infinite doesn't mean every

I was reading through Slashdot’s article on the crumbling possibilities of space elevators, and came across an interesting quotation:

An infinite universe is no guarantee that everything will happen. There are many infinities. For example, there are an infinite number of numbers between three and four, but none of them are five.

That was interesting to me, as it kind of effects something I am interested in – abiogenesis; the idea that life can appear out of semi-random chemical interaction (i.e.; no God).

One of the most popular arguments against abiogenesis is:

The probability of a self-reproducing molecule appearing by chance is so small that it should be considered impossible.

My favourite argument against that is:

In an inifinite universe, every configuration of molecules is not only probable, but inevitable.

The slashdot quote appears to negate that, by saying that even in an infinite universe, there may be impossible configurations. This is correct, but doesn’t really affect my belief in abiogenesis – my justification can be saved by adding one single word:

In an inifinite universe, every possible configuration of molecules is not only probable, but inevitable.

i.e.; in the original quote, it is impossible to have a number 5 which appears between 3 and 4, even though there are an infinite numbers that do appear between 3 and 4. However, the opposite is true – every possible number which is greater than 3 and lesser than 4 is most definitely part of that infinite set of 3<n<4.

So, if there is a molecular configuration which supports life and is possible to replicate in this universe, then it is inevitable that it will appear at some time, given that the universe is infinite.


  1. Just some thoughts from the top of my head it may be gibberish but see if you can follow my train of thought.
    So there is an infinate number of numbers between 3 and 4 for eample some of the numbers are 3.1, 3.2, 3.3, 3.4, 3.5…. ok there is a 5 being used a number reprentation from outside the group so a concept from outside is used within for example 5/10ths or half and what is 5 but the half way point of the digits. So I am wondering if the numbers between 3 and 4 are a subset and can not exist without the other numbers so since one exist the other must hence 5 is still a possibility since the two must both exist. So we have dependent or coexisiting infinities where one must exist if the other does and if that happens all infinities must be accounted for.

    I don’t think I explained that well, it is not one of my stong points. I hope you understand the concept.

  2. I understand what you mean. You are saying that, to represent the numbers between 3 and 4, we utilise symbols which also represent numbers outside that range.

    That’s an interesting point, which says that we can at least describe concepts that are currently outside our experience, using symbols that are within it (ie; it should be possible to describe an object which cannot exist in this universe, without getting into brain-melting multiple-dimensions).

    I think this is like the Platonic idea of life being a silhouette – we see the silhouette, whereas life is actually much larger than that.

  3. I think it goes a little farther then symbols but into concepts, objects and or ideas.

    In order to have the infinity of numbers between 3 and 4 we must have the infinity of positive numbers and the infinity of numbers and all the infinities within.

    Which makes me now think that the infinity of numbers between 3 and 4 is just a section of a larger group and not the whole set, so using the universe as our anaology. I think the numbers between 3 and 4 could be the number of suns in the universe and none are a planet, but both are part of the universe.

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