Author Topic: Does math exist?  (Read 9471 times)

Offline josephpalazzo

(No subject)
« Reply #15 on: June 06, 2013, 05:50:01 AM »
Quote from: "Solitary"
:-$ Don't even think about imaginary numbers.  :-k   :Hangman:  I just thought about an infinity of infinitesimals meeting at aleph.  :rolleyes:  Bill


The word is suggestive - they only exist in your imagination. For once mathematicians got it right.

Offline Plu (OP)

(No subject)
« Reply #16 on: June 06, 2013, 06:19:40 AM »
I think I'm starting to get an idea of the issue now. It's something that I've struggled with in programming as well, and that seems to be a common problem (one that seems to continue to exist because most people kinda ignore it)

In a way, seabear actually pointed out the crux of the matter. Do colors exist? Do words exist? I don't think it's really semantics. It's our brain trying to make sense of things, and being so good at it that most people forget it's doing it.

It's the disconnect between what is and what we experience of it. The way we mentally and automatically model things in our minds and then assign labels to them. It's a really cool and reliable system. The problem arises when we try to communicate with other people who have their own models of things and we forget that neither of us has the real thing in our minds, just a personal perception.

Is there such a thing as 'red'? In the real world, no. In our minds, yes. But no two labels representing 'red' are the same, and that's where the issues seem to arise. That's why people often can't agree on whether a specific shade of red is 'red' or 'purple' or 'bordeaux' or whatever.

Math, in a way, is the same thing. It's just even harder to grasp because unlike a normal language, it's pretty universal. But then you realise it's not, when you remember things like roman numerals, non-base-10 number system, the many different ways to calculate the same thing, etc.
Math is just a way of describing reality. And like all descriptions, it's imperfect, but it's workable. (More workable than most other languages, which leave a lot of margin for error). And we keep looking for better ways to describe reality in terms of math, which is where a lot of our progress comes from.

But I think this disconnect between reality and mathematics, where reality is leading and math is trying to describe it, is a crucial thing to keep in mind. In the same way that 'red' is an attempt to describe the bombardment of billions of unrelated photons hammering on your eye, math is merely a way to make sense of everything that is actually happening.

And if we forget that math is the descriptor (or View) of reality and that reality is the actual data (or Model) being described, we will start to ascribe properties to math like "It's real", and then we might not research alternatives anymore. I think a large part of human ingenuity and 'thinking outside the box' arises from people remembering that language is just a description of reality, and that sometimes you need to try a different language to describe reality and see if better solutions come up.

Philosophical? Not at all. Critically important, I'd say. The ability to look at a rock and describe it as "nut cracking tool" or "sharpening tool" was the first step towards intelligent thought. And that's basically just the ability to look at a part of reality, and to try different Views on it until you find one that helps you solve a problem at hand.

So is a rock a nutcracker, or a sharpening tool, or just a rock?
Or are they just different Views of the same Model and can we use different languages to solve different problems?
Is math real, or is it imagined? Or maybe it's just another language we use to try and make sense of reality, because that's what we do all day long, without even thinking about it?

...

Yeah I was kinda bored, sorry about that :P

Re: Does math exist?
« Reply #17 on: June 06, 2013, 09:13:27 AM »
Great post!  =D>  Bill
There is nothing more frightful than ignorance in action.

(No subject)
« Reply #18 on: June 06, 2013, 09:40:38 AM »
Quote from: "josephpalazzo"
Quote from: "Solitary"
:-$ Don't even think about imaginary numbers.  :-k   :Hangman:  I just thought about an infinity of infinitesimals meeting at aleph.  :rolleyes:  Bill


The word is suggestive - they only exist in your imagination. For once mathematicians got it right.

Great!  Now the only thing I can think about is Euler's number and pi!
Winner of WitchSabrinas Best Advice Award 2012


We can easily forgive a child who is afraid of the dark; the real
tragedy of life is when men are afraid of the light. -Plato

Offline josephpalazzo

(No subject)
« Reply #19 on: June 06, 2013, 09:44:54 AM »
Quote from: "Plu"
I think I'm starting to get an idea of the issue now. It's something that I've struggled with in programming as well, and that seems to be a common problem (one that seems to continue to exist because most people kinda ignore it)

In a way, seabear actually pointed out the crux of the matter. Do colors exist? Do words exist? I don't think it's really semantics. It's our brain trying to make sense of things, and being so good at it that most people forget it's doing it.

It's the disconnect between what is and what we experience of it. The way we mentally and automatically model things in our minds and then assign labels to them. It's a really cool and reliable system. The problem arises when we try to communicate with other people who have their own models of things and we forget that neither of us has the real thing in our minds, just a personal perception.

Is there such a thing as 'red'? In the real world, no. In our minds, yes. But no two labels representing 'red' are the same, and that's where the issues seem to arise. That's why people often can't agree on whether a specific shade of red is 'red' or 'purple' or 'bordeaux' or whatever.

I know someone who is color-blinded. He cannot distinguish red against a purple background. IOW, he cannot distinguish different shades of red, and this was identified as a particular chromosome that goes back to his grand-father. Apparently, it skips a generation. So we have in our genetic makeup the ability to see different colors. Independently of our perception, colors are different wavelengths of light, and so they exist on their own. And human perception would have a commonality - we all have a shared portion of the same genes. When one of those object is missing, we can identify it as in this case.
Quote
Math, in a way, is the same thing. It's just even harder to grasp because unlike a normal language, it's pretty universal.

We don't have proof of that. We cannot to this day translate any language from other species into our own language. There is no guarantee that math would suddenly be a universal language. There are certain species that do behave if the numbers are changes. For instance, bears are known to attack people, but if there is a number greater than 4 or 5, can't remember exactly the number, but over that number, bears will not attack. Other species seem to differentiate between small numbers, that is between one and many, but other than that, math being a universal concept is a hypothesis that remains unproven.

 

Quote
Math is just a way of describing reality.

Yes, and so are words, that's why there are both languages. It just turns out that our evolved brain treats them in separate spheres. Perhaps the reason why we have the ability to develop it more than any other species. No one believes that a dolphin could learn algebra, let alone simple arithmetic operations like adding fractions.


Quote
And like all descriptions, it's imperfect, but it's workable. (More workable than most other languages, which leave a lot of margin for error). And we keep looking for better ways to describe reality in terms of math, which is where a lot of our progress comes from.

The advantage with math is with measurement and geometry, which is what is needed to investigate the universe. Language does a poor job in that department.



Quote
And if we forget that math is the descriptor (or View) of reality and that reality is the actual data (or Model) being described, we will start to ascribe properties to math like "It's real", and then we might not research alternatives anymore. I think a large part of human ingenuity and 'thinking outside the box' arises from people remembering that language is just a description of reality, and that sometimes you need to try a different language to describe reality and see if better solutions come up.

Agree.

Quote
Philosophical? Not at all. Critically important, I'd say. The ability to look at a rock and describe it as "nut cracking tool" or "sharpening tool" was the first step towards intelligent thought. And that's basically just the ability to look at a part of reality, and to try different Views on it until you find one that helps you solve a problem at hand.


Philosophy is concerned with why-questions; science, with how-questions. So it is no wonder that technology flourished when science divorced itself from philosophy. Oddly, that took place some 500 years ago. Until then, the two were taught as one subject.


Quote
Or are they just different Views of the same Model and can we use different languages to solve different problems?
Is math real, or is it imagined? Or maybe it's just another language we use to try and make sense of reality, because that's what we do all day long, without even thinking about it?

With QM, we know that language utterly fails, and math is the only appropriate language. Tho' we will always need to communicate it with language. But looking at the history of QM, the controversies are still around us. Once in a while some magazines or website will proclaim that an experiment has proven Einstein was right on QM, spooky action at a distance has reared its ugly head again, when in reality, that has never happened.

...

Quote
Yeah I was kinda bored, sorry about that :P

No need to apologize. :-D

Offline josephpalazzo

(No subject)
« Reply #20 on: June 06, 2013, 09:51:01 AM »
Quote from: "Jason78"
Quote from: "josephpalazzo"
Quote from: "Solitary"
:-$ Don't even think about imaginary numbers.  :-k   :Hangman:  I just thought about an infinity of infinitesimals meeting at aleph.  :rolleyes:  Bill


The word is suggestive - they only exist in your imagination. For once mathematicians got it right.

Great!  Now the only thing I can think about is Euler's number and pi!

e = (1 + 1/n)[sup:2diui4mr]n[/sup:2diui4mr], n= 1,2,3...

? = 4/1 - 4/3 + 4/5 -4/7 + 4/9 - 4/11 + 4/13 +...

(No subject)
« Reply #21 on: June 06, 2013, 01:46:37 PM »
Quote from: "josephpalazzo"

e = (1 + 1/n)[sup:366qe3hp]n[/sup:366qe3hp], n= 1,2,3...

? = 4/1 - 4/3 + 4/5 -4/7 + 4/9 - 4/11 + 4/13 +...

Winner of WitchSabrinas Best Advice Award 2012


We can easily forgive a child who is afraid of the dark; the real
tragedy of life is when men are afraid of the light. -Plato

Offline josephpalazzo

(No subject)
« Reply #22 on: June 06, 2013, 02:57:42 PM »
LOL.

Offline Plu (OP)

(No subject)
« Reply #23 on: June 06, 2013, 03:23:30 PM »
Quote from: "josephpalazzo"
I know someone who is color-blinded. He cannot distinguish red against a purple background. IOW, he cannot distinguish different shades of red, and this was identified as a particular chromosome that goes back to his grand-father. Apparently, it skips a generation. So we have in our genetic makeup the ability to see different colors. Independently of our perception, colors are different wavelengths of light, and so they exist on their own. And human perception would have a commonality - we all have a shared portion of the same genes. When one of those object is missing, we can identify it as in this case.

I was actually thinking about adding an example about the colorblind, but decided against it. But colorblind people are another good example of the difference between the Model and the View. Just because you can't see color, doesn't mean it isn't there. But the color 'red' doesn't mean anything to the colorblind person; it's just another part of reality that's left out when observing it. But it seems strange to us, because others can see the color and so it's clear to us that the colorblind person is "missing" something.

Yet nobody feels the same way about the IR-spectrum, even though none of us can see that either. It's just a part of the Model left out in our View of the world, that nobody misses but it still there.

Quote
Quote
Math, in a way, is the same thing. It's just even harder to grasp because unlike a normal language, it's pretty universal.

We don't have proof of that. We cannot to this day translate any language from other species into our own language. There is no guarantee that math would suddenly be a universal language.

Actually I stated on the line right after this one that I don't think "math" is a universal language, as justified by the fact that we've gone through multiple mathematical languages, most of which were discarded along the way.
 
But good points :)

Offline Sal1981

(No subject)
« Reply #24 on: June 06, 2013, 07:31:14 PM »
math is very much like language.

It's a construct. We make it real, with a chalk on a black-board, or a pen on paper, or a keyboard on a screen.

If you want to argue that numbers exist outside of those constructs, I think you're just arguing for nonsensical things, like square circles and married bachelors. Which is pointless philosophical meandering.
"The first principle is that you must not fool yourself - and you are the easiest person to fool" --- Richard P. Feynman

Re: Does math exist?
« Reply #25 on: June 06, 2013, 11:06:28 PM »
Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.
"There is a saying in the scientific community, that every great scientific truth goes through three phases. First, people deny it. Second, they say it conflicts with the Bible. Third, they say they knew it all along."

- Neil deGrasse Tyson

Offline josephpalazzo

(No subject)
« Reply #26 on: June 07, 2013, 08:08:25 AM »
Quote from: "Plu"
Yet nobody feels the same way about the IR-spectrum, even though none of us can see that either. It's just a part of the Model left out in our View of the world, that nobody misses but it still there.

We need to look at our eyes as detectors. We can see a part of the spectrum, but we can compensate with other detectors to capture the other frequencies that escape our eyes -- the same way for our ears. Dogs pick up frequencies we can't. It just means their ear-detectors are better than ours.

Quote


Actually I stated on the line right after this one that I don't think "math" is a universal language, as justified by the fact that we've gone through multiple mathematical languages, most of which were discarded along the way.
 
But good points :)

That's true. We have certain maths that have never been used to describe anything in the real world, just like we have words that don't describe anything real -- leprechauns, fire-breathing dragons, invisible pink unicorns... god.  :-D

EDIT: fix tags
« Last Edit: June 07, 2013, 09:09:07 AM by josephpalazzo »

Offline josephpalazzo

(No subject)
« Reply #27 on: June 07, 2013, 08:13:13 AM »
Quote from: "Seabear"
Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

(No subject)
« Reply #28 on: June 07, 2013, 08:45:10 AM »
Quote from: "josephpalazzo"
Quote from: "Seabear"
Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

Didn't we send those time capsule thingees out into space? Yanno in case aliens found the capsule ?  I could google it for sure but I just don't want to.
So.... I think if the earth and all its inhabitants were blown into molecules yes- there's a tiny record of us somewhere in space.  Aww screw it - I googled:
http://www.theatlantic.com/technology/a ... ne/265718/
I am currently experiencing life at several WTFs per hour.

Offline josephpalazzo

(No subject)
« Reply #29 on: June 07, 2013, 09:07:14 AM »
Quote from: "WitchSabrina"
Quote from: "josephpalazzo"
Quote from: "Seabear"
Then by the same token I suppose we can say that languages don't really exist either. Or music. Or emotion. Or any abstract concept, for that matter. Including, ironically, philosophy.

Again, it's just a game of semantics, playing with an overly literal application of the word 'exist'.

If the earth was completely destroyed to smithereens, vaporized to single molecules, who would ever know of our alphabet, art, music, or any construct, real or mental that was ever done on this planet?

Didn't we send those time capsule thingees out into space? Yanno in case aliens found the capsule ?  I could google it for sure but I just don't want to.
So.... I think if the earth and all its inhabitants were blown into molecules yes- there's a tiny record of us somewhere in space.  Aww screw it - I googled:
http://www.theatlantic.com/technology/a ... ne/265718/

Got me there... let me rephrase this: If the earth + all the freaking probes  were completely destroyed to smithereens, vaporized to single molecules...

 :twisted: