Discussion in 'Off-Topic' started by Souron, Apr 10, 2010.
Of course that means math isn't just in your mind then!
@Birdjaguar: quit calling things by names and then try to make that flat grid that Souron talked about. It's still impossible. There are objective truths in the world even if we all turn into Zen buddhists overnight.
That is a classic example of the Fibonacci sequence and the Golden Ratio.
Link to video.
Link to video.
Praise the Mathematical Lord.
well that depends....
The question: do mathematical concepts (right word?) exist independently of our minds and the system of math that we have created around them?
How does explaining why there are no pentagon shaped honeycombs mean that that math is something universal and exists beyond our human brains?
If we can find Fibonacci sequences and gold ratios in nature, does that mean that these universal concepts are influencing evolution? How would they do so?
If these concepts exist outside of people, where do they exist and what is their relationship to the physical universe?
Now one could say that we see things in nature and from them we develop the concepts. Interesting, but I would bet it is not supported by facts.
Mathematics is a representation of an abstract system used for computation and analysis. As such, it is a framework within which everything is perfect and follows certain rules. This makes it easy to perform calculations and to figure out answers to questions that the framework was designed to examine. (by perfect I mean that every object has a defined and certain purpose and that each time you add 2 and 2 together you'll get the same result, assuming you are working in the same vector space)
It so happens that the sorts of questions we can analyze with this system can be applied to almost everything in life that's related to counting, measuring, figuring out certain problems, etc. That's why math is so powerful as a tool! With it you can figure out that once you eat an apple, it will be gone, or that if you mix 4 apples with 2 apples you will have 6 apples, which can last you 6 days if you eat an apple a day. That can be a life saving conclusion to reach, and math makes it happen.
But either way, neither the system, nor the objects in it, such as numbers, exist in any tangible way. It is just an abstract system that's useful for answering certain questions.
The examples of fibonacci occurring in nature might make you think: "but wait! maybe there's more to it, or something!" But nope, not really, it's just a sequence that happens to be frequently naturally occurring. I mean, keep adding up the previous 2 numbers, I can see why certain natural processes might take on that form, it's a very simple formula.
the discovery/innovation of certain mathematical concepts were for sure inspired by nature. be it a guy sitting under a tree, swimming with a bunch of cows, looking at a snail, or eating a salad, the relationship between nature and math is apparent. It is that connection between the two that makes it easy for you to look at nature and say: "Wow.. math!".. or to look at math and say: "Wow.. nature!"
But that is not where math comes from. Math is just an abstract system that we have built ourselves. The parallels between math and nature are there because math is built using some very basic and naturally occurring axioms. It makes sense that we can see a hint of math in naturally formed objects, such as galaxies, snails, and planets.
I was wrong, it doesn't depend. It would just be.
Several definitions of numbers have been presented in this thread, and it is not apparent that they are consistent.
Here's a list:
1) Pete Atoms observed that numbers represent the concept "how much more", effectively of ratios. This seems to be a physical property.
2) Birdjaguar seems to claim that numbers are a convention, much like language. Most other posters appear to disagree.
3) suiraclaw and ParadigmShifter seem to be saying that numbers are things that are constructed from a small set of axioms and operations. They are therefore purely abstract mathematical concepts.
4) Duo claims numbers are the physical property associated with quantity.
And what does Souron say?
I wouldn't have started this thread if I knew the answer.
Have you thought that it might have been the other way around?
There is a lot of evidence to show that disjointed human civilisations derived unique topologies to understand their environment. I hypothesise that counting could be an extention of topological thinking.
In the Mideast numbers and writing developed over many, many years from the increasing need for complex accounting.
Brief summary of Denise Schmandt-Besserat's work on the origins of counting:
The abacus predates the invention of zero so place notation came first, but in a non-written form.
Numbers were around a long time before formal mathematical systems were developed. As such the definition of what a number is has changed over the years.
I am assuming we are discussing numbers, as they exist in a modern mathematical framework. As such, they are abstract mathematical formulations.
Integers and rational numbers (fractions) are natural constructs though. (Negative numbers represent debt, fractions represent ratios of lengths or division of goods).
It's just real numbers that had to be "discovered". Irrational numbers were discovered pretty early on by a student of Pythagoras (apparently he was drowned for discovering them). Transcendental real numbers were discovered much later on.
Complex numbers were invented as well to form an algebraically closed extension field to the real numbers.
It's true that the construction, and axioms that define particular number sets have changed over the years. But I do not think that effects a layman definition of a number. And I think a layman is qualified to give a reasonable definition of a number -- numbers are not advanced mathematics.
But the philosophy of mathematics can far exceed the layman's understanding and interest. As far as I'm concerned (a laymen), math just works. It's the way I feel about a lot of things in science, I don't need to understand the intricacies of different concepts, but the application of those concepts are evident and pervasive in everyday life. A layman doesn't need or care to know what gravity is, but the applications of the theory are fundamental to our way of life.
What do you mean natural constructs?
In that negative numbers represent debt (or going below the zero of a scale, e.g. temperature).
Fractions used when cutting cakes or pies into equal sized pieces.
Separate names with a comma.