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As an exclusive club, it's a feature. As pursuit for knowledge it's a tragedy. There are many highly intelligent people who are differently able to absorb math
by ganzuul 6y ago
As an exclusive club, it's a feature. As pursuit for knowledge it's a tragedy.
There are many highly intelligent people who are differently able to absorb mathematical literature. Consider, perhaps, if the gender imbalance is caused by the time needed to take care of children and a household. - Time which mathematics in its current state unfairly demands.
Human brains are structurally not very different. If raw compute is about the same across individuals then the progress of academia relies on people with highly differing form of intelligence. An obvious example is people on the spectrum with seemingly absent emotional intelligence but vast capacity for abstract creativity. There should be many more types of intelligence available to us given a better communication protocol.
Since I'm firmly in the camp of gaining knowledge for the benefit of mankind, I think the camp which instead of descriptive names gives names like "Hausdorff" or "Abelian" to important mathematical concepts are intellectual looters and a detriment to the field. As you seem to say we are in the same camp, I hope you see the conflict in gatekeeping.
- vertbhrtn 6y agoWhat descriptive alternative would you use for "abelian group"?
- gizmo686 6y agocommutative group (which happens to be another name they often go by).
- archgoon 6y agoWhich is just a synonym for abelian. You're not about to guess what 'commutative group' is from it's name any more than you're going to guess what an 'abelian group' is, unless you have already learned what commutative or abelian means in the specific context of algebra. I'm always baffled that programmers, who freely adopt frameworks and languages with mostly meaningless names (which incidentally makes them easier to google for), continue to insist that names are the major stumbling block in learning math. It's utter nonsense. You pick up the names and terminology quickly enough (or look them up if you forget); the hard part is applying them.
- ganzuul 6y agoNo, to commute is plain English. Abelian is not.
- Someone 6y agoI doubt many lawmen would be able to infer the meaning of “communicative” from today’s meaning of “to commute”. https://www.merriam-webster.com/dictionary/commute https://www.merriam-webster.com/dictionary/commute defines it as ”change, alter”, “convert”, or “compensate”, or as a synonym for “to commutate”, with meaning “to reverse every other half cycle of (an alternating current) so as to form a direct current” (first used, according to that dictionary in 1890; https://projecteuclid.org/download/pdf_1/euclid.rmjm/1181070017 https://projecteuclid.org/download/pdf_1/euclid.rmjm/1181070... claims Kronecker introduced the term “Abelian group” in 1870) https://dictionary.cambridge.org/dictionary/english/commute https://dictionary.cambridge.org/dictionary/english/commute doesn’t give any definition close to the mathematical meaning, either. Unless dictionaries 150-ish years ago had significantly closer descriptions of the term, “Abelian”, being a new term not loaded with pre-existing definition might be the better choice for naming this property.
- ganzuul 6y ago"Commutative" communicates something. "Abelian" communicates nothing. "Order-independent" like I suggested communicates a lot.
- Someone 6y agoDoes it? I think that could describe “associative” equally well as “commutative”. Edit: “symmetric” might be an alternative for Abelian because the Cayley table (https://en.wikipedia.org/wiki/Cayley_table https://en.wikipedia.org/wiki/Cayley_table) of an Abelian group is symmetric. I’m not sure that’s immediately clear enough for laymen, though.
- ganzuul 6y ago
- vertbhrtn 6y agoAnd same for "Hilbert space" please :)
- ganzuul 6y agoThe set of an order-independent operator, perhaps.
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