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It’s because it’s the hardest field to bullshit. Everything is black and white and you can’t just make up fake data. On the converse, psychology and economics

It’s because it’s the hardest field to bullshit. Everything is black and white and you can’t just make up fake data. On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. This is because they are the easiest to falsify, and their results are interpreted according to less precise epistemology. There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge). Also, the general public isn’t interested in pure maths, so there are less incentives to fake data so you can get a nice press release, or so you can publish your new book, or so that the government bureaucrat will subsidise your ‘research.’

j16sdiz 3y ago
> There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge). see Brouwer–Hilbert controversy ?
- keithalewis 3y ago
  Neither Brouwer nor Hilbert claimed the other was wrong, only which axioms they preferred to use.
  - gnulinux 3y ago
    This is not true at all, Brouwer truly thought the original Aristotelian concept of the "law of excluded middle" was epistemologically unfounded. I would recommend his original paper introducing intuitionistic mathematics but it's very dense. You can refer to: https://plato.stanford.edu/entries/brouwer/ https://plato.stanford.edu/entries/brouwer/ Later, he argued he found mathematical proofs of counterexamples of LEM. From above source: > “Intuitionist Reflections on Formalism” of 1928 identifies and discusses four key differences between formalism and intuitionism, all having to do either with the role of PEM or with the relation between mathematics and language. Brouwer emphasises, as he had done in his dissertation, that formalism presupposes contentual mathematics at the metalevel. He also here presents his first strong counterexample, a refutation of PEM in the form ∀x∈R(Px∨¬Px), by showing that it is false that every real number is either rational or irrational. See the supplement on Strong Counterexamples.
lelanthran 3y ago
> On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. If you think that psychology and economics have problems with reproducibility and fraud, you haven't seen the social sciences!
- brutusborn 3y ago
  [flagged]
  - shaunn 3y ago
    Aren't all sciences were born from philosophy? Graduating from the journey of understanding the meaning of something and graduating to measuring it to further understand why the world works the way it works? Social sciences, economics, and medicine are relatively immature (hundreds of years versus thousands) compared to the hard sciences. These fields all apply the scientific method to the best degree available and the subject matter is pretty complex therefore results are difficult to reproduce. They could do a better job at self-regulation, but maybe that's part of its maturation process. Humans with their personalities and motivations are harder to "science".
    - brutusborn 3y ago
      Yes, I would say that science is a branch of epistemology that uses evidence to generate knowledge to increase predictive power. I think the difference between hard and soft sciences is just how tangible your predictions are. Soft fields are definitely harder to research, but instead of acknowledging this, many soft researchers ignore epistemological limits to make their research sound ‘harder.’ A good example is this psych researcher deriving equations of emotion based on fluid mechanics [O]. Somehow people in these fields don’t understand and/or care and allow this bullshit to continue. I think many or most soft research programs are currently in “degenerate” territory (Lakotos) [0] https://www.narratively.com/p/nick-brown-smelled-bull https://www.narratively.com/p/nick-brown-smelled-bull
  - dbspin 3y ago
_the_inflator 3y ago
I somewhat disagree and would invite Georg Cantor to this discussion about acceptance towards new paradigms and black/white in Mathematics. After all, Mathematics is not a natural science and hereby consensus must be reached.
- brutusborn 3y ago
  What do you mean by the last sentence? My understanding was that most maths research used proofs that didn’t rely on any consensus? I may well be wrong, would love some examples.
  - foota 3y ago
    There can be uncertainty about unproven results (e.g., P vs NP), or about results that are too complicated for people to verify (there have been a number of these, where the proof essentially creates a new branch of mathematics).
  - suoduandao2 3y ago
    I think they mean consensus about which axioms to accept. There could be competing schools of mathematics along those lines, I think there just happens not to be.
    - defrost 3y ago
      Hardly 'competing', more like (say) Commodore-64 demo Vs nVidia GPU demo scenes - you pick your arena and push what can be done with constraints (axioms). In mathematics you might compare groups that work with Vs without the Axiom of Choice, you can can have one group satisfied by an existence proof that asserts X exists otherwise a contradiction must exist and another group that only accept existence proofs that demonstrate a means to construct an example of X. The habeas corpus divide :-)
      - FieryTransition 3y ago
        But is a Hilbert system easier to run in a computer since there are many axioms which clarifies the cases where contradictions or some inference rules are used which might be hard to program? For example, on the top of my head, in predicate logic, how would you encode an inference rule like exists elimination? It's tricky enough for me to think about, but to be able to encode a computer with it, is harder, and I can't remember if something like this falls under the undecidable problems category or not.
bumby 3y ago
I’ve heard it’s own version of pontoons though. In particular, that it’s becoming so dense that enough people aren’t revalidating the proofs. There’s been examples on HN of published proofs that existed for years and years before someone pointed out they’re wrong. To a non-mathematician this sounds like it’s own version of the replication problem.
- grungegun 3y ago
  This is somewhat overblown, and only really an issue for some particular theorems and obscure corners of mathematics. And this isn't a recent problem, Hilbert's proof of Nullenschtatz in the early 20th century had logical errors, but is otherwise true. If a proof is used by 3 people it won't have much scrutiny, but once major results start to be based on the proof, it'll get reviewed more carefully and either accepted or rejected in the long run. The ABC conjecture is probably the biggest example.

j16sdiz 3y ago

> There’s no ‘Austrian school’ vs ‘Chicago school’ in maths (to my knowledge). see Brouwer–Hilbert controversy ?

keithalewis 3y ago
Neither Brouwer nor Hilbert claimed the other was wrong, only which axioms they preferred to use.
- gnulinux 3y ago
  This is not true at all, Brouwer truly thought the original Aristotelian concept of the "law of excluded middle" was epistemologically unfounded. I would recommend his original paper introducing intuitionistic mathematics but it's very dense. You can refer to: https://plato.stanford.edu/entries/brouwer/ https://plato.stanford.edu/entries/brouwer/ Later, he argued he found mathematical proofs of counterexamples of LEM. From above source: > “Intuitionist Reflections on Formalism” of 1928 identifies and discusses four key differences between formalism and intuitionism, all having to do either with the role of PEM or with the relation between mathematics and language. Brouwer emphasises, as he had done in his dissertation, that formalism presupposes contentual mathematics at the metalevel. He also here presents his first strong counterexample, a refutation of PEM in the form ∀x∈R(Px∨¬Px), by showing that it is false that every real number is either rational or irrational. See the supplement on Strong Counterexamples.

lelanthran 3y ago

> On the converse, psychology and economics seem to have the most problems in terms of reproducibility and fraud. If you think that psychology and economics have problems with reproducibility and fraud, you haven't seen the social sciences!

brutusborn 3y ago
[flagged]
- shaunn 3y ago
  Aren't all sciences were born from philosophy? Graduating from the journey of understanding the meaning of something and graduating to measuring it to further understand why the world works the way it works? Social sciences, economics, and medicine are relatively immature (hundreds of years versus thousands) compared to the hard sciences. These fields all apply the scientific method to the best degree available and the subject matter is pretty complex therefore results are difficult to reproduce. They could do a better job at self-regulation, but maybe that's part of its maturation process. Humans with their personalities and motivations are harder to "science".
  - brutusborn 3y ago
    Yes, I would say that science is a branch of epistemology that uses evidence to generate knowledge to increase predictive power. I think the difference between hard and soft sciences is just how tangible your predictions are. Soft fields are definitely harder to research, but instead of acknowledging this, many soft researchers ignore epistemological limits to make their research sound ‘harder.’ A good example is this psych researcher deriving equations of emotion based on fluid mechanics [O]. Somehow people in these fields don’t understand and/or care and allow this bullshit to continue. I think many or most soft research programs are currently in “degenerate” territory (Lakotos) [0] https://www.narratively.com/p/nick-brown-smelled-bull https://www.narratively.com/p/nick-brown-smelled-bull
- dbspin 3y ago

_the_inflator 3y ago

I somewhat disagree and would invite Georg Cantor to this discussion about acceptance towards new paradigms and black/white in Mathematics. After all, Mathematics is not a natural science and hereby consensus must be reached.

brutusborn 3y ago
What do you mean by the last sentence? My understanding was that most maths research used proofs that didn’t rely on any consensus? I may well be wrong, would love some examples.
- foota 3y ago
  There can be uncertainty about unproven results (e.g., P vs NP), or about results that are too complicated for people to verify (there have been a number of these, where the proof essentially creates a new branch of mathematics).
- suoduandao2 3y ago
  I think they mean consensus about which axioms to accept. There could be competing schools of mathematics along those lines, I think there just happens not to be.
  - defrost 3y ago
    Hardly 'competing', more like (say) Commodore-64 demo Vs nVidia GPU demo scenes - you pick your arena and push what can be done with constraints (axioms). In mathematics you might compare groups that work with Vs without the Axiom of Choice, you can can have one group satisfied by an existence proof that asserts X exists otherwise a contradiction must exist and another group that only accept existence proofs that demonstrate a means to construct an example of X. The habeas corpus divide :-)
    - FieryTransition 3y ago
      But is a Hilbert system easier to run in a computer since there are many axioms which clarifies the cases where contradictions or some inference rules are used which might be hard to program? For example, on the top of my head, in predicate logic, how would you encode an inference rule like exists elimination? It's tricky enough for me to think about, but to be able to encode a computer with it, is harder, and I can't remember if something like this falls under the undecidable problems category or not.

bumby 3y ago

I’ve heard it’s own version of pontoons though. In particular, that it’s becoming so dense that enough people aren’t revalidating the proofs. There’s been examples on HN of published proofs that existed for years and years before someone pointed out they’re wrong. To a non-mathematician this sounds like it’s own version of the replication problem.

grungegun 3y ago
This is somewhat overblown, and only really an issue for some particular theorems and obscure corners of mathematics. And this isn't a recent problem, Hilbert's proof of Nullenschtatz in the early 20th century had logical errors, but is otherwise true. If a proof is used by 3 people it won't have much scrutiny, but once major results start to be based on the proof, it'll get reviewed more carefully and either accepted or rejected in the long run. The ABC conjecture is probably the biggest example.