Habits of highly mathematical people • Hacker News Board

Re: Habits of highly mathematical people

#51

Post by nercht12 » Sat, Jul 30, 2016, 4:34 PM UTC

unfamiliar wrote: post #37

raldu wrote: post #18

Earlier quoted context omitted.

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

I strongly disagree with the claim that philosophers fit this description. As a mathematician, it often seems to me that 90% of philosophy is spent arguing about things with extremely loose definitions. As a result, you can argue from the same starting point and come to completely different conclusions (as separate philosophers often do), because the starting point was already self-contradictory for some interpretati…

Define "loose". Edit: Jokes aside, nothing is really "strictly-defined" as we would like it to be since definitions (even the most rudimentary ones) are based on -what we might call- statistical sets of observations. We come to the conclusion that an apple is a round object because we've seen an apple from multiple angles. Math accepts axioms, but those axioms are based on accepting definitions that are rudimentary observations. What is "1"? The idea of "1" can only be understood in terms of experience - hardly "rigorously defined".

Re: Habits of highly mathematical people

#52

Post by redipiny » Sat, Jul 30, 2016, 4:39 PM UTC

unfamiliar wrote: post #37

raldu wrote: post #18

Earlier quoted context omitted.

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

I strongly disagree with the claim that philosophers fit this description. As a mathematician, it often seems to me that 90% of philosophy is spent arguing about things with extremely loose definitions. As a result, you can argue from the same starting point and come to completely different conclusions (as separate philosophers often do), because the starting point was already self-contradictory for some interpretati…

One of the problems of philosophical discourse, imo, is that it seems to be impossible to give mathematically rigorous definitions of concepts like 'good' or 'moral' or even 'knowledge' that somebody won't be able to disagree with by counter example.

What you sometimes see among philosophers is that even definitions that are the result of many iterations are still treated more like rules of thumb than precise definitions. Or they at least acknowledge that their definition is probably flawed, and proceed carefully.

Some proceed as if they are doing math.

Re: Habits of highly mathematical people

#53

Post by [deleted] » Sat, Jul 30, 2016, 4:49 PM UTC

[deleted]

Re: Habits of highly mathematical people

#54

Post by GarrisonPrime » Sat, Jul 30, 2016, 4:50 PM UTC

louprado wrote: post #41

> The most common question students have about mathematics is “when will I ever use this?” The author then goes on to provide 6 semi-abstract reasons as to why abstract reasoning matters. Since this question is most likely to be asked by a child, it is code for "how can math-skills make me money or get me a job." Upon hearing the author's answers, 13 year old me would conclude, "it doesn't, and math is as useless as…

The point of the article isn't to show that the math will be used. The point is that people who ask such a question are missing the point.

"Education is what remains after one has forgotten what one has learned..." - Albert Einstein

Re: Habits of highly mathematical people

#55

Post by yummyfajitas » Sat, Jul 30, 2016, 5:09 PM UTC

unfamiliar wrote: post #37

raldu wrote: post #18

Earlier quoted context omitted.

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

I strongly disagree with the claim that philosophers fit this description. As a mathematician, it often seems to me that 90% of philosophy is spent arguing about things with extremely loose definitions. As a result, you can argue from the same starting point and come to completely different conclusions (as separate philosophers often do), because the starting point was already self-contradictory for some interpretati…

For example, many of the moral dilemmas that get tossed around as interesting become trivial to answer once you give a mathematically rigorous definition to words like "good", "moral", "utilitarian" or whatever.

Yes, but the while the conclusions become trivial, actually coming up with those rigorous definitions is not.

I'm not going to provide examples because they are likely to start a flamewar. But if you search for words like "normative" or "core principle" in my comment history, you can see how difficult it is to actually come up with those rigorous definitions. The problem is that when you do, you either come up with unsatisfying arbitrary definitions, or else you wind up implying peripherally related conclusions you probably dislike.

Yes, I am definitively guilty of being "highly mathematical" (and also highly economical and philosophical), and it pushes me to recognize incoherence in mainstream "thought".

Re: Habits of highly mathematical people

#56

Post by jknoepfler » Sat, Jul 30, 2016, 5:21 PM UTC

maroonblazer wrote: post #7

Couldn't this also be titled "Habits of high rational people", with mathematics simply being one application? I'm not a mathematician and was miserable at math in school, but I apply these habits in the business world every day. They help me cut through a lot of crap that comes from other people's sloppy/lazy thinking. >Anyone who has gone through an undergraduate math education has known a person (or been that perso…

I do think there is something unique about training in the 'hard' analytic disciplines (math, computer science, physics, etc.). In particular, one learns to be wrong often, and that the result of one's hard-fought intellectual effort is often objectively incorrect. At the very least, math accelerates the process of discovering this, and so is a very good teacher of intellectual humility.

The fact that you jumped to 'other people's sloppy thinking' as your first example is somewhat telling. The point is that your whole perspective can shift from thinking that you're smarter than other people and need to correct their mistakes, to understanding how to collaborate with other smart people over difficult problems while everyone is making and correcting mistakes.

Re: Habits of highly mathematical people

#57

Post by wutbrodo » Sat, Jul 30, 2016, 5:25 PM UTC

auggierose wrote: post #23

Very good article. I might add that a further pitfall in being "highly mathematical" is when you assume that the person you are communicating with is also "highly mathematical" and therefore has similar habits. That's not true MOST OF THE TIME and can lead therefore to severe misunderstandings.

IME you get used to this pretty rapidly, and what you're left with KS even better: the ability to translate between the two modes of communication (and expose the lack of rigor in one, which often leads to its proponent discovering errors in their assumptions).

Re: Habits of highly mathematical people

#58

Post by wutbrodo » Sat, Jul 30, 2016, 5:36 PM UTC

There's one habit in particular that he didn't really touch on that has been one of the most impactful parts of getting my math degree on my thinking.

There seems to be a gap between formal definitions and what we feel actual definitions are. Every once in a while, a professor would prove something that was clearly right, but felt like a violation of some unstated implicit part of a definition (for example, that the set of all vector spaces is itself a vector space). Despite feeling wrong, I couldn't come up with a particular reason that it wasn't right (short of falling back on some weasel word like "technically that's correct"). Math education forces that gap out into the open, and makes you pay more than lip service by building more and more theorems on top of it. The real world effect is to make you examine whether there's some actual value in this definitional gap (which can then be explicitly stated) or whether it's just fallacy.

I know far too many people who are comfortable with stopping at "this doesn't feel correct despite me having no counterargumemt to its 'proof' ". I've never been inclined that way but my math education certainly sharpened my ability to avoid this.

Re: Habits of highly mathematical people

#59

Post by BariumBlue » Sat, Jul 30, 2016, 5:40 PM UTC

jknoepfler wrote: post #56

maroonblazer wrote: post #7

Couldn't this also be titled "Habits of high rational people", with mathematics simply being one application? I'm not a mathematician and was miserable at math in school, but I apply these habits in the business world every day. They help me cut through a lot of crap that comes from other people's sloppy/lazy thinking. >Anyone who has gone through an undergraduate math education has known a person (or been that perso…

I do think there is something unique about training in the 'hard' analytic disciplines (math, computer science, physics, etc.). In particular, one learns to be wrong often, and that the result of one's hard-fought intellectual effort is often objectively incorrect. At the very least, math accelerates the process of discovering this, and so is a very good teacher of intellectual humility. The fact that you jumped to '…

The "hard analytical disciplines" require understanding the fundamentals of whatever they work with, in order to process those fundamentals together into a useful effect.

Getting meaning across via words is fundamentally the same process.

Re: Habits of highly mathematical people

#60

Post by wolfgke » Sat, Jul 30, 2016, 5:45 PM UTC

sidek wrote: post #21

raldu wrote: post #18

Earlier quoted context omitted.

Nice spot on. The described qualities would also apply to philosophers, logicians, etc. I think a broader term would be, habits of highly "analytical" people.

Philosophers? Using precise definitions? Maybe some philosophers do... But not most.

The much larger problem is that philosophers can't agree on one (or at least few) axiomatic base(s) they want to base their argumentations on. Thus lots of philosophical discussions are rather of the kind "we have different axioms and thus come to different conclusions".