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I feel like mathematicians should make the same effort for non mathematicians. Why do all these weird terms even matter to anyone else besides a self selected

by yters 7y ago

I feel like mathematicians should make the same effort for non mathematicians. Why do all these weird terms even matter to anyone else besides a self selected group of mathematicians? If they don't, why should anyone care about such things, just as the author asked why mathematicians should care about formal proof systems? Academia in general is so used to not having to justify their interests to anyone else that many seem to live in their own isolated little worlds. Gone are the days when the 'uni' in university meant a unified realm of knowledge. We should rename 'university' to be 'diversity.' However, the origin story of academia with Greek philosophy sought to not merely subsist in rapidly fracturing groups of special interest, but to also seek the unifying underlying ideas. Similarly with the scholastics in the medieval era, which actually birthed our university system. I believe academia has lost its way, which may spell its end. Which is unfortunate for our civilization, as it is so fundamentally tied to the quest for wisdom and knowledge.

kragen 7y ago
Why should mathematicians want non-mathematicians to care? The evidence to date shows that non-mathematicians do things like starting wars, electing Trump, dying of heroin overdoses, circulating conspiracy theories about climate change, sentencing Socrates to death, chopping down the Academy for firewood, putting Archimedes to the sword, burning the books and burying the scholars under Qin Shi Huang, burning Giordano Bruno, killing Galois in a duel, only recognizing Leonardo for his paintings, stripping the German Jewry of their professorships (those they didn't simply murder first, like Gödel's mentor Moritz Schlick), and drugging Turing until he grew breasts and killed himself. The best the mathematicians can hope for is to evade the attentions of the non-mathematicians so they can be left in peace with their theorems and their olive groves. The theorems are true and beautiful whether the non-mathematicians care or not. Governments burn libraries. Governments manifest the will of the common people. I, too, believe that academia has lost its way. Over the entry of the Academy it said, "Do not enter, non-geometers." We should return to that policy; allowing theologians and such peddlers of nonsense into the academy was an unavoidable concession during medieval times, but it is one we should walk back.
- klyrs 7y ago
  Non-mathematicians build mathematics buildings, harvest and press chalk into sticks, grow the food and coffee we process into theorems (mathematicians are significantly more likely to od on amphetamines, btw), attend the calculus courses we desperately need for funding, clean our chalkboards and empty our wastebins... the list goes on and on. And yes there are mathematicians who vote for Trump. All you've proven with that tirade is a bound on the radius of your own filter bubble.
  - kragen 7y ago
    Mathematicians are perfectly capable of doing all those self-care things, as monks do in every monastery. (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.) I don't know of a single mathematician who has ODed on amphetamines, although of course amphetamines have been popular with mathematicians since they were discovered; and I know of only one who voted for Trump (Dan Kleitman), although undoubtedly others exist. The doses of amphetamines conducive to doing mathematics are about two orders of magnitude lower than the lethal doses, so it seems unlikely that someone who takes them to improve concentration rather than for euphoria would OD accidentally, as heroin users frequently do. Funding is only necessary to the extent that it helps keep the torch-wielding villagers away from the gate. To the extent that it subjects mathematical research to political tests, it is not only unnecessary, but counterproductive. If my filter bubble includes Bruno, Socrates, Mozi, Gödel, Turing, and Archimedes, I think its radius is adequate. I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians, think that all those killings of mathematicians I listed were reasonable and justified, and would like to silence any criticism of them.
    - JadeNB 7y ago
      > I don't know of a single mathematician who has ODed on amphetamines, and only one who voted for Trump (Dan Kleitman) I'm a mathematician who thinks that your sequence of posts here isn't serving the purpose you seem to think it does. I don't think that addressing it point by point serves much purpose, but these two claims bothered me particularly, so I single them out for response. I speak to your second point first: surely you don't think that there is only one mathematician who voted for Trump? Unless you do, it is irrelevant that you only know one; there are surely lots of others out there. I didn't, and I don't know any mathematician that I know did, but I know at least a few mathematicians who I know voted for GWB, and I imagine that there have to be at least a few other Trump voters in my mathematical circle. The first part in particular, in addition to the same quibble about what it matters whether or not you personally know such people (as opposed to whether or not they exist), probably requires an overly restrictive definition of 'mathematician' as "someone with academic credentials, or other official recognition, as a practitioner of mathematics". I personally don't think that's a good definition of a mathematician, and I don't think that advancing such definitions is a good thing for the future of our profession.
bawolff 7y ago
> Why do all these weird terms even matter to anyone else besides a self selected group of mathematicians? Why should anyone care about anything?
- kragen 7y ago
  What is good, Wolff, and what is not good? How do we know these things?
miscPerson 7y ago
Mathematics is modern ontology. We’re not great at predicting which parts of ontology are eventually useful in other fields — mostly physics and other hard science, but more recently computer science, economics + finance, and even things like sociology and linguistics. So we let the people who self-select to be ontologists guide what the field researches — and this has generally been fairly effective. Certainly more effective than if we’d only looked at things which had immediate, obvious use. Complex numbers, widely used in science and engineering, were once regarded as suspect abstract nonsense. That’s why they’re called “imaginary numbers”: it was a pejorative name that stuck. We have cryptography, computers, modern physics, and modern finance to show for our efforts, among other things. It simply takes time (like, decades to centuries) for new ontological ideas to propagate to other fields. We’re hoping that formalizing into HoTT and other computer friendly systems will allow us to align with software development, and speed the process up. That seems to be going well, and at an accelerating pace. The hope is that HoTT and category theory give us a framework to do exactly what you propose — more easily specify and interlink knowledge. Expect results around 2050. It took around 40-60 years for category theory to have a big impact — but now it is in fields as far away from mathematics as linguistics. Hopefully HoTT will get there a little faster, but it’s still going to take decades to go from niche research to widely used in mathematics to widely used across disciplines. So, to summarize: 1. Because we’re bad at predicting the future and abstract math has often turned out to be useful later. 2. Mathematics is trying to do exactly what you propose with knowledge, via exactly the programs this blog is talking about.
- yters 7y ago
  I disagree that all knowledge, or even the most important items of knoknowledge, are reducible to mathematics.
  - miscPerson 7y ago
    Could you explain why you disagree? I’d also accept an example of knowledge you don’t believe is expressible in mathematics.
- kragen 7y ago

by yters 7y ago

kragen 7y ago

Why should mathematicians want non-mathematicians to care? The evidence to date shows that non-mathematicians do things like starting wars, electing Trump, dying of heroin overdoses, circulating conspiracy theories about climate change, sentencing Socrates to death, chopping down the Academy for firewood, putting Archimedes to the sword, burning the books and burying the scholars under Qin Shi Huang, burning Giordano Bruno, killing Galois in a duel, only recognizing Leonardo for his paintings, stripping the German Jewry of their professorships (those they didn't simply murder first, like Gödel's mentor Moritz Schlick), and drugging Turing until he grew breasts and killed himself. The best the mathematicians can hope for is to evade the attentions of the non-mathematicians so they can be left in peace with their theorems and their olive groves. The theorems are true and beautiful whether the non-mathematicians care or not. Governments burn libraries. Governments manifest the will of the common people. I, too, believe that academia has lost its way. Over the entry of the Academy it said, "Do not enter, non-geometers." We should return to that policy; allowing theologians and such peddlers of nonsense into the academy was an unavoidable concession during medieval times, but it is one we should walk back.

klyrs 7y ago
Non-mathematicians build mathematics buildings, harvest and press chalk into sticks, grow the food and coffee we process into theorems (mathematicians are significantly more likely to od on amphetamines, btw), attend the calculus courses we desperately need for funding, clean our chalkboards and empty our wastebins... the list goes on and on. And yes there are mathematicians who vote for Trump. All you've proven with that tirade is a bound on the radius of your own filter bubble.
- kragen 7y ago
  Mathematicians are perfectly capable of doing all those self-care things, as monks do in every monastery. (By contrast, non-mathematicians are unable to build anything larger than a small hut without help from mathematicians in the form of geometry.) I don't know of a single mathematician who has ODed on amphetamines, although of course amphetamines have been popular with mathematicians since they were discovered; and I know of only one who voted for Trump (Dan Kleitman), although undoubtedly others exist. The doses of amphetamines conducive to doing mathematics are about two orders of magnitude lower than the lethal doses, so it seems unlikely that someone who takes them to improve concentration rather than for euphoria would OD accidentally, as heroin users frequently do. Funding is only necessary to the extent that it helps keep the torch-wielding villagers away from the gate. To the extent that it subjects mathematical research to political tests, it is not only unnecessary, but counterproductive. If my filter bubble includes Bruno, Socrates, Mozi, Gödel, Turing, and Archimedes, I think its radius is adequate. I think the downvoting of my "tirade" to -2 has shown that non-mathematicians hate and fear mathematicians, think that all those killings of mathematicians I listed were reasonable and justified, and would like to silence any criticism of them.
  - JadeNB 7y ago
    > I don't know of a single mathematician who has ODed on amphetamines, and only one who voted for Trump (Dan Kleitman) I'm a mathematician who thinks that your sequence of posts here isn't serving the purpose you seem to think it does. I don't think that addressing it point by point serves much purpose, but these two claims bothered me particularly, so I single them out for response. I speak to your second point first: surely you don't think that there is only one mathematician who voted for Trump? Unless you do, it is irrelevant that you only know one; there are surely lots of others out there. I didn't, and I don't know any mathematician that I know did, but I know at least a few mathematicians who I know voted for GWB, and I imagine that there have to be at least a few other Trump voters in my mathematical circle. The first part in particular, in addition to the same quibble about what it matters whether or not you personally know such people (as opposed to whether or not they exist), probably requires an overly restrictive definition of 'mathematician' as "someone with academic credentials, or other official recognition, as a practitioner of mathematics". I personally don't think that's a good definition of a mathematician, and I don't think that advancing such definitions is a good thing for the future of our profession.

bawolff 7y ago

> Why do all these weird terms even matter to anyone else besides a self selected group of mathematicians? Why should anyone care about anything?

kragen 7y ago
What is good, Wolff, and what is not good? How do we know these things?

miscPerson 7y ago

Mathematics is modern ontology. We’re not great at predicting which parts of ontology are eventually useful in other fields — mostly physics and other hard science, but more recently computer science, economics + finance, and even things like sociology and linguistics. So we let the people who self-select to be ontologists guide what the field researches — and this has generally been fairly effective. Certainly more effective than if we’d only looked at things which had immediate, obvious use. Complex numbers, widely used in science and engineering, were once regarded as suspect abstract nonsense. That’s why they’re called “imaginary numbers”: it was a pejorative name that stuck. We have cryptography, computers, modern physics, and modern finance to show for our efforts, among other things. It simply takes time (like, decades to centuries) for new ontological ideas to propagate to other fields. We’re hoping that formalizing into HoTT and other computer friendly systems will allow us to align with software development, and speed the process up. That seems to be going well, and at an accelerating pace. The hope is that HoTT and category theory give us a framework to do exactly what you propose — more easily specify and interlink knowledge. Expect results around 2050. It took around 40-60 years for category theory to have a big impact — but now it is in fields as far away from mathematics as linguistics. Hopefully HoTT will get there a little faster, but it’s still going to take decades to go from niche research to widely used in mathematics to widely used across disciplines. So, to summarize: 1. Because we’re bad at predicting the future and abstract math has often turned out to be useful later. 2. Mathematics is trying to do exactly what you propose with knowledge, via exactly the programs this blog is talking about.

yters 7y ago
I disagree that all knowledge, or even the most important items of knoknowledge, are reducible to mathematics.
- miscPerson 7y ago
  Could you explain why you disagree? I’d also accept an example of knowledge you don’t believe is expressible in mathematics.
kragen 7y ago