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Sharon Turner

EAP Teacher (English for Academic Purposes), Sabanci University

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Does infinity exist?

I have been reading a lot about mathematics and astrophysics over my summer holidays. The question I have in my head right now is 'Does infinity exist?' or is it just a term to express what we cannot compute or understand yet?

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    Aug 23 2011: I think infinity exists only as a means of description, such as found in mathematics for example, or any other thing that exists only in the abstract. I do not believe that it has any real existence in the universe such as infinite mass or infinite size. The word 'infinity' is a descriptive term and not a measure of size, and I therefore do not see how it can be applied to anything 'real', as real things can be measured.

    I have come across web sites, and maybe you have also, that claim that atoms can be subdivided down into infinity, and that they contain tiny universes within them, and no doubt tiny people as well. Although science has not yet been able to prove we have reached the ultimate elementary particle from which all complexity is built, there is very strong theoretical and experimental evidence to show that quarks could be it. Smaller than quarks enters the realm of energy, not particles, as in string theory. As matter has been subdivided down from complex objects, to parts of the whole, to molecules, to atoms, to particles, to quarks, at each stage we see a simpler model, each stage is less complex than the previous level. All of which is in perfect agreement with the Big Bang model that describes how all matter is built up from simple to more complex elements, stage by stage. So when breaking down complex objects into smaller parts, it would come as a bit of a surprise if suddenly an entire universe popped up at even smaller scales than wave energy. Entire universes tend to be a bit complex!

    However, if string theory is shown to be correct, then tiny loops, or strings, of vibrating wave energy may be the smallest, but they are not particles anyway, and strictly speaking quarks aren't either, as they can not exist independently outside of a particle.
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      Aug 27 2011: Thank you Nina for this clear and comprehensive answer. I have also been reading about quarks etc. over the summer and smaller scales etc. Can everything real be measured though? How about pure numbers? (I think this is the term?!? They have no scale attached as yet. Do you think that we will produce a scale for them?
      • Aug 28 2011: Numbers are an abstract concept and although they seem natural to us, they are not real phenomena, so the notion of size doesn't really apply to them in the same sense that the notion of sound or color doesn't apply to them (i.e. we cannot say what is the size of 17 in the same way that we cannot say what is the color or sound or smell of 39).

        We can, however, discuss the size of a number relative to another number (i.e. 7 is larger than -4 or 0 is greater than -1 etc.) or its absolute value (i.e. its distance on the real line (the x-axis) from the origin) which is usually called the magnitude of a number.

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