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.’
Not to troll, but these kinds of comments: opinion -> caveat I know nothing about this, are growing more common on hacker news. Maybe consider if you're adding value by expressing your opinion in view of your awareness that it's completely uninformed?
That’s a fair call. I didn’t mean that I know absolutely nothing, just admitting that I don’t read much sociology.
My philosophy is that it’s still useful to give an opinion on something that interest you, even if it is probably wrong. If I am wrong, someone can correct me and I learn.
Also I suspect admitting ignorance leads to replies arguing in better faith since a discussion isn’t adversarial (I admit I’m not married to my opinion because I’m ignorant)
“There is a cult of ignorance in the United States, and there has always been. The strain of anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that 'my ignorance is just as good as your knowledge.”
Absolutely nothing wrong with forming opinions in the absence of deep understanding. We do it all the time. It can be fun and usefully provocative to engage in discussions as an interested but ill informed outsider. Providing first principles objections can even force people to question their assumptions when engaging or explaining.
But, and it's a huge but - expressing a broad opinion on an issue, when knowing nothing about it - as opposed to say asking a good faith question - isn't particularly useful to anyone.
My comment started a couple threads of discussion, and I learned something new about pure Mathematics. You are getting “useful to me” and “useful to anyone” mixed up.
I think Asimov would disagree with your interpretation.
“I believe that every human being with a physically normal brain can learn a great deal and can be surprisingly intellectual. I believe that what we badly need is social approval of learning and social rewards for learning.
We can all be members of the intellectual elite and then, and only then, will a phrase like "America's right to know" and, indeed, any true concept of democracy, have any meaning.”
What level of expertise do you think is required to comment on something? Would you consider yourself well versed in Internet ethics?
Also, your comment ironically expresses a broad opinion instead of asking good faith questions.
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".
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)
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.
If you did write a paper that assumed different axioms to the norm you would just state that you had done so! Because mathematics is axiomatic, mathematicians are happy to play around with axioms as long as it leads to something interesting.
Ah that makes sense, but do they really matter? If I want to use calculus to design the thickness of a bridge, does the selection of fundamental axioms matter at all?
Don’t all roads lead to Rome? It’s like an engineer deciding to use SI or Imperial units, people have their opinions but at the end of the day both work.
I think in theory, there could be very different axioms that both have so many open questions that competing schools vie for the best talent to explore 'their' space. Whether that's a situation likely to ever occur I have no idea.
I may just be a biased engineer, but until you find a way to apply your theoretical maths, surely it doesn’t matter if there are theoretical differences between approaches?
In the same way some heterodox political philosophies may result in new moral systems, but it doesn’t really matter that these moral systems are different to the status quo, until someone uses it as an ideology for their revolution.
It’s probably good to have a variety of theory to choose from, except when your different theories result in different practical outcomes.
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.
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.
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).
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.
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.
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/
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.
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.’