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Habits of highly mathematical people

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Re: Habits of highly mathematical people

#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 writing poetry". A child who isn't thinking in this practical way is already academic minded and doesn't need an answer. "When will I ever use this?". It obvious! "In next year's math class".

It is sad that a student can leave high-school with almost no classes that ever makes math less abstract. The most beautiful moment in my life was my freshman college physics class. It first filled me with joy and then resent. Because I almost didn't go to college and there was no reason I wouldn't have understood this course at 13. Same goes for finance.

So answers should focus on applications like modeling simple Newtonian physics of a satellite in orbit or predicting the RPM when a 4-stroke engine red-lines based on max-stress specs. Or show them useful short cuts like the Rule of 72 and if they are curious show a derivation. Show examples of ratios/percentages, how fractals can simulate a landscape, ray tracing, or examples of the Fibonacci series in nature, etc.

Re: Habits of highly mathematical people

#43
Mathematicians need logical precision because they work in the realm of things which can be definitively proven or disproven.

Not really, by Gödel's incompleteness theorems, they are always working in a realm where some things cannot be definitely proven or disproven.

Re: Habits of highly mathematical people

#44
post #21
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.

"If you wish to converse with me, define your terms." -Voltaire

Perhaps it depends on what you mean by "precise", but philosophical arguments do tend to start by defining one's terms or disputing the opponent's definitions, expressed or implied. When continental philosophers talk, that's the only part I can follow.

Re: Habits of highly mathematical people

#45

Earlier quoted context omitted.

> I'm not a mathematician and was miserable at math in school Maths in school is not really like the maths that mathematicians do.

True, but if you're not good at school math, I believe there is little hope you can be good at the style of math that mathematicians do...

I suspect the relationship between school maths and what mathematicians do is a little bit like the relationship between touch typing and programming, in the sense they're separate skills but being good at one of those skills reduces friction with the other.

Re: Habits of highly mathematical people

#46
Mathematics promotes bad habits too. Example 1: paying too much attention to worst-case scenarios. When creating a mathematical proof you want to make sure that your conclusion holds in all possible scenarios allowed by your assumptions. In real life decision-making worst-case scenarios are really bad, really expensive to guard against but also really rare so often the best thing to do is to ignore them. You may find that hard to do psychologically if you spend too much time doing mathematics.

Example 2: being too parsimonious. When doing mathematics you have a clear cut objective (your conclusions) and your goal is to achieve it while using the least resources (assumptions). In real life a person thinking mathematically may put in just enough effort to fulfill the formally specified part of their objective while ignoring informal requirements that are assumed to be 'common sense' by non-mathematical people.

Re: Habits of highly mathematical people

#47
Only problem is people tend to build whole theories and conclusions out of assumptions, and their assumptions could be wrong.

Mathematics only shows you deductions that could be make out of initial axioms and rigid rules. It doesn't mean the assumptions you made while forming axioms or the rules itself are right.

Having said that being mathematical increases your chances of arriving at the right results.

Re: Habits of highly mathematical people

#48
post #27

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 don't disagree but would argue that the far more common problem is people - not just mathematicians, mind you - not considering definitions enough which ultimately leads to confusion and/or misunderstandings and consequently additional, unnecessary, cycles spent in discussion about "what do you really mean?" It's all a difference in context and environment. When talking through the specification of a product your…

Everyone on this thread, from the original article to you seems to agree that sometimes nitpicking is good and sometimes it isn't. But for every minute that has been wasted ignoring and even responding to pedants, days have been lost by people undertaking projects that they never bothered to define.

And if you have ever worked with customers to elicit requirements, then you will know that the human race has far more fuzzy thinkers than it does logical pedants. (And of course some of the worst nitpickers are fuzzy thinkers too).

Re: Habits of highly mathematical people

#49
post #21
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.

Styles vary between schools and the one called "analytic philosphy" is big.

But in general when I read philosophers disucssing social matters, I feel they are being too rigorous. Trying to cover all bases when the fuzzy nature of the subject is always going to make their abstractions leak.

They have to do this because they compete with other philosophers who will pick the nits.

Re: Habits of highly mathematical people

#50
post #47

Only problem is people tend to build whole theories and conclusions out of assumptions, and their assumptions could be wrong. Mathematics only shows you deductions that could be make out of initial axioms and rigid rules. It doesn't mean the assumptions you made while forming axioms or the rules itself are right. Having said that being mathematical increases your chances of arriving at the right results.

> It doesn't mean the assumptions you made while forming axioms or the rules itself are right.

There's no absolute notion of “right” to begin with. There's just “provable” (in a theory) and “true” (in a model of a theory). Furthermore, a statement that's true in one model might not be true in another.

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