Q&A: Infinity
Infinity
Question
Is infinity possible in reality?
A. After all, if reality has existed for an infinite amount of time, we would never have reached this moment, since we would have had to pass through infinitely many moments before the present moment. That would imply that infinity is not possible, at least not in reality.
B. On the other hand, any stretch of time, even the most minimal one, is infinite.
For example, from 12:00 to 12:00 and one second,
one second has passed; that second contains infinitely many decimal numbers, meaning that from 12:00 to 12:00 and one second,
we have passed through one second that is infinitely many decimal numbers.
An infinity of decimal numbers is equivalent to any other quantitative infinity: an infinity of minutes, hours, and so on.
If so, how did we ever get to the time 12:00 and one second at all? After all, in order to reach the time “12:00 and one second,” we were required to pass through infinitely many decimal numbers, which means an infinite amount of time.
In summary, is infinity possible in reality?
If not, you will have to explain seconds, or time in general, in reality—use the paradox I presented in your answer;
and if infinity is possible in reality, you will have to solve the paradox presented at the beginning. Thank you for addressing this.
Answer
There are many misunderstandings here, mainly in mathematics. These are questions typical of Greek and medieval philosophers, but they do not trouble someone who knows a bit more modern mathematics.
A. You assume that if the universe has existed for an infinite time, then there is some point at which it begins and from there we move forward until we reach ourselves. But there is no such point. At most, you can argue that if you go backward in time, you will never reach an edge. The process you described is not well-defined. By the way, contemporary physics says that the world has not existed for an infinite time, but for about 14 billion years.
B. The fact that there are infinitely many points there does not mean it is an infinite amount of time. Every second on the timeline is made up of infinitely many points. So what? This is basically the (mistaken) paradox of Achilles and the tortoise.
Discussion on Answer
Who said anything about atheism?
I explained it. The fact that there are infinitely many points says nothing at all about the length of the segment. As for the paradox of Achilles and the tortoise, there are surely detailed explanations online.
You didn’t, I just mentioned it just in case.
If there are infinitely many time-points, and each point has a value greater than 0, wouldn’t that be an infinite amount of time?
^If* the night is confusing me
I also posted this in another question, looking for the answer.
A point has no length. But this really isn’t the place for math lessons.
Imagine a 1×1 square. Its area is 1. Now divide it in half and color it in. Of what remains, divide it in half and color that in. And so on to infinity. There are infinitely many addends, but you would agree that the area does not exceed the area of the square, which is 1.
What matters is not the infinite series itself, but whether it converges or diverges. Any series of accumulated seconds converges.
In addition, it is not true that an infinity of prime numbers is equivalent to every other infinity. Even among infinities, there is infinity that is countable (for example, the natural numbers) and infinity that cannot be counted (for example, the real and complex numbers).
A. I’m not an atheist; these are just questions that occurred to me.
As for the Big Bang, I read too many physicists who claim that it is not the beginning of the universe, but only the farthest point we can currently investigate… so I’m not sure what I think.
B. I’d be happy for an explanation of why this is a mistaken paradox.