7 ms·

Lost in Math?

143 points by ernesto95 8y ago

BucketSort 8y ago
Related: Dijkstra's comments on mathematics and CS - http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1243a.html 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.
- tmountain 8y ago
  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 other "design pattern" resources. I think there's still a lot of opportunity to bring these ideas to the masses in the way that Evan Czaplicki , the author of Elm, is trying to do. The challenge in doing so seems to be finding the right level of abstraction to expose people to with the goal of maximizing benefit while simultaneously minimizing the prerequisite knowledge you're requiring folks to take on to participate.
  - BucketSort 8y ago
    I think it depends on what you are doing. If you are just doing API plumbing, the idea of introducing more rigor into the process may seem somewhat absurd. If you are doing real programming, however, Haskell allows you to elegantly structure and think about a problem. Certainly in parsing applications Haskell is a no brainier, Pandoc is written in Haskell for example. People are saying Rust is going to be the chosen one that brings it all together. For anyone interested in Haskell, I recommend starting with http://learnyouahaskell.com/ http://learnyouahaskell.com/ (very friendly, intuitive and light) then doing these exercises: https://github.com/data61/fp-course https://github.com/data61/fp-course.
    - tmountain 8y ago
      I'm mostly in agreement with you with the caveat that I've seen lots of "throwaway code" turn into production code that folks end up depending on. These days, if something seems like it has even a remote chance of being adopted into a production system, I'll try to make sure that it's on a solid foundation. Also, in terms of learning Haskell and its cousins, my advice is to start building stuff right away. It's easy to read about this stuff almost endlessly and never do anything productive with any of it. After learning Haskell, I got into Elm and then later PureScript. PureScript has really opened the door for me regarding getting some of these concepts out into the real world. It's really fun and feels rewarding to actually take advantage of some of the constructs that seemed pretty alien and abstract for a long time.
      - BucketSort 8y ago
        It is actually quite important to read up on Haskell if you don't have a background in modern FP. It isn't like other languages where you just see what's different from what you already know. There's a lot of conceptual stuff that helps understand what's going on. I actually started by jumping in myself, so I just wrote programs that were quite bad in Haskell terms. I usually recommend jumping into a language right away too, but it really really helps to understand some Haskell concepts at a conceptual level that is hard to understand from just jumping into the code. If one wants to jump right in, they can just do that FP course which is all exercises and skip the book, but I assure you that most noobs will be completely lost. It's like starting someone off in calculus with derivatives, completely skipping over limits and the geometrical underpinnings.
        tmountain 8y ago
        I should clarify that by "jumping in", I'm suggesting getting to a structural foundation that includes monads, applicative functors, monads, and their ilk, and then moving into writing code. I say this because I spent a few years learning this stuff without doing anything remotely practical, and I think that's too long.
    - mywrathacademia 8y ago
  - doppelganger27 8y ago
    What's the name of the podcast?
    - tmountain 8y ago
      The Haskell Cast. This is the episode I was referring to. It's pretty good. https://www.youtube.com/watch?v=O3EjNRgypXg https://www.youtube.com/watch?v=O3EjNRgypXg
- gowld 8y ago
  "practical" is highly debated.
  - deleted 8y ago
    [deleted]
dnautics 8y ago
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". In the FP communities, I do sometimes see people overoptimize for TCO. 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.
- gowld 8y ago
  Hmm? My queues and stacks are >100 deep. My graph traversals are >100 deep. My recursive calculations are >100deep Dynamic programming wouldn't be relevant if non-tail recursion was always good enough in practice.
  - dnautics 8y ago
    I was obviously referring to a different you. Yes, there are (many) cases when tco is 100% a great idea.
- tathougies 8y ago
  > 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.
  - deleted 8y ago
    [deleted]
  - chopin 8y ago
    I agree as it is important to know your boundaries. But I also like the GP prefer legible over performant code whenever it is obvious that I am not going to need more performance. In almost all cases I encountered the necessity to optimize code the reason was I/O bound. I don't recall any instance of algorithmic performance being a problem.
dkarl 8y ago
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 sake of beauty. The charge is that people who are supposed to be applying mathematics to reality are instead prioritizing mathematics and neglecting reality. To extend the analogy to CS, he must be talking about researchers supposedly trying to model real systems but instead just chasing beautiful math, but he isn't specific. Is it obvious to people in the know who or what he's talking about? For practical programmers, I think the problem is the reverse of being "lost in math." Practical programmers use extremely general theoretical results because they don't want to do math, not because the math is more beautiful. If they applied the information they know about their particular problem, they could get more useful mathematical results, but since they want to stay as far away from (doing) theory as possible, they use whatever facts they remember from class, which are ironically the most purely theoretical ideas because those are the simplest and easiest to remember.
- BucketSort 8y ago
  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.
  - chopin 8y ago
    >In their defense, this is why what they do is called theoretical physics. In my opinion, theoretical physics is about explaining observable phenomena in a falsifiable way (I am with Popper here). Otherwise an omnipotent god would be an equally good explanation for a given phenomenon.
paulpauper 8y ago
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
- sls 8y ago
  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-science-reviews-lost.html http://backreaction.blogspot.com/2019/02/a-philosopher-of-sc...
  - masteranza 8y ago
    There's no need for anyone to read her book, because it's just a pile of garbage written by someone who doesn't have a clue about modern physics. Hossenfelder is an armchair physicist who failed in her discipline and started writing books for profit. The very idea of naturalness is basically the thing people hope the machines will someday do - namely think and be able to explain what is actually going on through fleshing out noise from the essential mechanisms. The stuff she writes on her blog are so stupid it's beyond belief. First she criticizes theorists (who write far more reasonable and far less philosophical articles than she) for using advanced mathematics and exploring various possibilities, a minute later she criticizes experimenters for trying to build a better particle collider. She's a person who would gladly see the resources flowing to the less skilled wannabe-physicists with no real knowledge, because she's one of them.
throwawaymath 8y ago
> 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.
- deleted 8y ago
  [deleted]
- vladislav 8y ago
  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.
karozagorus 8y ago
It's terrible that nobody got punished for it, I hope Bitcoin will solve all of our problems soon.
andrewmatte 8y ago
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.
- lamename 8y ago
  Can you give an example of beauty (or assumed beauty I guess) just being oversimplification?
  - mhh__ 8y ago
    Although I admittedly only do mathematics through physics, I can't really think of any. If it's oversimplified, it's wrong and therefore not beautiful. Beauty is often given after discovery rather than on the way
- lalalandland 8y ago
  Is't a large part of the history of physics about doing away with wrong assumptions based on beauty? Circular orbits of planets etc.
  - mhh__ 8y ago
    Not recently. Dirac did believe his equation had to be right as it was so elegant, however it turns out we now interpret it differently now
  - masteranza 8y ago
    Except that you've got the point completely upside down! At first people didn't believe in heliocentrism because it used circular orbits, and instead used to believe that the universe is better described from the geocentric point of view which was one ginormous mess from the mathematical point of view. Then people realized that the beautiful addition of conical curves solves the problem completely. I say 'beautiful' because clearly you don't have a sense of mathematical beauty. Mathematical beauty is not only the simplicity of the solutions, but also it's robustness and fluid way in which it fits into the rest of our knowledge. The real simplification that came from it is far deeper than any 'circular orbits' picture you imagine. Naturalness and search for beauty can never be proved wrong. Those principles can perhaps only be applied prematurely, before enough data is collected.
salty_biscuits 8y ago
If you count all the work in AI/ML then the criticism has been overwhelmingly in the other direction, i.e. to much "just trying stuff to see what happens" and not enough "really understanding what is going on". Always seemed like a weak criticism to me honestly. You can advance theory, or you can advance through experimental insight. Neither is the right or wrong path, just whichever seems like the best way to make progress given the state of current knowledge.
- m463 8y ago
  I think AI/ML has changed things. I think Computer Science used to be more aligned with math, in the sense that the mathematics courses most people took in school were overwhelmingly symbol manipulation. Just like CS. Now I think things are not only more data driven, any sort of "undertanding" might be prioritized away forever, unless some adversarial network requires it. :)
- kevinventullo 8y ago
  Yeah, I feel ML would have been a more apt analogy than complexity theory. For some problems it's an ugly, "brute force" approach that works really really well.
drilldrive 8y ago
Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity of properly abstracting and insight to the resulting formal theory. I feel that physicists care more about such intuitive ideas than anybody else. Regardless, you only can become lost in math if you have bad premises. Mathematics is a relative subject, abstracting the arbitrary of reality to axioms. And if the axioms do not hold, the theory is bunk. It will always be the case that more granularity is required in real-life situations. Mathematics is precise and sound; it's not gospel.
- speedplane 8y ago
  > Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity and insight. Beauty is a subjective emotion, it's not so easy to quantify. You may not find mathamatics beautiful due to it's clarity and insight, but many others would precisely because of that. And it's not just math. Beautiful paintings, architecture, legal arguments, religions, etc., are often believed to be beautiful because of the clarity and insight they provide as well.
- mikorym 8y ago
  > And if the axioms do not hold, the theory is bunk. You assume the axioms hold. That is what an axiom is: an assumption. > Mathematics is precise and sound; it's not gospel. We do think that mathematics is precise. We don't really know if it is sound (unless I am missing something). For example, what is a set? It is not a "collection of things". Rather, it is an object in some mathematical setting. The topic of whether mathematics is "correct" is something else. We can all go out and build a DIY logical machine from scratch and see for ourselves that the mathematics we use give the results that we expect. Applied mathematics in this sense concerns itself with mathematics that suitably describe real situations.
  - drilldrive 8y ago
    >We don't really know if [mathematics] is sound. My apologies, I was hoping to be concise. I meant to say that mathematics is sound relative to the assumptions, which is exactly correct. But if the assumptions do not hold in reality (and they never quite do), then the theory as a whole is slightly off. I mean to say that mathematics is never 'correct' with reference to reality, but of course is always 'correct' with reference to the axioms.
mikorym 8y ago
> the theoretical physicist Sabine Hossenfelder asserts that mathematical elegance led physics astray I feel the other way around: Applied mathematicians and physicists led the pure mathematicians astray. But I say this for a different reason. I feel that physics has become convoluted with a plethora of theories where this same beauty is interpreted wildly differently by different people. In other words, people all have different ways of thinking, different notions of beauty, and ultimately, this manifests into different (competing) notions in physics. These may even be equivalent notions and they may embody the desired perspective on beauty, but instead of consolidation there is extended differentiation. My point is that physics has become ugly exactly because of physicists' ignorance towards mathematical elegance in favour of personal beauty. I don't think physics can become consolidated without exactly a stark appreciation for elegance. IMO this is why category theory took so long to start appearing in physics: The physicists are caught up in their own idea of beauty rather than the mathematical tradition of finding the minimal sufficient proofs and theories (which I call elegance).

143 points by ernesto95 8y ago

Related: Dijkstra's comments on mathematics and CS - http://www.cs.utexas.edu/users/EWD/transcriptions/EWD12xx/EWD1243a.html 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.

tmountain 8y ago
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 other "design pattern" resources. I think there's still a lot of opportunity to bring these ideas to the masses in the way that Evan Czaplicki , the author of Elm, is trying to do. The challenge in doing so seems to be finding the right level of abstraction to expose people to with the goal of maximizing benefit while simultaneously minimizing the prerequisite knowledge you're requiring folks to take on to participate.
- BucketSort 8y ago
  I think it depends on what you are doing. If you are just doing API plumbing, the idea of introducing more rigor into the process may seem somewhat absurd. If you are doing real programming, however, Haskell allows you to elegantly structure and think about a problem. Certainly in parsing applications Haskell is a no brainier, Pandoc is written in Haskell for example. People are saying Rust is going to be the chosen one that brings it all together. For anyone interested in Haskell, I recommend starting with http://learnyouahaskell.com/ http://learnyouahaskell.com/ (very friendly, intuitive and light) then doing these exercises: https://github.com/data61/fp-course https://github.com/data61/fp-course.
  - tmountain 8y ago
    I'm mostly in agreement with you with the caveat that I've seen lots of "throwaway code" turn into production code that folks end up depending on. These days, if something seems like it has even a remote chance of being adopted into a production system, I'll try to make sure that it's on a solid foundation. Also, in terms of learning Haskell and its cousins, my advice is to start building stuff right away. It's easy to read about this stuff almost endlessly and never do anything productive with any of it. After learning Haskell, I got into Elm and then later PureScript. PureScript has really opened the door for me regarding getting some of these concepts out into the real world. It's really fun and feels rewarding to actually take advantage of some of the constructs that seemed pretty alien and abstract for a long time.
    - BucketSort 8y ago
      It is actually quite important to read up on Haskell if you don't have a background in modern FP. It isn't like other languages where you just see what's different from what you already know. There's a lot of conceptual stuff that helps understand what's going on. I actually started by jumping in myself, so I just wrote programs that were quite bad in Haskell terms. I usually recommend jumping into a language right away too, but it really really helps to understand some Haskell concepts at a conceptual level that is hard to understand from just jumping into the code. If one wants to jump right in, they can just do that FP course which is all exercises and skip the book, but I assure you that most noobs will be completely lost. It's like starting someone off in calculus with derivatives, completely skipping over limits and the geometrical underpinnings.
      - tmountain 8y ago
        I should clarify that by "jumping in", I'm suggesting getting to a structural foundation that includes monads, applicative functors, monads, and their ilk, and then moving into writing code. I say this because I spent a few years learning this stuff without doing anything remotely practical, and I think that's too long.
  - mywrathacademia 8y ago
- doppelganger27 8y ago
  What's the name of the podcast?
  - tmountain 8y ago
    The Haskell Cast. This is the episode I was referring to. It's pretty good. https://www.youtube.com/watch?v=O3EjNRgypXg https://www.youtube.com/watch?v=O3EjNRgypXg
gowld 8y ago
"practical" is highly debated.
- deleted 8y ago
  [deleted]

dnautics 8y ago

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". In the FP communities, I do sometimes see people overoptimize for TCO. 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.

gowld 8y ago
Hmm? My queues and stacks are >100 deep. My graph traversals are >100 deep. My recursive calculations are >100deep Dynamic programming wouldn't be relevant if non-tail recursion was always good enough in practice.
- dnautics 8y ago
  I was obviously referring to a different you. Yes, there are (many) cases when tco is 100% a great idea.
tathougies 8y ago
> 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.
- deleted 8y ago
  [deleted]
- chopin 8y ago
  I agree as it is important to know your boundaries. But I also like the GP prefer legible over performant code whenever it is obvious that I am not going to need more performance. In almost all cases I encountered the necessity to optimize code the reason was I/O bound. I don't recall any instance of algorithmic performance being a problem.

dkarl 8y ago

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 sake of beauty. The charge is that people who are supposed to be applying mathematics to reality are instead prioritizing mathematics and neglecting reality. To extend the analogy to CS, he must be talking about researchers supposedly trying to model real systems but instead just chasing beautiful math, but he isn't specific. Is it obvious to people in the know who or what he's talking about? For practical programmers, I think the problem is the reverse of being "lost in math." Practical programmers use extremely general theoretical results because they don't want to do math, not because the math is more beautiful. If they applied the information they know about their particular problem, they could get more useful mathematical results, but since they want to stay as far away from (doing) theory as possible, they use whatever facts they remember from class, which are ironically the most purely theoretical ideas because those are the simplest and easiest to remember.

BucketSort 8y ago
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.
- chopin 8y ago
  >In their defense, this is why what they do is called theoretical physics. In my opinion, theoretical physics is about explaining observable phenomena in a falsifiable way (I am with Popper here). Otherwise an omnipotent god would be an equally good explanation for a given phenomenon.

paulpauper 8y ago

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

sls 8y ago
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-science-reviews-lost.html http://backreaction.blogspot.com/2019/02/a-philosopher-of-sc...
- masteranza 8y ago
  There's no need for anyone to read her book, because it's just a pile of garbage written by someone who doesn't have a clue about modern physics. Hossenfelder is an armchair physicist who failed in her discipline and started writing books for profit. The very idea of naturalness is basically the thing people hope the machines will someday do - namely think and be able to explain what is actually going on through fleshing out noise from the essential mechanisms. The stuff she writes on her blog are so stupid it's beyond belief. First she criticizes theorists (who write far more reasonable and far less philosophical articles than she) for using advanced mathematics and exploring various possibilities, a minute later she criticizes experimenters for trying to build a better particle collider. She's a person who would gladly see the resources flowing to the less skilled wannabe-physicists with no real knowledge, because she's one of them.

throwawaymath 8y ago

> 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.

deleted 8y ago
[deleted]
vladislav 8y ago
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.

karozagorus 8y ago

It's terrible that nobody got punished for it, I hope Bitcoin will solve all of our problems soon.

andrewmatte 8y ago

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.

lamename 8y ago
Can you give an example of beauty (or assumed beauty I guess) just being oversimplification?
- mhh__ 8y ago
  Although I admittedly only do mathematics through physics, I can't really think of any. If it's oversimplified, it's wrong and therefore not beautiful. Beauty is often given after discovery rather than on the way
lalalandland 8y ago
Is't a large part of the history of physics about doing away with wrong assumptions based on beauty? Circular orbits of planets etc.
- mhh__ 8y ago
  Not recently. Dirac did believe his equation had to be right as it was so elegant, however it turns out we now interpret it differently now
- masteranza 8y ago
  Except that you've got the point completely upside down! At first people didn't believe in heliocentrism because it used circular orbits, and instead used to believe that the universe is better described from the geocentric point of view which was one ginormous mess from the mathematical point of view. Then people realized that the beautiful addition of conical curves solves the problem completely. I say 'beautiful' because clearly you don't have a sense of mathematical beauty. Mathematical beauty is not only the simplicity of the solutions, but also it's robustness and fluid way in which it fits into the rest of our knowledge. The real simplification that came from it is far deeper than any 'circular orbits' picture you imagine. Naturalness and search for beauty can never be proved wrong. Those principles can perhaps only be applied prematurely, before enough data is collected.

salty_biscuits 8y ago

If you count all the work in AI/ML then the criticism has been overwhelmingly in the other direction, i.e. to much "just trying stuff to see what happens" and not enough "really understanding what is going on". Always seemed like a weak criticism to me honestly. You can advance theory, or you can advance through experimental insight. Neither is the right or wrong path, just whichever seems like the best way to make progress given the state of current knowledge.

m463 8y ago
I think AI/ML has changed things. I think Computer Science used to be more aligned with math, in the sense that the mathematics courses most people took in school were overwhelmingly symbol manipulation. Just like CS. Now I think things are not only more data driven, any sort of "undertanding" might be prioritized away forever, unless some adversarial network requires it. :)
kevinventullo 8y ago
Yeah, I feel ML would have been a more apt analogy than complexity theory. For some problems it's an ugly, "brute force" approach that works really really well.

drilldrive 8y ago

Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity of properly abstracting and insight to the resulting formal theory. I feel that physicists care more about such intuitive ideas than anybody else. Regardless, you only can become lost in math if you have bad premises. Mathematics is a relative subject, abstracting the arbitrary of reality to axioms. And if the axioms do not hold, the theory is bunk. It will always be the case that more granularity is required in real-life situations. Mathematics is precise and sound; it's not gospel.

speedplane 8y ago
> Coming from a mathematics background, I personally do not care so much for the 'beauty' of mathematics, and am moreso interested in clarity and insight. Beauty is a subjective emotion, it's not so easy to quantify. You may not find mathamatics beautiful due to it's clarity and insight, but many others would precisely because of that. And it's not just math. Beautiful paintings, architecture, legal arguments, religions, etc., are often believed to be beautiful because of the clarity and insight they provide as well.
mikorym 8y ago
> And if the axioms do not hold, the theory is bunk. You assume the axioms hold. That is what an axiom is: an assumption. > Mathematics is precise and sound; it's not gospel. We do think that mathematics is precise. We don't really know if it is sound (unless I am missing something). For example, what is a set? It is not a "collection of things". Rather, it is an object in some mathematical setting. The topic of whether mathematics is "correct" is something else. We can all go out and build a DIY logical machine from scratch and see for ourselves that the mathematics we use give the results that we expect. Applied mathematics in this sense concerns itself with mathematics that suitably describe real situations.
- drilldrive 8y ago
  >We don't really know if [mathematics] is sound. My apologies, I was hoping to be concise. I meant to say that mathematics is sound relative to the assumptions, which is exactly correct. But if the assumptions do not hold in reality (and they never quite do), then the theory as a whole is slightly off. I mean to say that mathematics is never 'correct' with reference to reality, but of course is always 'correct' with reference to the axioms.

mikorym 8y ago

> the theoretical physicist Sabine Hossenfelder asserts that mathematical elegance led physics astray I feel the other way around: Applied mathematicians and physicists led the pure mathematicians astray. But I say this for a different reason. I feel that physics has become convoluted with a plethora of theories where this same beauty is interpreted wildly differently by different people. In other words, people all have different ways of thinking, different notions of beauty, and ultimately, this manifests into different (competing) notions in physics. These may even be equivalent notions and they may embody the desired perspective on beauty, but instead of consolidation there is extended differentiation. My point is that physics has become ugly exactly because of physicists' ignorance towards mathematical elegance in favour of personal beauty. I don't think physics can become consolidated without exactly a stark appreciation for elegance. IMO this is why category theory took so long to start appearing in physics: The physicists are caught up in their own idea of beauty rather than the mathematical tradition of finding the minimal sufficient proofs and theories (which I call elegance).