Discussion»Questions»Science and Technology» The field of study known as mathematics and all of its rules and tenets; do you believe it's all man-made, or does it exist independently? ~
Does that mean that without mankind having described it, would it still exist? Does mankind have to acknowledge that two plus two equals four, or is it still true without mankind recognizing it? ~
Math is man-made, an extension of human logic. A fellow named Godel made quite a fuss when he published a proof that math can not be proved to be valid, it can only be proved to be internally consistent. That agrees with what I keep telling people: "Math is only valid when it describes reality."
Math is manmade, a form of deductive reasoning. Mathematical laws are man’s tested method of defining the unfailing consistencies found in the natural world.
The way in which we count is artificial but even allowing for the inconsistencies in Nature, the fundamental physical mechanisms follow behaviour that can be traced and described by counting - i.e. mathematically.
The artificiality in mathematics really comes down to how we describe things - but those things still happen in the proportions they do whether we analyse them or not; and irrespective of such details as the base of our number-system.
For a simple example, light travels at a set speed, but it doesn't matter if we measure it in metres or miles per second. Similarly, the ratio of circumference to diameter of a circle is always pi - no matter the units into which we divide the two measurements (as long as they are the same).
If this were not so, if Physics especially was not consistent and regular to an extent that yields readily to maths, we would not be able to discuss it like this - we would not even have electricity.
It is entirely man-made. Sometimes it can be fruitfully correlated to reality but that should only be done where the correlation holds true. Durdle mention the radius of the circle above. Here is an test for you: 1> Find a Horse saddle. 2> draw a circle on it using a pair of calipers 3> Measure the circumference of the circle you drew as best you can. 4> I am pretty sure that your 'circle on a saddle' will have a circumference a good bit greater than diameter*pi it is only on flat surfaces that that formula holds
This post was edited by JakobA the unAmerican. at May 4, 2018 4:51 PM MDT
Clause 4 doesn't prove anything other than the given point that the measured circle lies on a single, flat plane. Well, that is assumed unless otherwise stated.
I'm sure you can calculated the circumference of a "circle" drawn on an arcuate surface, provided the surface itself can be described mathematically, though the method would certainly be far beyond me. (I'd guess it involves a lot of calculus.)
However, if mathematics is entirely artificial then how come it describes so many natural phenomena so well? The only artificiality really, is in such details as the base of the counting system and the number of degrees we apportion to a circle - but even if you change them the rules themselves would still hold.
Pi may be called by some other number, but provided you are consistent in units, the diameter/circumference ratio (in one plane!) would be similar.
The characteristics of right-angled triangles, and the rules of simple harmonic motion and of the harmonic series, would still apply.
The acceleration due to gravity would be same for any given location, even if you count by different divisions of distance and time units: in fact we do that, by using either foot & second or metre & second units - but the physical event still follows the same rule.
Mathematics shows us what in Nature is numerically consistent, mainly in physics and chemistry; but it also shows those phenomena which are not. That does not prove maths is somehow weak or artificial; it proves not all of Nature can be analysed numerically so helps us understand better, both the regular and the irregular natural processes. Notwithstanding arithmetical syntheses like matrices and set theory, the only things man-made in maths, at a fundamental level, are number bases and the relative sizes of measurement units.
We have a simple formula to calculate where a thrown object will land, or any point along it's travel. If you consider a point outside the launch and landing, the math is consistent, telling you negative altitude and negative time. Those results are mathematically valid, but in the case of a thrown object they do not describe reality.
Math is not inherently related to reality. Mankind made it up. It reliably describes reality, but it is capable of unreal results too.
"... an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?
In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality..."
it is only on flat surfaces that that formula holds
This post was edited by JakobA the unAmerican. at May 4, 2018 4:51 PM MDT
Element 99 