Does math exist?

[josephpalazzo]

There are 5 sheep over there only means: over there, there is a sheep, and then another one, and another one, and another one, and one more. That we group them under the symbol 5 is just a mental construct. All math are mental construct. Now, like language, it is a tool our minds can use to understand the universe.

I define mathematics as a principle, rather then a language or mental construct, as universal laws and forces outside of human interaction or interpretation follows mathematical principles (which we then observe, analyze, predict, etc, and communicte using symbols to define them, such as numbers and equations).

To put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

I doubt it very much that mother nature says: I better accelerate that rock at 9.8m/sec[sup:ga9rtgxh]2[/sup:ga9rtgxh] -- especially that at one point it's 9.802; at another, 9.81034... in fact it's a different quantity at every single point on the crust of the earth, and slightly different two millimeters above that crust, etc..   All the laws of nature are described in a language that we understand, and math is part of that language.  Just to calculate one term in the Feynman's diagram for two electrons scattering at a given angle requires to evaluate more than three hundred sub-terms, each of those is as ugly as it can get. There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

[Sulaco]

If we define it as a principle, it should follow that there is only one way to do it;

Not that there is one way, so long as it's a series of properties that are consistent and deemed true.

ie.. the addition of an extra unit to a series will always equate to the value higher then the previous.

So to state that mathematics is a language by human construct is to state that the likes of Addition only exists because we forumated it. Though the example I mentioned above would still be true whether man was around to recognise it or not.

There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

I think we're completely missing each other here.

Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

[Solitary]

To put it another way; do we call a spectrum of light that is beyond our capability of processing, color? (for example ultraviolet light). Or a frequency of sound beyond human capability of hearing, sound?

Yes for the first question, that's why it is called ultra"violet" Just because there are no "color" names for the ones we can't see don't mean they don't have color, they are called nonspectral colors and yes for the second question because scientifically it is a sound: the energy that produces the stimulus of hearing even if we don't hear it. Solitary

[Plu]

If we define it as a principle, it should follow that there is only one way to do it;

Not that there is one way, so long as it's a series of properties that are consistent and deemed true.

ie.. the addition of an extra unit to a series will always equate to the value higher then the previous.

So to state that mathematics is a language by human construct is to state that the likes of Addition only exists because we forumated it. Though the example I mentioned above would still be true whether man was around to recognise it or not.

Addition only generates higher values if you add positive numbers, with negative numbers it generates lower ones and with the number 0 it doesn't change anything. But that's actually trivial compared to the real issue, which is that the whole concept of defining what it means to be an object is something humans do.

In nature, there is nothing to really add, because without human interference there is no way to determine where one thing ends and another begins. That's something we do. There are no seperate objects in nature, just a giant ball of matter and energy. We set borders on objects so that we can make sense of the world, and then created rules to determine what happens when we interact with those objects.

(Also it's totally possible to create mathematical systems where adding things positive values doesn't always generate higher outcomes; for example modulo based ones. You can even make ones based entirely on multidimensional vectors, where the concept of "higher" doesn't even really make sense. The only reason any mathematical rule you know holds, is because we defined this system as such and it happens to work really well. But few people are taught why math actually works, so they see it as more than it really is.)

[Sal1981]

Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

This is just hair-splitting words: there is uniformity in nature is what you're getting at, right?

If nature wasn't uniform, then it wouldn't be predictable and we'd be unable to form any meaningful thought to begin with ... if reality itself even existed in such a total weird foam of chaos.

[josephpalazzo]

There is no principle in nature that says that it has to be mathematical, none whatsoever. You are fantasying if you beleive such principle exists. Or you haven't done the kind of calculations that I have done -- an estimate of more than 100 thousands in my lifetime.

I think we're completely missing each other here.

Nature does operate by mathematical standards/principles, hence why it exists and we're able to formulate it into a language (called maths).

You're confusing the model we hold in our minds with reality. The model is always a work in progress, hopefully getting close to what is reality, but it's never the real world, just a model. Hence a mental construct.

[Sulaco]

Addition only generates higher values if you add positive numbers, with negative numbers it generates lower ones and with the number 0 it doesn't change anything. But that's actually trivial compared to the real issue, which is that the whole concept of defining what it means to be an object is something humans do.

In nature, there is nothing to really add, because without human interference there is no way to determine where one thing ends and another begins. That's something we do.

What of other life-forms that have shown to understand mathematics? It's one of the means by which we measure the intelligence of a species.

Which raises the question as to at what point did a species begin to identify mathematics?

There are no seperate objects in nature, just a giant ball of matter and energy. We set borders on objects so that we can make sense of the world, and then created rules to determine what happens when we interact with those objects.

Are you proposing that intelligent life is what determines existence from non-existence? Or rather shapes what we observe and interact with into something we call reality?

So therefore before life formed on Earth, nothing existed? And then because life came into existence, which evolved into the beings we are today, it therefore validates the existence of the Universe before life came about?

[Plu]

What of other life-forms that have shown to understand mathematics?

We have no way of knowing whether they use our math or a different internal object representation of it; and because most only know basic counting and addition, there are dozens of systems available that they could be using that would generate the same results.

The Romans could do what pigeons and monkeys do, and their mathematical system was nothing like the current one. (And not nearly as capable as the one we use now, but it still worked in many basic cases.)

Are you proposing that intelligent life is what determines existence from non-existence?

No, I'm not. I'm proposing that life (in general) determines its own set of boundaries between objects, and that those boundaries do not exist in reality. Even with life in the picture, there are no seperate objects in nature. We just look at things and our brain organises them for us so that it appears to be full of objects, but when you look at things really closely you will notice that there are no dividing lines other than what our brain draws for us so that we can make sense of things.

Forgetting that our brain filters input and draws the dividing lines for us lets you think that the universe is clearly divided into different kinds of things, but it isn't. It's all just a handful of natural laws operating on subatomic particles that, given the scale of things that we experience, seems to generate things.

Existance and non-existance have nothing to do with it. It is merely the thing that seperates one object from another that exists only in our heads, and it still only exists in our heads. There are still no objects in nature, our brain just describes things in the form of objects because it needs to simplify reality into something we understand.

[Eve]

An interesting video on the topic of whether or not math is even a real thing.

http://www.youtube.com/watch?feature=pl ... bNymweHW4E

I'd like to hear your opinions. I'm still trying to figure out my own :P

Math do not exist in the nature. Math is a way to describe things. Math is like a symbol. They(symbols) don't exist in the nature but they are great ways to describe things.
Math is truth. Is "truth" something that exists in the nature? No. The same is math.
 :-D

[Sulaco]

Are you proposing that intelligent life is what determines existence from non-existence?

No, I'm not. I'm proposing that life (in general) determines its own set of boundaries between objects, and that those boundaries do not exist in reality. Even with life in the picture, there are no seperate objects in nature.

hmmm.. forces creates a seperatation between all things, even on a sub-atomic level. If there was no seperation between them to define one subset from another (ie objects), nothing would exist.

If anything I consider life as being a collective construct of particles, held together by a series of forces and laws, that is able to identify other objects formed.

Likewise with mathematics, we identify the existence of mathematics and use symbols to explain it. The use of symbols is language .. so to define mathematics as a language, is also partially correct, but it isn't just that - as is sound isn't just the frequencies that we're able to process and identify - but also the frequency itself, even if it's beyond our capability to hear it.

[Plu]

hmmm.. forces creates a seperatation between all things, even on a sub-atomic level.

Forces create a seperation between atoms and sub-atomic particles, but those seperations aren't clearly outlined on the macro-scale. There is no accurate way to determine where the human body ends and the air surrounding it begins, and there are many things living on the edges of the human body (and inside it) that are living things in their own right but make up an essential part of the human.

The mere task of determining which of the trillions of bacteria inside us are part of our bodies and which are not alone is daunting, let alone seperating them on the atomic level where you have to seperate the skin from the dead skin from the dust from the bacteria.

It's not really a clear-cut object that is formed. The lines we see where things end and begin are added by our brain; there aren't such clear lines in the real world. Everything is made up of a ball of everything, and constantly changing with particles falling off or reacting with other particles. Even things that don't seem to change are constantly changing on a sub-atomic level.

[josephpalazzo]

Likewise with mathematics, we identify the existence of mathematics and use symbols to explain it. The use of symbols is language .. so to define mathematics as a language, is also partially correct, but it isn't just that - as is sound isn't just the frequencies that we're able to process and identify - but also the frequency itself, even if it's beyond our capability to hear it.

You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

[entropy]

You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

I think I'm missing something here. To help me understand your point better, could you explain what you mean in terms of, say, Planck's Constant? I don't mean the arbitrariness of whatever measuring units (e.g., joules or electron-volts) that may be chosen to express Planck's Constant, but I had thought that Planck's Constant was not arbitrary, instead that it is a basic quantized factor of electromagnetic radiation and matter.

[josephpalazzo]

You're talking about quantification, which is also a human construct. We quantify such things as weight, distance, time, human population, and Da Vinci's  Mona Lisa, but all of that is quite arbitrary, nothing that really exist in nature but our own human inventions.

I think I'm missing something here. To help me understand your point better, could you explain what you mean in terms of, say, Planck's Constant? I don't mean the arbitrariness of whatever measuring units (e.g., joules or electron-volts) that may be chosen to express Planck's Constant, but I had thought that Planck's Constant was not arbitrary, instead that it is a basic quantized factor of electromagnetic radiation and matter.

It is a constant just like the speed of light or Newton's constant. Sometimes these constants are set equal to one, simply because all measurement units are arbitrary to start with. Again, showing that quantification is arbitrary.

Leaving aside their arbitrariness in measuring units, they also represent fundamental concepts in the laws of physics. We are no longer in the realm of math, here but in the scientific theoretical description of the fundamental structure of the universe, which is also a human construct. Is there an objective reality? Most likely, but our theories are our own description of that reality. We hope in our endeavor that our scientific description comes close to how the universe functions, it doesn't mean that the universe has to obey our limited concepts. Planck constant arises in QM, which brings this quite in focus. In classical physics, we can place all things into two sets: things that are particle-like (they bounce when they meet) and things that are wave-like (they go right through each other when they meet). Yet, at sub-atomic level, these two classifications don't hold - there are things which can have properties from both of these categories. So here we are confronted with the limitations of our human construct. We were forced to invent other concepts, such as non-commutative algebra, which is not intuitive at all, to deal with that weird reality - which in a strange way, shows that we can overcome our limitations with a little imagination.

EDIT: OTOH, these calculations in QM can really get ugly. Here's one possible way to get the Higgs boson.



The calculations behind such a diagram are partially shown here in one of my blogs.
http://soi.blogspot.ca/2011/09/gauge-th ... anism.html

I don't believe that mother nature goes through those calculations for every Higgs boson she produces. This theory is our clumpsy way to understand her.
 :P
EDIT 2: typo mistakes

[AllPurposeAtheist]

See? I knew math was just a diabolical plot concocted by the evil woman who posed as my 4th grade teacher... Mrs Stepp!