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How has mathematics gotten so abstract?

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Re: How has mathematics gotten so abstract?

#41

Post by TZubiri »

jlongr wrote: post #18
roel_v wrote: post #17

Earlier quoted context omitted.

Did you bother to google his handle? While I don't know his pure mathematics credentials, he's nerd-famous enough to not warrant an introduction. In fact, you not recognizing it says something about you.

>he's nerd-famous enough to not warrant an introduction What is nerd-famous supposed to be. He's at the center of some subjective in-group that exists in your head?

To be fair, we are on hacker news. I did once use on of his programs, American Fuzzy Lopper (fake advertisement lawsuit incoming if its not american). So he is not nobody apparently

Re: How has mathematics gotten so abstract?

#43

Post by pdpi »

myrmidon wrote: post #29
pdpi wrote: post #21

Earlier quoted context omitted.

> Pure mathematics is regarded as an abstract science, which it is by definition. I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

You could turn the argument around and say that math must be a science because it builds on falsifiable hypotheses and makes testable predictions. In the end arguing about whether mathematics is a science or not makes no more sense than bickering about tomates being fruit; can be answered both yes and no using reasonable definitions.

> In the end arguing about whether mathematics is a science or not makes no more sense than bickering about tomates being fruit

That's the thing, though — It does make sense, and it's an important distinction. There is a reason why "mathematical certainty" is an idiom — we collectively understand that maths is in the business of irrefutable truths. I find that a large part of science skepticism comes from the fundamental misunderstanding that science is, like maths, in the business of irrefutable truths, when it is actually in the business of temporarily holding things as true until they're proven false. Because of this misunderstanding, skeptics assume that science being proven wrong is a deathblow to science itself instead of being an integral part of the process.

Re: How has mathematics gotten so abstract?

#44

Post by TuringTest »

rob74 wrote: post #24

How has mathematics gotten so abstract? My understanding was that mathematics was abstract from the very beginning . Sure, you can say that two cows plus two more cows makes four cows, but that already is an abstraction - someone who has no knowledge of math might object that one cow is rarely exactly the same as another cow, so just assigning the value "1" to any cow you see is an oversimplification. Of course, simp…

> My understanding was that mathematics was abstract from the very beginning.

It wasn't; but that's a common misunderstanding from hundreds of centuries of common practice.

So, how has maths gotten so abstract? Easy, it has been taken over by abstraction astronauts(1), which have existed throghout all eras (and not just for software engineering).

Mathematics was created by unofficial engineers as a way to better accomplish useful activities (guessing the best time of year to start migrating, and later harvesting; counting what portion of harvest should be collected to fill the granaries for the whole winter; building temples for the Pharaoh that wouldn't collapse...)

But then, it was adopted by thinkers that enjoyed the activity by itself and started exploring it by sheer joy; math stopped representing "something that needed doing in an efficient way", and was considered "something to think about to the last consecuences".

Then it was merged into philosophy, with considerations about perfect regular solids, or things like the (misunderstood) metaphor of shadows in Plato's cave (which people interpreted as being about duality of the essences, when it was merely an allegory on clarity of thinking and explanation). Going from an intuitive physical reality such as natural numbers ("we have two cows", or "two fingers") to the current understanding of numbers as an abstract entity ("the universe has the essence of number 'two' floating beyond the orbit of Uranus"(2)) was a consequence of that historical process, when layers upon layers of abstraction took thinkers further and further away from the practical origins of math.

[1] https://www.joelonsoftware.com/2001/04/21/dont-let-architect...

[2] https://en.wikipedia.org/wiki/Hyperuranion

Re: How has mathematics gotten so abstract?

#45

Post by _9ptr »

pdpi wrote: post #21
Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

> Pure mathematics is regarded as an abstract science, which it is by definition. I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

He probably means science in a wider sense as opposed to the anglo-american narrower sense where science is just physics, chemistry, biology and similar topics.

Re: How has mathematics gotten so abstract?

#47

Post by wvlia5 »

thadt wrote: post #2

This reminds of of that one time when I was on a date with a girl from the history department who somehow bemusedly sat through my entire mini-lecture on comparing infinite sets. Twenty years and three kids later, she'll still occasionally look me straight in the eye and declare "my infinity is bigger than your infinity."

Once I taught the binomial coefficient formula to a girl after sex

Re: How has mathematics gotten so abstract?

#48

Post by fidotron »

azan_ wrote: post #31
fidotron wrote: post #30

Unlike Zeno's famous example the paradox which does better at explaining the problem is https://en.wikipedia.org/wiki/Coastline_paradox which Mandelbrot seemed particularly keen on. The tendency towards excessive abstraction is the same as the use of jargon in other fields: it just serves to gatekeep everything. The history of mathematics (and science) is actually full of amateurs, priests and bored aristocrats that…

Theirs no such thing as excessive abstraction in math, because abstraction is the point. Is category theory “excessive abstraction” in your opinion?

> because abstraction is the point.

Formal reasoning is the point, which is not by itself abstraction.

Someone else in this discussion is saying Euclid's Elements is abstract, which is near complete nonsense. If that is abstract our perception of everything except for the fundamental [whatever] we are formed of is an abstraction.

Re: How has mathematics gotten so abstract?

#50

Post by weinzierl »

pdpi wrote: post #21
Tazerenix wrote: post #13

>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition . Arnol'd argued vehemently and much more convincingly for the viewpoint that all mathematics is (and must be) linked to the natural sciences. >On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs…

> Pure mathematics is regarded as an abstract science, which it is by definition. I'd argue that, by definition, mathemtatics is not, and cannot be, a science. Mathematics deals with provable truths, science cannot prove truth and must deal falsifiability instead.

Pure mathematics is just symbol pushing and can never be science. It is lot of fun though and as it turned out occasionally pretty useful for science.
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