This came up from a few years back, in reaction to Paul Krugman writing of Isaac Asimov’s classic story: “In Foundation, we learn that a small group of mathematicians have developed ‘psychohistory,’ the aforementioned rigorous science of society.” I wrote:
I read the Foundation books as a child. I remember the “psychohistory” part, of course, but not that it was invented by mathematicians. That seems so retro! Back in the day, there were only a few sorts of technical academic fields, and one of these was mathematics. Thus you had Mandelbrot inventing fractals, Turing inventing computer science, and Ulam inventing the H-bomb.
Nowadays, I think of mathematicians as a sort of eccentric band of specialists, working for decades on problems that only they care about, while earning money teaching intro calc and training graduate students to work for Steven A. Cohen. I’m not saying that’s a fair impression–it would be just as correct for a mathematician to describe statisticians as an eccentric band of mathematical plodders who make a virtue of their mediocrity and call it practicality–but it’s the impression I get. If I were writing a novel about an exciting new science, I might have it be invented by a biologist or a computer scientist or even a rogue economist, but I probably wouldn’t think that something so applied would come out of the minds of a band of mathematicians.
Again, no slam on mathematicians. We wouldn’t expect such a breakthrough from a statistician or a political scientist either. Maybe not even from a physicist!
That said, in the twelve years since the above post appeared, deep learning has taken over the world, and there’s a lot of math in deep learning. And there was a front-page article in the newspaper today on quantum computing, and that’s all about physics. Still, I think the expectation now is that any exciting new science will be invented by a computer scientist. Above I also included economists, but I think the status of that field has declined since its early-2000s peak, so we can forget them. I still think there’s still an outside chance that a biologist or chemist could become the next scientific superhero.
What has happened in economics that makes you think it peaked in the early 2000s and declined afterwards?
Alex:
I’m not saying that I think economics peaked then; I’m saying that I think the status of economics peaked then.
Ah ok, thanks for the clarification. Why do you think the status of economics peaked in the early 2000s and declined afterwards? The 07-08 financial crisis and aftermath, and that most economists didn’t see it coming or even didn’t think it was possible, or something else?
Alex:
Just the natural ups and downs of public esteem. In the early 2000s, economics was hot: Krugman got the NYT column, Freakonomics presented economists as heroes, it was the era of econ triumphalism. The financial crisis was a turning point, but I think if it hadn’t been that, it would’ve been something else, some new flavor of the month. The new culture heroes are the AI people, or maybe the bitcoin scammers or the Ted talkers. Academic economists are still around, but there’s less of a perception that they are special people with all the answers.
Remember that “One of the easiest ways to differentiate an economist from almost anyone else in society” line? That could well be the peak of economics triumphalism, and it was from 2010.
I think economics is important, just not as important as some economists and journalists seemed to think during the first decade of this century.
FWIW, a couple of years ago Tyler Cowen (self) published a book in which he set out to determine which was the greatest economist of all time: https://goatgreatesteconomistofalltime.ai/en. He ends up naming four. In the process of making the rounds about the book he re-asserted something he’s been saying for awhile: for the last decade or three economics has been about technical improvements within the same range of topics. He doesn’t think there are any great new economic ideas out there.
Is he right about that? How would I know, I’m not an economist. OTOH, I think there are great new ideas out there all over the place. We just need to find them. Why would I think that? Because there is no reason to believe that the sequence David Hays and I outlined in this paper is at an end: https://www.academia.edu/243486/The_Evolution_of_Cognition
My fan fiction contribution along the “rogue economist” line:
> Shandess said, “You have asked for a private audience, Speaker, on a matter of importance. Could you please summarize the matter for me?”
> And Gendibal, speaking quietly, almost as though he were describing what he had just eaten at dinner, said, “First Speaker, regression discontinuity can give bogus results!”
Andrew: you might also keep an eye on materials science.
See especially Emerging technologies section in
https://en.wikipedia.org/wiki/Materials_science
and
https://deepmind.google/discover/blog/millions-of-new-materials-discovered-with-deep-learning/
There were some very good critiques of Deepmind’s materials “discoveries.” I can’t remember which were best, but see e.g. Link; “These errors unfortunately lead to the conclusion that no new materials have been discovered in that work”
Computational methods are great, but one of the reasons I went into experiment rather than theory is that plenty of fine theory falls apart when faced with reality. There’s no substitute for actually building / making things!
Thanks for link, interesting.
For sure, one must always build the real stuff … and if useful, do the big work of being able to do so a scale.
I might have said more: the DeepMind stuff is early, reminds me a bit of protein folding in the early 1990s, when algorithms often went off the deep end. Anyway, there clearly was some overclaiming, but also:
“In our view, three materials have been successfully synthesized as predicted.
In any case, the compounds in question were reported relatively recently, between 2021 and 2023. In fact, the authors of the Google DeepMind paper clarified that they took snapshots of the ICSD in 2021 and thus did not include materials discovered since in their training set. They rightfully view it as a success that materials they predicted based on a 2021 snapshot were since discovered.”
This seems another example of design processes that must explore large state spaces, for which any computational improvements are helpful, even if they are far less than perfect in early days. I’m also reminded of car crash simulations. When we drastically reduced the cost of doing those in the 1990s, i.e., as parallel 64-bit micros overtook vector supercomputers, car companies could try out many more crashes by computer … but of course, always had to do some real ones, much more expensive.
“…must explore large state spaces…”
And reality is a really huge state space.
I have a series of blog posts where I compare chess and language from a computational point of view. I start with what I call the “geometric footprint.” The geometric footprint of chess is quite small and simple, an 8 by 8 board, a small set of pieces with simple shapes, each capable of simple, well-defined moves. In combination with a small set of rules we get a very large, but mathematically well-behaved state space (a tree). The geometric footprint of language, OTOH, is ill-defined and unbounded, with the referents of many words having no specifiable physical geometry, and no end to the number of possible words. And the rules, they’re ill-defined as well. We end up with a much larger state space we don’t know how to define. No wonder combinatorial explosion killed “classical” symbolic approaches to language.
Yes I think you made the right choice to go into experimental biomolecular research rather than theory! At least up to now real advances in biology have come from experiment and its potential for making surprising and unpredicted field-changing observations. However much computational methods might be speeding up high-throughput and massively comprehensive data analysis it still relies on data from experiment. Of course if computational data analysis is your thing then go for it – it’s an exciting time to be a computational biologist.
Here’s where I see fast and significant advances from computational bioinformatics/machine learning in the next few years:
1. the identification of potential drugs to address rare (and maybe not so rare) diseases, through training computational methods to scour the scientific literature and medical databases for so-far-unrecognised significance of the effects of molecules that might be relevant for interventions in particular diseases. A sort of computational beefing-up of the approaches David Fajgenbaum has been using.
2. the interpretation of massive amounts of (experimental) genome sequences from a vast number of organisms to refine evolutionary relationships. This is already giving tons of info about the nature of Last Universal Common/Eukaryotic Ancestor (LUCA and LECA) and the molecular origins of multicellularity from single celled organisms that lead to the Cambrian Metazoa and human genetic diversity.
I would expect each of these to show a burst of major advance in the next decade and then return to a more steady progression, much as computational methods for protein structure prediction (based on 50 years of experimental data) exploded in significance just a few years ago and are likely to settle down as hugely useful tools. There’s only so much (which is a lot!) that can be done with existing data. So I expect that major advances in medicine in the next few decades will come from experimental developments in stem cell manipulation for tissue regeneration and replacement in degenerative disorders, reversal of somatic mutations for cancers and so on; not from computational develoments.
Of course predictions aren’t easy, especially about the future…
I happened just to be reading this post about the hype of Java (the programming language) in the 90s, and how it became entrenched and ubiquitous on all it’s non hyped features and became dull. I think there’s a big parallel with field prestige. Physics got a lot more prestige coverage from the speculative and not useful string theory than it did from, say, the routine and highly successful exercise of photonics or quantum mechanics in computing. And Economics got a lot more prestige from the reckless dilettantism of Freakonomics than it did from the normie macro or niche applied micro policy that most economists actually do.
So it’d be fun to imagine what routine and successful fields suddenly become hot and prestige based on a frivolous but exciting fringe.
https://dylanbeattie.net/2021/07/01/java-is-criminally-underhyped.html
The omission of psychology is a sign of confusion here.
Surely it is to the philosophers that we must look for new science? It’s in their job description.
To be sure, I don’t think mathematicians have been much involved in the development of deep learning. I think physicists have a better track record of contributing to it in fact. Some of the authors of OpenAI’s scaling laws paper were physicists.