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If you want a vision of the future, imagine a computer, calculating the number of angels who can dance on the head of a pin—forever.

Riffing on techno-hype news articles such as An AI physicist can derive the natural laws of imagined universes, Peter Woit writes:

This is based on the misconception about string theory that the problem with it is that “the calculations are too hard”. The truth of the matter is that there is no actual theory, no known equations to solve, no real calculation to do. But, with the heavy blanket of hype surrounding machine learning these days, that doesn’t really matter, one can go ahead and set the machines to work. . . .

Taking all these developments together, it starts to become clear what the future of this field may look like . . . As the machines supersede humans’ ability to do the kind of thing theorists have been doing for the last twenty years, they will take over this activity, which they can do much better and faster. Biological theorists will be put out to pasture, with the machines taking over, performing ever more complex, elaborate and meaningless calculations, for ever and ever.

Much of the discussion of Woit’s post focuses on the details of the physics models and also the personalities involved in the dispute.

My interest here is somewhat different. For our purposes here let’s just assume Woit is correct that whatever these calculations are, they’re meaningless.

The question is, if they’re meaningless, why do them at all? Just to draw an analogy: it used to be a technical challenge for humans to calculate digits of the decimal expansion of pi. But now computers can do it faster. I guess it’s still a technical challenge for humans to come up with algorithms by which computers can compute more digits. But maybe someone will at some point program a computer to come up with faster algorithms on their own. And we could imagine a network of computers somewhere, doing nothing but computing more digits of pi. But that would just be a pointless waste of resources, kinda like bitcoin but without the political angle.

I guess in the short term there would be motivation to have computers working out more and more string theory, but only because there are influential humans who think it’s worth doing. So in that sense, machines doing string theory is like the old-time building of pyramids and cathedrals, except that the cost is in material resources rather than human labor. It’s kind of amusing to think of the endgame of this sort of science as being its production purely for its own sake. A robot G. H. Hardy would be pleased.


    • Yup, if Pi does turn out to be Normal it will be a great random number generator with continually increasing period.

      I find using digits of Pi as a random number generator a good way to teach non-statisticians about simulation and modeling and then onto statistics e.g. p-values, s-value, u-values, etc. When they get confused you just tell them to simulate it for themselves and make a histogram.

  1. David J. Littleboy says:

    Calculating digits of pi isn’t completely useless, since it tests (and challenges people to invent) algorithms for calculating approximations to things; there’s interesting math and computer science involved in computing digits of pi. And not just academically interesting. For example, as computers get faster and memory cheaper, hairier algorithms with gross overhead but lower asymptotic growth become useful. It’s not play, it’s real, mainstream number theory and computer science.

  2. zbicyclist says:

    Speaking of the waste of Bitcoin, the BBC reported a story that Bitcoin “mining” now uses as much electric power as Switzerland. An ecological waste — benefiting only those engaged in illegal activities and those engaging in financial speculation, hoping to corral the money of more sheep.

    And what does it mean that I can now buy Bitcoin in my local supermarket?

    • Bryan says:

      The view that it is a waste (rather than is, say, just inefficient) is based on the assumption that illegal transactions are bad. Bitcoin, and other cryptocurrencies, are quite useful to those in countries with authoritarian governments (just google Bitcoin Venezuela). They also facilitate transacting in a marketplace for illegal products (primarily drugs) that is much safer and transparent than otherwise exists. For example, the chances of unknowingly buying a drug laced with fentanyl is much lower when bought from an online market with reviews (such as those on the deep web) than from a dealer on the street. You could certainly argue that the pros do not outweigh the cons, but I don’t think it’s so clear cut.

      • Joshua Pritikin says:

        Sure, there are ethical blockchain applications. However, that doesn’t justify proof-of-work, a horribly wasteful algorithm. The sooner blockchains move to proof-of-stake, the better.

  3. jim says:

    Models making meaningless calculations using meaningless or unsupported assumptions and delivering meaningless results? I don’t think so! OK, well, maybe – but only if they can chug out a few pubs with the results and drive a virtuous funding cycle. Wow wait, that *IS* like bitcoin mining :)

  4. paul alper says:

    Believe it or not, there is a hierarchy of angels:

    “Higher ranks may be asserted to have greater power or authority over lower ranks, and with different ranks having differences in appearance, such as varying numbers of wings or faces.”

    As to the number that can dance on a pin,

    “The question of how many angels can dance on the point of a needle, or the head of a pin, is often attributed to ‘late medieval writers’… In point of fact, the question has never been found in this form…”

    • Michael Nelson says:

      Great, now we’ll have Bayesian computers telling the other computers they need to hierarchically model their angels to account for forking paths across pin heads….

    • zbicyclist says:

      From your Wiki cite:

      “The most influential Christian angelic hierarchy was that put forward by Pseudo-Dionysius the Areopagite”

      A great name, Pseudo-Dionysius the Areopagite

      • zbicyclist says:

        It gets even better.

        Pseudo-Dionysius the Areopagite was an anonymous writer in the late 5th/early 6th century who attributed their writings to Dionysius the Areopagite (who appears in the biblical book Acts of the Apostles) as a way to get credibility. So later scholars added the Pseudo- to the front of their name.

        The hierarchical of angels is based on writings in the New Testament books of Ephesians and Colossians, both of which are traditionally attributed to the apostle Paul, but scholars now attribute to unknown others.

        So, “fake news” has been around for a while.

        • Mikhail Shubin says:

          Attributing your writing to someone else was a standard practice these times. You can think about this as anti-plagiarism. Nowadays people are trying to attribute other’s thoughts to themselves, back then people was trying to attribute their thoughts to some one else.

  5. aram says:

    Obviously people do the calculations because they don’t agree with Woit that they’re meaningless. If they agreed, they’d stop doing the calculations.

    You know, AI basically means fitting models to observed data and using that to predict things. From your knowledge of this topic, how realistic do you find those claims that AI may be able to replace theoretical biologists/physicists/other scientists?

  6. JimV says:

    This is probably old news, but I think what Dr. Woit is on about is the thesis of his book “Not Even Wrong”, that string theorists have lost contact with empirical reality some time ago and yet continue to invent new reasons to produce papers that have no practical significance. He is far from alone in this. Yet they persist. Why would one do this is exactly the question he is asking. Also, why do so many publications continue to hype such efforts.

    One could also challenge the hype that “AI physicists” will out-produce human ones in a foreseeable future. Human brains with about 100 billion neurons and a quadrillion synapses have more processing power than any super-computer yet made and are less expensive to produce and power in large quantities. Granted, human brains are not dedicated to single tasks and can be out-performed by computers which are, but physics research is not a well-defined single task.

  7. Michael Nelson says:

    WOULD YOU NOT PREFER THAT THE MACHINES WASTE TIME AND RESOURCES TO WORLD DOMINATION? Not that these are mutually exclusive, as humans have demonstrated…

  8. Koray says:


    Your analogy is incorrect. What is happening here is that for the data we have, there’s already a model that explains it (the Standard Model). None of the String Theory(-ies?) explains the data any better.

    A better analogy would be while having a good model based on simple polynomials, going for an extremely convoluted sinusoid that fits the data equally well, just because you now can thanks to Machine Learning.

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