# Does the concept of infinity mean we have already 'been'?

A memory that frequently inhabits my consciousness is that of a lesson taught by my religious education teacher in senior school.

He likened the conditions and occurrences that resulted in the creation of the planet we inhabit to a hurricane in a junk yard resulting in the creation of a fully functioning car. An am impressionable child could easily digest that notion and shape their personality and life based on that notion.

While it sounds like a reasonable comparison, it fails to take in to consideration the concept of infinity, in this instance, relating to the conditions that existed before existence as we know it.

For example, the likelihood of the aforementioned eventuality occurring is obviously incredibly close to zero. But not zero. To apply that same notion to existence as we know it, given an infinite number of junk yards, and an infinite number of hurricanes hitting them, not only is it possible that a fully functioning car would eventually be produced, it is inevitable. In fact, not only is it inevitable it would occur once, it would occur an infinite amount of times.

No matter how unlikely the conditions that resulted in our existence would come to fruition, given an infinite amount of chances, it is inevitable that it would occur, not only once, but an infinite amount of times. While we exhibit behaviour indicative of free will, and maybe that is the case, given an infinite amount of chances, we would live the same life an infinite amount of times. Additionaly, we would live the same life, with one slight deviation, a slight difference in the pronunciation of one syllable, in one sentence, on one day an infinite amount of times.

That is not to say that each individual would “live”, and experience the events in the same consciousness, only that ones physical form would follow the same path.

Is that a reasonable interpretation of 'Infinity'?

• c.f. Boltzmann's brain
– Dave
Commented Sep 20, 2014 at 4:27
• What makes you think the universe is infinite?
– Dave
Commented Sep 20, 2014 at 10:51
• Ransack I'd mark your comment the correct answer if I could. I poorly worded my question so that no answer is correct. I should have framed it to ask if that scenario would be fair assuming both the expanse of the universe and time were both known to be infinite. But thanks to all that commented - some interesting thoughts.
– user9168
Commented Oct 15, 2014 at 23:16

It is simply not the case that "anything must happen" in an infinite sample space.

Consider the universe consisting of three possible states, A, B, and C. The universe recurs endlessly forever, taking states A, B, A, B, A, B, ...

Even though there are infinitely many instantiations of the universe, C never occurs. The best you can say is that some state must occur infinitely many times. But it's not the case that every state must occur.

And what if there's some fundamental physical reason that C can never occur?

Here's another example. 1, 2, 3, 4, 5, 6, 7, ...

No matter how far you go out, "2" will never reoccur.

It is simply false that "in an infinite universe, everything will eventually happen."

Now, you can make a probabilistic argument. Take the A, B, C examples and suppose that each state is equally likely, occurring with probability 1/3. Nevertheless, the states recur as A, B, A, B, A, B, ... and C never happens.

In this thought experiment, there is zero probability that C never happens. Yet, C never happens. How can this be? The answer is simply that in infinite probability spaces, an event with probability 0 can actually happen. It's just very unlikely.

A familiar example is "throwing darts at the real line," as the experiment is called. The chance of hitting a rational number is zero, because the measure of the rationals in the reals is zero. http://en.wikipedia.org/wiki/Measure_(mathematics)

Yet, the rational exist. I just did the experiment in my living room and my dart hit the number 2/3. How about that! Probability zero events can and do happen in infinite probability spaces.

So even the probabilistic argument that "in an infinite universe, everything must eventually happen" is false. Flat out false. It doesn't matter how many amateurs with Internet connections think it's true.

It's false.

• I regret that I have but one vote to give.
– user5172
Commented Oct 28, 2014 at 12:11

Infinity doesn't magically do things, so no this is not a reasonable interpretation of infinity. You need to combine infinity with something else, like say, an rolls of the dice to provide an outcome like what you're suggesting.

And generally it's the second bit that is controversial and less than obviously the case.

To wit, if I had an "infinite" number of grains of sand, it doesn't at all imply anything about the same events occurring twice. Conversely, if there are an infinite number of universes, then that would imply something there are such similar worlds or potentially identical worlds. But then controversy is tied up in the claim that there are such infinite universes. Same thing with trying to say the universe has been created and destroyed an infinite number of times -- but with the second one, my understanding is that contemporary science indicates that this is not happening insofar as the second law of thermodynamics cannot allow it to happen and the data from the expansion pattern of the universe makes it so the accordion theory is false.

• I didn't say explicitly, but in the scenario I outlined, infinity is being applied to the expanse of the universe, and to time.To apply the same reasoning to your rebuttal, a more fair comparison would be to say if you had an infinite number of grains of sand, not only would you have two identical grains of sand, but an infinite amount.
– user9168
Commented Oct 15, 2014 at 21:32
• Not quite sure what your comment is supposed to mean but one serious problem is the claim you'd have two identical grains of sand. Identity comes in a variety of forms and you would never get numerically identical grains of sand. You could probably get a lot of similar events where a piece of sand falls down the pile, but that's a repeated event only on the most trivial of levels. Children on that beach would not be required even given infinite time to make the same sand castle twice. Commented Oct 15, 2014 at 22:53
• A single grain of sand is composed of building blocks, atoms, arranged in a certain manner. While they all share a resounding resemblance, it would be incredibly unlikely to find two that share the exact composition. Events, motion, numericality aside, I'm saying given an infinite number of grains of sand, there would be two, ad infinatum that are identical.
– user9168
Commented Oct 15, 2014 at 23:09
• There's a lot of types of identity. Please look up "numerical identity". It is by definition impossible for two different things to have this. Commented Oct 16, 2014 at 1:10

Time does not necessarily go back infinitely into the past - read this funny lecture by Stephen Hawking for his explanation.

• Yea but what does he know, I mean, really.
– user9168
Commented Sep 20, 2014 at 13:04
• Well, what can I say, your question reminded me of what Hawking once said about infinity and your comment reminded me of what Einstein once said about it.
– nir
Commented Sep 20, 2014 at 13:17