Michael Nielsen

I'm all for new publishing models in academia, but this post doesn't address the fundamental difference between the web in general and academic papers: expert curation.

The web's "curation" works (to whatever degree it does) because there are thousands, if not millions of people who can rate the quality of most articles/essays/websites. But in many scientific fields, there are often only a very small number of people who would be qualified to review a particular paper (usually well under a hundred, sometimes as few as a handful).

And make no mistake, this is a numbers game -- there's the well known 100/10/1 rule for content websites (for every 100 viewers, there are 10 who rate content, and only 1 who creates content). The exact numbers vary quite a bit from website to website, but the point is that it's orders of magnitude difference. That's all fine if your initial pool of people is huge, but if you start with 20 qualified people...you see the issue.

Another related point not addressed is that peer review is fairly demanding work. You're not just saying "accept" or "reject", but you're obliged to write a page or two suggesting the strong and weak points of the paper, things to improve, etc. You need some mechanism for enforcing this (even if it's via social norms), otherwise review quality deteriorates quite severely, which in turn affects paper quality.

In lieu of this article, I'd recommend seeing lectures by (or essays by) Michael Nielsen, who's thought about this…

I feel compelled to point out (as is done here http://michaelnielsen.org/blog/quantum-computing-for-everyone/) that it is possible that no such explanation exists. My understanding is that most people doing theoretical research in quantum computing don't need to have intuitive explanations for their results, since the calculations work themselves out. This is a depressing but honest observation.

I found quantum mechanics courses very frustrating for exactly this reason, especially in grad school, when the calculations became especially dense and the rationale impenetrable (I have since left physics). Occasionally there would be some little gem of insight into a particular phenomena where the result could be explained in a clear way, but the default approach was to just "do the calculation".

I can't explain exactly how a quantum computer works (because I don't understand it myself) but I will say that the reason the kind of analogy given above might make sense from a quantum mechanical perspective is that the state of the system and the operations that mutate the state have semantics different from classical computers. In particular, the state of the system is given by a bunch of complex numbers, which you can think of as a collection of arrows on the plane. The length and direction that these arrows are pointed in determines the probability for a bit having a particular sign. For example if an arrow is aligned more east-to west the measured classical bit will more likely…

As an arrogant 20-something year old, I disagree :P.

An important distinction to make here is whether you're teaching someone to intuitively reason about something or to logically calculate it precisely.

I think as long as someone grasps the basics of high school math and has a decent working memory, they should be able to learn how to calculate anything precisely given that you break it down into simple steps. If you don't know how to do that, you have no clue what you're doing.

Then there's intuitive reasoning. I think for most things, if you're familiar with a topic, you should be able to teach it in a way that makes sense. Of course there's exceptions -- some people are incredibly brilliant, but lack social awareness. I think that's the exception rather than the average case.

But not all topics are so easily reduced. There's probably some exceptions. The strongest that comes to mind is quantum computing. As many times as you can explain things like superdense coding, there's still a sense of "magic". Where the results of the math seem unnatural. And you go back through each step and try to figure out where things went weird. But each step is a logical progression from the beginning.

On that note, Michael Nielson's "Quantum Computing for the Determined" is one of the most well-taught courses I've found, and does a very good job of stepping the viewer through a very complicated topic. Michael Nielson clearly knows what he's doing…

This is fascinating to me. A couple comments and links.

Here is a course on proof theory that uses Coq [1]. It is actually the course that Vladimir Voevodsky took when he was trying to understand proof and type theory [2], [3]. While writing the midterm paper, he discovered homotopy type theory [4]. More details on the bitcoin scripting language can be found in the excellent blog post by Michael Nielsen[5].

If the escrow model is implemented, you can actually imagine the mathematical proof market maker acting like a bank, loaning out or otherwise investing bitcoins while the world waits for a verified proof; say, of the abc conjecture [6a] or the goldbach conjecture [6b]. This might be one small way to disrupt Wall St [7a], [7b]. In particular, such a market, when more highly developed, provides skilled mathematicians and scientists incentives to work on math and ( computer ) science problems in an open source format that benefits everyone - since everyone can look at and learn from their proofs - rather than quantitative trading in a closed format that actually causes long term social harm and political instability [IMHO]. I am thinking here of Goldman Sachs and Renaissance Technology founded by James Simons. Imagine if an incentive structure existed that encouraged all these smart folks to work on what is essentially verifiable open source software [8].

[1] http://www.cs.princeton.edu/courses/archive/fall09/cos441/index.php
[2]…

All these academics that lay low then pop up with problems and call Deolalikar's contribution unfixable infuriate me.

They bring out the worst in the same way that bad QA employees do. They create no wealth and add little value. They slow down and confuse the process. But in the end they are still necessary. There is something to be said about how one reports such problems. Most here know a great QA person that reports relevant problems in a intelligent manner and is there to help find solutions. Versus the QA person that just cranks out an endless stream of wonky insane problems. All make you look bad and all are difficult to reproduce, understand or address.

It's my understanding that his approach is a radical and new way to attempt to solve the P!=NP problem. So it's no surprise that at first glance the vast majority of average math and computer scientists would think it was not a valid approach. And, again no surprise to me, that has ended up to be the case. I don't pretend to understand this flaw or Deolalikar's paper. But I do understand the type of person that posts comments like that...

It looks like the math community has settle on a wiki to unofficially collect news and information on the paper:

http://michaelnielsen.org/polymath1/index.php?title=Deolalikars_P!%3DNP_paper

Unless I misread, I don't believe I saw anything that implied that the poster was claiming that anyone with a modicum of smarts could contribute significantly to the study of elliptic curves as relates to Diophantine equations. That being said, there are a mind-boggling number of extremely specific sub-specialties in mathematics, each of which would demand a significant investment of time from even a very intelligent person to reach a deep understanding of the state of the art. The fact that only a handful of folks are sufficiently versed in a particular sub-specialty to evaluate a long, involved and presumably brilliant proof attempt that draws significantly upon the state of the art of that sub-specialty does not imply that only a handful of folks are sufficiently intelligent to evaluate the proof. This reminds me of the recent attempt on the P/NP problem by Vinay Deolalikar - plenty of extremely talented mathematicians watched from the sidelines because they did not have sufficient specialized knowledge to properly evaluate the proof; though, that did not imply that the proof was particularly brilliant or even correct (http://michaelnielsen.org/polymath1/index.php?title=Deolalikar%27s_P!%3DNP_paper).