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An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

Math like the alphabet is a mental construct. OTOH, geometry is physics... don't get me started.

I think that everything is math and people who believe in irrational numbers should be killed.

A lot of mathematicians think math is a discovery and exist in reality. I think it is an invention used to describe quantum reality that can't be described pictorially, or our world that can be described pictorially.  Good question though. Bill

I have often wondered what philosophers think about when not serving fries or glasses of pinot grigio.....now I know.

:-$  I'm drinking my Old Vine Zinfandel now.  :rolleyes:  Bill

Nothing beats beer and pizza.

 :P

I dunno, do "words" really exist? What about colors?

It's philosophical bullshit like this that makes me want to kick someone in the balls.

For something that may not really "exist", it sure does a fantastic fucking job of allowing us to do things like make the computer you are reading this on work as designed. Things it would be impossible to do without it.

There are no numbers in your computer, except on your keyboard. Inside of your computers is a bunch of wires and switches.

I don't think anyone is going to argue that math doesn't work. But that doesn't mean that math is a tangible thing. And there's a big difference in approach to it between "it's a real, tangible thing" and "it's just stuff we make up".

Semantics

Quote from: "aitm"I have often wondered what philosophers think about when not serving fries or glasses of pinot grigio.....now I know.

Thank you. I was not aware that Pinot Grigio was the correct wine to serve with fries.

See?  Philosophy DOES have some actual use.

Quote from: "missingnocchi"I think that everything is math and people who believe in irrational numbers should be killed.

They are needed in college algerbra... not saying its right.

:-$ Don't even think about imaginary numbers.  :-k   :Hangman:  I just thought about an infinity of infinitesimals meeting at aleph.  :rolleyes:  Bill

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.

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

Great post!  =D>  Bill

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!

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.

QuoteMath, 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.

 

QuoteMath 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.

QuoteAnd 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.

QuoteAnd 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.

QuotePhilosophical? 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.

QuoteOr 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.

...

QuoteYeah I was kinda bored, sorry about that :P

No need to apologize. :-D

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 +...

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 +...

(//http://imgs.xkcd.com/comics/complex_conjugate.png)

LOL.

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

QuoteMath, 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 :)

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.

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'.

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.

QuoteActually 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

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?

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/ (http://www.theatlantic.com/technology/archive/2012/11/a-time-capsule-launched-into-space-for-aliens-to-find-when-all-the-humans-are-gone/265718/)

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/ (http://www.theatlantic.com/technology/archive/2012/11/a-time-capsule-launched-into-space-for-aliens-to-find-when-all-the-humans-are-gone/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:

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

 :twisted:

It's ok.  You're waaay ahead of me on this.  I don't speak 'math'.  I mean I Really don't speak 'math'.  This thread already exceeds my learned-level.  lol

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?

Does something have to exist for all time in order to exist at all?

Quote from: "missingnocchi"

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?

Does something have to exist for all time in order to exist at all?

Good question for Jesus.

Quote from: "missingnocchi"

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?

Does something have to exist for all time in order to exist at all?

The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

Don't things exist in their relation to Other things? Otherwise how would we know?  As in - item B laying on the table exists because I can see it laying there............or you might see it there......... or Colanth might see it there.  If no one sees it and records mentally the existence of said object - how else do we know?
It's the human mind where things are logged, categorized, recognized and recorded or observed & reported or tested.  Kind of qualifies our argument against a supernatural being - like a god --- there's no human recorded data of such an observance; no proof. Things exist in relation to something else - like observation.
Sure things like Item B might exist without me...............   but at some point a human will need to record the evidence of item B. Or there's no items B.

Quote from: "WitchSabrina"

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

Don't things exist in their relation to Other things? Otherwise how would we know?  As in - item B laying on the table exists because I can see it laying there............or you might see it there......... or Colanth might see it there.  If no one sees it and records mentally the existence of said object - how else do we know?
It's the human mind where things are logged, categorized, recognized and recorded or observed & reported or tested.  Kind of qualifies our argument against a supernatural being - like a god --- there's no human recorded data of such an observance; no proof. Things exist in relation to something else - like observation.
Sure things like Item B might exist without me...............   but at some point a human will need to record the evidence of item B. Or there's no items B.

Here you are talking about knowledge, and not existence. In terms of philosophy ( ha, hum) we've moved from metaphysics to epistemology.  :-D

 So how do I know that tree or that table exists?

So for that, we need to look at  truth, belief, justfication, and different schools espousing certain things like the empirical method, or logiccal rational thinking, or revelation/insight, etc.


You've just open another can of worms.  :Hangman:

Quote from: "josephpalazzo"Here you are talking about knowledge, and not existence. In terms of philosophy ( ha, hum) we've moved from metaphysics to epistemology.  :-D

 So how do I know that tree or that table exists?

So for that, we need to look at  truth, belief, justfication, and different schools espousing certain things like the empirical method, or logiccal rational thinking, or revelation/insight, etc.


You've just open another can of worms.  :Hangman:

Sorry.  Go back to math.  I can't speak math.  I was just kinda chiming in.  Ignore my ramblings.
 :rolleyes:

I was expecting sarcasm! What happened?  :P

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

If the earth exploded, no one would know about the tree.

But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist. Because even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way. I think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist? Can you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.

Quote from: "missingnocchi"

Quote from: "josephpalazzo"The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.

If the earth exploded, no one would know about the tree.

But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist.

It exists as a mental construct, just like our alphabet.

QuoteBecause even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way.

The universe would exist. Its human description would not, since the humans upholding those mental construct don't exist anymore. Where would those human thoughts exist???

QuoteI think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist?

Physics is a human description of the universe, a model that we have refined over the years with constant observations, experiments and hypothesis. Therefore it is a mental construct produced by our minds.

QuoteCan you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.

I believe you are conflating two things: the mental constructs - ideas, theories, thoughts, beliefs, theories, physics, math etc - exist as long as they are hold by human brains. And the things these mental construct describe - particles, stars, the universe, etc. which exist independently of our thoughts.

Erg, nominalism. Well, I'd have to say no. This is like a discussion I had the other day with a proponent of a version of the transcendental argument for the existence of God, wherein they repeatedly claimed that the "laws" of informal logic exist and are "invariant, universal", etc, and that was (somehow) evidence for the existence of God. But that misses is that when you say "A=A" (law of identity, LoD), that statement isn't itself the law of identity but just that, a statement referring to what we mean by the LoD. Also forgetting that they are ways of drawing proper inferences and that they can't be denied without being coherent. Basically, it's a language thing really.

And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Quote from: "GurrenLagann"Erg, nominalism. Well, I'd have to say no. This is like a discussion I had the other day with a proponent of a version of the transcendental argument for the existence of God, wherein they repeatedly claimed that the "laws" of informal logic exist and are "invariant, universal", etc, and that was (somehow) evidence for the existence of God. But that misses is that when you say "A=A" (law of identity, LoD), that statement isn't itself the law of identity but just that, a statement referring to what we mean by the LoD. Also forgetting that they are ways of drawing proper inferences and that they can't be denied without being coherent. Basically, it's a language thing really

.

Yep, math is nothing but LoD + the substitution principle.  

QuoteAnd I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Quote from: "josephpalazzo"

Quote from: "GurrenLagann"And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Doesn't Gödel's Incompleteness theorem also imply that there can be an infinite amount of mathematical structures or something?

Quote from: "josephpalazzo"

QuoteAnd I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Hm, I thought that's basically what I said? I wasn't very clear at the end there I see. Damn my lazy fingers. ;)

Quote from: "Sal1981"

Quote from: "josephpalazzo"

Quote from: "GurrenLagann"And I think that mathematics is similar to those, though it lacks a truly logical basis (damn you Gödel!).

Hmm. I'm not sure what you're trying to say here. Gödel's theorem just shows that any system must start with a set of axioms - truths taken to be given. If one wants to prove/disprove one of those assumptions, you need to go out of the system, but you will end up with other assumptions, if you enlarge the system to include the new assumptions, you're back to square one. Hence, no system is ever completed.

Doesn't Gödel's Incompleteness theorem also imply that there can be an infinite amount of mathematical structures or something?

I don't know about infinite number, but theoretically yes. There are no complete systems, so as long as humans are creative, new ones can always be found.

I hate questions like this. This is like saying "If a tree falls in the woods and no one is around to hear it does it make a sound?"

Yes and no.

Physically speaking air is moved and the energy released by the objects hitting each other will move air which makes sound, even if it is not heard by others.

Math is a language, like speed is to a car. Speed is not physical, but you use the word "speed" to describe the observed.

1 orange, 1 house, 1 girl, 1 insect, 1 planet. Math exists as an abstraction like speed is to a car. You can have a bike going 20mph and a car going 20mph.

So again, a major problem with this entire line of argument is that it can be applied equally to any number of other concepts to declare them "non-existent".

Music is a perfect example. It's just sound, and we apply a symbolic notation in order to describe it. However, if you try to argue that music doesn't really exist, people will think you are an imbecile.

Language is another example. I guess we can conclude that it doesn't really exist either, since we use symbols to notate and describe it. And, it follows therefore that literature doesn't exist, either.

I suppose Chemistry isn't really real, either, since elements aren't actually floating around with the alphabetical symbols we use to describe them, and *gasp*, MATH is used to balance the equations!

It's a bit fucking absurd, really.

Quote from: "Seabear"So again, a major problem with this entire line of argument is that it can be applied equally to any number of other concepts to declare them "non-existent".

Music is a perfect example. It's just sound, and we apply a symbolic notation in order to describe it. However, if you try to argue that music doesn't really exist, people will think you are an imbecile.

Language is another example. I guess we can conclude that it doesn't really exist either, since we use symbols to notate and describe it. And, it follows therefore that literature doesn't exist, either.

I suppose Chemistry isn't really real, either, since elements aren't actually floating around with the alphabetical symbols we use to describe them, and *gasp*, MATH is used to balance the equations!

It's a bit fucking absurd, really.

I think you're missing a bit about what people mean when they ask this. The thrust behind it isn't exactly like asking if music or language exist, since they clearly do as they are our rooted in sounds and symbols. However, when it's asked whether or not mathematics exist, what is meant is what makes reality so amenable to consistent descriptions by mathematics. In other words, is it because there is something that inherently roots reality to that description?

That, I think, is what people mean in this case.

QuoteHowever, if you try to argue that music doesn't really exist, people will think you are an imbecile.

While really, they are the imbiciles for not even listening to a perfectly understandable justification for why you think it doesn't exist while still being a useful thing to talk about at the same time.

Quote from: "Seabear"So again, a major problem with this entire line of argument is that it can be applied equally to any number of other concepts to declare them "non-existent".

Music is a perfect example. It's just sound, and we apply a symbolic notation in order to describe it. However, if you try to argue that music doesn't really exist, people will think you are an imbecile.

Language is another example. I guess we can conclude that it doesn't really exist either, since we use symbols to notate and describe it. And, it follows therefore that literature doesn't exist, either.

I suppose Chemistry isn't really real, either, since elements aren't actually floating around with the alphabetical symbols we use to describe them, and *gasp*, MATH is used to balance the equations!

It's a bit fucking absurd, really.

You're conflating two different ideas: one is about existence ( what is real), the other is about knowing if something is real. Take the sentence, "this is a tree". Am I talking about something real? Well, we can find out. Find a tree. Point to it. Find fossils of trees, etc. And so we can establish that a tree does exist. But what about the sentence itself, "this is a tree," is that real? We can say that it exists as scribbles on a piece of paper, or pixels on your screen, or some configuration of your neurons in your brain so that you can think about it when you read it. But if humans didn't exist, the sentence would never have been uttered or written down in the first place. It's not that trees wouldn't exist, but the sentence itself, "this is a tree" wouldn't. This applies to language as a whole. Without humans our language - alphabet, words, sentences, etc - wouldn't exist. Math is also a language, and without humans, it has no existence. The universe doesn't go around calculating the value of pi = 3.14159625... or that if you fall, it must be at 9.80 m/s[sup:3birdy7v]2[/sup:3birdy7v], etc. Those are mental constructs that have only meaning to us, humans.

Quote from: "josephpalazzo"

Quote from: "missingnocchi"If the earth exploded, no one would know about the tree.

But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist.

It exists as a mental construct, just like our alphabet.

That doesn't address any points that I brought up.

Quote

QuoteBecause even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way.

The universe would exist. Its human description would not, since the humans upholding those mental construct don't exist anymore. Where would those human thoughts exist???

The descriptions would not exist, but the features that they describe would.

Quote

QuoteI think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist?

Physics is a human description of the universe, a model that we have refined over the years with constant observations, experiments and hypothesis. Therefore it is a mental construct produced by our minds.

It's only produced by our minds if you stop right there, close your ears and shout, and ignore the obedience of the universe to certain laws (for lack of a better word) which Physics the study tries to describe. When someone says that Physics is independent of the human mind, they are not talking about the study, they are talking about the real universe as it pertains to what is described in the study.

Quote

QuoteCan you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.

I believe you are conflating two things: the mental constructs - ideas, theories, thoughts, beliefs, theories, physics, math etc - exist as long as they are hold by human brains. And the things these mental construct describe - particles, stars, the universe, etc. which exist independently of our thoughts.

I believe I went out of my way to make a distinction between those things, and that you have spent this entire thread ignoring everyone who does so, and insisting on seeing an imaginary conflation.

Quote from: "missingnocchi"

Quote from: "josephpalazzo"It exists as a mental construct, just like our alphabet.

That doesn't address any points that I brought up.

You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

QuoteThe descriptions would not exist, but the features that they describe would.

If humans don't exist then those features are perceived by whom? Who is there to describe them, God?

QuoteIt's only produced by our minds if you stop right there, close your ears and shout, and ignore the obedience of the universe to certain laws (for lack of a better word) which Physics the study tries to describe. When someone says that Physics is independent of the human mind, they are not talking about the study, they are talking about the real universe as it pertains to what is described in the study.

Physics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

QuoteI believe I went out of my way to make a distinction between those things, and that you have spent this entire thread ignoring everyone who does so, and insisting on seeing an imaginary conflation.

I believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

QuoteHowever, if you try to argue that music doesn't really exist, people will think you are an imbecile.

Come to think of it, I think it is the very fact that someone once thought to himself "music doesn't exist, it's just ripples in the air of moving molecules" that gave us the ability to record and play back "music".

The difference between the classical idea of "music" and the way a computer generates it is incredibly large, and it is only by realising that describing something as "music" is just that; describing a physical effect; that allows for the idea of capturing it on a recording device.

At no point in its mechanical design does a microphone or speaker ever do anything with what we call "music".

Quote from: "josephpalazzo"You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

When you stated a contrary position with no elaboration or reference to my argument. It would be like if I replied to this part of your post with "You failed to address the point."

QuoteIf humans don't exist then those features are perceived by whom? Who is there to describe them, God?

Does someone need to be there to describe them? If you believe so, make an argument for it. That's not even close to being a given, but it seems to be at the heart of your argument.

QuotePhysics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

Physics, as a study, and as an idea, is what you say it is. But the laws and patterns we see in nature and use physics to describe are really there, independent of us. And it is in this way that I use the word physics. They are independent of the concept of "pattern" and "law", those are just imperfect descriptive terms.

QuoteI believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

Worse than being childish is being willfully obtuse. And when you refuse to acknowledge a clearly explained difference between the idea of a term used to describe something and the actual object being described, that is what you are doing. When I say that something has a "feature", I'm not referring to some metaphysical quality that exists independent of our minds, I'm saying that the real thing exists in the way that the feature describes. Not only in that way, or separately in that way, or whatever other human ideas you insist on telling me I am projecting onto the thing. Just in that way.

All this poking and playing at linguistics without actually addressing the issue in communication is drowning what could have been an interesting debate.

Quote from: "missingnocchi"

Quote from: "josephpalazzo"You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

When you stated a contrary position with no elaboration or reference to my argument. It would be like if I replied to this part of your post with "You failed to address the point."

QuoteIf humans don't exist then those features are perceived by whom? Who is there to describe them, God?

Does someone need to be there to describe them? If you believe so, make an argument for it. That's not even close to being a given, but it seems to be at the heart of your argument.

QuotePhysics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

Physics, as a study, and as an idea, is what you say it is. But the laws and patterns we see in nature and use physics to describe are really there, independent of us. And it is in this way that I use the word physics. They are independent of the concept of "pattern" and "law", those are just imperfect descriptive terms.

QuoteI believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

Worse than being childish is being willfully obtuse. And when you refuse to acknowledge a clearly explained difference between the idea of a term used to describe something and the actual object being described, that is what you are doing. When I say that something has a "feature", I'm not referring to some metaphysical quality that exists independent of our minds, I'm saying that the real thing exists in the way that the feature describes. Not only in that way, or separately in that way, or whatever other human ideas you insist on telling me I am projecting onto the thing. Just in that way.

All this poking and playing at linguistics without actually addressing the issue in communication is drowning what could have been an interesting debate.

Now this is what happens when we start down that slippery slope of philosophical bullshittery...its all fun and games until someone pokes someone in the eye...

Quote from: "missingnocchi"

Quote from: "josephpalazzo"You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

When you stated a contrary position with no elaboration or reference to my argument. It would be like if I replied to this part of your post with "You failed to address the point."

To my question, "In what way did I fail to address that point?" Yes, you have failed to address that question. My answer was clear as it could be. Which part of, "It (math) exists as a mental construct", don't you understand?

Quote

QuoteIf humans don't exist then those features are perceived by whom? Who is there to describe them, God?

Does someone need to be there to describe them? If you believe so, make an argument for it. That's not even close to being a given, but it seems to be at the heart of your argument.

Exactly, to describe anything implies the existence of someone doing the describing. Learn how to use words properly, instead of being wishy-washy.

Quote

QuotePhysics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

Physics, as a study, and as an idea, is what you say it is. But the laws and patterns we see in nature and use physics to describe are really there, independent of us. And it is in this way that I use the word physics. They are independent of the concept of "pattern" and "law", those are just imperfect descriptive terms.

Again you fall into the same trap: you're confusing between the thing that exist, in this case the universe, and knowing about that thing, which is in this case, physics which by your own words, is a "the laws and patterns we see in nature", which again implies our existence to do the studying and the seeing. The fact that you had to add,  "those are just imperfect descriptive terms", more than anything support my claim: those are description done by someone, humans. Try harder next time to understand the differences between (1)  when we talk about the existence of a thing, which BTW pertains to the realm of metaphysics, and (2) when we talk about knowing about things, which pertains to the realm of epistemology.  

Quote

QuoteI believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

Worse than being childish is being willfully obtuse. And when you refuse to acknowledge a clearly explained difference between the idea of a term used to describe something and the actual object being described, that is what you are doing. When I say that something has a "feature", I'm not referring to some metaphysical quality that exists independent of our minds, I'm saying that the real thing exists in the way that the feature describes. Not only in that way, or separately in that way, or whatever other human ideas you insist on telling me I am projecting onto the thing. Just in that way.

All this poking and playing at linguistics without actually addressing the issue in communication is drowning what could have been an interesting debate.

Well so far, you have demonstrated you're not so quick in grasping simple concepts. Your learning abilities are dysmal. But perhaps you will surprise me with a better understanding if only you would get rid of your misplaced bad attitude and focus on where you can improve yourself.

Quote from: "aitm"

Quote from: "missingnocchi"

Quote from: "josephpalazzo"You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

When you stated a contrary position with no elaboration or reference to my argument. It would be like if I replied to this part of your post with "You failed to address the point."

QuoteIf humans don't exist then those features are perceived by whom? Who is there to describe them, God?

Does someone need to be there to describe them? If you believe so, make an argument for it. That's not even close to being a given, but it seems to be at the heart of your argument.

QuotePhysics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

Physics, as a study, and as an idea, is what you say it is. But the laws and patterns we see in nature and use physics to describe are really there, independent of us. And it is in this way that I use the word physics. They are independent of the concept of "pattern" and "law", those are just imperfect descriptive terms.

QuoteI believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

Worse than being childish is being willfully obtuse. And when you refuse to acknowledge a clearly explained difference between the idea of a term used to describe something and the actual object being described, that is what you are doing. When I say that something has a "feature", I'm not referring to some metaphysical quality that exists independent of our minds, I'm saying that the real thing exists in the way that the feature describes. Not only in that way, or separately in that way, or whatever other human ideas you insist on telling me I am projecting onto the thing. Just in that way.

All this poking and playing at linguistics without actually addressing the issue in communication is drowning what could have been an interesting debate.

Now this is what happens when we start down that slippery slope of philosophical bullshittery...its all fun and games until someone pokes someone in the eye...

You can't define anything precisely. If we attempt to, we get into the paralysis of thought that comes to philosophers, one saying to the other: "You don't know what you're talking about!" The second one says: "What do you mean by 'talking'? What do you mean by 'you'? What do you mean by 'know'?"
 
-- Richard Feynman

Quote from: "aitm"

Quote from: "missingnocchi"

Quote from: "josephpalazzo"You said,  "math does exist, I responded, "It exists as a mental construct". In what way did I fail to address that point?

When you stated a contrary position with no elaboration or reference to my argument. It would be like if I replied to this part of your post with "You failed to address the point."

QuoteIf humans don't exist then those features are perceived by whom? Who is there to describe them, God?

Does someone need to be there to describe them? If you believe so, make an argument for it. That's not even close to being a given, but it seems to be at the heart of your argument.

QuotePhysics is not an object that can do the describing. It is people using physics as a very efficient tool to describe the universe. As such, it is a mental construct, unless physics has a mind of its own?!?

Physics, as a study, and as an idea, is what you say it is. But the laws and patterns we see in nature and use physics to describe are really there, independent of us. And it is in this way that I use the word physics. They are independent of the concept of "pattern" and "law", those are just imperfect descriptive terms.

QuoteI believe you're confused, and you are too childish to recognize where your thoughts aren't very clear.

Worse than being childish is being willfully obtuse. And when you refuse to acknowledge a clearly explained difference between the idea of a term used to describe something and the actual object being described, that is what you are doing. When I say that something has a "feature", I'm not referring to some metaphysical quality that exists independent of our minds, I'm saying that the real thing exists in the way that the feature describes. Not only in that way, or separately in that way, or whatever other human ideas you insist on telling me I am projecting onto the thing. Just in that way.

All this poking and playing at linguistics without actually addressing the issue in communication is drowning what could have been an interesting debate.

Now this is what happens when we start down that slippery slope of philosophical bullshittery...its all fun and games until someone pokes someone in the eye...

I think you should send "philosophical bullshittery" into urban dictionary.
yep

Quote from: "josephpalazzo"To my question, "In what way did I fail to address that point?" Yes, you have failed to address that question. My answer was clear as it could be. Which part of, "It (math) exists as a mental construct", don't you understand?

I understand what you SAID perfectly. I just don't think it addresses my argument in a meaningful way. My argument was worded to specifically draw a line between the mental construct of math and the real relationships it describes. Your argument was basically "No u."

QuoteExactly, to describe anything implies the existence of someone doing the describing. Learn how to use words properly, instead of being wishy-washy.

True, I could have been clearer. What I meant was "Does someone need to be there to describe them in order for them to exist?"

QuoteAgain you fall into the same trap: you're confusing between the thing that exist, in this case the universe, and knowing about that thing, which is in this case, physics which by your own words, is a "the laws and patterns we see in nature", which again implies our existence to do the studying and the seeing. The fact that you had to add,  "those are just imperfect descriptive terms", more than anything support my claim: those are description done by someone, humans. Try harder next time to understand the differences between (1)  when we talk about the existence of a thing, which BTW pertains to the realm of metaphysics, and (2) when we talk about knowing about things, which pertains to the realm of epistemology.  

No, I'm specifically differentiating between the two things, and you are continuing to imagine conflation. What I am saying is that the various relationships that constitute the real world, the universe, exist as the real counterparts to our descriptions of them, independent of the descriptions themselves, and that this is just as true for math as it is for physics, chemistry and biology. That just because math doesn't have a physical component to study, doesn't mean that the relationships it describes are any less a real part of our universe.

QuoteWell so far, you have demonstrated you're not so quick in grasping simple concepts. Your learning abilities are dysmal. But perhaps you will surprise me with a better understanding if only you would get rid of your misplaced bad attitude and focus on where you can improve yourself.

Boy but do we think highly of ourselves. Aren't you afraid of the fall?

Quote from: "missingnocchi"

Quote from: "josephpalazzo"Again you fall into the same trap: you're confusing between the thing that exist, in this case the universe, and knowing about that thing, which is in this case, physics which by your own words, is a "the laws and patterns we see in nature", which again implies our existence to do the studying and the seeing. The fact that you had to add,  "those are just imperfect descriptive terms", more than anything support my claim: those are description done by someone, humans. Try harder next time to understand the differences between (1)  when we talk about the existence of a thing, which BTW pertains to the realm of metaphysics, and (2) when we talk about knowing about things, which pertains to the realm of epistemology.  

No, I'm specifically differentiating between the two things, and you are continuing to imagine conflation. What I am saying is that the various relationships that constitute the real world, the universe, exist as the real counterparts to our descriptions of them, independent of the descriptions themselves,

Fine, that's a little bit better expressed than your previous post.

Quoteand that this is just as true for math as it is for physics, chemistry and biology.

Math doesn't describe anything in the real world. It is an abstraction based on the identity law and the law of substitution. Instead of saying, "there's a sheep there, and a sheep next to it", I can substitute, "there are two sheep over there". It's the same reality, just a different description.  

Quote

QuoteWell so far, you have demonstrated you're not so quick in grasping simple concepts. Your learning abilities are dysmal. But perhaps you will surprise me with a better understanding if only you would get rid of your misplaced bad attitude and focus on where you can improve yourself.

Boy but do we think highly of ourselves. Aren't you afraid of the fall?

I'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

I also run this blog:

http://soi.blogspot.ca/ (http://soi.blogspot.ca/)

Quote from: "josephpalazzo"Fine, that's a little bit better expressed than your previous post.

I'm overjoyed at your approval.

QuoteMath doesn't describe anything in the real world. It is an abstraction based on the identity law and the law of substitution. Instead of saying, "there's a sheep there, and a sheep next to it", I can substitute, "there are two sheep over there". It's the same reality, just a different description.  

If those laws are as true in reality as they are on paper, then there must be a reason for it. An existence in our universe that causes them to be true. If it's only in between the lines, a coincidence of literally universal proportions, so be it. I would contend that that's unlikely, though.

QuoteI'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

Bold words to say to a stranger from another country on the Internet. I don't know how you sleep at night.

QuoteI'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

(//http://images.picturesdepot.com/photo/c/cartman_respect_my_authority-11123.jpg)

Quote from: "Seabear"

QuoteI'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

[ Image (//http://images.picturesdepot.com/photo/c/cartman_respect_my_authority-11123.jpg) ]

while I love the touche' your siggy line makes it rather moot.

Quote from: "aitm"

Quote from: "Seabear"

QuoteI'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

[ Image (//http://images.picturesdepot.com/photo/c/cartman_respect_my_authority-11123.jpg) ]

while I love the touche' your siggy line makes it rather moot.

Sure, whatever.

Quote from: "missingnocchi"

Quote from: "josephpalazzo"Fine, that's a little bit better expressed than your previous post.

I'm overjoyed at your approval.

You should be. My students pay a lot of money to get it (in tuition fees).

Quote

QuoteMath doesn't describe anything in the real world. It is an abstraction based on the identity law and the law of substitution. Instead of saying, "there's a sheep there, and a sheep next to it", I can substitute, "there are two sheep over there". It's the same reality, just a different description.  

If those laws are as true in reality as they are on paper, then there must be a reason for it. An existence in our universe that causes them to be true. If it's only in between the lines, a coincidence of literally universal proportions, so be it. I would contend that that's unlikely, though.

Our models get better because we continuously refined them with new discoveries and new theories. Take for instance Bequerel's discovery that uranium gave off radiation. Until then, no one suspected that a rock could give off energy on its own. And all the prevailing theories about matter at the time could not explain that phenomenon. It took the works of the Curies, Einstein, Rutherford, Bohr, Schroedinger and Heisenberg before we had a theory that could describe it with Quantum Mechanics.

But at the end of the day, we only have a model that describes more or less the reality out there. Never confuse the model with reality. The model is what we create in our minds.

Quote

QuoteI'm a university professor, teaching physics for the last 25 years, and I'm very demanding. Don't ever get into my class. You have no chance of passing.

Bold words to say to a stranger from another country on the Internet. I don't know how you sleep at night.

I sleep very well, thank you, and when I don't, I blog.

It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

Quote from: "Plu"It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

Indeed, math is one of the greatest invention, along with the alphabet, and it took us from cave-dwelling to landing on the moon.

Quote from: "Plu"It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

I have a yard stick  (no pressure boys)

*hands on hips*  Now.............  *ahem* Who's dick am I measuring?   Line em up!


 :rollin:  :rollin:  :rollin:

Yard stick? Whut?
I'm so bad at math
 :rollin:

:-#









 :popcorn:

Quote from: "aitm":-#









 :popcorn:

gotta have a little bit of fun - eh?

Quote from: "josephpalazzo"

Quote from: "Plu"It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

Indeed, math is one of the greatest invention, along with the alphabet, and it took us from cave-dwelling to landing on the moon.

So, it took us from rocks to more rocks. I kid, I kid.  :)

Quote from: "Plu"An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

Short answer, no.

Suppose you have a monitor with a length x and a width x giving you an area of x^2. You know the area of a monitor is c, and you want to find the distance x. So you build the equation x^2=c and solve it. This will create 2 equations. x = sqrt(c) and x=-sqrt(c). One of them make sense in reality, the other is tossed.

Mathematics doesn't have the limitation of our reality.

Quote from: "SixNein"

Quote from: "Plu"An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

Short answer, no.

Suppose you have a monitor with a length x and a width x giving you an area of x^2. You know the area of a monitor is c, and you want to find the distance x. So you build the equation x^2=c and solve it. This will create 2 equations. x = sqrt(c) and x=-sqrt(c). One of them make sense in reality, the other is tossed.

Mathematics doesn't have the limitation of our reality.

Sure it does.  The first answer is sometimes called the real root.

Quote from: "Plu"An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

No controversy just mental masturbation woo garbage.

YES math exists. PERIOD.

This is as stupid as saying speed doesn't exist.

Quote from: "WitchSabrina"

Quote from: "Plu"It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

I have a yard stick  (no pressure boys)

*hands on hips*  Now.............  *ahem* Who's dick am I measuring?   Line em up!
 :rollin:

You are measuring from the base right?  And girth?  And are you taking the angle of the erection into account?

QuoteSure it does.  The first answer is sometimes called the real root.

Both of those numbers in my example were real; however, one was a negative number. We toss the negative number because it has crossed the physical limitations of distance.

Mathematics is more like a game where axioms can be made up about anything.

Quote from: "Brian37"

Quote from: "Plu"An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

No controversy just mental masturbation woo garbage.

YES math exists. PERIOD.

This is as stupid as saying speed doesn't exist.

Quite a limiting view on reality you have there, I fear.

QuoteMathematics is more like a game where axioms can be made up about anything.

Yep. That's the beauty of it. Math is greater than reality in a way, it's just that some of it doesn't really do anything useful. But sometimes taking a short-cut through non-reality allows you to go back to reality and do something useful... (see: imaginary numbers)

Quote from: "WitchSabrina"

Quote from: "Plu"It seems my topic is devolving into some kind of dick-measuring context. It's a good thing math allows us to objectively compare such things, I guess?

I have a yard stick  (no pressure boys)

*hands on hips*  Now.............  *ahem* Who's dick am I measuring?   Line em up!


 :rollin:  :rollin:  :rollin:

Yard stick? Whut?
I'm so bad at math
 :rollin:

I had twelve inches, but now it is limp and I no longer use it as a "rule."  :shock:  :cry:  Solitary

Quote from: "SixNein"

QuoteSure it does.  The first answer is sometimes called the real root.

Both of those numbers in my example were real; however, one was a negative number.

Oops, my bad.  After a quick glance I ASSumed you had a real and an imaginary root.

Negative speed is real and useful in some contexts.

Quote from: "Colanth"

Quote from: "SixNein"

QuoteSure it does.  The first answer is sometimes called the real root.

Both of those numbers in my example were real; however, one was a negative number.

Oops, my bad.  After a quick glance I ASSumed you had a real and an imaginary root.

Negative [s:1w3sppbc]speed[/s:1w3sppbc] velocity is real and useful in some contexts.

 :P

I tried to be kind.  I've found that many people think that "velocity" is just a fancy way of saying speed.  But you're right, of course - vectors go in all directions, but length has no direction.

The things that mathematics represents are real. Mathematics itself is merely a language that humans use to represent those things, so, in that sense, it's as real as any other language.

Quote from: "Jmpty"The things that mathematics represents are real. Mathematics itself is merely a language that humans use to represent those things, so, in that sense, it's as real as any other language.

It's a question of distinguishing "form" from "content". In its form math, like language, is a human construct. In its content, it may represent real things, but not necessarily so.

Does pi have a quintillionth digit? Does anyone know what it is? If not, how can it "exist' when it's not in any mind?

Actually, the problem mathematical ontology with regards to irrational numbers is for nominalists, not Platonists. Nominalists tend to say that numbers are just an abstraction that sentient beings apply to groups of things. But clearly that cannot be the entire case, because what grouping are you abstracting from when you, say, take the square root of two?

I'd say that I'm a nominalist, but there are interesting challenges to it, and the number of adherents to it (37%) among philosophers is slightly  below Platonists (39%).

So, is mathematics an invention, discovery, or both? In my opinion it is a tool. Solitary

Quote from: "Unbeliever"Does pi have a quintillionth digit? Does anyone know what it is? If not, how can it "exist' when it's not in any mind?

Pi (= circumference/diameter) is derived from geometry, and geometry is determined by the laws of physics, hence pi is part of the real world.

Quote from: "Unbeliever"Does pi have a quintillionth digit? Does anyone know what it is? If not, how can it "exist' when it's not in any mind?

Yes.  Pi has been calculated to over 10 trillion digits.  

It's 2.

Edit: Source (//http://www.numberworld.org/misc_runs/pi-5t/details.html)

I am an uneducated hick, and I haven't read the entire thread, YET, but I think about this kind of thing a lot.: The language of math is a perfect language, but we have not completely mastered it yet. The universe and everything in it can be described by 1+1=2, or whatever is extrapolated from that perfect statement. We just haven't done all the math yet. There can't be a universe with different laws, because 1+1 can only equal 2. You can play semantics and describe the unit "1" as some kind of set I suppose, but you aren't really changing anything. It's perfect, just not complete.

So my answer to the original post is, "Yes, math exists, everywhere, regardless of perception, it's shapes sizes and behaviors are all extrapolated from the most basic statement: 1+1 always equals 2."

It's funny though that we are discussing this on a computer, which is a great evidence that math is a perfect language. After I read the rest of the thread I may have more to say.

"Math" is just an example of a set of languages that describe things. It's not perfect, nor is there only one. It's the best one we have though. (Which is the primary reason why the others aren't in use anymore, they're simply not as good as this one)

I think I disagree about math not being perfect. I think it is perfect, but incomplete.

You said it is not even the only one. But another one (like what? Base Twelve or something?) would simply use other symbols for the same constructs.

I really don't think there is much disagreement here, except on semantics. All of us would probably agree that the universe exists regardless of human perception. Unless there is a semantic problem with the word, "exists".

As an uneducated hick though, I am put off by a lot of the arguing-at-the-person that takes place on these boards. Name-calling is beneath all of us.

QuoteYou said it is not even the only one. But another one (like what? Base Twelve or something?) would simply use other symbols for the same constructs.

Actually the way the Romans handled things was pretty wildly different from any numbers system we have today. Although that may well have been their downfall as well.

Different numbers systems are widely used today, computer sciences still commonly uses binary and hexadecimal (16 digit) number systems.

Clocks and time also still use a pretty interesting mess of concepts and measurements.

The fact you can have multiple different maths that do pretty much the same thing show that math is a human construct, not a universal constant. Now whether the concept behind math is perfect... I don't know. I guess not, since the concept behind math is just describing what we see happen in the world.

I guess I would say that mathematical symbols are a human construct, but the patterns being described are indeed a "universal constant". So the language is written in everything, so to speak. I think it's more discovery than invention.

So I come down on the side of "Math Exists". In fact I think it may be the only thing that does.

But I'm just an uneducated hick.

Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

Quote from: "Colanth"Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

I couldn't have said it better. Can I steal that?  :P

I think I may be having a definition problem with "math". If you define it to be the symbols and systems we use to describe the relationships between quantities, then I certainly agree that it is a human construct. But If you define it to BE the relationships and quantities, then I think it "exists".

But I am just an uneducated hick.

If you define it to BE the relationships and quantities, you're defining it completely different from most people, though.

That is probably true. Like I said:uneducated hick. Thanks for discussing it with me. Not exactly dinner conversation around here. It's fun to articulate it all though. Helps me reason.

What word should I apply to the mathematically described relationships between quantities, if not "math"?

Quote from: "Solomon Zorn"What word should I apply to the mathematically described relationships between quantities, if not "math"?

Single word?  I can't think of one.  How about "the mathematically described relationships between quantities"?

Quote from: "josephpalazzo"

Quote from: "Colanth"Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

I couldn't have said it better. Can I steal that?  :P

Sure.  Send the royalty checks to the forum. :)

Once again, Colanth nails it. I've made it a point to not post until after he does, just to look more astute by agreeing with him.  :-D

I think math is real in the same sense that language is real. Although I have a hard time defining abstractions themselves. And that stuff like the circumference of a circle divided by it's diameter gives an irrational constant number blows my mind. A lot of stuff in math does that for me.

Quote from: "Colanth"

Quote from: "Solomon Zorn"What word should I apply to the mathematically described relationships between quantities, if not "math"?

Single word?  I can't think of one.  How about "the mathematically described relationships between quantities"?

Can I call it the MDRBQ for short? 8-)

(A little uneducated hick humor.)

Can I amend it to say, "mathematically described consistent patterns in the relationships between quantities"?

So MDCPRBQ is my acronym!  8-)  

(Oh, that felt good! - A little mental masturbation is healthy for an uneducated hick!)

As long as you actually understand what you're doing (it sounds as if you do), have at it.

Quote from: "stromboli"Once again, Colanth nails it. I've made it a point to not post until after he does, just to look more astute by agreeing with him.  :-D

Just for that I'm instituting a new policy - I'm not posting until I see your response. Þ

Quote from: "Colanth"Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

I am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.  :rolleyes:

Quote from: "GurrenLagann"

Quote from: "Colanth"Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

I am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.  :rolleyes:

Language can describe reality, but not all language reflects reality as it can be used to describe fantasy, like religion... :)

Similarly, math can describe reality, but not all math describes that.

Quote from: "GurrenLagann"

Quote from: "Colanth"Quantities exist.  Relationships exist.  But math is purely a human construct - a language.

But that's not what it means to ask whether or not math exists. What is being asked is if there is a referrent in reality that mathematics refers to, or why does mathematics oftentimes seem so intertwined with reality (see geometry) if it does not exist?

If you ask the wrong question, you get a meaningless answer.

QuoteI am in a room. I exist. The room exists. But does 'in' exist? Clearly 'in' is describing something actual, a relationship, but there is no apparent referrent, nor does such seem to make sense. But it clearly describes something, and I'm using English to describe it. I'm not sure if this comparison is really accurate (probably isn't), but I'll probably think of a better one later.

[/quote]You objectively exist.  The room objectively exists.  "in" exists as a descriptive word, but it doesn't objectively exist.

So "does math exist" is an incomplete question, since 'exist' is ambiguous.  Ask an unambiguous question and you can get an unambiguous answer.

You know, I think this entire argument is a disguised piece of Platonism trying to sneak in. A lot of people who assert "math exists" — especially if they're mathematicians — mean that there's this abstract object called a "two" out there that really exists. Of course this notion is wrong, because no single object can be a "two" — 'two' is what we label the notion and relationships between pairs of objects. We see a lot of pairs of objects, notice the underlying unity between them, and label that unifying relationship "two." We do similarly with "one" on singular objects, "three" on triplets, "four" on quadruples, and so on. We observe that combining a "one" group with a "two" group forms a "three" group, and so on, and label the entire mess of combining relationships "addition". Even if all humans disappeared and all mathematical knowledge destroyed, a singular object combined with a pair of objects will form a triplet of objects — the underlying fact is still there, even if the description does not.

I think that, despite your assertions to the contrary, Joseph, that you acknowledge this particular sense in which math is real, and not just a language. The physical laws that you teach your students and use to predict what will happen and test your theories are all highly mathematical in nature. The grounding the math has in reality doesn't merely anchor the mathematical descriptions, but allow you to predict what will happen to high accuracy. Math gives you not just descriptions, but tools to turn descriptions into predictions.

And no, the fact that mathematics can be used to describe completely imaginary situations is neither here nor there, as physics can be used to describe situations equally as imaginary and downright impossible, like gedanken experiments, or the imaginary physics of the Drive and the Field in Larry Niven's Mote in God's Eye world.

It's all in your head. Math is a lie. We must abolish all science based upon this false mental construct.

(//http://trdforums.org/data/attachments/1/1765-eec2ca63d89c0fcb2ec17a5a515eaea4.jpg)

Lol, I didn't notice the troll face at first. :p

I was going to let this slide but..that Feynman quote is childish. I guess famous smart people can have bouts of "the stupid" like the rest of us mortals.

Quote from: "josephpalazzo"You can't define anything precisely. If we attempt to, we get into the paralysis of thought that comes to philosophers, one saying to the other: "You don't know what you're talking about!" The second one says: "What do you mean by 'talking'? What do you mean by 'you'? What do you mean by 'know'?"
-- Richard Feynman

First off, precision isn't all or nothing it comes in degrees. This is a prime example of the black and white fallacy.
Secondly, there is much to be criticized when it comes to how philosophy has been done traditionally like philosophers wanting perfect necessary and sufficient conditions for just about every important idea, but asking for clarification of problems isn't one of them. It's basic problem solving 101: define the terms of the problem or question before you even try to answer or solve it. Why? Because some "problems" aren't even real problems. Many unanswerable questions are unsolvable because they are so ill defined. Also how the hell are you going to solve a problem you don't even understand?
By the way: If someone claims, "God exists" is it so "unreasonable" to ask the speaker what is meant by "god" and "exists?"

That's all I wanted to add.

Quote from: "Colanth"

Quote from: "stromboli"Once again, Colanth nails it. I've made it a point to not post until after he does, just to look more astute by agreeing with him.  :-D

Just for that I'm instituting a new policy - I'm not posting until I see your response. Þ

We're gonna be circling the campfire with uncooked hot dogs, in that case.

So?  You never ate an uncooked hot dog?  They're good.

This thread reminds me of a guy I knew years back that insisted that there was a special meaning to numbers, and the numbers 1333 in particular. He said he saw it by looking through (or past) pictures and imagery, he saw it on public business signs, he even saw it by adding up numbers as frivolous as the license plates of a car on TV. He believed that the government was trying to force this number into the public so it could counter-act the alien coalition that also is trying to send humanity the number 1333 to save them from ultimate destruction.

I still remember him flipping out when I told him that numbers only have a "spiritual", mental/psychological or emotional impact when you assign that value to them. If you do not assign such values, they are void and without such properties. He got very mad and was in a hysterical breakdown and almost crashed the car. I feel bad for his parents and all the problems he caused them but then again but it is their fault for enabling him and never doing anything to discipline him or get him proper mental help that he needed.

Yep.

Quote from: "Colanth"But math is purely a human construct - a language.

I disagree.

As with any universal law, principle or force, our recognition of it doesn't suddenly give rise to its' existence. We merely attribute a word and definition to something we recognise as either a part of reality, or as a concept in opposition to something that exists in reality.

If we take the color red, it exists as the color that it is because we exist to define it, but the spectrum of light that gives rise to what we interpret and label as 'red' exists whether we're around to recognise it or not.

Quote from: "Sulaco"

Quote from: "Colanth"But math is purely a human construct - a language.

I disagree.

As with any universal law or force, our recognition of it doesn't suddenly give rise to its' existence. We merely attribute a word and definition to something we recognise as either a part of reality, or as a concept in opposition to something that exists in reality.

If we take the color red, it exists as the color that it is because we exist to define it, but the spectrum of light that gives rise to what we interpret and label as 'red' exists whether we're around to recognise it or not.

There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

Quote from: "josephpalazzo"There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

I define mathematics as a principle, rather then a language or mental construct, as universal laws and forces outside of human interaction or interpretation follows mathematical principles (which we then observe, analyze, predict, etc, and communicte using symbols to define them, such as numbers and equations).

To put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

If we define it as a principle, it should follow that there is only one way to do it; which is the way that it is.

Yet we can define many ways to do the exact same thing, and what we call current math is merely one of them that happens to work fairly well (but is still rough, contradictionary and incomplete in various areas)

We can define colors in many ways, but there is only one wave-length spectrum. We can also define our maths in many ways; but there doesn't seem to be any natural construct that we map it to. That's why we have fields like abstract mathematics that don't even describe real things anymore but still work.

Quote from: "Sulaco"

Quote from: "josephpalazzo"There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

I define mathematics as a principle, rather then a language or mental construct, as universal laws and forces outside of human interaction or interpretation follows mathematical principles (which we then observe, analyze, predict, etc, and communicte using symbols to define them, such as numbers and equations).

To put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

I doubt it very much that mother nature says: I better accelerate that rock at 9.8m/sec[sup:ga9rtgxh]2[/sup:ga9rtgxh] -- especially that at one point it's 9.802; at another, 9.81034... in fact it's a different quantity at every single point on the crust of the earth, and slightly different two millimeters above that crust, etc..  :twisted: All the laws of nature are described in a language that we understand, and math is part of that language.  Just to calculate one term in the Feynman's diagram for two electrons scattering at a given angle requires to evaluate more than three hundred sub-terms, each of those is as ugly as it can get. There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

Quote from: "Plu"If we define it as a principle, it should follow that there is only one way to do it;

Not that there is one way, so long as it's a series of properties that are consistent and deemed true.

ie.. the addition of an extra unit to a series will always equate to the value higher then the previous.

So to state that mathematics is a language by human construct is to state that the likes of Addition only exists because we forumated it. Though the example I mentioned above would still be true whether man was around to recognise it or not.

Quote from: "josephpalazzo"There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

I think we're completely missing each other here.

Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

QuoteTo put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

Yes for the first question, that's why it is called ultra"violet" Just because there are no "color" names for the ones we can't see don't mean they don't have color, they are called nonspectral colors and yes for the second question because scientifically it is a sound: the energy that produces the stimulus of hearing even if we don't hear it. Solitary

Quote from: "Sulaco"

Quote from: "Plu"If we define it as a principle, it should follow that there is only one way to do it;

Not that there is one way, so long as it's a series of properties that are consistent and deemed true.

ie.. the addition of an extra unit to a series will always equate to the value higher then the previous.

So to state that mathematics is a language by human construct is to state that the likes of Addition only exists because we forumated it. Though the example I mentioned above would still be true whether man was around to recognise it or not.

Addition only generates higher values if you add positive numbers, with negative numbers it generates lower ones and with the number 0 it doesn't change anything. But that's actually trivial compared to the real issue, which is that the whole concept of defining what it means to be an object is something humans do.

In nature, there is nothing to really add, because without human interference there is no way to determine where one thing ends and another begins. That's something we do. There are no seperate objects in nature, just a giant ball of matter and energy. We set borders on objects so that we can make sense of the world, and then created rules to determine what happens when we interact with those objects.

(Also it's totally possible to create mathematical systems where adding things positive values doesn't always generate higher outcomes; for example modulo based ones. You can even make ones based entirely on multidimensional vectors, where the concept of "higher" doesn't even really make sense. The only reason any mathematical rule you know holds, is because we defined this system as such and it happens to work really well. But few people are taught why math actually works, so they see it as more than it really is.)

Quote from: "Sulaco"Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

This is just hair-splitting words: there is uniformity in nature is what you're getting at, right?

If nature wasn't uniform, then it wouldn't be predictable and we'd be unable to form any meaningful thought to begin with ... if reality itself even existed in such a total weird foam of chaos.

Quote from: "Sulaco"

Quote from: "josephpalazzo"There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

I think we're completely missing each other here.

Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

You're confusing the model we hold in our minds with reality. The model is always a work in progress, hopefully getting close to what is reality, but it's never the real world, just a model. Hence a mental construct.

Quote from: "Plu"Addition only generates higher values if you add positive numbers, with negative numbers it generates lower ones and with the number 0 it doesn't change anything. But that's actually trivial compared to the real issue, which is that the whole concept of defining what it means to be an object is something humans do.

In nature, there is nothing to really add, because without human interference there is no way to determine where one thing ends and another begins. That's something we do.

What of other life-forms that have shown to understand mathematics? It's one of the means by which we measure the intelligence of a species.

Which raises the question as to at what point did a species begin to identify mathematics?

Quote from: "Plu"There are no seperate objects in nature, just a giant ball of matter and energy. We set borders on objects so that we can make sense of the world, and then created rules to determine what happens when we interact with those objects.

Are you proposing that intelligent life is what determines existence from non-existence? Or rather shapes what we observe and interact with into something we call reality?

So therefore before life formed on Earth, nothing existed? And then because life came into existence, which evolved into the beings we are today, it therefore validates the existence of the Universe before life came about?

QuoteWhat of other life-forms that have shown to understand mathematics?

We have no way of knowing whether they use our math or a different internal object representation of it; and because most only know basic counting and addition, there are dozens of systems available that they could be using that would generate the same results.

The Romans could do what pigeons and monkeys do, and their mathematical system was nothing like the current one. (And not nearly as capable as the one we use now, but it still worked in many basic cases.)

QuoteAre you proposing that intelligent life is what determines existence from non-existence?

No, I'm not. I'm proposing that life (in general) determines its own set of boundaries between objects, and that those boundaries do not exist in reality. Even with life in the picture, there are no seperate objects in nature. We just look at things and our brain organises them for us so that it appears to be full of objects, but when you look at things really closely you will notice that there are no dividing lines other than what our brain draws for us so that we can make sense of things.

Forgetting that our brain filters input and draws the dividing lines for us lets you think that the universe is clearly divided into different kinds of things, but it isn't. It's all just a handful of natural laws operating on subatomic particles that, given the scale of things that we experience, seems to generate things.

Existance and non-existance have nothing to do with it. It is merely the thing that seperates one object from another that exists only in our heads, and it still only exists in our heads. There are still no objects in nature, our brain just describes things in the form of objects because it needs to simplify reality into something we understand.

Quote from: "Plu"An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)

I'd like to hear your opinions. I'm still trying to figure out my own :P

Math do not exist in the nature. Math is a way to describe things. Math is like a symbol. They(symbols) don't exist in the nature but they are great ways to describe things.
Math is truth. Is "truth" something that exists in the nature? No. The same is math.
 :-D

Quote from: "Plu"

QuoteAre you proposing that intelligent life is what determines existence from non-existence?

No, I'm not. I'm proposing that life (in general) determines its own set of boundaries between objects, and that those boundaries do not exist in reality. Even with life in the picture, there are no seperate objects in nature.

hmmm.. forces creates a seperatation between all things, even on a sub-atomic level. If there was no seperation between them to define one subset from another (ie objects), nothing would exist.

If anything I consider life as being a collective construct of particles, held together by a series of forces and laws, that is able to identify other objects formed.

Likewise with mathematics, we identify the existence of mathematics and use symbols to explain it. The use of symbols is language .. so to define mathematics as a language, is also partially correct, but it isn't just that - as is sound isn't just the frequencies that we're able to process and identify - but also the frequency itself, even if it's beyond our capability to hear it.

Quotehmmm.. forces creates a seperatation between all things, even on a sub-atomic level.

Forces create a seperation between atoms and sub-atomic particles, but those seperations aren't clearly outlined on the macro-scale. There is no accurate way to determine where the human body ends and the air surrounding it begins, and there are many things living on the edges of the human body (and inside it) that are living things in their own right but make up an essential part of the human.

The mere task of determining which of the trillions of bacteria inside us are part of our bodies and which are not alone is daunting, let alone seperating them on the atomic level where you have to seperate the skin from the dead skin from the dust from the bacteria.

It's not really a clear-cut object that is formed. The lines we see where things end and begin are added by our brain; there aren't such clear lines in the real world. Everything is made up of a ball of everything, and constantly changing with particles falling off or reacting with other particles. Even things that don't seem to change are constantly changing on a sub-atomic level.

Quote from: "Sulaco"Likewise with mathematics, we identify the existence of mathematics and use symbols to explain it. The use of symbols is language .. so to define mathematics as a language, is also partially correct, but it isn't just that - as is sound isn't just the frequencies that we're able to process and identify - but also the frequency itself, even if it's beyond our capability to hear it.

You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

Quote from: "josephpalazzo"You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

I think I'm missing something here. To help me understand your point better, could you explain what you mean in terms of, say, Planck's Constant? I don't mean the arbitrariness of whatever measuring units (e.g., joules or electron-volts) that may be chosen to express Planck's Constant, but I had thought that Planck's Constant was not arbitrary, instead that it is a basic quantized factor of electromagnetic radiation and matter.

Quote from: "entropy"

Quote from: "josephpalazzo"You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

I think I'm missing something here. To help me understand your point better, could you explain what you mean in terms of, say, Planck's Constant? I don't mean the arbitrariness of whatever measuring units (e.g., joules or electron-volts) that may be chosen to express Planck's Constant, but I had thought that Planck's Constant was not arbitrary, instead that it is a basic quantized factor of electromagnetic radiation and matter.

It is a constant just like the speed of light or Newton's constant. Sometimes these constants are set equal to one, simply because all measurement units are arbitrary to start with. Again, showing that quantification is arbitrary.

Leaving aside their arbitrariness in measuring units, they also represent fundamental concepts in the laws of physics. We are no longer in the realm of math, here but in the scientific theoretical description of the fundamental structure of the universe, which is also a human construct. Is there an objective reality? Most likely, but our theories are our own description of that reality. We hope in our endeavor that our scientific description comes close to how the universe functions, it doesn't mean that the universe has to obey our limited concepts. Planck constant arises in QM, which brings this quite in focus. In classical physics, we can place all things into two sets: things that are particle-like (they bounce when they meet) and things that are wave-like (they go right through each other when they meet). Yet, at sub-atomic level, these two classifications don't hold - there are things which can have properties from both of these categories. So here we are confronted with the limitations of our human construct. We were forced to invent other concepts, such as non-commutative algebra, which is not intuitive at all, to deal with that weird reality - which in a strange way, shows that we can overcome our limitations with a little imagination.

EDIT: OTOH, these calculations in QM can really get ugly. Here's one possible way to get the Higgs boson.

(//http://i243.photobucket.com/albums/ff277/josephpalazzo/180px-BosonFusion-Higgs_svg.png) (//http://s243.photobucket.com/user/josephpalazzo/media/180px-BosonFusion-Higgs_svg.png.html)

The calculations behind such a diagram are partially shown here in one of my blogs.
http://soi.blogspot.ca/2011/09/gauge-th ... anism.html (http://soi.blogspot.ca/2011/09/gauge-theory-and-higgs-mechanism.html)

I don't believe that mother nature goes through those calculations for every Higgs boson she produces. This theory is our clumpsy way to understand her.
 :P
EDIT 2: typo mistakes

See? I knew math was just a diabolical plot concocted by the evil woman who posed as my 4th grade teacher... Mrs Stepp! :evil:

Quote from: "josephpalazzo"

Quote from: "entropy"

Quote from: "josephpalazzo"You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

I think I'm missing something here. To help me understand your point better, could you explain what you mean in terms of, say, Planck's Constant? I don't mean the arbitrariness of whatever measuring units (e.g., joules or electron-volts) that may be chosen to express Planck's Constant, but I had thought that Planck's Constant was not arbitrary, instead that it is a basic quantized factor of electromagnetic radiation and matter.

It is a constant just like the speed of light or Newton's constant. Sometimes these constants are set equal to one, simply because all measurement units are arbitrary to start with. Again, showing that quantification is arbitrary.

Leaving aside their arbitrariness in measuring units, they also represent fundamental concepts in the laws of physics. We are no longer in the realm of math, here but in the scientific theoretical description of the fundamental structure of the universe, which is also a human construct. Is there an objective reality? Most likely, but our theories are our own description of that reality. We hope in our endeavor that our scientific description comes close to how the universe functions, it doesn't mean that the universe has to obey our limited concepts. Planck constant arises in QM, which brings this quite in focus. In classical physics, we can place all things into two sets: things that are particle-like (they bounce when they meet) and things that are wave-like (they go right through each other when they meet). Yet, at sub-atomic level, these two classifications don't hold - there are things which can have properties from both of these categories. So here we are confronted with the limitations of our human construct. We were forced to invent other concepts, such as non-commutative algebra, which is not intuitive at all, to deal with that weird reality - which in a strange way, shows that we can overcome our limitations with a little imagination.

EDIT: OTOH, these calculations in QM can really get ugly. Here's one possible way to get the Higgs boson.

[ Image (//http://s243.photobucket.com/user/josephpalazzo/media/180px-BosonFusion-Higgs_svg.png.html) ]

The calculations behind such a diagram are partially shown here in one of my blogs.
http://soi.blogspot.ca/2011/09/gauge-th ... anism.html (http://soi.blogspot.ca/2011/09/gauge-theory-and-higgs-mechanism.html)

I don't believe that mother nature goes through those calculations for every Higgs boson she produces. This theory is our clumpsy way to understand her.
 :P
EDIT 2: typo mistakes

I misunderstood what you meant. I had just read Plu's post that I took to be about the distinction between what is our bodies and what is not is arbitrary (with respect to our bodies, I agree with that). I think I saw your response in that light, but if I understand you correctly now, you were making a different point - that the particular form of mathematical quantification we give to observed events is arbitrary. I had thought maybe you were saying that all observed distinctions are arbitrary (like an extension of the point Plu was making about the distinction of our body from non-body). If reality is utterly and completely physically continuous, then I could see how one could make the case that all distinctions would necessarily have to have some arbitrariness to them, but if at some identifiable fundamental level, reality is discrete rather than continuous, then that would imply that some observed distinctions are not necessarily arbitrary.

Quote from: "entropy"... if at some identifiable fundamental level, reality is discrete rather than continuous, then that would imply that some observed distinctions are not necessarily arbitrary.

In regard to the Planck constant, its discreteness had the value of bringing back the concept of "particle" to the nature of light. What is often lost today is that in 1905, the wave model was a permanent fixture in the minds of the leading scientists of the times. Maxwell's equation reigned surpreme, and Hertz discovery of electromagnetic waves that could be sent wireless over the Atlantic was a marvel to behold. So when an unknown clerk at the Swiss patent office published a paper, emphatically showing that light was made of particles, that idea was first met with derision. It was not until the 1920's that Einstein's idea of the particle model, and the ensuing wave/particle duality, took hold.

In regard to our discussion, that some concepts, which are mental constructs, are continuous or discrete does not settle whether or not something would be arbitrary.  In scientific matters, often it's a question that a model will prevail if it has predictive powers. When QM was finally developped, it predicted the existence of anti-matter, that matter was made of two distinct types of matter - bosons and fermions, each obeying its own statistic laws - and the anomalous electron magnetic dipole, we knew then we had a theory unparalled in the annals of history. But we should never forget that these theories are our own making, regardless if we look at them in regard to our understanding of the universe as triumphant or clumsy.  :P

Gut feeling tells me that realtiy is continuous instead of discrete, despite Planck sizes.  :-D

nah, this seems something that we might know better when we can actually experiment at such tiny scales. I don't see how we could though. I wouldn't be surprised that it's something weird, like both discrete and continuous.

Haven't really bothered reading the whole thread, but here are my points on the matter:

Maths is a tool, nothing more. It simply let's us quantify the properties of the universe. Mathematical notation is not universal, but the properties that it describes are. I am quite certain that if intelligent aliens exist, they probably understand the concept of Pythagorean Theorem, for example. Sure, they would write it in a completely bizarre and in-understandable way, but the concept remains the same, because it is a universal property, independent of mathematical notation. Of course, all of this requires the invention of a triangle, but I have no problem in believing that it can be re-invented by other species than humans.

We could also consider the application of mathematics in the field of physics. The laws of physics would most likely be known to an intelligent alien species and we have every reason to believe that they would create tools in order to describe and quantify these laws. Since the laws of physics are universal, their descriptions and quantification should also be universal. Of course, their notation would be completely different and inconceivable, but the underlying principles would be the same.

In general, math is a language and it varies (it is not universal), but the properties that it describes are universal. The laws of physics, mathematical theories, ratios and constants are all there, "embedded" in the universe. They are accessible to a being that is capable of intellectual thought. The only problem is - different beings will describe them in different notations.

Define exist.
2 apples + 2 apples = 4 apples.
2 books + 2 books = 4 books.
Math is mental reflection of how things happen in the world.

If the earth is destroyed, and if humans are the only conscious beings in the universe but now no longer exist, who is doing the counting?

Do numbers exist then?

I'm a mathematician and I'm certain that math does exist independent of us. Pi number is a proof of that.
It can't be found anywhere in nature yet it is infinite and can be calculated with infinite precision.
It never changes. It is true anywhere and anytime.
So yeah math does exist.

It exists in the minds of human. The universe couldn't care if you say, "Over there there is a sheep, and another sheep next to it"; OR "over there, there are two sheep". You are just describing the same reality, one with just words, and the other one contains a math equation 1+1 = 2. Math is just another language, invented by humans.  Mind you, it has a lot of practicality.

Quote from: josephpalazzo on March 26, 2014, 06:57:56 PM
It exists in the minds of human. The universe couldn't care if you say, "Over there there is a sheep, and another sheep next to it"; OR "over there, there are two sheep". You are just describing the same reality, one with just words, and the other one contains a math equation 1+1 = 2. Math is just another language, invented by humans.  Mind you, it has a lot of practicality.

If life will form on some other planet and they calculate number pi it will be the same as it is here. Precisely the same.
And you can't find it anywhere in the nature.

I agree that language and symbology aside the formula's , the methodology remains a constant, for as Rex said "Pi" should be "Pi" however you spell it or formulate it. However, if indeed the universe can present a time and location fluctuation or if a constant aboard an object at light speed can present an "Schordingers cat" scenario, then mathematics as we know may be moot, one apple two apple, gone one apple, now here is three apple.......oy vey.

Quote from: aitm on March 26, 2014, 10:52:23 PM
I agree that language and symbology aside the formula's , the methodology remains a constant, for as Rex said "Pi" should be "Pi" however you spell it or formulate it. However, if indeed the universe can present a time and location fluctuation or if a constant aboard an object at light speed can present an "Schordingers cat" scenario, then mathematics as we know may be moot, one apple two apple, gone one apple, now here is three apple.......oy vey.

Everything you said is in no way related to quantum physics and mathematics.

QuoteIf life will form on some other planet and they calculate number pi it will be the same as it is here. Precisely the same.

It will be the same ratio to an arbitrary length, but I doubt it would be the same number as they'd be unlikely to even use as many digits as we do, let alone the same arbitrary shapes and directions to write them down.

I was talking about the ratio. Who cares about which numbers are used?

Depends on what parts you think make up math. If you rebuild it from the ground up, I'm pretty sure a ratio like pi would still exist, but you'd have to wonder if that ratio is an inherent part of the concept of math, or just a side effect of our use of it. Math could still perform a lot of functions without knowledge of pi.

Quote from: rex on March 26, 2014, 11:29:49 PM
Everything you said is in no way related to quantum physics and mathematics.

Excellent, then I made my point.

Quote from: Plu on March 27, 2014, 08:08:00 AM
Depends on what parts you think make up math. If you rebuild it from the ground up, I'm pretty sure a ratio like pi would still exist, but you'd have to wonder if that ratio is an inherent part of the concept of math, or just a side effect of our use of it. Math could still perform a lot of functions without knowledge of pi.

What I am saying is that math contains objects and variables which are eternal and can't be found in nature. Which kind of hints me some sort of mathematical dimension.

Constants such as Pi and natural logarithm e are calculated a priori, they exist only in maths - but even with that, that's a number that would only exist if someone is around to discover it, it's just more sophisticated than comparing 2 set amounts of something existing in nature.

Quote from: Sal1981 on March 27, 2014, 09:33:12 AM
Constants such as Pi and natural logarithm e are calculated a priori, they exist only in maths - but even with that, that's a number that would only exist if someone is around to discover it, it's just more sophisticated than comparing 2 set amounts of something existing in nature.

Yeah but if there is nobody to discover law of gravity doesn't mean law of gravity doesn't exist.
If there is nobody to discover distance doesn't mean distance doesn't exist. If there is nobody to measure time doesn't mean time doesn't exist.

The fact that there is no observer doesn't change information.
As for mathematics I think eternal constants are telling me something. Perfect circle can't be found anywhere. Yet the more close you get to a perfect circle yet closer it's ratio to it's diameter comes to Pi.
And Pi can be calculated on paper, in computer, in the mind. Yet it's still the same.
So it is independent of observers. Independent of nature. And is eternal. I'm certain it does exist.

Pi can be approached, but never calculated.

Quote from: rex on March 27, 2014, 09:44:23 AM
Yeah but if there is nobody to discover law of gravity doesn't mean law of gravity doesn't exist.
If there is nobody to discover distance doesn't mean distance doesn't exist. If there is nobody to measure time doesn't mean time doesn't exist.

The fact that there is no observer doesn't change information.
As for mathematics I think eternal constants are telling me something. Perfect circle can't be found anywhere. Yet the more close you get to a perfect circle yet closer it's ratio to it's diameter comes to Pi.
And Pi can be calculated on paper, in computer, in the mind. Yet it's still the same.
So it is independent of observers. Independent of nature. And is eternal. I'm certain it does exist.

This seems like a question of what came first, chicken or the egg. I think that without reality or an observer to make a note of it, we wouldn't have the diameter to circle ratio.

I can easily see that the ratio exists independently of me, but I can also see that it's an invention of thinking minds that discover these ratios. You can't get there without both, reality and a reasoned language to describe it. Without ever seeing a circle, you wouldn't think of that ratio, likewise without a language, i.e. maths, you wouldn't think of a ratio if you saw a circle-like object in reality.

This is the reason why I think you need minds first (and the language to describe it) and circle-like objects secondly to make account of a constant we call Pi thereof.

Quote from: rex on March 26, 2014, 07:11:48 PM
If life will form on some other planet and they calculate number pi it will be the same as it is here. Precisely the same.
And you can't find it anywhere in the nature.

Pi is the ratio between the circumference of a circle and its diameter. It's really a geometric concept, hence it's physical, just like a tree is physical. In terms of math, it's a ratio, which is a division, which is the inverse of multiplication, which is another way of adding groups, and addition is just another language that is more practical to say, "I have two sheep", then saying, "I have a sheep and another sheep."

Now, I do agree that we can describe reality with symbols, which are human constructs: the alphabet and math. But these two form different languages. Pi is just a convenient way to say the circumference over diameter: two things I can measure with a ruler of an object that exist in the real world.

Quote from: josephpalazzo on March 27, 2014, 10:51:40 AM
Pi is the ratio between the circumference of a circle and its diameter. It's really a geometric concept, hence it's physical, just like a tree is physical. In terms of math, it's a ratio, which is a division, which is the inverse of multiplication, which is another way of adding groups, and addition is just another language that is more practical to say, "I have two sheep", then saying, "I have a sheep and another sheep."

Now, I do agree that we can describe reality with symbols, which are human constructs: the alphabet and math. But these two form different languages. Pi is just a convenient way to say the circumference over diameter: two things I can measure with a ruler of an object that exist in the real world.

What I am talking about is that pi is 3.14... not 3.15... or 3.13...
It will always be 3.14...
Another thing is that you can calculate it very precisely on paper or in your mind and then when you test it in reality it will be very accurate.
Now how could that come about?

Besides all the different mathematical fields work well together. It's a part of the whole thing which we can't see completely yet.
As for minds who gives the fuck about them?
The triangle would still be a^2 + b^2 = c^2 even if there was no one to know it.
Math is independent of both reality and minds.

Quote from: rex on April 04, 2014, 03:43:25 PM
What I am talking about is that pi is 3.14... not 3.15... or 3.13...
It will always be 3.14...
Another thing is that you can calculate it very precisely on paper or in your mind and then when you test it in reality it will be very accurate.
Now how could that come about?

Which part of "It's really a geometric concept, hence it's physical" don't you understand?

QuoteBesides all the different mathematical fields work well together. It's a part of the whole thing which we can't see completely yet.

Indeed, mathematical description plays a vital role in our understanding of the real world. But so do words.

QuoteAs for minds who gives the fuck about them?

If minds don't exist, then words don't, and likewise with numbers.

QuoteThe triangle would still be a^2 + b^2 = c^2 even if there was no one to know it.

Again, you are describing a geometric object, which like a tree or a cat, would exist independently of a human mind.

QuoteMath is independent of both reality and minds.

With no minds in the universe, who would be counting? God??

Quote from: josephpalazzo on April 04, 2014, 06:49:22 PM
Which part of "It's really a geometric concept, hence it's physical" don't you understand?


Indeed, mathematical description plays a vital role in our understanding of the real world. But so do words.

If minds don't exist, then words don't, and likewise with numbers.


Again, you are describing a geometric object, which like a tree or a cat, would exist independently of a human mind.


With no minds in the universe, who would be counting? God??

Look here bitch.
2+2=4 even if NOBODY IS FUCKING COUNTING. It's not 5 or 3 or 2. It's 4. ALWAYS 4.

Now as for geometry objects. Find me perfect triangle or circle in nature.

Quote from: rex on April 24, 2014, 05:14:42 PM
Look here bitch.
2+2=4 even if NOBODY IS FUCKING COUNTING. It's not 5 or 3 or 2. It's 4. ALWAYS 4.

[lmgtfy]Tautology[/lmgtfy]

QuoteNow  as for geometry objects. Find me perfect triangle or circle in nature.

Nothing is ever perfect, but lots of stuff which are triangular or circular.

Quote from: josephpalazzo on April 24, 2014, 06:12:49 PM
[lmgtfy]Tautology[/lmgtfy]



Nothing is ever perfect, but lots of stuff which are triangular or circular.

Pi applies to perfect circles. The more digits you count the more perfect it gets.
So there is perfection which can't be found in nature yet it can be calculated. And it is independent of minds since destruction of all minds information is still true.

Quote from: rex on April 25, 2014, 03:03:06 AM
Pi applies to perfect circles. The more digits you count the more perfect it gets.
So there is perfection which can't be found in nature yet it can be calculated. And it is independent of minds since destruction of all minds information is still true.

How can anything get more perfect??? It's either perfect, or not. Anything that has to get more perfect wasn't perfect to start with.

Quote from: josephpalazzo on April 25, 2014, 10:24:11 AM
How can anything get more perfect??? It's either perfect, or not. Anything that has to get more perfect wasn't perfect to start with.

What the fuck are you talking about?
The pi is transcendental number. It's unlimited. But you can calculate any number of digits with a mathematical series. And even if geometry of the universe is different mathematicians in another universe can come up with flat space and calculate pi and it will have same digits.

Quote from: rex on April 25, 2014, 04:07:38 PM
What the fuck are you talking about?
The pi is transcendental number. It's unlimited. But you can calculate any number of digits with a mathematical series. And even if geometry of the universe is different mathematicians in another universe can come up with flat space and calculate pi and it will have same digits.

Pi is the ratio of circumference to diameter. A civilization could be aware of this ratio without ever expressing it as a number.

Quote from: josephpalazzo on April 25, 2014, 05:23:33 PM
Pi is the ratio of circumference to diameter. A civilization could be aware of this ratio without ever expressing it as a number.

Yes and the ratio is always the same. It never changes.

Quote from: rex on April 25, 2014, 08:21:08 PM
Yes and the ratio is always the same. It never changes.

So is the speed of light, Planck's constant, and Newton's constant. But so what? Numbers are just a convenient way to express certain realities, but we also do the same with words or pictures. You have to be able to dissect between "reality" and "description of reality" - the latter being done with written words, pictures, sound (oral communication), and numbers, all of which are human constructs. When I say, "this is a tree", that is a statement which I can make by writing it or saying it orally. It is a human construct. The tree has its own existence, independently of whether I say that statement or not. But the statement only exists because there are humans who can utter or scribble that statement. Similarly, I can say, "on the other side of the road, there is a sheep, next to it, another sheep, next to that one, another sheep". Or I can say, "on the other side of the road, there are 3 sheep." There is no different reality in these two descriptions, but in the second one, I described that reality with a more convenient way, using 1+1+1 = 3. But both are "descriptions of reality", that is, human constructs. If I had 17 sheep instead of 3, the first type of description - enumerating them one by one - would be quite inconvenient and boring to say the least, but it would still be a valid "description of reality." Of course with math, I can do a lot more abstractions than if I didn't have math - trying to do Quantum Mechanics (see here (http://soi.blogspot.ca/2014/02/the-essential-quantum-mechanics.html)) or General Relativity (see here (http://soi.blogspot.ca/2014/01/the-essential-general-relativity.html)) without math would be nearly impossible. I can make a similar argument with language: without it, how far do you think we would have progressed in our understanding of the universe? Not much. We have a better understand of the real world with language, math, art, music, etc. - all human constructs. It's testimony of the creativity of the human mind.

Quote from: Plu on June 05, 2013, 02:29:45 PM
An interesting video on the topic of whether or not math is even a real thing.

<!-- m -->http://www.youtube.com/watch?feature=pl ... bNymweHW4E (http://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E)<!-- m -->

I'd like to hear your opinions. I'm still trying to figure out my own <!-- s:P -->:P<!-- s:P -->

I just think of math as a language.
6+6=12 is identical to
six plus six equals twelve

Now, just ask yourself. "Does english exist?"
I'd have to say yes since we are using english right now. Would english exist if there were never any people? No, but this doesn't mean that words that describe concepts invalidate the concept if the words don't exist.

For example "2" doesn't exist anywhere. You can always point to two things, or to the symbol "2" but never actually to "2". Twoness is a concept. That concept exists even if there is no language like math or english to give it a label.

You could now probably argue (if you were really argumentative) whether or not concepts exist if there are no brains to conceptualize them. It seems to me that concepts are always available to be conceptualized even in the absence of any brains.