Originally Posted by

**sunshinewarrior**
Thanks for that Dr Rocket. Can I ask a related question about infinity?

A former teacher of maths once told me that the universe could not be infinitely old because it is impossible, mathemtically, to cover an infinite 'distance' and arrive at a specific point, ergo, it would not be possible to have a speicifc present if there had been an infinite past.

Something about this argument sounded shady to me, but my maths was not good enough to say whether:

a. his mathematics was faulty, or

b. his analogy between time and number was faulty

Any ideas?

It sounds to me like he may have been applying a mathematical model that is inappropriate.

From the way that you state the position it sounds like he was saying something like "If the universe is a deterministic dynamical system then the behavior is determined by the doefficients of the differential equations that describe it plus the initial conditions. So, if the universe is infinitely old there are no initial conditions and hence later states cannot be determined."

There is a problem with that statement. If you could measure the state at any point then you can apply the differential equations to determine the behavior at later points. If the equations are "nice" you may also be able to determine past behavior.

If he is making some other assertion with respect to "infinity" then the problem is even more murky. Analytic functions, those describable by an infinite Taylor series, are completely determined by their value on any set with a limit point. So, for instance if you know the value of such a function on the unit interval, it is completely determined over the entire real line. Penrose at least believes that the universe is describable with analytic functions (of several variables).

His argument to me sounds more philosophical than mathematical, and not particularly penetrating philosophy. In the 1950's Herman Bondi, a pretty decent mathematician, advocated a steady-state cosmology. With that comes an infinite time. Later knowledge shows that idea to not be a good one from the perspective of physics, but I think it does show that an infinite age for the universe is a possibility that would be accepted as mathematically valid.