Recent content by PeroK

Everything. A finite open interval can be defined to have a midpoint in the obvious way. Compactification and Hausdorff distance have nothing to do with a basic question of mathematical terminology.

A quick search suggests that midpoint normally applies to a (finite) line segment.

There is no geometric midpoint. Whether zero is an algebraic midpoint depends entirely on how you define midpoint. More generally, things in mathematics are what they are defined to be. If you don't have a usable definition, then all bets are off.

My post related to the diameter of an object. If the length of the diameter increases at almost 2c, then the circumference of a circular object can increase at over 6c. And a circle could transform into an irrelugar shape with a much greater circumference in an almost arbitrarily short time...

This is not necessarily true. The diameter of an object could expand at twice the speed of light.

What you see in a scenario like this depends on the travel time of light from an event on Earth to your spaceship. This sort of effect is not in itself relevant to the theory of relativity. Indeed, in classical mechanics, you could in principle exceed the speed of light and you would see all...

If you want to go beyond popular science, then you could try An Introduction to Modern Cosmology by Andrew Liddle. This is at an accessible undergraduate level. Alternatively, you could start by studying Special Relativity. My recommendation would be Morin. If you search for that. The first...

The simplest mathematical example that illustrates an infinite universe is the number line. With 0 in the middle (although, geometrically, there is no definitive middle), the positive integers (1,2,3 ...) to the right, and the negative integers to the left. The line is infinite in both...

It seems that NASA is (temporarily) shut down. https://www.nasa.gov/shutdown/ :frown:

Which option for Velotic did you use?

This thread has highlighted that ultimately it is perhaps a matter of personal taste whether "nature is fundamentally probabilistic" or not. Let's go back to the simple example of a single radioactive atom. Taken at face value, there is nothing in the description of the atomic state that...

The obvious point is that you are not working on a specific problem, but on a grand unification of everything. If you were doing your own medical research, say, you might find something interesting. But, if you were working on the elixir for eternal life (simultaneously curing all cancers...

Physics books hopefully and not pulp fiction.

Here it is (note that this is an Advanced, research-level paper). It might be useful to see that physics isn't just about having an idea. The idea has to be refined and fully expressed mathematically. https://arxiv.org/abs/2503.24263 Note that it might be nonsense!

The best model for the universe suggests that its expansion will continue forever. There's no evidence that the universe will eventually contract and result in a big crunch, followed by a repeat of the Big Bang. That simplestic model does not fit the data. There are some advanced ideas about...