Habits of highly mathematical people • Hacker News Board

Re: Habits of highly mathematical people

#111

Post by rafaquintanilha » Sun, Jul 31, 2016, 3:22 PM UTC

ktamura wrote: post #63

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 studied math and computer science. Walked out of a math Ph.D. program before starting one) >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. That's possible. The OP does not claim that the traits he listed apply if and only if you are a mathematician. It'…

I find it ironic how OP's claim is easily ruled out by basic mathematical argument.

Re: Habits of highly mathematical people

#112

Post by dev1n » Sun, Jul 31, 2016, 4:57 PM UTC

mathgeek wrote: post #15

dev1n wrote: post #4

Earlier quoted context omitted.

Isn't there an old quip about how poor mathematicians are at arithmetic? ;)

I don't recall. How are poor mathematicians at arithmetic? ;)

lol my bad.

Re: Habits of highly mathematical people

#113

Post by nercht12 » Mon, Aug 08, 2016, 3:06 AM UTC

catnaroek wrote: post #69

nercht12 wrote: post #51

Earlier quoted context omitted.

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 o…

> definitions (even the most rudimentary ones) are based on -what we might call- statistical sets of observations Mathematical definitions are usually abstractions of concrete observations, but they aren't the observations themselves. This is why coming up with a mathematical definition often requires more work than coming up with any other kind of definition. > What is "1"? The idea of "1" can only be understood in…

> Mathematical definitions are usually abstractions of concrete observations, but they aren't the observations themselves. This is why coming up with a mathematical definition often requires more work than coming up with any other kind of definition. ... 1 is very rigorously defined: As a natural number, it's the successor of 0. As an integer, rational, real or complex number, it's the result of mapping the natural number 1 into Z, Q, R or C in a suitable way (compatible with the semiring structure of N).

That's all nice and dandy for mathematicians, but such is still meaningless (from an overall perspective) because ultimately you end up with recursive definitions. "The successor" of "0" means nothing because "successor" isn't defined, unless you define it via dimensions (or something else). Once you try to define dimension or otherwise, you have to define dimension, which leads to defining counting, which leads back to defining 1. Appealing to experience is the only way to end the cycle.

That said, it's perfectly fine to talk about a system within itself, but it's applicability to anything real (which is what I'm concerned with - my apologies if that's not where you're going) is limited to whatever can be described in terms of reality.

Re: Habits of highly mathematical people

#114

Post by catnaroek » Thu, Aug 11, 2016, 4:40 PM UTC

nercht12 wrote: post #113

catnaroek wrote: post #69

Earlier quoted context omitted.

> definitions (even the most rudimentary ones) are based on -what we might call- statistical sets of observations Mathematical definitions are usually abstractions of concrete observations, but they aren't the observations themselves. This is why coming up with a mathematical definition often requires more work than coming up with any other kind of definition. > What is "1"? The idea of "1" can only be understood in…

> Mathematical definitions are usually abstractions of concrete observations, but they aren't the observations themselves. This is why coming up with a mathematical definition often requires more work than coming up with any other kind of definition. ... 1 is very rigorously defined: As a natural number, it's the successor of 0. As an integer, rational, real or complex number, it's the result of mapping the natural n…

> "The successor" of "0" means nothing because "successor" isn't defined

The existence of a successor function is postulated, because it's an axiom of the theory of natural numbers. It's up to individual models of the theory to define this function concretely.