maths largely was invented to explain empirical things, you have an apple and you add one and you get two apples, then you can figure out that if you add two more apples you have four.
I guess it depends on whether the axioms that everything is based on come from explaining physical situations or not, and I have no idea whether this is common or if it can even be decided reliably.
Being a physics major has probably muddled my brain up beyond repair for thinking about most of this though
Early mathematics was probably based on abstraction from empirical finding sure.
Ugg the caveman sees that he has a rabbit for Uggette, his wife, and Ugg Jr. He also sees that he could put a rabbit on each of the rocks outside his cave and there would be a rabbit for each rock and no rabbits left for him to eat, etc.
However that works.
But it's very difficult to see how empirical observation could be the basis of virtually any mathematics aside from the natural numbers and the very basic functions that operate on them. How does one empirically observe zero, or negative numbers, or that pi*r^2 is the relationship between the radius of a circle and its circumference (how does one deduce pi from empirical observation to begin with?).
Well yeah, math is always a tool to describe the real world to varying degrees of abstraction.
There was never a question like "what came first, pi or the circle?"
I'm pretty proud of that sentence btw, that is TV material 8-)
autono-wally, erotibot300 on
0
Options
FishmanPut your goddamned hand in the goddamned Box of Pain.Registered Userregular
edited February 2010
Shit, it shows you how fucking snowed under at work I am that I didn't even notice this thread until now.
I'm setting up camp over here. My skills and tools are rusty from disuse, but by Gods, I'm ready for a good old fashioned proof.
Just as soon as I finish testing and compling this code.
Maths develops alongside other disciplines pretty often, but also based on just math, too.
And when you go from the notion that it started out as a tool to describe the 'real world' , I find it pretty easy to accept on some level that, the better this took gets, the better it describes the world it started out with describing.
autono-wally, erotibot300 on
0
Options
FishmanPut your goddamned hand in the goddamned Box of Pain.Registered Userregular
I did a bunch of work on differential equations on fractals. All the mathematicians in the area insisted that it was pure pure pure and had no applications.
Turns out there's a secretive military contractor company building our fractals as antennae, exploiting them for the wave-propagation properties we discovered.
All is number, ladies and gents.
I really dislike military funding of research, it just means it's going to be steered the wrong way and the best stuff is going to be kept secret
it's probably better than no funding, but I'm not sure
But if history has taught us anything, it's that if you're a valuable weapons developer, you're never out of a job, even if your country loses a fucking world war!
But if history has taught us anything, it's that if you're a valuable weapons developer, you're never out of a job, even if your country loses a fucking world war!
the treatment of the paperclip scientists is pretty abhorrent, yep. Especially Mr. Werner "Oh I love space so much the jews just got in the way I didn't know anything!" Von Braun.
Also fuck Fritz Haber, and Grignard while I'm at it.
"He moved to Cambridge, England, for a few months, during which time Ernest Rutherford pointedly refused to shake hands with him (Haber), due to his involvement in poison gas warfare."
I did a bunch of work on differential equations on fractals. All the mathematicians in the area insisted that it was pure pure pure and had no applications.
Turns out there's a secretive military contractor company building our fractals as antennae, exploiting them for the wave-propagation properties we discovered.
All is number, ladies and gents.
I really dislike military funding of research, it just means it's going to be steered the wrong way and the best stuff is going to be kept secret
it's probably better than no funding, but I'm not sure
Looking at my probable stipends for next year has made me realize that I would gladly kill lots of people (indirectly) for moola.
But my point was that math doesn't just go from real world -> abstract. Sometimes a wholly abstract object turns out to have practical applications.
Let F be the set of all forums
Let T be the set of all threads
Let P be the set of all posts
Define FOR(t) as the function mapping a thread t to its parent forum
Define CON(t,p) as the function mapping a thread t to the set of strings comprising its post numbered p
∀ f ∈ F, A t ∈ T FOR(t)=f, ∃ p ∈ P, lim (|t| → ∞) CON(t,p) ⊇ {"Nazis","Hitler"}
Posts
Early mathematics was probably based on abstraction from empirical finding sure.
Ugg the caveman sees that he has a rabbit for Uggette, his wife, and Ugg Jr. He also sees that he could put a rabbit on each of the rocks outside his cave and there would be a rabbit for each rock and no rabbits left for him to eat, etc.
However that works.
But it's very difficult to see how empirical observation could be the basis of virtually any mathematics aside from the natural numbers and the very basic functions that operate on them. How does one empirically observe zero, or negative numbers, or that pi*r^2 is the relationship between the radius of a circle and its circumference (how does one deduce pi from empirical observation to begin with?).
There was never a question like "what came first, pi or the circle?"
I'm pretty proud of that sentence btw, that is TV material 8-)
I'm setting up camp over here. My skills and tools are rusty from disuse, but by Gods, I'm ready for a good old fashioned proof.
And when you go from the notion that it started out as a tool to describe the 'real world' , I find it pretty easy to accept on some level that, the better this took gets, the better it describes the world it started out with describing.
I really dislike military funding of research, it just means it's going to be steered the wrong way and the best stuff is going to be kept secret
it's probably better than no funding, but I'm not sure
kpop appreciation station i also like to tweet some
don't know what i'm going to do afterwards, probably take a year off then do phd
the treatment of the paperclip scientists is pretty abhorrent, yep. Especially Mr. Werner "Oh I love space so much the jews just got in the way I didn't know anything!" Von Braun.
Also fuck Fritz Haber, and Grignard while I'm at it.
"He moved to Cambridge, England, for a few months, during which time Ernest Rutherford pointedly refused to shake hands with him (Haber), due to his involvement in poison gas warfare."
god damn rutherford was awesome
kpop appreciation station i also like to tweet some
But my point was that math doesn't just go from real world -> abstract. Sometimes a wholly abstract object turns out to have practical applications.
http://numberblog.wordpress.com/
∀
Let T be the set of all threads
Let P be the set of all posts
Define FOR(t) as the function mapping a thread t to its parent forum
Define CON(t,p) as the function mapping a thread t to the set of strings comprising its post numbered p
∀ f ∈ F, A t ∈ T FOR(t)=f, ∃ p ∈ P, lim (|t| → ∞) CON(t,p) ⊇ {"Nazis","Hitler"}
it's a lot easier than godel's proofs
but it still makes my head hurt