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Does math exist?

Started by Plu, June 05, 2013, 02:29:45 PM

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entropy

Quote from: "josephpalazzo"
Quote from: "entropy"
Quote from: "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.

[ Image ]

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

I misunderstood what you meant. I had just read Plu's post that I took to be about the distinction between what is our bodies and what is not is arbitrary (with respect to our bodies, I agree with that). I think I saw your response in that light, but if I understand you correctly now, you were making a different point - that the particular form of mathematical quantification we give to observed events is arbitrary. I had thought maybe you were saying that all observed distinctions are arbitrary (like an extension of the point Plu was making about the distinction of our body from non-body). If reality is utterly and completely physically continuous, then I could see how one could make the case that all distinctions would necessarily have to have some arbitrariness to them, but if at some identifiable fundamental level, reality is discrete rather than continuous, then that would imply that some observed distinctions are not necessarily arbitrary.

josephpalazzo

Quote from: "entropy"... if at some identifiable fundamental level, reality is discrete rather than continuous, then that would imply that some observed distinctions are not necessarily arbitrary.

In regard to the Planck constant, its discreteness had the value of bringing back the concept of "particle" to the nature of light. What is often lost today is that in 1905, the wave model was a permanent fixture in the minds of the leading scientists of the times. Maxwell's equation reigned surpreme, and Hertz discovery of electromagnetic waves that could be sent wireless over the Atlantic was a marvel to behold. So when an unknown clerk at the Swiss patent office published a paper, emphatically showing that light was made of particles, that idea was first met with derision. It was not until the 1920's that Einstein's idea of the particle model, and the ensuing wave/particle duality, took hold.

In regard to our discussion, that some concepts, which are mental constructs, are continuous or discrete does not settle whether or not something would be arbitrary.  In scientific matters, often it's a question that a model will prevail if it has predictive powers. When QM was finally developped, it predicted the existence of anti-matter, that matter was made of two distinct types of matter - bosons and fermions, each obeying its own statistic laws - and the anomalous electron magnetic dipole, we knew then we had a theory unparalled in the annals of history. But we should never forget that these theories are our own making, regardless if we look at them in regard to our understanding of the universe as triumphant or clumsy.  :P

Sal1981

Gut feeling tells me that realtiy is continuous instead of discrete, despite Planck sizes.  :-D

nah, this seems something that we might know better when we can actually experiment at such tiny scales. I don't see how we could though. I wouldn't be surprised that it's something weird, like both discrete and continuous.

Biodome

Haven't really bothered reading the whole thread, but here are my points on the matter:

Maths is a tool, nothing more. It simply let's us quantify the properties of the universe. Mathematical notation is not universal, but the properties that it describes are. I am quite certain that if intelligent aliens exist, they probably understand the concept of Pythagorean Theorem, for example. Sure, they would write it in a completely bizarre and in-understandable way, but the concept remains the same, because it is a universal property, independent of mathematical notation. Of course, all of this requires the invention of a triangle, but I have no problem in believing that it can be re-invented by other species than humans.

We could also consider the application of mathematics in the field of physics. The laws of physics would most likely be known to an intelligent alien species and we have every reason to believe that they would create tools in order to describe and quantify these laws. Since the laws of physics are universal, their descriptions and quantification should also be universal. Of course, their notation would be completely different and inconceivable, but the underlying principles would be the same.

In general, math is a language and it varies (it is not universal), but the properties that it describes are universal. The laws of physics, mathematical theories, ratios and constants are all there, "embedded" in the universe. They are accessible to a being that is capable of intellectual thought. The only problem is - different beings will describe them in different notations.

vsenetak

Define exist.
2 apples + 2 apples = 4 apples.
2 books + 2 books = 4 books.
Math is mental reflection of how things happen in the world.

josephpalazzo

If the earth is destroyed, and if humans are the only conscious beings in the universe but now no longer exist, who is doing the counting?

Do numbers exist then?

rex

I'm a mathematician and I'm certain that math does exist independent of us. Pi number is a proof of that.
It can't be found anywhere in nature yet it is infinite and can be calculated with infinite precision.
It never changes. It is true anywhere and anytime.
So yeah math does exist.

josephpalazzo

It exists in the minds of human. The universe couldn't care if you say, "Over there there is a sheep, and another sheep next to it"; OR "over there, there are two sheep". You are just describing the same reality, one with just words, and the other one contains a math equation 1+1 = 2. Math is just another language, invented by humans.  Mind you, it has a lot of practicality.

rex

Quote from: josephpalazzo on March 26, 2014, 06:57:56 PM
It exists in the minds of human. The universe couldn't care if you say, "Over there there is a sheep, and another sheep next to it"; OR "over there, there are two sheep". You are just describing the same reality, one with just words, and the other one contains a math equation 1+1 = 2. Math is just another language, invented by humans.  Mind you, it has a lot of practicality.
If life will form on some other planet and they calculate number pi it will be the same as it is here. Precisely the same.
And you can't find it anywhere in the nature.

aitm

I agree that language and symbology aside the formula's , the methodology remains a constant, for as Rex said "Pi" should be "Pi" however you spell it or formulate it. However, if indeed the universe can present a time and location fluctuation or if a constant aboard an object at light speed can present an "Schordingers cat" scenario, then mathematics as we know may be moot, one apple two apple, gone one apple, now here is three apple.......oy vey.
A humans desire to live is exceeded only by their willingness to die for another. Even god cannot equal this magnificent sacrifice. No god has the right to judge them.-first tenant of the Panotheust

rex

#145
Quote from: aitm on March 26, 2014, 10:52:23 PM
I agree that language and symbology aside the formula's , the methodology remains a constant, for as Rex said "Pi" should be "Pi" however you spell it or formulate it. However, if indeed the universe can present a time and location fluctuation or if a constant aboard an object at light speed can present an "Schordingers cat" scenario, then mathematics as we know may be moot, one apple two apple, gone one apple, now here is three apple.......oy vey.
Everything you said is in no way related to quantum physics and mathematics.

Plu

QuoteIf life will form on some other planet and they calculate number pi it will be the same as it is here. Precisely the same.

It will be the same ratio to an arbitrary length, but I doubt it would be the same number as they'd be unlikely to even use as many digits as we do, let alone the same arbitrary shapes and directions to write them down.

rex

I was talking about the ratio. Who cares about which numbers are used?

Plu

Depends on what parts you think make up math. If you rebuild it from the ground up, I'm pretty sure a ratio like pi would still exist, but you'd have to wonder if that ratio is an inherent part of the concept of math, or just a side effect of our use of it. Math could still perform a lot of functions without knowledge of pi.

aitm

Quote from: rex on March 26, 2014, 11:29:49 PM
Everything you said is in no way related to quantum physics and mathematics.

Excellent, then I made my point.
A humans desire to live is exceeded only by their willingness to die for another. Even god cannot equal this magnificent sacrifice. No god has the right to judge them.-first tenant of the Panotheust