from quite a few participants, my scientific debate with Aram Harrow regarding quantum fault tolerance is essentially over. Some good food for thought, I hope. As always, there is more to be said on the matter itself, on the debate, and on other”meta” matters, but it is also useful to put it now in the background for a while, to continue to think about quantum fault tolerance in the slow pace and solitude, as I am used to, and also to move on in other fronts, which were perhaps neglected a little.

Here are the links to the eight posts: My initial post “Perpetual Motion of The 21st Century?” was followed by three posts by Aram. The first “Flying Machines of the 21st Century?” the second “Nature does not conspire” and the third “The Quantum super-PAC.” We had then two additional posts “Quantum refutations and reproofs” and “Can you hear the shape of a quantum computer?.” Finally we had  two conclusion posts: “Quantum repetition” and “Quantum supremacy or quantum control?

### EDP 22-27

We had six new posts on the Erdos Discrepancy Problem over Gowers’s blog (Here is the link to the last one EDP27). Tim contributed a large number of comments and it was interesting to follow his line of thought.  Other participants also contributed a few comments. One nice surprise for me was that the behavior of the hereditary discrepancy for homogeneous arithmetic progression in {1,2,…,n} was  found by Alexander Nikolov and  Kunal Talwar. See this post From discrepancy to privacy and back and the paper. Noga Alon and I showed that it is ${\tilde{\Omega}(\sqrt{\log n})}$ and at most ${n^{O(\frac{1}{\log\log n})}}$, and to my surprise Alexander and Kunal showed that the upper bound is the correct behavior. The argument relies on connection with differential privacy.

### Möbius randomness and computation

After the $AC^0$-prime number theorem was proved by Ben Green, and the Mobius randomness of all Walsh functions and monotone Boolean function was proved by Jean Bourgain, (See this MO question for details) the next logical step are low degree polynomials over Z/2Z . (The Walsh functions are degree 1 polynomials.) The simplest case offered to me by Bourgain is the case of the Rudin-Shapiro sequence. (But for an ACC(2) result via Razborov-Smolensky theorem we will need to go all the way to polynomial of degree polylog.) I asked it over MathOverflaw. After three months of no activity I offered a bounty of 300 of my own MO-reputations. Subsequently, Terry Tao and Ben Green discussed some avenues and eventually Tao solved the problem (and earned the 300 reputation points). Here is a very recent post on Möbius randomness on Terry Tao’s blog.

### Influences on large sets

In my post Nati’s Influence I mentioned two old conjectures (Conjecture 1 dues to Benny Chor and Conjecture 2) about influence of large sets on Boolean functions. During Jeff Kahn’s visit to Israel we managed to disprove them both. The disproof is inspired by an old construction of Ajtai and Linial.

### Tel Aviv, New Haven, Jerusalem

Last year we lived for a year in Tel Aviv which was a wonderful experience: especially walking on the beach every day and feeling the different atmosphere of the city. It is so different from my Jerusalem and still the people speak fluent Hebrew. I am now in New Haven. It is getting cold and the fall colors are getting beautiful. And it also feels at home after all these years. And next week I return to my difficult and beautiful  (and beloved) Jerusalem.

# The Quantum Fault-Tolerance Debate Updates

In a couple of days, we will resume the debate between Aram Harrow and me regarding the possibility of universal quantum computers and quantum fault tolerance. The debate takes place over GLL (Godel’s Lost Letter and P=NP) blog.

## The Debate

### Where were we?

My initial post “Perpetual Motion of The 21st Century?” presented my conjectures regarding how noisy quantum computers and noisy quantum evolutions really behave.

Aram’s first post was entitled “Flying Machines of the 21st Century?” It mainly dealt with the question “How is it possible that quantum fault-tolerance is impossible (or really really hard) while classical fault tolerance is possible (and quite easy). Aram claimed that my conjectures, if true, exclude also classical computers.

Aram’s second post entitled “Nature does not conspire” dealt mainly with correlated errors. Aram claimed that it is unreasonable to assume strong correlation of errors as my conjectures imply and that the conjectured relation between the signal and noise is in tension with linearity of quantum mechanics.

Aram’s third  post “The Quantum super-PAC”  raised two interesting thought-experiments and discussed also intermediate models.

Each post ended with a small rejoinder, and included a short description of the ealier discussion.  The discussion was quite extensive and very interesting.

### What’s next

Aram and Steve Flammia wrote an interesting manuscript with appealing counterexamples to my Conjecture C. Our next planned post (it now has appeared) will discuss this matter.

Next, I will conclude with a post discussing Aram’s two main points from his first and second posts and some related issues which I find important.

These posts are mostly written but since Aram was busy with pressing deadlines we waited several weeks before posting them. I also enjoyed the break, as the extensive discussion period was quite tiring.

## A very short introduction to my position/approach

1) The crux of matter is noise

# Updates, Boolean Functions Conference, and a Surprising Application to Polytope Theory

## The Debate continues

The debate between Aram Harrow and me on Godel Lost letter and P=NP (GLL) regarding quantum fault tolerance continues. The first post entitled Perpetual  motions of the 21th century featured mainly my work, with a short response by Aram. Aram posted two of his three rebuttal posts which included also short rejoiners by me. Aram’s first post entitled Flying machines of the 21th century dealt with the question “How can it be that quantum error correction is impossible while classical error correction is possible.” Aram’s  second post entitled Nature does not conspire deals with the issue of malicious correlated errors.  A third post by Aram is coming and  the discussion is quite interesting. Stay tuned. In between our posts GLL had several other related posts like Is this a quantum computer? on how to tell that you really have a genuine quantum computer , and Quantum ground day that summarized the comments to the first post.

## Virgin Island Boolean Functions

In the beginning of February I spend a week in a great symposium on Analysis of Boolean Functions, one among several conferences supported  by the Simons foundation, that took place at St. John of the Virgin Islands.

Irit Dinur and me

Ryan O’Donnell who along with Elchanan Mossel and Krzysztof Oleszkiewicz (the team of “majority is stablest” theorem) organized the meeting, live blogged about it on his blog. There are also planned scribes of the lectures and videos. I posed the following problem (which arose naturally from works presented in the meeting): What can be said about circuits with n inputs representing n Gaussian random variables, and gates of the form: linear functions, max and min.

## A surprising application of a theorem on convex polytopes.

(Told to me by Moritz Schmitt and Gunter Ziegler)

A theorem I proved with Peter Kleinschmidt and Gunter Meisinger asserts that every rational polytope of dimension d>8 contains a 3-face with at most 78 vertices or 78 facets. (A later theorem of Karu shows that our proof applies to all polytopes.) You would not expect to find a real life application for such a theorem. But a surprising application has just been given.

Before talking about the application let me say a few more words about the theorem. The point is that there is a finite list of 3-polytopes so that every polytope of a large enough dimension (as it turns out, eight or more) has a 3-face in the list. It is conjectured that a similar theorem holds for k-faces, and  it is also conjectured that if the dimension is sufficiently high you can reduce the list to two polytopes: the simplex and the cube. These conjectures are still open. (See this post  for related open problems about polytopes.) For k=2, it follows from Euler’s theorem that every three-dimensional polytope contains a face which is a triangle, quadrangle, or pentagon, and in dimension five and up, every polytope has a 2-face which is a triangle or a rectangle.