Originally posted by Raui
View Post
If you honestly believe that all Socially defined things are not "reality", then I suggest you put that belief a test. go rob a bank (but don't hurt anyone), and when you get caught, see if you can convince the judge that the Socially defined penalty for the crime is NOT a reality.
I'm sorry, but some Socially defined things are as "real" as anything can be. They were defined the way they are, because the proof of experience, over the years, has caused them to be defined that way.
Math is NOT ONLY A TOOL, except to non- pure mathematicians. Mathematics may be used by some people as a tool in their attempts to describe/model physical "reality", but to pure mathematicians, Mathematics has a "reality" unto "itself".
Unlike our physical "reality", it is a WELL "defined reality" that is logically proven correct, consistent and interrelated.
Yes, there are some areas of Mathematics that are still in the discovery stage (because some of their concepts have not, as yet, been proven to be true or false and are just mathematical theories/ assumptions, but for the most part, mathematics is well defined, logically consistent and most of its Theorems have been proven to be true. (Again, I remind you, that its "truthfulness has NOTHING to do with "physical reality".)
On a 2 dimensional "flat" surface (something that can NOT exist in the physical reality WE LIVE IN, if Relativity is "true"), the sum of the interior angles of a triangle will always equal 180 degrees, where a degree is always defined as the size of the angle created between two adjacent radii of a circle. whose arc length along the circumference of that circle between those two radii is 1/360th of the circumference of the circle. (And again a "circle, is NOT an object that can exist in our physical "reality, but it DOES EXIST in the "mathematical" "world" of 2 dimensions).
Likewise the sum of the angles in a triangle drawn on the surface of a sphere (another object that can NOT exist in our physical reality) is greater than 180 degrees.
Like most people you confuse Mathematics' main purpose with having something to do with our physical reality. Any such comparison, where that is true, is purely accidental as far as Mathematics is concerned.
Let me illustrate with a story about the difference between a physicist and a mathematician:
There was once a professor of Philosophy who wants to determine what was the difference between the way a physicist thinks and a mathematician, so he devised a test.
In a room he had a table with a glass of water on it and a chair.
He brought the physicist in first and asked him to move the glass of water from the table to the chair and explain why he did what he did.
The physicist moved the glass of water from the table to the chair along a relatively straight line and said, "I have learned that the shortest distance between two points is a straight line." ((( as an aside, that statement may NOT be true in the Universe in which we live, if Space is in fact curved))).
The physicist then left, the glass was replaced on the table and the mathematician was invited in and give the same problem.
He moved the water from the table to the chair along a relatively straight line and said, "I learned in Math that the shortest distance between two points is a straight line."
He left the room and the physicist came back in, with the glass still on the chair.
The philosopher then asked him to move the water from the chair to the floor. The physicist picked it up and lowered it to the floor in a relatively straight linear motion and said the same thing he had said before.
He left, the glass was returned to the chair and the mathematician brought back in and given the same challenge, with the same results.
He left, the glass was put back on the table and the physicist came back in.
He was told to now take the water from the table to the floor and explain.
He picked it up, moved it directly from the table to the floor along a relatively straight line and quoted the same reason.
He left, the glass was replaced on the table and the mathematician was brought back in and given the same challenge.
He said, "That is easy, I already know how to get the glass from the table to the chair and from the chair to the floor". So he picked up the glass, moved it first to the chair and then from there to the floor.
Now, what is the difference?
The physicist works with "models", he used his Math "skills" to make a model for finding a scientific process for moving the glass between any two different points in space and then using that method to solve the last problem.
Whereas, the mathematician took the bigger problem and broke it down into two smaller problems, each of which he already knew how to solve, and used that knowledge to solve the original problem.
Pure mathematicians aren't studying "physical reality" they are studying the various relationships between their mathematical constructs in their "mathematical reality".
If those relationships have anything in common with physical reality, then THAT is for physicists to be concerned with. Pure mathematicians could care less. Physicists take Math classes, so they can learn enough Math to use it in forming their models. Most pure mathematicians don't concern themselves with Physics and physical "reality", they study Math for Math's sake.
When I studied Mathematics, the fact that it was a "reality" unto itself. One that does not change over time, was one of the things that caused it to be attractive to me. (Unlike Science, where "reality" is so uncertain and "scientific explanations are constantly changing.)
In Mathematics, things it deals with are true because its relationships have been "proven" to be logically consistent. (Again, I remind you that Mathematics has a "reality" unto itself and though some of its principals and relationships may be used by other people to try to model the external world, whether or not those attempts to use it for such purposes yields any useful results, that, to a pure mathematician, is totally unimportant.)
In Spherical Geometry, Pi has "exactly" the same mathematical value it has in Euclidean flat plane Geometry. the same mathematical "rules" apply and the same Calculus calculations define it in either system.
Just because something is written in a book, no matter how logical it may "sound", doesn't necessarily make it "a true fact".
Let a = b
now multiply both sides by a
Then a^2 = ab
now subtract b^2 from both sides
Then a^2 - b^2 = ab - b^2
now factor both sides
(a + b) (a - b) = b(a-b)
now divide both sides by (a-b)
Then(a + b) = b
but b = a
Then 2a = a
now divide both sides by a
Then 2 = 1
See what happens when you violate some of the rules in Math?
Rick
Comment