I also know the story of the “Grothendieck prime”, 57—the fact that 57 isn’t prime illustrating Grothendieck’s complete disregard for concrete examples, and his lack of need for them.

In any case, 1957 was the year when Grothendieck’s mother passed away. It’s also in 1957 that he started to rebuild the foundations of algebraic geometry. Thus the number 57, if not prime in the arithmetic sense, was certainly prime to his heart. My opinion is that AG had become a mathematician – reinventing measure theory without even knowing about Lebesgue – to put up with the disappearance of his father. Later on, he might have turned into a leading algebraic geometer partly to avoid thinking about his mother’s death. However, by 1970 he went through what’s called today a professional burnout – first campaigning for ecology, then retiring alone in the region where he’d lived most of his youth. Which makes me think of the title of Marilyn Monroe’s last and uncompleted movie: “Something’s got to give…”

]]>haha, I was kidding about “memristors”, but then I just saw this:

“A new memristor-based device could be used to build brainlike systems and base-10 computers”

http://spectrum.ieee.org/semiconductors/memory/sixstate-memristor-opens-door-to-weird-computing

]]>A similar example is the following: from the magnetic permeability and the electric permittivity of vacuum it’s possible to define a quantity that has the dimensions of velocity and whose numerical value is that of the speed of light. However, within electrostatics and magnetostaics this velocity desn’t have physical meaning. Only once time-dependent phenomena in electromagnetism have been consistently described, does it turn out that this velocity does have physical significance. But its significance as a limiting velocity in fact emerges once special relativity is understood-since for any wave equation the velocity parameter is a limiting velocity; but it turns out that only electromagnetic waves can’t be described as the vbrations of more fundamental degrees of freedom. ]]>

It’s a comment on the article. ]]>

Your timeline is missing quite a bit between 1985 and 1998.

]]>**Scott** asserts “With quantum computing, the problem of decoherence was acknowledged by experts from the very beginning, and has by now been thought through in immense detail. We understand a lot both about why quantum fault-tolerance should work in principle, and about why realizing it experimentally is so hard.”

The literature paints a picture of our evolving understanding of decoherent dynamics that is considerably more nuanced than *that!* The following chronological sequence of five articles is commended to *Shtetl Optimized* readers:

**Feynman (1982)** *Simulating physics with computers* Feynman asks “Can a quantum system be probabilistically simulated by a classical universal computer?”

**Deutsch (1985)** *Quantum theory, the Church-Turing principle and the universal quantum computer* Deutsch introduces the crucial notion of universality in quantum computing.

**Preskill (1998)** *Quantum computing: pro and con* Preskill summarizes a decade’s hard-won understanding of fault-tolerant quantum dynamics; admirably balancing optimism against skepticism in regard to the feasibility of FTQC.

**Zangwill (2014)** *The education of Walter Kohn and the creation of density functional theory* Meanwhile Walter Kohn leads an exodus that regards Hilbert space as the resolution of an underlying, lower-dimension, algebraically tractable state-space, in which Feynman’s quantum simulation objective can be achieved by classical means.

**Murcko (2014)** ** Accelerating drug discovery: the accurate prediction of potency** Quantum chemists assert that Feynman’s promised land of cheap, fast, accurate, reliable, large-scale quantum simulation has been reached in practice … and these simulations crucially exploit noise for purposes of high-accuracy free energy perturbation (FEP) estimates.

———

**Falsifiable prediction** It will be news to many *Shtetl Optimized* readers (as it was news to me) that Walter Kohn was a teen-age *Kristallnacht* refugee, who spent the war in a *Canadian* (!) internment camp.

Kohn’s name therefore joins the remarkably long roster of imprisoned/interned algebraic geometers and dynamicists that includes also Galois, Weil, Grothendieck, Kähler, and Koblitz.

**Semi-serious question** Why does imprisonment seemingly foster an enduring passion (and an outstanding aptitude!) for algebraic geometry and dynamics?

**A pivotal challenge** How can quantum computing viably “pivot” (per Scott Adams’ remarks of #57) in view of ever-more-credible claims that Feynman’s 1982 quantum simulation objective has been achieved?

**Most usefully** Andrew Zangwill’s biography of Walter Kohn is heartily recommended to *Shtetl Optimized* readers, for its sympathetic in-depth portrait of a life well-lived in science and mathematics, spent grappling with tough quantum problems.

———

**Readings**

@article{Feynman:1982hs, Author = {R. P. Feynman},

Journal = {International Journal of Theoretical

Physics}, Number = {6–7}, Pages = {467–488}, Title

= {Simulating physics with computers}, Volume = 21,

Year = 1982}

@article{Deutsch:1985aa, Author = {{Deutsch}, D.},

Journal = {Royal Society of London Proceedings

Series A}, Month = jul, Pages = {97-117}, Title =

{Quantum theory, the Church-Turing principle and the

universal quantum computer}, Volume = 400, Year =

1985}

@article{Preskill:1998aa, Author = {{Preskill}, J.},

Journal = {Royal Society of London Proceedings

Series A}, Month = jan, Pages = {469}, Title =

{Quantum computing: pro and con}, Volume = 454,

Year = 1998}

@article{Zangwill:2014aa, Author = {Zangwill,

Andrew}, Journal = {Archive for History of Exact

Sciences}, Number = {6}, Pages = {775-848}, Title =

{The education of {W}alter {K}ohn and the creation

of density functional theory}, Volume = {68}, Year =

{2014}}

@inproceedings{Murcko:2014aa, Author = {Mark

Murcko}, Booktitle = {Advances in Drug Discovery and

Development}, Month = {24 September}, Note = {URL:

\url{https://www.youtube.com/watch?v=wa59ZgflJD}},

Organization = {Chemical \&\ Engineering News

(Virtual Symposium)}, Title = {Accelerating drug

discovery: the accurate prediction of potency},

Year = {2014}}

Scottargues [#55] “But there’s no need to debate this in the abstract! I’ll tell you what:build a memcomputingmachine, then show that you can use it to factor 1000-digit RSA challenge numbers into primes (as you must be able to do, if you can[resp. quantum computing]solve NP-complete problems). As soon as you do this, I’ll readily admit that I was wrong.[resp. scalably error-correct]

Let’s review some responses to this particular criticism of quantum computing, with a view toward discerning therein a viable response to Scott’s criticism of memcomputing.

——————–

**Tim Gowers’ question and Scott’s answer**

Tim Gowersasks [onMathOverflowin 2009] “Are there any interesting examples of random NP-complete problems?”

Scott Aaronsonanswers [onMathOverflowin 2010] “It’s been one of the great unsolved problems of theoretical computer science for the last 35 years!\(\ \)[…] “For [natural distributions], alas, we generally don’t haveanyformal hardness results”.

**Implication** Memcomputers might credibly claim practical efficacy in solving random instances of problem-classes that *formally* have NP-complete reductions, but whose random instances in practice almost always don’t … and this claim would not contravene *any* established results in complexity theory.

——————–

**Narratives by Gowers and Mazur** Tim Gowers’ recent weblog post “ICM2014 — Barak, Guralnick, Brown” extended his 2009 *MathOverflow* question as follows:

Tim Gowers’ dream“I’ve spent a lot of time in the last few years thinking about the well-known NP-complete problem where the input is a mathematical statement and the task (in the decision version) is to say whether there is a proof of that statement of length at most \(n\ \)— in some appropriate formal system.”“The fact that this problem is NP-complete does not deter mathematicians from spending their lives solving instances of it.”

“What explains this apparent success? I dream that there might be a very nice answer to this question, rather than just a hand-wavy one that says that the instances studied by mathematicians are far from general.”

Recent thoughtful follow-on essays by Tim Gowers (“Vividness in mathematics and narrative”, 2012) and Barry Mazur (“Visions, dreams, and mathematics”, 2012) are commended to *Shtetl Optimized* readers (BibTeX appended).

——————–

**Pivotal narratives** By what strategy can the quantum computing and memcomputing communities pursue the Gowers/Mazur program? Scott Adams’ recent on-line essay “The Pivot” (2014, BibTeX appended) provides a general strategy

Scott Adamssays “The most fascinating phenomenon in the start-up world is called the pivot. That word has been used in every meeting I’ve attended. There’s more to it than you think.”“A pivot is when a start-up quickly changes from one product to another or from one business model to another. The valley is full of stories about companies that started with a lame idea and hit it big after a pivot.”

“Another fascinating phenomenon in the valley is that every entrepreneur and investor seems genuinely interested in helping strangers succeed. I would go so far as to call it the defining feature of the start-up culture.”

“The dominant worldview in Silicon Valley is that if you aren’t trying to make the world better, you’re in the wrong line of work. The net effect is that the start-up culture is shockingly generous. If you need something for your start-up, folks will happily help you find it. I would have predicted the opposite.”

**Pivotal opportunities** For reasons that Scott [Aaronson] articulated (as quoted the beginning of this comment)\(\ \)— reasons that apply forcibly to *both* quantum computing and memcomputing\(\ \)— it’s time for both disciplines to pivot from their original hardware-centric objectives.

**Falsifiable prediction** Quantum computing and memcomputing *both* will pivot toward algorithm-deliverables, that run on *classical* Turing machines, that are implemented upon *ordinary* von Neumann hardware architectures … and are programmed in *nonstandard* languages (*e.g.* “G”).

—————

**Readings**

@incollection{Gowers:2012aa, Address =

{Princeton}, Author = {Timothy Gowers},

Booktitle = {Circles disturbed: the

interplay of mathematics and narrative},

Editor = {Doxiades, Apostolos K. and

Mazur, Barry}, Pages = {211--231},

Publisher = {Princeton University

Press}, Title = {Vividness in

Mathematics and Narrative}, Year =

{2012}}

```
```@incollection{Mazur:2012aa, Address =

{Princeton}, Author = {Barry Mazur},

Booktitle = {Circles disturbed: the

interplay of mathematics and narrative},

Editor = {Doxiades, Apostolos K. and

Mazur, Barry}, Pages = {183--210},

Publisher = {Princeton University

Press}, Title = {Visions, Dreams, and

Mathematics}, Year = {2012}}

`@misc{Adams:2014aa, Author = {Scott`

Adams}, Howpublished = {The Scott Adams

Weblog}, Month = {Jun 16,}, Title = {The

Pivot}, Year = {2014}}

It’s really too bad the author didn’t suggest to build those UMM devices with “memristors” /S

]]>But there’s no need to debate this in the abstract! I’ll tell you what: build a memcomputing machine, then show that you can use it to factor 1000-digit RSA challenge numbers into primes (as you must be able to do, if you can solve NP-complete problems). As soon as you do this, I’ll readily admit that I was wrong.

]]>