Does Mathematics Exist Independently of the Universe?

[Aggie]

This may be more of a philosophical exercise than a real debate, but I thought it fit here.


If the physical universe did not exist, and there was NOTHING - would mathematical principles, theoretically speaking, still hold true?
Taken another way, do numbers and their relationships exist completely independently of things that can be counted?


I realize that if there was nothing whatsoever, there would be no significance to mathematics nor a way of discovering / using maths, but would it exist?

[Griffin NoName]

Zero would not exist without mathematics so if zero is nothing then yes mathematics would exist.

[Aggie]

Is null and zero the same thing, or distinct?

[Sibling Zono (anon1mat0)]

Mathematics are by definition an abstraction from the generalization of the natural world. An easier way to probe the subject (unless we want to delve into the classic "if a tree falls in the forest..."*) is to consider a different universe with different rules, then we could make an abstraction based on the rules of said universe and define the math of it. In fact you could claim that said consideration has been used already in things like imaginary and complex numbers.

Another approach is to see the problem from a computer simulation perspective, that is, the universe depicted in the simulation doesn't exist yet the rules by which it behaves are clearly defined.

*if you want to go that route, is an abstraction possible without the consciousness capable of conceiving it?

[Aggie]

Another approach is to see the problem from a computer simulation perspective, that is, the universe depicted in the simulation doesn't exist yet the rules by which it behaves are clearly defined.

Ah, but in this example, the parameters of the simulation are necessarily set by the user, i.e. the rules are pre-determined.  For our universe, the natural laws are set with specific constants involved, which one could tweak in a simulation.  However, it might be useful to use hypothetical alternate universes to delve into this a little more - if there are multiple universes which are based on different constants or laws from ours, is the math otherwise the same in all of them, necessarily?

[Sibling Zono (anon1mat0)]

My guess is Yes and No, I imagine that while the operations may have different results (ie, 1+1=3) the general rational structure should be quite similar, given that the main point of math is consistency.

[Swatopluk]

It is still an open question, whether 'our' math is the only possible.
Also there are things that cannot be done with math in this universe (e.g. to exactly solve the three-body problem).
There are even discussions whether this world can be described by math by mere chance or whether it is a necessity.
But for that matter physicists debate whether inertial mass, active gravitational mass and passive gravitational mass are identical and whether that is a necessity.

[Sibling DavidH]

I know no maths or philosophy but it seems to me that if no objects existed, and thus no distances, masses or whatever, then there would be nothing for mathematics to describe, not to mention no intelligence to do the describing.

[Swatopluk]

Mathematicians love to describe nonexisting things (that's 'pure' math) and can get very angry, if someone finds a useful application (applied=tainted).

[Sibling DavidH]

Yes, but that's done by physical brains starting from mathematics developed from the counting of objects.  Were there no objects there could not even be the concept of number or distance.  Add in the fact that nobody's there to do any thinking ...

The Whooples of planet Fooplegloop^* have a language, even though they don't exist, but that's only because my head is there to give it a home.

_{*It's a very harmonious and musical language, unlike that of the evil Ng.}

[Swatopluk]

But the premise of the discussion was that an 'independent' math could be available for a conscience developing absent our universe.
I could of course shortcut the discussion adn say that an 'independent' math would be platonism and since Platon was a digestive rear exit I could not accept that idea .

[Griffin NoName]

Is null and zero the same thing, or distinct?

Null is normally signified by an empty cell* whereas zero is represented by a zero. This distinguishes between deliberately indicating zero where null indicates nothing has happened. eg. we do know Mr Baker the Plumber's son does not want any muffins rather than we don't know if he wants any. So yes, null and zero are distinct.

One could argue either way, therefore. Null may be distinct from zero but represents nothing none the less so for the purposes of our current discussion it can be treated the same as zero = nothing. On the other hand null may only be represented by a boundary that defines waht is null - therefore a boundary must exist, therefore something exists to form the boundary, therefore it is not nothing.

*there are plenty of null cells in the Monastery !

[Aggie]

Yes, but that's done by physical brains starting from mathematics developed from the counting of objects.  Were there no objects there could not even be the concept of number or distance.  Add in the fact that nobody's there to do any thinking ...

This much can be addressed by imagining an absence of intelligent life in our universe, or on our planet, for that matter.  If humankind was wiped out tomorrow, including all recorded information, would mathematics cease to exist?

Even in an alternate matter-and-energy containing universe, things presumably can be described by some version of physics, which would be based on some version of mathematics; perhaps even a universe without matter and energy but with space and time could be described mathematically (although I'm starting to lose grip on whether that would be a universe at all?).  In all these cases, mathematics could most definitely be said to exist, IMHO, whether an intelligent mind was present or not.

But with nothing, I'm a bit muddled at whether even a pure abstract can exist.  At first glance, one would think that the concept of infinity would still hold (because there'd be infinite nothingness), but if there's no space, time, matter or energy to quantify, there would be no infinity.  I'm still skeptical of whether zero would exist in a meaningful way, because that implies there is something to quantify - one could accurately say there are zero Whooples of planet Fooplegloop on Earth, but only because they can be conceived of and described (by David).  In nothingness, saying there is zero energy or zero matter is more meaningless than saying there are zero Whooples, because they cannot even be conceived of.


Hmm... I'm dragging my next set of thoughts elsewhere, because they are too for this discussion.

[Griffin NoName]

Yes, but that's done by physical brains starting from mathematics developed from the counting of objects.  Were there no objects there could not even be the concept of number or distance.  Add in the fact that nobody's there to do any thinking ...

This much can be addressed by imagining an absence of intelligent life in our universe, or on our planet, for that matter.  If humankind was wiped out tomorrow, including all recorded information, would mathematics cease to exist?

Some animals and birds can count, usually along the lines of one, two, a lot. So humankind may be irrelevant.

[Sibling Zono (anon1mat0)]

Many birds up to seven. 

[ivor]

A bird does my accounting...

[Aggie]

Some animals and birds can count, usually along the lines of one, two, a lot. So humankind may be irrelevant.

Intelligent life in general, then.  The main point being that mathematics IMHO is capable of existing without life, given that the organization of the solar system, galaxy, universe etc. follow mathematical principles.

[Swatopluk]

A bird does my accounting...

The software used by the German federal agency colelcting the income tax is named ELSTER (magpie; as in thieving...)

The main point being that mathematics IMHO is capable of existing without life, given that the organization of the solar system, galaxy, universe etc. follow mathematical principles.

We still don't know that. We can describe it by math but as said above not even solve rather 'simple' things like the 3-body problem (only approximate).
We also can describe atoms as pieces of wood connected by metal wire

[Lindorm]

Some animals and birds can count, usually along the lines of one, two, a lot. So humankind may be irrelevant.

Intelligent life in general, then.  The main point being that mathematics IMHO is capable of existing without life, given that the organization of the solar system, galaxy, universe etc. follow mathematical principles.

But aren't those mathematical principles very much a thing in the eye of the beholder?

[Sibling DavidH]

  In the brain of, anyway!

[Lindorm]

Having spent the evening ironing and packing for tomorrow's upcoming trip, I can report that the collars of ladies' blouses are positively non-euclidian surfaces!

Now, did I hear Erich Zann play on his violin in the background... ? 

[Aggie]

But aren't those mathematical principles very much a thing in the eye of the beholder?

Colour is very much a thing in the eye of the beholder - one can easily say that colour does not exist independently of eyes (and some colours do not exist in some eyes), yet the wavelengths of light that are perceived exist independently of eyes.  The equations that describe electromagnetic radiation can exist independently of EM radiation, and EM radiation obviously can exist without the equations being known....

[Aphos]

As a mathematician, I will weigh in on this question.

Mathematics is a branch of logic.  It is based on axioms and the logical consequences of those axioms.  Different axioms can be used, leading to different mathematics.

So, no, math is not part of the universe.  For example, the number ONE does not have a physical reality, though it can be used abstractly to represent a single item.

That said, however, math is a great tool for modeling the universe.

Up until about 1800, the development (or discovery, depending on your philosophy of mathematics) of math was driven largely by physics.  Starting about 1800, new abstract maths were developed.  Some of these have since found applications in real world problems, such as group theory being applied to quantum physics, but for the most part math has been done for math's sake over the last 200 years.

[Bob in a quantum-state-of-faith]

As a mathematician, I will weigh in on this question.

Mathematics is a branch of logic.  It is based on axioms and the logical consequences of those axioms.  Different axioms can be used, leading to different mathematics.

So, no, math is not part of the universe.  For example, the number ONE does not have a physical reality, though it can be used abstractly to represent a single item.

That said, however, math is a great tool for modeling the universe.

Up until about 1800, the development (or discovery, depending on your philosophy of mathematics) of math was driven largely by physics.  Starting about 1800, new abstract maths were developed.  Some of these have since found applications in real world problems, such as group theory being applied to quantum physics, but for the most part math has been done for math's sake over the last 200 years.

(emphasis mine)

Proving the old joke:

There once was an argument between a high priest and a prime minister and a mathematician, over which was better to have-- a wife or a mistress?

The priest argued that the wife was superior, for she was faithful and could be supportive.

The prime minister argued that the mistress was better, because of the elements of danger she represented, which added spice to the relationship.

The mathematician argued that it was best to have one of each-- and that each was aware of the other.  That way, you could tell your wife you were at your mistresses, and you could tell your mistress you were with your wife-- then you could get some real math done...

[Sibling DavidH]

There are three kinds of mathematician: those who can add up, and those who can't.