Transinfinite Numbers and Paradigms

A rare science post. I started to write this as a comment on a post by Dave Jorm, then put it here, because nothing annoys me more than people who use the comments section to try to write an article of their own.

Dave wrote about Transinfinite Numbers. This is not really a response to that, but a different post on the same subject.

You see, funnily enough, I had a discussion with a work mate on this very subject today, as you do.

He was saying that the complete set of integer numbers was an unbounded, infinite set. I said that he didn't know that, and that it had never been experimentally verified. He then said that the proof is that you can think of any number, and then just add 1. And then just add 1 to that, and so on.

The problem with this proof is that you may run out of numbers. Just like on a computer. If you exceed the number of bits allocated for a number, it becomes negative, or rolls over, or causes an overflow.

Similarly, we do not know the extent of the universe. It is possible that it is infinite, and in my opinion it is probably designed in such a way that overflows cannot cause system crashes. However, we don't know that until we run into the condition that will cause it to crash.

Just like software design. Theoretically your system works fine, until someone who doesn't know what they are supposed to do jumps on it and starts using it. Similarly, theoretically you just keep adding 1 and there is another number there. But maybe not...

It's the axiomatic assumption of Western science at work: "The laws are the same everywhere and at all times for all people". Without this fundamental assumption you cannot extrapolate from a small example to some larger generalization. It works in a lot of case, most cases, maybe all cases. But maybe not.

Just as we had to extend the paradigm of Newtonian physics to Einsteinian physics to resolve dilemmas that we encountered as we expanded our experience, we may find that we have to abandon or recognize the limitations of other paradigms. In fact it's inevitable. History shows us that the progress of empirical science means exploring one paradigm to its limit, then finding out that it is actually a special case that has an application at a certain level, and we need another paradigm that transcends it to explain the situation more fully.

According to the Vedic understanding, fundamental laws of physics are experienced differently at different times, in different places, and for people at different levels of consciousness at the same time in the same place.

This allows the Vedic paradigm to present consciousness as a phenomenon categorically distinct from matter and energy. The modern hand wavy idea that consciousness is merely an emergent property of the brain is not supported by the Vedic conception. It's a separate phenomenon entirely. The Vedas have their own analogies to explain this. One is that consciousness is that which experiences, whereas matter and energy are that which is experienced. This is referred to as ksetra and ksetra-jña, or the field and the knower of the field.

Anyway, we'll find science and the Vedic conception converging more and more as we empirical science advances and is forced to change paradigms. This journey is discussed in the famous book "The End of Science", by John Horgan. Truth is truth, and whether you get there the long way or the short way, it's the same destination. Bahunam janmanam ante.

That's enough of that. The conversation evolved from there, and Brian, my work mate, explained to me that no matter where you are in the universe (as far as he knows), it looks like everything else is receding from you. He gave an analogy of a balloon that is being blown up. No matter where you are on the surface of the balloon, every other point on the balloon is receding from you.

How that works in three dimension space, or rather four dimension space-time, I'm not sure. I was trying to imagine how to model that in my head, or a software physics simulation engine. What does that look like, where everything is receding from everything else. Surely that would mean that something was moving toward something else?

Anyway, my godsister Carana Renu has a Ph.D. in Astrophysics. Maybe she knows something more about it. Next time I see her I'll ask her about it.