But the new law doesn’t look like the old law plus a special clause exempting the exception. It looks like a single, universal, mathematically simple, coherent statement, and it is then very clear that the old law was simply the approximate behavior of the new law under certain special conditions, the way that Newton’s old laws of motion are simply the approximate behavior of Special Relativity under conditions in which the relative motion of particles is very slow compared to lightspeed.
The universality of the law is not a sophistry; the universe really does look that way.
A while ago, I came across a mathematics problem involving the calculation of the length of one side of a triangle, given the internal angles and the lengths of the other two sides. Eventually, after working through the trigonometry of it (which I have now forgotten, but could re-derive if I had to), I realised that it incorporated Pythagoras’ Theorem, but with an extra term based on the cosine of one of the angles. The cosine of 90 degrees is zero, so in a right-angled triangle, this extra term disappears, leaving Pythagoras’ Theorem as usual.
The older law that I knew turned out to be a special case of the more general law.
I wish that I had slept properly. My comprehension skills have dwindled to the point that I am completely unable to grasp even the simplest statements. Perhaps this material is too advanced for me. I need to study science before returning to this forum. I need to stop being a willingly blind and childish idiot.
But the new law doesn’t look like the old law plus a special clause exempting the exception. It looks like a single, universal, mathematically simple, coherent statement, and it is then very clear that the old law was simply the approximate behavior of the new law under certain special conditions, the way that Newton’s old laws of motion are simply the approximate behavior of Special Relativity under conditions in which the relative motion of particles is very slow compared to lightspeed.
The universality of the law is not a sophistry; the universe really does look that way.
A while ago, I came across a mathematics problem involving the calculation of the length of one side of a triangle, given the internal angles and the lengths of the other two sides. Eventually, after working through the trigonometry of it (which I have now forgotten, but could re-derive if I had to), I realised that it incorporated Pythagoras’ Theorem, but with an extra term based on the cosine of one of the angles. The cosine of 90 degrees is zero, so in a right-angled triangle, this extra term disappears, leaving Pythagoras’ Theorem as usual.
The older law that I knew turned out to be a special case of the more general law.
I wish that I had slept properly. My comprehension skills have dwindled to the point that I am completely unable to grasp even the simplest statements. Perhaps this material is too advanced for me. I need to study science before returning to this forum. I need to stop being a willingly blind and childish idiot.