Where do we place Mathamatics?

[Boanerge]

I placed this thread in the Philosophy section because well, i figure exploring the whole of Mathamatics is something a philopher would do. But where does Mathamatics belong? Its not really science, nor is it really religion, but both make use of Mathamatics. What is it? Is it something that holds this world together? Or is it dependant on certain conditions? For example We can use a thermometer here on earth but would the same measuring instrument be useful any where else? And then we have Literature, which also uses mathamatics. Such as "Two wrongs do not equal a right." Is Mathamatics wisdom? Can it speak? what can it teach us? Is it Independant? Can it be?​

What is mathamatics exactly? IT seems to be used alot but yet alone... is it a language?​

any thoughts?​

 

[Philosoft]

An excellent question. Let me throw out a definition I've seen:

A science, or group of related sciences dealing with the logic of quantity, shape and arrangement.

 

[MoonlessNight]

But where does Mathamatics belong?

It's probably best described as a Science, though Philosophy works too.

Or is it dependant on certain conditions?

I'm not really sure what you mean here. Mathematical applications certainly depend on certain conditions. That's bascially the idea behind functions. But Math itself should work the same under any conditions, as long as it is applied correctly. That is, Math can be used incorrectly and so not seem to work under certain conditions, but there is no set of conditions where mathematical laws stop working (so 2 never equals 1, no matter what's happening). Of course that's an assumption about how the universe works, but since it's seemed to hold everywhere humanity has ever gone, it's a pretty good assumption.

For example We can use a thermometer here on earth but would the same measuring instrument be useful any where else?

Well, this isn't Math really. But like above, we assume that it would work anywhere because we assume the universe works the same everywhere.

Is Mathamatics wisdom?

Depends on your definition of wisdom.

Can it speak? what can it teach us?

Again, it depends by what you mean by those words.

Is it Independant?

Well, it is not dependent on anything (unless you don't consider logic Mathematics). That is, a new discovery in Physics would never cause us to reconsider how Mathematics works.

 

[taedium]

I think of math more as a philosophy, you create a set of properties and derive a system of rules from those properities. Science is more real-world, math is abstract and need not apply directly to anything in the real-world.

 

[billwald]

Mathematics seems built into the fabric of the universe. If we should meet space aliens the one thing we can be sure of is their basic math will be the same as ours.

 

[professor frink]

I think of math more as a philosophy, you create a set of properties and derive a system of rules from those properities. Science is more real-world, math is abstract and need not apply directly to anything in the real-world.

The set of properties or assumtions upon which mathematics is based are not really "created" so to speak. They are either based on observation, or are considered self evident. For instance, the sum of the angles of a triange is pi radians (in two space), or if a = b and b=c, the a=c. Thus if math is philosophy, so then is the field of thermodynamics, the laws of which are based either on observation, or self evidence. (Only the zeroth law is based on self evidence, stating that if X is in thermal eqilibrium with Y and Y is in thermal equilibrium with Z, then X is in thermal equilibrium with Z).

 

[victorhadin]

I like to think of mathematics in general as a toolbox. A knowledge of mathematics alone will not aid you in understanding the world we live in, but it is essential to creating working theoretical models; vital to the scientific process.

You cannot build a bridge without steel or stone. Equally, you cannot build a working theoretical model without mathematical methods.

Wherever you need to predict the behaviour of the physical world, of currency interactions, of movement and systems, you need mathematical tools. This does not mean that knowledge of mathematics implies knowledge of those systems, but knowledge of those systems demands relevant mathematical knowledge.

 

[Kirei]

What IS mathematics ? I think mathematics is the set of rules and properties that can be extracted from a few basic axioms. In that optic, philosophy, science and religion are branches of mathematics that deal with their own sets of axioms.

 

[Boanerge]

I like to think of mathematics in general as a toolbox. A knowledge of mathematics alone will not aid you in understanding the world we live in, but it is essential to creating working theoretical models; vital to the scientific process.

Can i add the same for the Vice Versa? Without any knowledge of Mathamatics, we would not understand any working theoretical model.

The way i see it is that if you have a very strong foundation on mathamatics you can understand many things, and you can actually fill in the blanks (For example you receive a set of patterns and you want to know what the rest of the pattern would be) because math remains consistant, or the underlying pattern... This only works because, as was stated, Math is not something we created. We simply gave a name to that which was already there.

I was reading a little about Pathagoras and over looked how they said that he had some "secret" math religion with followers which he never talked about. How is this so? And if one were to make a religion or belief with math, and so does another on the other side of the planet, would their beliefs differ?

I think they would if you break the laws of common sequences and operations. But this would also be like a language, like Pig latin and skipping every letter, where it means something to one person but means nothing to another. So maybe Pathogoras found this math pattern, maybe by adding the digits of a number while multiplying it by the sums of its first and last numbers, and discovered something.

Perhaps i made this up right now, but could these kinds of formulas actaully mean something? or are they as meaningless as scrambled letters? And if they do mean something, could they be a means of "Mathamatical Poetry?" expressing the deeper things of the mathamatical world. That would be interesting.

 

[Radagast]

But where does Mathamatics belong?

Roger Penrose, in his 1994 book Shadows of the Mind expresses this in terms of three worlds (similar to the three worlds of Karl Popper):

1. The physical world or Universe “out there”—electrons, trees, planets, and stars—which is studied by science and which we see when we open our eyes.

2. Our mental world of feelings and thoughts, which include our perceptions of the physical objects that we see and touch.

3. The “Platonic” world of eternal ideas, especially including mathematics. Before Time and the Universe were created, it was true that 2+2=4. This fact was discovered (is discovered everyday, in kindergarten), not invented. As Penrose says (echoing Augustine) the existence of this Platonic world:

“rests on the profound, timeless, and universal nature of these concepts, and on the fact that their laws are independent of those who discover them… It has always been true that each natural number is the sum of four squares [e.g. 100=64+16+16+4], and it did not have to wait for Lagrange to conjure this fact into existence.” (Section 8.7)

The Christian perspective places the mathematical ideas of world 3 in the mind of God, who both created the Universe and our minds. That's why mathematics works so well.

-- Radagast

 

[jayem]

I would expand on part of Roger Penrose's definition. Mathematics comes from how our brain works. The set of mental rules we use to describe how our brain perceives the world, specifically the quantitative aspects. It is a mental construct. Similar to logic and language. No higher brain function--no mathematics.

 

[Chilldogg77]

The Christian perspective places the mathematical ideas of world 3 in the mind of God, who both created the Universe and our minds. That's why mathematics works so well.

Here's where it gets interesting. Could it be any other way than it is? Could there be a universe in which each natural number was not the sum of four squares? Also, mathematics can't exist without either creation(a quantity of things, something with angles, etc.) or someone intelligent enough to think about math. I once took a philosophy quiz online that tested how logically consistent your ideas were. My only "red flag" was when I said that God could make 4 sided triangles and any other mathematically impossible thing if He chose to. That's more of a question of definitions, but I think the sum of four squares thing is a better example. Mathematics depends on God's mind and God's creation for its existence. So it seems that God does not just know about math, but created math when he created the universe to be as it is. Perhaps it couldn't be any other way because it comes from God who is perfect, so logic and math are flawless, and are made perfectly. I don't know, but we never had this discussion in any math class I've been in.

 

[Radagast]

...Could it be any other way than it is? Could there be a universe in which each natural number was not the sum of four squares?

It's difficult to imagine how that could be possible. One can imagine physics being different, and biology being different, but one can't imagine mathematics being different...

Mathematics depends on God's mind and God's creation for its existence. So it seems that God does not just know about math, but created math when he created the universe to be as it is.

Or perhaps before that --- if you believe in the Trinity, then the number 3 existed before the universe was created...

I don't know, but we never had this discussion in any math class I've been in.

A shame, isn't it?

-- Radagast

 

[jaguar]

if you believe in the Trinity, then the number 3 existed before the universe was created...

I think you're spot on here, Radagast. I would suggest that we have to believe that God really is three persons. In other words, 'threeness' is one of his attributes, (along with unity).

The implications of this are tremendous. Whereas time, matter,and the laws of physics are all created, mathematics in some sense was around before creation and thus in some sense is part of God. Not that God has 'parts' of course... I'm struggling to express this - can anyone help me out?

 

[seebs]

I consider mathematics to be probably a necessary truth, but certainly "real". I'm sort of a Platonist on the issue; I think that the numbers preexist our awareness of them. I don't even know whether they're "created" as part of the universe, or whether they're simply part of what it means to talk about creating a universe.

 

[burrow_owl]

. Perhaps it couldn't be any other way because it comes from God who is perfect, so logic and math are flawless, and are made perfectly.

Godel would take exception with this statement, which is why I'd resist the identification of math with the mind of god. I'd prefer not to think that the mind of God is either inconsistent or incomplete.

 

[Radagast]

I don't think Goedel's results apply to God, who knows truth in a different way from us.

Goedel's results apply to our formalisations of mathematics, I think.

-- Radagast

 

[burrow_owl]

Goedel's results apply to our formalisations of mathematics, I think.

Are you suggesting that there's some 'essence of math' in the platonic heavens that exists as distinct from math as formal logic? That'd certainly be a curious thing to behold (pure Math).

 

[Radagast]

There are two parts to mathematics: truth and proof. I think God knows the truth (e.g. is every even number the sum of two primes?) without proving it the way we do (with rules and axioms).

-- Radagast

 

[TScott]

Or perhaps before that --- if you believe in the Trinity, then the number 3 existed before the universe was created...

So the Trinity is based on boolean logic? 1+1+1=1