Scientific Research Is Unreliable, Unreliable Scientists Report

Math is to scientists what weight training is to athletes.

Puny athletes are not great performers, mathematically inept scientists are not great either.

Originally Posted by Papewaio

Math is to scientists what weight training is to athletes.

Puny athletes are not great performers, mathematically inept scientists are not great either.

Biology is Chemistry.
Chemistry is Physics.
Physics is Math.

Essentially, everything is math.

Originally Posted by rvg

Essentially, everything is math.

Of course!

Mathematics isn't about calculations. Mathematics is a way of thinking, the calculations are just a result of that way of thinking.



EDIT: Oh, and I nearly forgot to add that mathematics is also the only true absolute truth in the universe.

Yep. The best thing about math is that it's universal.

Oh, and I nearly forgot to add that mathematics is also the only true absolute truth in the universe.

It would be more accurate to say that math is the only currently known absolute truth.

Mathematics doesn't exist in the universe. It exists in our heads. It is a made up tool we use to add precision to our attempts to categorize, describe, and where possible predict existence. Mathematics is perfect because it is a mental construct and not, per se, real.

Still all, a damned useful tool.

Mathematics is not really an "absolute truth". There are many cases of needing to pick your definitions and axioms just right for it to work out. You have to agree to 0^0 being 1, for instance or lot's of things involving factorials fall apart. This gets significantly less trivial when it comes to subjects such as topology and set theory which is where some of the most deep results and insights come from. One particular example of this has to do with the nature of infinity and infinite sets. Consider a function f(x) which maps x from the set of Reals to the range -1 to 1 (exclusive) using:

Code: [View]

f(x) = x / (1 + (abs(x))

It's clear that f is 'onto' (the entire range -1 to 1 is covered) and 'one-to-one' (for each x there is a unique value of f(x)). Therefore by a counting analogy there are exactly as many instances of x (i.e numbers in the set of Reals) as there are values of f(x). However, notice that each value of f(x) is also a Real number and therefore part of the same set as x. Therefore ...


On the other hand "Mathematics" is not made up as in "fantasy". It is every bit as real as "a metre" or "a Newton" or any SI unit or physics concept you care to name. It's rather more real in some senses than most of those such as "distance" or "time" because we know] that at a fundamental level "distance" and "time" are conceptual crutches that reality does not admit whereas reality does admit the notions of "addition" or "multiplication".

Originally Posted by Tellos Athenaios

Mathematics is not really an "absolute truth". There are many cases of needing to pick your definitions and axioms just right for it to work out. You have to agree to 0^0 being 1, for instance or lot's of things involving factorials fall apart. This gets significantly less trivial when it comes to subjects such as topology and set theory which is where some of the most deep results and insights come from. One particular example of this has to do with the nature of infinity and infinite sets. Consider a function f(x) which maps x from the set of Reals to the range -1 to 1 (exclusive) using:

Code: [View]

f(x) = x / (1 + (abs(x))

It's clear that f is 'onto' (the entire range -1 to 1 is covered) and 'one-to-one' (for each x there is a unique value of f(x)). Therefore by a counting analogy there are exactly as many instances of x (i.e numbers in the set of Reals) as there are values of f(x). However, notice that each value of f(x) is also a Real number and therefore part of the same set as x. Therefore ...


On the other hand "Mathematics" is not made up as in "fantasy". It is every bit as real as "a metre" or "a Newton" or any SI unit or physics concept you care to name. It's rather more real in some senses than most of those such as "distance" or "time" because we know] that at a fundamental level "distance" and "time" are conceptual crutches that reality does not admit whereas reality does admit the notions of "addition" or "multiplication".

But what of that is mathematics? Is it the function and its solution, or is it rather the method of thinking which allowed its creation?

Spoiler Alert, click show to read: 

I omitted the conclusion because it's much more fun if you draw the inference yourself but if you insist: the range -1 to 1 (exclusive) contains exactly as many Reals as the entire set of Reals. For an encore, note how multiplication by some constant A or addition by some constant B yields a different function with exactly the same number of outputs but mapped onto a different range, which by analogy proves the same fact about that range. We have found a quantity which appears in the same instant both "smaller" than itself and also "larger" than itself.

This quantity is known as the cardinality of the continuum (c).

Originally Posted by HoreTore

But what of that is mathematics? Is it the function and its solution, or is it rather the method of thinking which allowed its creation?

The question is whether or not the same thinking applied differently can lead to incompatible results. To stick with the theme: http://en.wikipedia.org/wiki/Continuum_hypothesis