Seafang said:
Well I think it is necessary to distinguish between Physics and Mathematics.
Physics is presumably the study of observable phenomena; things we can actually 'see' and 'measure'.
Mathematics on the other hand is pure fiction; we made it all up in our heads. There is absolutely nothing in mathematics which exists in the real universe.
Nice statement! Where did this come from?
Let try
phys·ics (fzks)
(Physics)
n.
1. (used with a sing. verb) The science of matter and energy and of interactions between the two, grouped in traditional fields such as acoustics, optics, mechanics, thermodynamics, and electromagnetism, as well as in modern extensions including atomic and nuclear physics, cryogenics, solid-state physics, particle physics, and plasma physics.
And Mathematics is the universal language that this thread is requesting an answer for the age old question. The problem is the variant minds who offer their interpretation; do they know enough language to address this question?
Well Taoist, I am not sure of the meaning of your question; "where did this come from ?"
I thought it came from a post I just typed in and which you cited; that is where it came from. Does 'stuff' need some annointed source before it can be understood?
As for mathematics being a "Universal Language", nothing could be further from the truth. As I said it is all fictional and we humans made it up in our head. There's nothing fundamental about it.
Anybody can invent their own mathematics merely by stating some axioms, which then become assertions of truth, and then based on that you can twiddle knobs and see where it all leads.
For example suppose I assert the following axioms:
1/ Two points define a line, which passes through the two points.
2/ Two lines define a point, which lies at the intersection of the two lines.
3/ There are at least four points.
Can I do anything mathematically interesting with that set of axioms.
Well yes I can. For a start axiom 2 establishes that this must be a two dimensional mathematics, since in ordinary Euclidean geometry, I could have two lines which lie in different planes and never intersect anywhere, but when confined to a plane, any two lines intersect as asserted by the second axiom.
What about parallel lines you might ask; they don't intersect. Well maybe they don't in Euclidean geometry, but in this mathematics they do; axiom two says so. Does that mean there are no parallel lines in this mathematics? No it doesn't ; parallel lines exist, and they do intersect, in fact parallel lines intersect at a point on 'the line at infinity'. Which is the definition of the line at infinity. so now I have removed the parallel line anomaly, but can I do anything or prove anything with thatset of axioms.
Well I can prove as the first theorem, that there are at least seven points. This comes very simply from drawing the four points which axiom 3 says exist, (I suggest an irregular quadrilateral shape) and then using axiom 1 to draw the lines that form the four sides of that polygon.
Two more lines can be drawn namely the diagonals of the quadrilateral, and you will see that three new points exist, making a total of seven.
Unfortunately, I cannot prove that there are any more points than seven, but there are at least seven points.
Sounds pretty useless doesn't it. But in fact every single theorem of Euclidean plane geometry can be rigorously proved within the confines of this decidedly non-Euclidean geometrry. There are some surprises. Circles and the conic sections ellipse, parabola and hyperbola exist, although cones don't, and most surprising; whereas in Euclidean geometry, a circle is a special case of an ellipse, that is not true in this geometry, a circle becomes a special case of a hyperbola. Even more strange is that all possible circles intersect each other, and they do so at two special points called the circular points at infinity (they lie on the line at infinity).
Ellipses don't touch the line at infinity, parabolas touch the line at infinity at two coincident points, and hyperbolas cut the line at infinity at two points. If those two points are the circular points at infinity, the hyperbola is also a circle.
Now try findng something elsewhere in the universe that corresponds even vaguely to this mathematics which somebody a long time ago, made up from those three simple axioms.
Mathematics is about as universal as the baseball world series.