Tuesday, 6 March 2012

Infinity, eternity and cosmology

Infinity is any number divided by zero and does not exist in reality. It is purely a mathematical fiction, totally meaningless. For instance, it arises when certain values are fed into a mathematical equation, causing some term in the equation to be divided by zero. E.g.  Speed = distance travelled divided by the time taken. If a marble rolls forward in zero time its speed is infinite, regardless of whether it rolls forward a millimetre or a billion light years.

To assume it has any physical meaning or even any place in a mathematical expression other than to show the that the expression breaks down under certain circumstances, leads to profound absurdities.  It is the number beyond which no greater number can be imagined and there is no such number. Eternity is also meaningless – it just means an infinite amount of time. Here are just a few examples to show how meaningless are infinity and eternity within the realm of science.

 1. Infinity x infinity = infinity

2. Infinity divided by infinity = ????

3.Infinity – infinity = ????

4. Infinity squared, cubed or raised to any power, even to the power of infinity = infinity (‘raised to the power of infinity’ means multiplied by itself an infinite number of times)

5. Hilbert, a German mathematician (1862-1943) proposed a hotel with an infinite number of rooms, all occupied, specifically to illustrate the irrationality of infinity as a quantitative concept. A visitor turns up and asks for a room. The reception clerk says the hotel is full but he can make the first room vacant  by moving the guest in the first room into the second room as the second room occupant is moved into the third room as the guest in the third room moves into the fourth etc. etc. There is always an extra room at the end because infinity is always higher than any number one can imagine. In Hilbert’s fully occupied hotel an infinite number of new guests could be accommodated by this kind of shuffling.

6. Eternity. If the universe was eternal it would have existed for an infinite time and it would mean that everything had already happened an infinite number of times and one of the events that would have happened would be the end of the universe so the universe should not be here now. This does not accord with our observations.

Infinity and eternity have a place in poetry and metaphor, where they have qualitative rather than numerical meanings. Infinite love, infinite mercy and eternal life, for instance. No theory of science can use the concept of infinity with any expectation of being taken seriously. If an equation includes infinity it can only be as an expression of the equation’s limitations within certain boundary conditions.

Neverthless, some cosmologists use this concept with abandon, ignoring the fallacies which it implies.

Oscillating universe

It has been proposed that the Big Bang resulted from a previous Big Crunch, by which a universe imploded in on itself: i.e. the Big Bang is really a Big Bounce. This process is said to have been  going on eternally. This is supposed to avoid the need to posit a creation from existential nothingness, which would mean invoking an act of creation (Heaven forbid). What this theory overlooks is that each cycle of expansion and contraction must cause a higher entropy than the prevous one. If this oscillating universe is eternal it means it should now be one of infinite entropy – totally disordered and extending infinitely into space. Last time I looked this was not the case.

Such a model would mean that there had to be a first Big Bang, in a previous universe, since each cycle would be smaller than the one which followed it  (followed it causally not temporally, since between the cycles time would not exist). This follows, I understand, from the fact that each cycle would use a smaller proportion of the energy content, which would mean higher entropy and, consequently, a larger sized universe than the preceding one.


To avoid having to explain how this universe began in such a miraculous way some cosmologists have speculated that there must be an infinite number of parallel universes, one of which was bound to have all the physical laws and constants in place for the creation of sentient beings and the universe which has been revealed to us by scientific investigation. This is a non-starter for two reasons:

/1/ An infinite number of universes, apart from being intrinisically meaningless because infinity itself is meaningless, would mean having one universe which did not have any parallel universes.  There would have to be an infinite number of universes and just one universe at the same time. It is therefore a logical paradox.

/2/ An infinite ensemble of bubble universes, which some have proposed, expanding in all directions, would mean there had to be a point from which they derived. The ‘problem’ (and it is only a problem for those who deny a creation event) therefore remains – the universe had a beginning (Gen 1:1).

A theorem with fundemental implications for cosmological models involving cyclic or expanding universes or multiverses was published by Borde, Guth and Vilenkin in 2003. It is explained on this Youtube video.

It is becoming increasingly difficult, if not impossible, to avoid the conclusion that the universe was created. Should most cosmologists become theists I wonder how cosmology would develop. Personally, I think it would be a great boon to the science of the real universe which is huge and full of untold layers of mystery. There is no need to resort to magic by proposing unprovable and unfalsifiable cosmological models.