Recent content by PeroK

... they are competing with humans for jobs. And they have largely won the competition with PF on student help.

It's better to think of an entangled system of two particles. The particles are not independent. A measurement of either particle is a measurement of the system. There is no causality, because the particles are part of the same system.

How do you know all this? Sounds like wishful thinking to me.

A singularity is where the mathematical model breaks down. The observable universe can't have expanded from a point in a physically meaningful way. You can, however, mathematically map a finite volume to a point. And that may or may not make sense physically. But, that mapping has no inverse...

History tells a different story. Look at the life expectancy of a slave on a sugar plantation. Or, the wholesale slaughter in WWI. The rich and powerful sent an entire generation of young men to the trenches.

Colour is a property of paint. But colour is a property of other things as well. Energy is not exclusively a property of matter. It can be a property of other things as well. E.g It might also be a property of the vacuum (dark energy). In any case, the main point is that matter is not...

Mass and energy are properties of matter (and of antimatter). Matter also has charge, spin and other properties, like colour charge etc.

It seems valid to me to see AI as potentially in direct competition to humans, in all respects. It's ironic that it requires continued human development of AI and that we may be creating the means of our own destruction. We've put ourselves at the mercy of economic and political forces that we...

It's not like that. A singularity is when a mathematical model breaks down. It's not a physical thing. Once you cross the event horizon, you only have a finite amount of time before the mathematical model breaks down. Most physicists expect that a theory of quantum gravity will explain what...

The natural numbers form a countably infinite set. You can partition the natural numbers into a finite collection of infinite sets. E.g. into odd and even numbers. Or, into sets depending on the remainder when divided by 10.

It's not very helpful to think of light as made of photons. There are two theories of light. First, there is classical electromagnetism, where charged particles create the electromagnetic field. There are no photons in classical electromagnetism. They are simply not part of the theory. A more...

We can also work backwards: $$a^3 \times a^{-1} = a^2$$$$a^2 \times a^{-1} = a^1 = a$$$$a \times a^{-1} = 1 (= a^0)$$$$1 \times a^{-1} = a^{-1} \dots$$In particular, there's no way that ##a^0 = 0## can fit that pattern in any shape or form.

I guess the rationale is this: Start with ##0##, add ##a## you get ##a##. Add ##a## again you get ##2a##. In this case you start with the additive identity (##0##). Start with ##0##, multiply by ##a## you get ##0##. And so on. That leads to nothing except ##a^n = 0## for all ##n##...

Why not define ##a^0 = 0##? And take it from there. For example: The usual index rule for all integers ##m, n## is: $$x^mx^n = x^{m + n}$$Whereas, your index rule is limited to non-zero integers ##m,n##: $$x^mx^n = x^{m + n} \ \ (m + n \ne 0)$$$$x^mx^n = 1 \ \ (m+n = 0)$$You could make a...

Yes, this is correct for the given problem. I hadn't understood it properly when I posted originally.