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#1 Rabbi Shapiro

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Posted 30 January 2011 - 05:37 PM

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?

Infinity, right?

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?
Infinity, right?

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.

Time
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.



#2 mamash

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Posted 28 August 2011 - 10:17 PM

I have a question about the infinity argument. You wrote, "the past cannot be an infinite amount of time because the past is over, and an infinite amount of time can never be over." I understand that an infinite amount of time can never be over, but why can't you reach points along the infinite path? If the yellow brick road never started and never ends, and I decide to start placing mile markers, I'll eventually reach mile marker 50 even though it extends infinitely in the past and into the future. Why can't someone argue that the reason we reached the point we are now b/c someone decided to start counting? Why does time hypothetically being infinite prevent the progression of time?

#3 Rabbi Shapiro

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Posted 29 August 2011 - 07:44 PM

I have a question about the infinity argument. You wrote, "the past cannot be an infinite amount of time because the past is over, and an infinite amount of time can never be over." I understand that an infinite amount of time can never be over, but why can't you reach points along the infinite path? If the yellow brick road never started and never ends, and I decide to start placing mile markers, I'll eventually reach mile marker 50 even though it extends infinitely in the past and into the future. Why can't someone argue that the reason we reached the point we are now b/c someone decided to start counting? Why does time hypothetically being infinite prevent the progression of time?

That road represents the progression of time. Think of it as stretching out as time goes on - let's say one foot per second of time. Now I ask you: That road at any given point, the road that was constructed one foot at a time, between the beginning of the road and any given point you choose - is there an infinite distance or a finite distance? There cannot be an infinite distance because you would never have enough time to build, foot by foot, an infinitely long road, since you'd need an infinite amount of time for that and you will never get that amount of time no matter how long you wait.

Your mistake is that you are assuming that the road pops into existence all at once - an infinitely long road. But it doesn't. Time happens one moment after the next. That road is built one segment at a time. And so, there will never have been enough time to have already built that road an infinite length.

#4 AYidOnTheWayUp

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Posted 09 December 2012 - 04:59 PM

I have seen brought down that the Torah is infinite, is the Torah infinite and if so how can the medrash say it say it was "created" 2000 years before the world was created? Furthermore what is the meaning of "2000 years" before creation if there was no time at that point?



#5 taon

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Posted 17 December 2012 - 12:43 PM

Another question, it says elsewhere that Torah was created 974 generations before the world. How could both be true? I heard that Hilchos Gedolos says the two amounts are the same (which would make a generation about two years, i don't know how that works). According to that, the answer to your question is the same as why 974 doros. Namely, because the Torah should have been given after 1000 generations, but Hashem saw we couldn't last that long without it, so He gave it to us after 26 generations. So the other 974 were removed and either somehow counted from before creation, or it was  as if they were counted from before creation.



#6 yuiop

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Posted 17 March 2013 - 08:04 PM

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?

Infinity, right?

You can't split it smaller than the indiviudal atoms, the quantity of which is finite.  (and a *different* finite number than that of the football field)



#7 Rabbi Shapiro

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Posted 17 March 2013 - 08:33 PM

For the record, you can, but this is totally irrelevant. The fact that you can't split them is only because we don't know a way to do it - not because the size of an atom is too small to split.

 

Put it this way - if you like, don't "split" the atom into two parts - on paper, just divide  the length of the diameter of the atom by two. Same idea.



#8 Hillel

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Posted 15 July 2013 - 06:58 AM

I understood that the Rambam in the Moreh does not believe one can prove that the world is not infitely old and that we know about the world having a beginning based on the Torah.  Is that a mistake?  If not, then how does the Rambam deal with this logical argument regarding infinity?



#9 Rabbi Shapiro

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Posted 04 August 2013 - 02:38 PM

I understood that the Rambam in the Moreh does not believe one can prove that the world is not infitely old and that we know about the world having a beginning based on the Torah.  Is that a mistake?  If not, then how does the Rambam deal with this logical argument regarding infinity?

It's not a contradiction. In fact, the Rambam himself uses the above argument to prove a first cause. 

 

The Rambam's issue with the infinity of the universe is not that we cannot prove that the universe has no cause. Rather, we cannot prove that there was ever a situation where the world did not exist. In other words, Hashem created the world such that it is now 5773 years old. Hashem could have certainly created the world "earlier" or "later" than that, such that the world would today be much older or less old than 5773 years.

 

Now let's assume there was never a point "before" Hashem created the world. Let's assume that there was never a "pause" before Hashem decided to create the world. Meaning, the world always existed together with Hashem. 

 

Now how old would the world be?

 

That's the Rambam's problem. The reason this problem exists is because since Hashem created time with the world,there really enver was any "before" the world. Still, the world is only 5733 years old and not much older. So time started 5733 years ago. Could Hashem have made the world so that today the world would be 5755 years old? Certainly. And had He done that, time would have been created 5755 years ago, not 5733 years ago.

 

But what does that mean? If there was no time before the world was created, how can we say that time could have been created "earlier" than it actually was?

 

We will never be able to comprehend this because, as I mentioned above, our minds cannot comprehend existence without time, since we have never experienced it.

 

So we cannot prove logically that the world is any younger than Hashem Himself.

 

But even if that were so, the world would still need a Cause to create it.