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Zuma's avatar

Would there be a mathematics if there were no mind to contemplate it?

Asked by Zuma (5893 points ) December 31st, 2009

This is a variation on the old philosophical potboiler, “If a tree falls in a forest and there is no one there to hear it, does it make any sound?” Only instead of making reference to a physical event, it refers to the non-physical world of mathematical objects. Is mathematical reality uniquely dependent on consciousness in a way that physical reality is not?

Does the unreasonable effectiveness of mathematics have any bearing on the matter?

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35 Answers

Violet's avatar

Great question! I would have to say the math would be there, even if there were no humans there to do the equations. For example E=mc^2, would still apply, even if we did not know about it. The same goes for πr^2. The circle still exists.

stranger_in_a_strange_land's avatar

Mathematics is merely a tool that homo sapiens has developed to help describe the world around us. So ithe answer is no. In the same was there would be no stone arrowheads if no one was there to make them. The universe would still function according to set principles, but the descriptive tools would not exist, or perhaps different (maybe better) tools in the minds of another species.

Haleth's avatar

What is the sound of one hand clapping?

stranger_in_a_strange_land's avatar

@Haleth A good classical koan.

Pazza's avatar

Do numbers really exist outside the mind, or are they just caracters we have developed to quantify reality?

I would have to agree with @stranger_in_a_strange_land.

I suppose a deeper question would be, does something have to be physical to exist?

@Haleth – If you define a clap as the noise that two hands make comming together in a specific manner, then one hand cannot clap.
If you define a clap as the specific movement of the hand then one hand can clap, but it wont’t make a noise :-)

LeopardGecko's avatar

There will always be “mathematics” no matter if you can comprehend it or not. Even Porifera use “mathematics”. The quotations are required for a question like this as we would not understand what it means to use “math” therefore there would be nothing “math” no branches of it. But there will always be numbers involved in everything. Mathematics is omnipresent just as sound as.

HumourMe's avatar

Not as we know it, just like there wouldn’t be physics, chemistry or science. It’s our enquiring minds that have brought about the things we know today. The concept of mathematics and science would still exist because no one can doubt gravity, chemical reactions, mass etc. are present in our world, however without humans and our evolved brains that allow a “mind” no one would ever know they existed.

stranger_in_a_strange_land's avatar

@Haleth My solution to the koan was to clap my hand against an object other than my other hand. My Zen instructor considered that cheating though; I’m not wired correctly for Zen

LostInParadise's avatar

It seems we have been around this one before. To be able to step back and think of mathematics as mathematics requires a sentient being, but mathematics exists independently of us. In that sense we have no choice but to be Platonists. The laws of the universe or multiverses are expressed in mathematical terms. We did not make these laws up. Indeed quantum mechanics is so alien to our everyday experience that it is questionable whether anyone could have thought of it on his or her own, yet by empirical testing these laws were discovered.

Could there be some place where mathematics does not apply? I can’t even imagine what such a place would be like. If this place has identifiable parts then they can be counted and would be subject to the laws of arithmetic.

stranger_in_a_strange_land's avatar

@LostInParadise But our version of mathematics may not be the correct key to the universe/multiverse. We are continuously refining our tools, i.e. String Theory, that in two hundred years time may be as valid as the 18th century Phlogiston Theory debunked by Lavoissier et.al.

Blondesjon's avatar

There will always be mathematics. It’s not a language we made up. It is a language we translated. It is the language of the Universe.

Gossamer's avatar

despite the existance of the mind mathmatics would continue on…math is forever…it can not be destroyed or denied….no matter if its counting or exponential growth…math will exist if we understand it or not

dpworkin's avatar

It turns out that since sound is a psychophysical phenomenon, the Bishop Berkeley question has been solved – the falling tree makes no sound until the sound is interpreted. However, sound is not structure, it is just the phased compression and decompression of air molecules. Mathematics, however, may be inherent, and I make my guess based on the fact that structures like the Fibonacci Series show up so often in nature.

HasntBeen's avatar

What exists independently of thought is “regularities” in the behavior or structure of real things. So, for example, the orbits of planets are determined by the nature of gravity and laws of motion, etc. We have developed mathematics as a language for expressing and working with these kinds of regularities. But certainly the symbols and ideas of mathematics are a function of human thought. The regularities are not.

janbb's avatar

Let us not forget fractals as well.

Zuma's avatar

@janbb Yes, indeed. It now appears that everything from quantum wierdness to the structure of spacetime, to the branching of capillaries and synapses, to the turbulence of clouds, to the distribution of galaxies all conform to fractal geometry. In fact, one promising candidate for explaining quantum gravity—the holy grail that is hoped will reconcile quantum mechanics with general relativity—involves fractals.

See also, this commentary on Max Tegmark’s Mathematical Universe Hypothesis. and the original paper where he talks about how the knower and the known are all part of an emergent self-referential system.

LostInParadise's avatar

In all fairness, here is an opinion opposed to mine: Link (page 24)

ETpro's avatar

Here’s how it adds up. Math was there before anybody discovered it. It’s rather like gold, or diamonds. They don’t have to be discovered by man in order to exist. They benefit from discovery only in that they are then appreciated.

So it is with math. The hydrogen atom is one of the simplest things in the universe and it had the +1/-1 attractive equality of a proton and an electron worked out in a little over 300,000 years after the big bang.

Have a Happy New Year!

Zuma's avatar

@LostInParadise I just read that article and—correct me if I am wrong—it seems to me that the whole substance of his argument was “Ewww, Platonism! That’s religion!”

Pazza's avatar

Can you quantify the infinitly variable?

engineeristerminatorisWOLV's avatar

Long time back, a man was sitting underneath a tree and an apple fell.He derived the theory of gravitation from that incident .People around at that time didn’t have the optimum thinking level to acknowledge and applaude the great discovery and uttered,“Acceleration due to gravity?What on earth is that?”.Slowly with the advancement of physics and more works on gravity,people came to know that yes,such a thing do exist and they lauded the discovery years after the discoverer’s death(How pathetic!!!).Now, when you ask a school kid he says,“Gravitational force?What’s the big deal about that?That’s how my baby brother dropped his pants to wee last night”.
So, no matter how tough a concept is,there will come a time when people would be able to comprehend it.Similarly some mathematical works produced out of great minds are the treasures for the future.

LostInParadise's avatar

@Zuma , Yeah, that is my sense of it. The article also implies that if it can be shown that we are born with mathematical instincts then that rules out prior existence of math, which does not make a whole lot of sense. I just wanted to show that there are people on both sides of the issue.

Jeruba's avatar

Mathematics is a human construct, the product of human minds. It would not exist any more than telescopes would exist, even though the stars that can be seen through a telescope would certainly exist.

The finger pointing at the moon is not the moon.

Polly_Math's avatar

Would there be anything if there were no mind to contemplate it?

ETpro's avatar

@Jeruba Mathematics is a human observation of a construct that existed fromm the moment of the creation of the universe forward. The entire universe is ordered with mathematical precision and couldn’t otherwise exist. The attraction between a negatively charged electron (-1) and a positively charged proton (+1) is perfectly balanced in 1 -1 = 0, binding electrons to their quantum domains around the nucleus of an atom. If it were not so, atoms would self destruct and the universe would collapse into a scattered array of subatomic particles. It didn’t take human beings figuring that out to make it work. It started working about 13.7 billion years ago, and we just figured it out recently.

ETpro's avatar

@Polly_Math If there were nothing till man contemplated it, how did everything exist so that man could evolve?

Zuma's avatar

Since the discovery of the Mandelbrot set there has been a movement within mathematics to treat it almost as if it were a natural science, using computers to explore mathematical objects in mathematical space. It appears that there are all sorts of mathematical objects “out there” waiting to be discovered. Here, for example, is a gallery of my fractal art. Each series, and in fact several series, are explorations of a single formula.

ETpro's avatar

@Zuma WOW! Very beautiful. Thank you for the link.

LostInParadise's avatar

@Zuma , Is that your artwork? Very nice. It is not just the Mandlebrot set. The use of computers has given rise to what has been called experimental mathematics. link. I feel a little uneasy when computers are used to find a brute force solution to problems, but it certainly is a legitimate approach.

Zuma's avatar

Yes, it’s my artwork. (thanks) You’re right, it’s not just the Mandelbrot set. I saw a graphic a few years back which mapped musical harmony as a 3D object. Apparently, there are only certain cords that the human ear finds pleasing, and this is universal across human cultures, and possibly across species. Anyway, they map along one spine of this spiral spheroid tinker-toy structure. Apart from being very beautiful (and possibly fractal) it looks as though we are somehow “tuned” to respond aesthetically to certain mathematical structures, whether visual or auditory.

If you look at my Harmonic1 series, you will find what look like wave interference patterns like you might get if you filled a shallow pan half full with water and placed it on a vibrating surface, like a sub-woofer, and you placed objects in it at regular intervals, you could get these patterns by varying the frequency and the volume.

Fractals are everywhere and I suspect that they are integral to consciousness itself. I just picked up Ian Stewart and Jack Cohen’s and The Collapse of Chaos which looks as though it might shed some light on this.

Polly_Math's avatar

@ETpro I was being a bit facetious, but that is an excellent point.

ETpro's avatar

@Polly_Math I got the chuckle. It’s the old philisophical question of, “If a tree falls in a forrest herer there is no one to hear it, does it make a sound?” taken to a reductio ad absurdum. And I guess the answer to the reductio ad absurdum answers the one about the tree, as well.

Zuma's avatar

@ETpro @Polly_Math The mathematical physicist Paul Davies argues that there is a kind of “omnipotence” in the way that universal laws apply. This also implies a kind of “omniscience,” in that nothing escapes them; they apply everywhere without exception. In this respect, “mind” need not necessarily be human, but perhaps an embedded mathematical order that is “unreasonably effective,” accessible to consciousness, and the very embodiment of intelligence.

ETpro's avatar

@Zuma That’s close to how I feel things are ordered as well. Call it “The Force” if you like, in Star Wars fashion.

The Cray XT5 Jaguar Supercomputer is a network of 19,000 machines with 224,256 cores each having 300 million transistors. That amounts to 12.7 quintillion neural connections, or roughly 10,000 times the number of neurons in a human brain. It performs 1.75 petaflops. That’s 1.75 thousand trillion floating point operations per second.

The XT5 is connected to the Internet, letting it access all the knowledge, conjecture and absolute bunk known to man. It’s network connections give it “eyes” wherever there is an network connected camera and “ears” wherever there is a network connected microphone. It can even see into space and through radar and sonar. And yet it can’t program itself, and we can.

And it’s not just an issue of living neurons being of superior design. Whales, orcas and elephants all have more neurons in their brains than we do, and they can’t yet break out of their instinctual programming either. They are not aware of being aware.

It’s a fascinating puzzle why we, with such relatively limited computational power, have uniquely become self aware. Perhaps the Universe willed it to be so. If so, shouldn’t we wonder why?

Zyx's avatar

The universe can be quantified (yeah yeah, fuck uncertainty), which means it’s basically information; programming if you will, with math. So yeah, all the math we know is just a measure of the logic in nature. There’s loads of math that doesn’t do anything but might in other universes. Of course we can’t be sure what the fuck is out there but it seems pretty likely math is not limited to us.

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