# Is mathematics the language of the Universe? **URL:** \ **Category:** Great Debates\ **Created:** [August 23, 2011, 2:54pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784 "2011-08-23T14:54:55Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [August 23, 2011, 7:16pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/21 "2011-08-23T19:16:42Z")
Math is an amazingly useful tool in physics (although even there it is not the whole story: you cannot infer physical knowledge just from mathematics). It is a lot less useful (I am not saying it is no use at all) when we are trying to understand other aspects of reality, for instance, history. Yet history happens in the universe too. Math maybe fairly plausibly be called the language of physics, but it is not teh language of history. Other aspects of reality, such as biology, fall somewhere in between: math has considerable utility in biology, but it is very far from being its “language”. (I am aware that some people may think that biology and history, and everything else, ought to be reducible, in principle, to physics, to the motions of particles or the evolution of waveforms, or whatever. However, this is an unproven, and almost certainly unprovable metaphysical hypothesis, not a fact. Even if it is true, we can’t even begin to make the reduction) ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [August 23, 2011, 7:21pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/22 "2011-08-23T19:21:21Z")
> [@Smurfie](#): > > This is another face of the old Math debate…Do Mathematicians ‘discover’ new things or ‘invent’ new things. Actually I don’t think it is. I can agree that mathematicians discover new things without conceding that it is “the language of the universe.” **Mijin** makes a very good point, I think. I wish I’d said that. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [August 23, 2011, 7:37pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/23 "2011-08-23T19:37:01Z")
> [@Mijin](#): > > I don’t think the Universe is mathematical any more than it is based on the English language. > > How many points are there along a 1 metre line; I mean in the real, physical universe? > 1 / planck length? Infinity? Then how come I can do useful mathematics, and get correct answers, with a much lower granularity? > > The answer is because mathematics is just a tool for deriving non-obvious facts from obvious facts. It’s a means of manipulating information in a way we would find difficult without the intermediate step of representing it symbolically. > > That said, the fact that maths can be applied to the universe tells us _something_: that the universe is self-consistent and behaves in the same way as far as we can currently see. Aren’t your issues really just human inability to do the math? I mean, in theory, if we knew the starting conditions with perfect precision (ignoring Heisenberg for the moment) isn’t every future event predictable? Heisenberg certainly throws a spanner in those works but hypothetically, if you had the calculational power, you could do that. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 23, 2011, 7:49pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/24 "2011-08-23T19:49:15Z")
> [@Whack-a-Mole](#): > > Heisenberg certainly throws a spanner in those works but hypothetically, if you had the calculational power, you could do that. Lots of things can be reasoned about. Anything which follows rules can have its rules analyzed. For example, chess. If I had the calculational power, given the option to choose whether to be black or white, I could ensure that I never lost a game of chess. Does that mean math is the language of chess? (Genuine question here; I have no idea what it means to say that “X is the language of Y”). If that’s the sort of thing you’re talking about, then math is the language of _everything_. [Anything you can reason about you can, uh, reason about. Anything with rules can have its rules analyzed. Anything you can talk about, you can talk about abstractly. That’s all math is…] ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [August 23, 2011, 7:53pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/25 "2011-08-23T19:53:33Z")
> [@Indistinguishable](#): > > Does that mean math is the language of chess? (Genuine question here; I have no idea what it means to say that “X is the language of Y”). If that’s the sort of thing you’re talking about, then math is the language of _everything_. Reminds me of this [XKCD comic](http://xkcd.com/435/). In theory I think everything is reducible to math. Gets us into free will and all that jazz though. Perhaps Heisenberg’s theory allows for genuine unpredictability. Literally God rolling dice with the universe. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 23, 2011, 7:59pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/26 "2011-08-23T19:59:17Z")
What does unpredictability have to do with whether math is “the language of the universe”? If one analyzes situations such as “There is a die which unpredictably produces a value from 1 to 6; based on the value of the die, [something something]” and all their consequences, is that not just as much math as the analysis of deterministic situations? A non-deterministic function is just as much a mathematical concept as a deterministic function. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [August 23, 2011, 8:02pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/27 "2011-08-23T20:02:37Z")
I think the question resolves itself if one asks why people wonder about the unreasonable effectiveness of mathematics, but not about the unreasonable effectiveness of computers – since with computers, it is well known that any one (universal) computer can emulate any other (see [Turing completeness](http://en.wikipedia.org/wiki/Computational_universality)), so if reality is not ‘more complex’ than any computer, it’s trivial that computers can be used to simulate every aspect of the physical world. But actually, I think it’s not different with mathematics. Certainly, math has similar capacities to ‘emulate’ other systems as computers do – it must, since computers are mathematically describable. A famous example of this is Gödel numbering: you can mirror every statement you can make in a formal mathematical system within number theory, as simple (well, actually kind of complicated) arithmetical statements. This establishes the universality of mathematics. So, the reason mathematics can be used to model the physical universe is the same reason that computers can be used thus – universal systems are able to emulate, i.e. mirror the behaviour of, all other universal systems, or systems not more complex than that. Of course, reality might turn out to be ‘more complex’, i.e. non-computable, though I personally doubt it; but similarly, it might turn out that there are aspects of reality that can’t be modelled with mathematics, that we just haven’t discovered yet (though if we ever could discover such aspects, our deliberate thinking and modes of communication appearing quite computational in make-up, is an interesting question in itself). For more on this point of view, see [here](http://ratioc1nat0r.blogspot.com/2011/07/universal-universe-part-iii-answer-to.html). ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [August 23, 2011, 8:47pm UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/28 "2011-08-23T20:47:15Z")
We must have cross-posted. See my last post in the other thread. ---
**Author:** ![Hyperelastic](https://avatars.discourse-cdn.com/v4/letter/h/a3d4f5/32.png) [@Hyperelastic](https://boards.straightdope.com/u/Hyperelastic)\ **Post date:** [August 24, 2011, 12:31am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/29 "2011-08-24T00:31:03Z")
There is a [school of thought](http://en.wikipedia.org/wiki/Digital_physics) that the universe is just a big computer, solving the equations of mathematical physics. It’s a fringe view and not one I share. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 24, 2011, 12:50am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/30 "2011-08-24T00:50:15Z")
> [@Whack-a-Mole](#): > > Maybe both. > > 2+2=4 is discovered. > > As mentioned in the OP there apparently is modulo math which makes 2+2=0. > > I assume there are real world uses for that kind of math but I do not think that kind of math describes the universe we live in.’ Modulo is incredibly useful in Computer Science, where you deal with constraining large amounts of input to finite spaces. To use a VERY simple example, if you have a table with 8 slots, and want to store the number “27”, you do 27 mod 8, getting 3 (the remainder of 27/8), of course there are countless problems with this simple example, but that’s a simple example of how its useful – for enforcing bounds constraint. That said, as far as “the universe” goes, I hear modular arithmetic is very important in chemistry, but I don’t know anything as to HOW. ---
**Author:** ![XT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xt/32/456_2.png) [@XT](https://boards.straightdope.com/u/XT)\ **Post date:** [August 24, 2011, 1:07am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/31 "2011-08-24T01:07:47Z")
Mathematics is the language that humans use to describe the universe. It’s a human construct that allows us to describe how we think the universe works and to make predictions about the universe. -XT ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 24, 2011, 1:15am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/32 "2011-08-24T01:15:41Z")
> [@Whack-a-Mole](#): > > 2+2=4 is discovered. > > As mentioned in the OP there apparently is modulo math which makes 2+2=0. > > I assume there are real world uses for that kind of math but I do not think that kind of math describes the universe we live in.’ Of course it does. It just describes different aspects of that universe… [Just like “1 + x is guaranteed to be \>= 1” is true on some useful interpretations of what addition is (“If you add one item to a pile of items, you’ll definitely have at least one item overall”), while “1 + x is sometimes equal to 0” is true on some other useful interpretations of the language of addition (“If you go one mile to the right, and then follow up with a random movement, you might well end up 0 miles from where you started”] For example, suppose you’re keeping track of your car’s orientation by counting the number of left turns you make. 2 + 2 left turns is just as good as 0 left turns. In this context, 2 + 2 = 0 is an accurate and useful description of the universe. You wouldn’t want a driver who refused to accept 2 + 2 = 0 in this context. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 24, 2011, 1:24am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/33 "2011-08-24T01:24:11Z")
It’s nothing like that 2 + 2 = 4 is “discovered” and 2 + 2 = 0 is “invented”, if that’s what you’re proposing. That would be a ridiculous distinction… They’re both equally rules in some abstract games we’ve chosen to make up and spend time playing. Our interest in these particular games, of course, is often motivated by the desire to model patterns we’ve noticed in the universe or in other abstract games. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 24, 2011, 2:07am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/34 "2011-08-24T02:07:33Z")
I don’t think it’s fair to say math is the language of the universe any more than you can any other language is. Any given language is a more or less powerful way to describe the universe. Just because I’m not quite as PRECISE when I say “The moon orbits around the Earth” doesn’t mean I’m not describing the universe the same way math does. I can describe pretty much any physical property I want, it just may not be as succinct as math at describing the particulars. I can probably describe the exact meaning of a given input to a complicated function, even though depending on the language it may take three or four pages to do so. Math was invented, it just so happens to be a more powerful tool for writing down observations and predicting future outcomes than many other human languages in many cases. > [@bump](#): > > Math’s a way to represent what we see in the physical world, a language if you will. > > The ratio of a circle’s circumference to it’s diameter is constant, whether it’s denoted as 3.14159, 22/7, 3.11037 or 3.243F6. (pi, if you haven’t figured that out) > What people are trying to say when they say that “math’s the language of the universe” is that instead of saying that an alien would look at 3.14159 and recognize pi, that there are abundant examples of mathematical “rosetta stones” (pi, etc…) out there, so that we and any other species could relatively easily reconcile our respective mathematical systems. While this may be true, this is more of a sign that we happened to study the same things. I’m sure they have plain Glorkinese for “running” too, which almost all languages share a word for. It’s just the chances of them writing a document describing running similar enough to ours to decode are much smaller than the chances of them computing the area of a circle in a similar way to how we do it. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 24, 2011, 6:14am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/35 "2011-08-24T06:14:15Z")
It’s funny that π = 3.14… is ubiquitously held up as an example of the one universal mathematical constant that every sophisticated alien culture can be expected to have canonized as profoundly important, since any alien mathematical culture is more likely to have hit upon τ = 6.28… as the more natural, fundamentally significant “circle constant”. Our primary veneration of π (the number of radians in a _half_ revolution) is a bizarre historical anomaly, rather like making a big hullabaloo over sqrt(e) or 1 + the Euler-Mascheroni constant or some such thing. Sending it out into space is begging to be mocked (though if we do it in binary, we can hope the aliens don’t quite notice the factor of 2…). ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [August 24, 2011, 7:54am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/36 "2011-08-24T07:54:17Z")
> [@Smurfie](#): > > This is another face of the old Math debate…Do Mathematicians ‘discover’ new things or ‘invent’ new things. Precisely. > [@John\_Mace](#): > > The question is: did the universe “invent” math in order to exist (pardon the anthropomorphizing), or did humans invent math in order to understand the universe? I’m not sure how you would prove this, but it seems intuitively obvious to me that it’s the latter. Intuition says “Invention”. But how do we account for fractals such as the [Mandelbrot set](http://en.wikipedia.org/wiki/Mandelbrot_set)? The set continues on into infinity, so no human can hold it in his head at once. > [@Roger Penrose](#): > > … no one, not even Benoit Mandelbrot himself […] had any real preconception of the set’s extraordinary richness. The Mandelbrot set was certainly no invention of any human mind. The set is just objectively there in the mathematics itself. If it has meaning to assign an actual existence to the Mandelbrot set, then that existence is not within our mind, for no one can fully comprehend the set’s endless variety and unlimited complication. An alien civilization would come up with the same Mandelbrot set that we do, yet they probably wouldn’t create the plays of Shakespeare. [1] So the latter was created and the former discovered. Unfortunately, I find the idea of a discovered mathematics to be imponderable as well. If math is discovered, then it has an existence independent of the human mind. Math has no mass: is it measurable? I find this topic rather confusing. Penrose tentatively posits a Platonic world of mathematics, which is a reasonable model though it’s metaphysically unsettling. [Reverend Berkeley](http://en.wikipedia.org/wiki/George_Berkeley) would have probably said that the Mandelbrot set is situated in the mind of God. [1] Idea lifted from here: [The Reality of Fractals | Syntopia](http://blog.hvidtfeldts.net/index.php/2010/04/the-reality-of-fractals/) ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 24, 2011, 7:56am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/37 "2011-08-24T07:56:40Z")
> [@Indistinguishable](#): > > It’s funny that π = 3.14… is ubiquitously held up as an example of the one universal mathematical constant that every sophisticated alien culture can be expected to have canonized as profoundly important, since any alien mathematical culture is more likely to have hit upon τ = 6.28… as the more natural, fundamentally significant “circle constant”. Our primary veneration of π (the number of radians in a _half_ revolution) is a bizarre historical anomaly, rather like making a big hullabaloo over sqrt(e) or 1 + the Euler-Mascheroni constant or some such thing. Sending it out into space is begging to be mocked (though if we do it in binary, we can hope the aliens don’t quite notice the factor of 2…). Nah, the universe will be filled with quirks, specifically built around the circle constant, just to confound everyone. One alien with have found pi-squared, yet another will have 2\*tau, another still will SOMEHOW have their base circle constant be the pi[sup]tau[/sup]. One day we’ll eventually figure it all out and have a good laugh… which the aliens will misinterpret for a battle cry and throw us in the salt mines for threatening their peaceful existence. Edit: Even if we can’t hold the entirety of the Mandlebrot set in our minds at once, that doesn’t really matter, we can still hold the rules for constructing it. In language terms, we basically just invented a really witty turn of phrase for the math world that happens to be a good comeback to damn near everything. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 24, 2011, 8:19am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/38 "2011-08-24T08:19:11Z")
> [@Measure\_for\_Measure](#): > > An alien civilization would come up with the same Mandelbrot set that we do, yet they probably wouldn’t create the plays of Shakespeare. How about, say, tic-tac-toe? The rules are so simple and semi-natural that I can well imagine large numbers of alien civilizations independently coming up with it… Yet, in each case (including our own), I am also perfectly happy to say it was “invented” or “made up”\* by whoever, well, came up with it. I don’t feel that we should deny that person X invented Y for reasons Z just because some other person also independently invented essentially the same thing for similar reasons. (\*: While also, _at the same time_, I would not be surprised to discovered the existence of phenomena in the universe (even apart from the phenomenon of people playing tic-tac-toe) which were usefully modelled in some fashion or another by the abstract system of tic-tac-toe. Such that someone studying such phenomena might be motivated to codify and analyze tic-tac-toe even if it wasn’t a game which previously existed among their culture) ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 24, 2011, 8:28am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/39 "2011-08-24T08:28:38Z")
I’m also happy to describe ideas as both discovered and invented, I suppose. To invent the telephone is to discover a way of transmitting sound over long distances. To invent the wheel is to discover that a rolling, round object experiences mitigated friction. One can use either piece of language to describe the same accomplishment. ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [August 24, 2011, 11:33am UTC](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784/40 "2011-08-24T11:33:52Z")
> [@Indistinguishable](#): > > I’m also happy to describe ideas as both discovered and invented, I suppose. To invent the telephone is to discover a way of transmitting sound over long distances. To invent the wheel is to discover that a rolling, round object experiences mitigated friction. One can use either piece of language to describe the same accomplishment. Good point. Etymologically, the first means to “remove what was hiding something”, while the second means “to come upon something”. Neither, etymologically speaking, implies pure creative genius on the part of the finder. [Previous page](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784.md?page=1) [Next page](https://boards.straightdope.com/t/is-mathematics-the-language-of-the-universe/593784.md?page=3)