All proofs of something being noncomputable hinge on the assumption that infinite computing resources (computation and memory) do not exist. If we ask

Or phrased another way, what cannot be computed if we have infinite computational resources at our disposal? Is the answer "nothing"?

**February 17, 2014**

Maxwell's equations are taught in physics courses as the description of
light and magnetism. But those equations require mathematical concepts
(integrals and derivatives) that themselves are uncomputable. For example,
according to Maxwell a light ray passing through space involves energy
oscillating back and forth between the electric field and the magnetic field.
Maxwell's equations describe how at every point in space if there is a changing
magnetic field, this will give rise to an electric field. And if there is a
changing electric field, this will give rise to a magnetic field. Solving these
equations yields results that behaving like light beams travelling through
space. The solutions have sin() and cosine() elements, two functions of time
that are out of phase with each other.

Those functions require infinite precision in terms of *time* as well as
infinite precision in terms of *value*. This is typical of math, the
concepts in math can involve such imaginary, infinite precision. So there is
the question, if the universe we live in is described by equations that
themselves require infinite precision (and are therefore uncomputable by any
known computer), can the equations *really* be a description of what
is going on in the universe?

One thing we've observed about light coming to the earth, through telescopes.
It seems that the further away an object is, the more its light is red-shifted.
The common assumption is that means the object is moving away from us, and
the further away it is the faster it is moving away. This holds true for
pretty much every direction we look in. So people say, "Aha! This means there
was a Big Bang where everything blew up, and now we're seeing the aftermath
where everything is flying apart." But the Big Bang theory has so many glaring
holes in it that it *simply cannot* be a valid explanation of what
actually happened. There are objects in the universe older than the age of
the universe as demanded by the Big Bang theory. Moreover there are very
distant objects (quasars) that are unacceptably bright when considering their
red-shift. Halton Arp demonstrated that they are actually much, much closer
than commonly believed.

Ok, so we have a prevailing theory (Big Bang) that is part of the commonly
accepted explanation of reality, and part of that is Maxwell's equations for
describing how light moves around the universe. But Maxwell's equations depend
on infinite precision which itself is uncomputable. And light rays that have
been moving through space *for a very long time* seem to end up slowing
down (red shifting). Might there be some other explanation for the red-shifting
that will resolve all the issues?

Specifically, suppose the universe is computable, and there is not infinite precision anywhere (in time, or in space). Now that would mean that Maxwell's equations are only an approximation of the machinery that is active in the universe. Suppose the universe itself, operating with limited precision, exhibits waves moving through space that appear to remain unchanged (light) but suppose that there are effects that manifest themselves over very long periods of time. Specifically suppose a ray of light moving along appears to gradually slow down. This slowing down would appear identical to the red-shift associated with a light source moving away. Also suppose the slowing down is a necessary side effect of the fact that the universe is not operating with infinite precision. That is, suppose the slowing down in light frequency is a natural outcome of things like rounding errors in the computations.

Then we have a situation where the redshift we observe is *not* caused
by an exploding or expanding universe, and so there is no need to postulate
the Big Bang theory in the first place. So the universe can be very much
older than we've been assuming, and so the objects in the universe that are
so inexplicably old now will pose no problem at all. And finally, if the
universe *does not* demand infinite precision in order for its operation
we can feel a sense of relief that it is in fact computable.