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Is Math an Invention or a Discovery?

Invention
12
44%
Discovery
15
56%
 
Total votes: 27

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furball
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Post by furball » Thu Jun 16, 2005 4:20 pm

AquaRegia wrote: The argument is getting metaphysical: can an idea exist without a mind to conceive it? I maintain that after our solar system is dust and there is no one to remember French, French will no longer exist. But other planets will continue to orbit other starts according to GMm/r2, whether anyone is aware of it or not. In a sense, the universe IS math - not literature, or art, or history, or language, all of which are fantastic human inventions. Math is qualitatively different - something always there to be discovered.

Am I making any sense?
you are making perfect sense, and perfect non-sense as is necessarily the case for such metaphysical claims. simply put, you adopt here the viewpoint of god - of an omniscient being. only from this viewpoint could you claim with such confidence what the history of human science, religion and mysticism has to date been unable to show: the nature of reality past, present, and future.

you cling to mathematics as the most of certain of all branches of knowledge, with the idea that it is somehow more fundamental, more basic, more "true" in its descriptions of "reality" (given, of course, that we jettison the ludicrous notion that math itself is reality). in this regard, Blind Willie is right on when citing Wittgenstein. contrast early Wittgenstein with late Wittgenstein and you have a valuble lesson in scepticism.

math is a productive language for describing various phenomenon. it offers rules by which the world (or "reality") may be judged to abide. it is productive to the extent that these rules predict things. but just because the universe (that is, our universe) corresponds to mathematical rules (the parts we focus on) does not mean that it is guided by mathematical rules (note the focus on agency). correlation is not causation.

so while you would be foolish to treat casually (i.e., skeptically) GMm/r2 if you want to enjoy a long life, over 1000 years of philosophy has also shown you are very foolish if not sceptical of any claims as to what constitutes the foundations of reality (even if we limit them to only "our" reality).

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Post by Baden » Thu Jun 16, 2005 4:44 pm

Blind Willie wrote:
furball wrote:
Blind Willie wrote:For more dense answers, may I refer you to the works of Descartes, Frege, Russell, and Wittgenstein?
do they play lux? i haven't run into them.
They are unregistered. I assume that's why you haven't played with them :P
The scientist as "homo ludens": Heisenberg was an excellent chess-player and frequently played table-tennis with his students. He was a very fair loser, but always demanded a re-match to improve his skills.

Btw, had the luck to meet him personally a few times in my youth since his youngest doughter was a class-mate at my boarding school. Will never forget his friendly and modest attitude. We once asked him humbly to contribute an article for our school magazine. He commended our effort and sent us an essay with the remark that this essay ("Goethe's View of Nature and the World of Science and Technology") would be published first in our magazine.

There exists an english translation, but found no public link for it. For those who are able to read the original text:

http://www.geocities.com/Athens/6674/heisenberg.html

I read this essay dealing with many aspects of science-history and the term "abstraction" again and again and still discover new aspects.

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Baden
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Post by Baden » Thu Jun 16, 2005 5:14 pm

I don't want to get off-topic. But found an english translation of a Goethe-quoute Heisenberg used in his essay:

"Everything [...] is now "ultra," everything transcends... [überbieten], irresistibly, in thought as in action. No one knows himself any longer, no one grasps the element that sustains him and in which he functions [...]. Young people are stimulated too soon and then torn along in the whirlpool of time; wealth and speed is what the world admires and what it strives for; trains, express mail, steamships and all sorts of communicative facilities are what the civilized world aims at in outpacing itself."

Goethe

Written about 1830 and well worth to reconsider in the age of e-mail and world-wide-web.

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Mike
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Post by Mike » Thu Jun 16, 2005 5:24 pm

?Mike smiles as he reads the interchange of ideas regarding this post?

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Post by slayer » Thu Jun 16, 2005 6:07 pm

<< Slayer congratulates Mike and sends him a sack of Sri Lankan potatoes hand picked by Eskimoes from Formosa>>

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Baden
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Post by Baden » Thu Jun 16, 2005 7:44 pm

Mike wrote:?Mike smiles as he reads the interchange of ideas regarding this post?
Should we talk about "grammer" again?

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Post by Tracker » Thu Jun 16, 2005 8:13 pm

I don't know,all i know is,the more i know the more i know i don't know!

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Post by Blind Willie » Thu Jun 16, 2005 8:33 pm

furball wrote:math is a productive language for describing various phenomenon. it offers rules by which the world (or "reality") may be judged to abide. it is productive to the extent that these rules predict things. but just because the universe (that is, our universe) corresponds to mathematical rules (the parts we focus on) does not mean that it is guided by mathematical rules (note the focus on agency). correlation is not causation.
Right on the money fur.

To expand on this, I would add that the only reason the universe corresponds to mathematical rules is because these rules were written up based on observation of the universe. If the universe stops corresponding to these rules, what do we do? We either change the rules and rewrite math based on new observations, or shake our fist at the sky and yell "St00pid universe! Follow the rules!"

History has shown it seems to be best to change the rules, btw.

"Math" is a slippery term that we use to describe a lot of different things, both concrete and abstract. Confusion arises when we assume that we can lump all these different things together and try to get one solid definition of them.

Remember those preschool toys with the box with different shaped holes and pegs? The idea was to learn that the square peg fits in the square hole and the round peg fits in the round hole, etc. Questions like "Was math invented or discovered?" or "Does math exist independent of our observations?" assume that math is either a round or square peg and we just have to figure out which hole it fits in. In reality, math is a little more like Play-Doh and we can easily squish it into either hole.

Or, if you were like Little Blind Willie in preschool, you could just eat the Play-Doh and avoid this metaphysical confusion.

MMMMM.....Play-Doh...

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Post by sasquatch » Thu Jun 16, 2005 9:22 pm

AquaRegia wrote: You lost me here - this seems to illustrate exactly my point. Circles were round, the value of ? fixed - built into the universe itself - before anyone knew about it. Circles will STILL be round, and ? still ?, long after we, and the earth, and English and Swahili, have ceased to exist.
Aqua,
The perfect mathematical circle did not exist until man defined it. Even a man today can only theorize the perfect circle and is unable to draw or model it to anywhere near perfect precision. An exact model for "perfect" simply does not exist anywhere, yet the equation that describes the perfect circle helps to decode many general or approximate shapes around us. That is a wonderful simile for mathematics as a whole. The equations are accurate - if you simplify the variables to match the simplified perspective.

A 20 year old man 2000 years ago may have looked at the sun thru the opaque wall of his tent and said, "the sun is a perfect disc which rises and sets each day." Copernicus looked up 500 years later and saw the sun as a perfect sphere which we revolved around on a perfectly circular orbit. Newton described an imperfect sphere which we revolve around on an elliptical orbit while we ourselves are bulging in the middle by the forces of gravity. Today we have computer models that mimic the rolling surface of the sun complete with coronal mass ejections and complex electro magnetic fields and we realize it's circumference is infinitely more complicated than the equation that describes a perfect circle or sphere. It is more like the infinite length of a coastline than anything resembling geometric precision. So is the original description merely refined and the now 2020 year old man is still correct saying the sun is a perfect circle? I say, "No." I guess one man's refinement is another man's giant leap of perspective.

The cutting edge of quantum physics is far more unsettling and filled with more possibilities than absolutes and you have to consider the perspective to lend any relevance to the equations (sub atomic vs cosmological). That is why I say we are always jumping 50% closer to elusive mathematical perfection, but never arriving at the destination. We are always viewing the universe from our limited perspective and describing it with a complimentary limited language... a bunch of hairy fish that can't see the water they live in... Oh wait, that's just me :D

Sasquatch
:smt017

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Post by orlando » Sat Jun 18, 2005 2:40 am

Math always existed, it was discovered.

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Post by Vinny Vedi Vici » Sun Jun 19, 2005 6:20 pm

nice sas


it is my opinion that invention and discovery are similar and inventions are usually based upon discoveries, or discoveries are found using an invention. therefore, it is both.

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Post by furball » Sun Jun 19, 2005 6:41 pm

i discovered peanut butter
i invented peanut butter
i discovered the moon
i invented the moon
i discovered a spot on my nose
i invented a spot on my nose

hmm, not similar enough to offer a conclusion to this discussion imho.

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Post by orlando » Sun Jun 19, 2005 8:19 pm

i discovered sasquatch in the shower with a picture of orlando
i invented sasquatch in the shower with a picture of orlando

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Post by Baden » Sun Jun 19, 2005 8:26 pm

Baden wrote:You invent something new. You discover what is already there.
First time I quote meself. I think this is true.

Amen

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Post by furball » Sun Jun 19, 2005 9:26 pm

orlando wrote:i discovered sasquatch in the shower with a picture of orlando
i invented sasquatch in the shower with a picture of orlando
another thread crash lands on the planet orlando ...

<< furball goes off in search of survivors >>

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Post by vonibot » Sun Jun 19, 2005 9:46 pm

Baden nailed it on the head here so I will re-quote him, too:
Baden wrote:You invent something new. You discover what is already there.
Utility in action...

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Post by el toro » Sun Jun 19, 2005 10:49 pm

is there really anything new?

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Baden
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Post by Baden » Sun Jun 19, 2005 11:11 pm

y, some people might discover that they aren't inventive.

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Post by IrnBru001 » Mon Jun 20, 2005 12:22 am

atom wrote:second, given that the values given to certain recognizable elements (horses, eggs, quarks, nudists, etc...) are agreed upon it is a discovery as it unveils relations between these items in a comparable way.
false.... you are first assuming numbers to state an object, ie a horse only make sense by first assuming number or a quanity of horses. You'll need to first prove identity to use them as an example... and you can't use any reference to numbers or things to do so.

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Post by IrnBru001 » Mon Jun 20, 2005 12:29 am

yuck... I don't really want to get into this... but I'll spoil it for you all...
math is neither... math is false... as are all claims to knowledge... as is that past statement... as was that one... ad nausium.
I promise you these roads of thought only leading to drinking.

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Post by Kef » Mon Jun 20, 2005 12:34 am

2 + 3 = 5

it's all false, how can a sum be equal to a number?

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Post by Mike » Mon Jun 20, 2005 1:39 pm

Baden wrote:
Mike wrote:?Mike smiles as he reads the interchange of ideas regarding this post?
Should we talk about "grammer" again?


Qhat r u takin' abut?

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Post by slayer » Mon Jun 20, 2005 2:08 pm

Math is 90% attitude and 50% effort.

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Post by Kef » Mon Jun 20, 2005 2:48 pm

and 15ish% logic

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Mike
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Re: To Philosophize

Post by Mike » Fri Jun 03, 2016 2:51 am

well its been over 10 years now - anyone else want to weigh in on the 'math is a discovery vs math is an invention' debate?

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Re: To Philosophize

Post by n00less cluebie » Fri Jun 03, 2016 9:51 am

If the Universe is "real" Math is a discovery.

The Universe has been governed by laws that are represented with math for some 13 billion years before humans came onto the scene F=GMm/r^2 or E=mc^2 could not exist without math

Unless you're arguing that the physical laws of the universe did NOT exist before we came onto the scene, in which case we are living in some sort of simulated universe. Which is possible of course, but that's another debate

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Re: To Philosophize

Post by Red Beard » Fri Jun 03, 2016 7:57 pm

I always found drastic polarities to be a kind of odd thing. Can't it be both?

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Re: To Philosophize

Post by Symbiosis » Sat Jun 04, 2016 9:43 am

I would say math is an invention which closely maps to reality. Maps were an invention too.

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Re: To Philosophize

Post by Red Beard » Sat Jun 04, 2016 10:47 am

Yes! There's a phrase in semantics that correlates to what you said: "the map is not the territory". The map is what we're inventing, the territory is what we're discovering.

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