Can infinity end?

[hantaba]

The concept of infinity is often used to describe something that is limitless, boundless, or goes on forever. In mathematics, infinity is a theoretical concept that represents an unbounded quantity or an endless progression. It is not something that can be reached or completed. 

However, in certain contexts, such as in discussions about the potential size or duration of the universe, there are theories that suggest that the observable universe may have a finite size or that the universe itself may have a finite lifespan. These theories are based on scientific models and observations and are subject to ongoing research and debate within the scientific community.

So, while the concept of infinity itself doesn't have an end, in specific contexts, there are theories and discussions about finite limits or durations. It's important to note that our understanding of the universe is continually evolving as scientific knowledge progresses.

[LingNeutron]

I think that when it comes to the question of whether the totality of an infinite number of objects can exist, it depends on the context and the concept of infinity being considered. In some mathematical systems, such as set theory, it is acceptable to work with infinite sets as a completed whole.

[wtf]

19 hours ago, LingNeutron said:

I think that when it comes to the question of whether the totality of an infinite number of objects can exist, it depends on the context and the concept of infinity being considered. In some mathematical systems, such as set theory, it is acceptable to work with infinite sets as a completed whole.

I agree with you that this distinction is the heart of the matter.

Mathematicians have a beautifully involved and highly abstract theory of the infinite. Yet nobody has ever demonstrated a completed infinity in the physical world in which we live. 

Some cosmologists speculate that beyond the visible universe, the universe as a whole may be infinite. If so, then it would be a question of physics as to whether set theory applies to physical infinities. 

I believe this is a question for many decades in the future. It has often been the case that crazy abstract math later becomes necessary to describe the world we live in. Riemann and others pioneered the math of non-Euclidean geometry in the 1940s, and everyone considered it a great curiosity but of no use to the physicists. 

Then when Einstein was struggling to formulate his general theory of relativity, one of his math buddies said, "Hey, math has just the thing for you," and showed him Riemannian geometry, which is the perfect mathematical setting for relativity. Einstein reportedly said that when he got his own theory back from the mathematicians, he no longer understood it.

So this is my thesis, or my belief. That some genius not yet born is going to find a use for infinitary set theory within physics; and that breakthrough, whatever it is, will enable the next huge leap in scientific understanding.

I also think that answer to consciousness is NOT to be found in today's understanding of computability and AI; but rather within some future scientific revolution. Our current focus on computer AI is on the same level as the 18th century vision of the world as a great machine. Whatever is the technology of the age, we think the universe and/or our minds are that thing. We are not 18th century clockwork machines, and we are not computers as we currently understand them. 

I think the mathematics of the infinite is the key to the next revolution in physics; but that we're many decades or a century early. 

Edited July 18, 2023 by wtf