Take a six-inch stick and divide it in half. You now have two sticks made of three inches each. Now divide those halves in half. Keep dividing them over and over again. How many pieces can you divide them into?
OK, now take a football field, and divide it into half, and then again in half, and again and again. How many pieces can you divide it into?
This means that both a six inch stick and a football field are comprised of the same amount of pieces: Infinity. And that makes no sense.
If A/B=C, then CxB=A. So if six inches divided infinitely equals an infinite amount of pieces, that means if you take an infinite amount of pieces and line them up side by side, you’ll get a six-inch stick.
Or maybe a football field?!
The answer is, infinity is not a large number which you will reach if you count for a very long time. Infinity is unreachable. There is a never-ending (that is, an “infinite”) supply of finite numbers into which you can chop the stick – or the football field. Therefore, no matter how many times you chop up that football field, or that stick, the number of pieces will always be finite. You can keep chopping the pieces forever, but no matter how long you chop, you will never have an “infinite” amount of pieces. When we say you can keep chopping “for infinity” it doesn’t really mean you will ever chop the stick an infinite amount of times. Rather, it means you will never have to stop chopping - no matter how many times you have already chopped, you can always chop an additional time. You can go on like that forever. But because the amount of finite numbers never ends, the amount of slices you can chop that stick into never ends, and therefore, no matter how many times you chop that stick, and no matter how long you keep chopping, the amount of pieces that the stick – or football field – has been chopped into will always be a finite number. It will never reach “infinity.”
When we say that there is an infinite amount of finite numbers, we mean you can keep counting finite numbers forever. But no matter how long you count, you will never reach infinity, ever.
So if you are counting and counting and you have already reached a particular number, you can be sure that number is not infinity. Since infinity is not reachable, therefore, if you reached it, it is not infinity.
Now we are ready for our first question: The amount of time that has passed in all of history – if you were to add up every moment that has ever been, until now - will that amount of moments be finite or infinite?
If someone was alive from the beginning of time and had been counting all the moments of his life, all throughout the past until now – would he be still counting finite numbers or would he have already reached “infinity”?
Answer: He would still be counting finite numbers, since he could never reach infinity.
If the past would consist of an infinite amount of time, it would never be over. At no point would you be able to say “we have reached infinity”, since that point is unreachable.
The past, however, is over. Therefore, the amount of time that has already transpired in the past could never have reached infinity.
The past cannot be an infinite amount of time because the past is over, and an infinite amount of time can never be over.
As a syllogism:
If the amount of moments in the past is infinity, those moments would never be finished.
But the past has finished.
Therefore, the amount of moments in the past is not infinity.
This is based on the same idea as the answer to the stick-football field paradox, which appears problematic because it seems that even an inch can be divided up an infinite amount of times.
This means that an inch and a mile - which also is divisible an infinite amount of times - are really the same length.
But this is wrong, obviously, and the reason is because you can never divide up an inch, or a mile, an infinite amount of times. No matter how many times you divide up the distance, the resultant amount of parts will always be a finite number. So you will never, ever have an infinite amount of parts in any given line.
Infinity cannot be reached in real life, ever. You can never count until infinity. You can never have an infinite amount of anything that has magnitude. Therefore, if we already had a certain amount of moments in time, since each moment does take up time, the total amount of moments cannot be infinity.
And if the amount of time that has happened throughout history is finite, that means it had to have a beginning. There had to have been a first moment in time. If there was no first moment, then time would be infinite, and that would be impossible.
And since there had to have been a first moment in time, then something must have caused it to begin, because nothing happens without a cause. Time could not have just popped into existence without something causing it to do so. It makes no sense that something should cause itself to begin (see this post).
And the thing that caused time to begin must exist outside of time, because it was the cause of time. And if it exists outside of time, it must exist outside of space, because space can only exist within time.
And that means that the entity that created time:
1. Cannot change, because change means there is a “before” and “after”, and without time, it is not possible to have before and after.
2. It also means that the entity that created time was “always” here and “always” will be here. The cause of time had no beginning and can have no end, because to begin or to end cannot happen if there is no change.
3. It also means that this entity cannot be affected by any stimuli. Nothing can impact on it at all. Because that would entail a change, which cannot happen if something is not subject to time.