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Lost in Math?

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Re: Lost in Math?

#11

Post by BucketSort »

dkarl wrote: post #9

But complexity theory aims at describing the performance of A over the space of all problem instances and it does so by abstracting away from individual problem instances. I appreciate the effort to extend the story into CS, but I wonder if you have to be familiar with the particular work he's alluding to. The charge (as leveled against theoretical physics) is not that some people do pure mathematical work for the sa…

This has been a common point of complaint in Physics since Einstein, and probably before. The idea that you can come up with ideas about how the universe works in the absence of experimentation doesn't sit right with many scientists. There are many scientists, like Edward Witten, that are working on things that are purely mathematical at the moment, and to some it seems like an inbred mathematical fantasy. In their defense, this is why what they do is called theoretical physics.

Re: Lost in Math?

#12

Post by paulpauper »

But the seductive power of mathematical beauty has come under criticism lately. In Lost in Math, a book published earlier this year, the theoretical physicist Sabine Hossenfelder asserts that mathematical elegance led physics astray. Specifically, she argues that several branches of physics, including string theory and quantum gravity, have come to view mathematical beauty as a truth criterion, in the absence of experimental data to confirm or refute these theor

Her criticism has gotten more attention than justified by its merits. No one has argued that beauty holds precedent over truth

Re: Lost in Math?

#13

Post by throwawaymath »

> About 10 years ago, in the wake of the 2008 financial crisis, the Nobel Laureate economist Paul Krugman made the same point with respect to economics and mathematics in an influential article titled "How Did Economists Get It So Wrong?" His main answer was: mistaking mathematical beauty for truth. "As I see it," wrote Krugman, "the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth."

I appreciate the point the article is trying to make, but I think this example is shoehorned in. You can misuse math without it being because you're "seduced by the beauty" of it.

I do agree with the author's example in physics. I have seen a lot of beautiful math in physics; look at lie algebras, monstrous moonshine and representation theory. Quite a bit of modern physics PhD dissertations are actually just math dissertations, and the same holds for a significant amount of new research in the field.

On the other hand I haven't seen that in finance. Highly exotic (read: "beautiful") mathematics is extremely rarely used in financial engineering. Pricing derivatives is decidedly mundane work compared to the brain-meltingly abstract mathematics deployed in high energy particle physics research. That's not to say it isn't difficult - it is difficult! But difficulty is better described by the word "complex" rather than "beautiful", and then of course financial engineering is complex. Then we should be talking about how getting mired in complexity can be bad for accountability and transparency.

This is a different thesis than the one presented by the author. Being led astray because you've built extremely brittle financial products using layers of complicated math is not the same as being more preoccupied with the elegance of a grand unifying theory than its agreement with reality.

But hey, maybe I'm just being pedantic. You can misuse mathematics in a lot of ways.

Re: Lost in Math?

#14

Post by doppelganger27 »

tmountain wrote: post #4
BucketSort wrote: post #2

Related: Dijkstra's comments on mathematics and CS - http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EW... . I've personally been getting a lot of satisfaction from learning Haskell and seeing how the functional programming community is taking ideas from abstract mathematics, like category theory, and is turning them into practical ways of thinking about programming.

Me too. Listened to a podcast recently where they were talking about things like, "once you know what a monoid is, you start seeing them everywhere". I've tried to express these benefits to coworkers recently. Leveraging ideas from math allows you to take advantage of many decades of research and provides a structural foundation that's substantially more robust than things you might find in the gang of four book or o…

What's the name of the podcast?

Re: Lost in Math?

#15

Post by [deleted] »

throwawaymath wrote: post #13

> About 10 years ago, in the wake of the 2008 financial crisis, the Nobel Laureate economist Paul Krugman made the same point with respect to economics and mathematics in an influential article titled "How Did Economists Get It So Wrong?" His main answer was: mistaking mathematical beauty for truth. "As I see it," wrote Krugman, "the economics profession went astray because economists, as a group, mistook beauty, cla…

[deleted]

Re: Lost in Math?

#17

Post by tathougies »

dnautics wrote: post #3

I haven't been in the developer industry for too long, but excepting the haskell community, I would say that the way CS tends to treat math is as guardrails, as in, "you can't do that because of the halting theorem". "you might be butting up against computational complexity if you try doing it this way". "reconstruction of this data shard is impossible because you don't have enough points to determine the equation".…

> Your datastructure is never going to be more than 10-100 deep. Don't worry about it. Just write the most legible recursive algorithm, not the most performant.

What? Try computing the 1000th fibonacci number.

Re: Lost in Math?

#18

Post by vladislav »

throwawaymath wrote: post #13

> About 10 years ago, in the wake of the 2008 financial crisis, the Nobel Laureate economist Paul Krugman made the same point with respect to economics and mathematics in an influential article titled "How Did Economists Get It So Wrong?" His main answer was: mistaking mathematical beauty for truth. "As I see it," wrote Krugman, "the economics profession went astray because economists, as a group, mistook beauty, cla…

Agreed. There's a huge difference between mathematical beauty in theoretical physics and in economics, the latter not really being on the radar in modern math. The author is conflating mathematical beauty with the "fancy math" effect of being able to easily publish papers in fields that aren't very mathematical just by having equations as part of the analysis. It's not like economists have found some amazingly beautiful theory (by modern math standards), they just use math to promote/legitimize their work.

Re: Lost in Math?

#19

Post by andrewmatte »

I have long felt like "beauty" in mathematics is just oversimplification.

Ironic that intelligent mathematics types get caught up in what could be analogous to socially hurtful stereotypes.

I am going to follow the author.

Re: Lost in Math?

#20

Post by sls »

paulpauper wrote: post #12

But the seductive power of mathematical beauty has come under criticism lately. In Lost in Math, a book published earlier this year, the theoretical physicist Sabine Hossenfelder asserts that mathematical elegance led physics astray. Specifically, she argues that several branches of physics, including string theory and quantum gravity, have come to view mathematical beauty as a truth criterion, in the absence of expe…

In a recent blogpost [1], Hossenfelder responds to a review of her book. All but the first two paragraphs are basically a response to this idea. A brief excerpt:

> In most cases, however, physicists are not aware they use arguments from beauty to begin with (hence the book’s title). I have such discussions on a daily basis.

> Physicists wrap appeals to beauty into statements like “this just can’t be the last word,” “intuition tells me,” or “this screams for an explanation”. They have forgotten that naturalness is an argument from beauty and can’t recall, or never looked at, the motivation for axions or gauge coupling unification. They will express their obsessions with numerical coincidences by saying “it’s curious” or “it is suggestive,” often followed by “Don’t you agree?”.

[…]

> What physicists are naive about is not appeals to beauty; what they are naive about is their own rationality. They cannot fathom the possibility that their scientific judgement is influenced by cognitive biases and social trends in scientific communities. They believe it does not matter for their interests how their research is presented in the media.

Have you read the book or any of her posts about the ideas in the book? There are in fact a lot of people who do claim that research programs and research dollars should be prioritized because of ideas like naturalness or beauty, even when decades of increasingly expensive and time-consuming work has led to no support for the natural or beautiful hypothesis.

[1] http://backreaction.blogspot.com/2019/02/a-philosopher-of-sc...

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