|
|
|
|
|
|
by adrian_b
732 days ago
|
|
|
While in the mathematics of the later part of the 19th century and of the 20th century there have been developed many theories with very abstract concepts for which it may be claimed that those concepts have been invented in the minds of some mathematicians without a direct correspondence with the world experienced by them, such a claim would be false about almost any concept in the mathematics developed until the 19th century, because almost all older mathematical concepts are just abstractions of properties of the physical world. For instance, what happens when you connect the two electrodes of a battery to the pins of a semiconductor diode will differ depending on whether you negate the battery or not (i.e. you revert or not its connections). What happens with a ball (or with a thrown stone) will differ depending on whether its velocity is positive or negative, and so on. Additions and subtractions of physical quantities, therefore also negation, happen in the physical world regardless of the presence of sentient beings. Humans can recognize such properties of the world and give them names and integrate them in coherent mathematical models, but the base concepts are not inventions, they are the result of empirical observations. |
|
|
> What happens with a ball (or with a thrown stone) will differ depending on whether its velocity is positive or negative, and so on.
The velocity of a ball is a vector. Using a positive or negative number to describe it is a manner of convention. When you say that you threw a ball with “positive 7 mph” velocity, you need to explain what you mean.
One might argue that there really is a ball and that it has a velocity and that the velocity really is an element in a vector field originating [0] at the center of mass of the ball. Debating to what extent this is fundamentally true or is just a useful concept that people came up with would be interesting.
[0] In general relativity, space is not Euclidean (nor is it a flat Minkowski space), and velocity vectors are only really meaningful in association with a point in spacetime. You can read all about tangent bundles in Wikipedia :)