Kurt Gödel

We live in an age of ubiquitous information.

Information, thoughts, ideas. Everywhere.

But what is true and what is false?

What is designed to deceive, to prevent the reveal of a deeper secret?

How to test for truth?

We have our own first hand experience, and that of people we know and trust, at least on some subjects.

We have observations of all kinds, forecasts too.

Plus ca change, plus la meme shoes.

Now if the weather forecast says its 30C in Ottawa and I go outside and freeze, do I conclude they got the units or the sign wrong?

Over-time the thermometer in the pi should agree very well.

So if someone regularly reports a temperature different to the observation, what can we conclude?

It is questions like these Gödel explored and proved a remarkable theorem about mathematics.

Gödel proved that there were some statements in mathematics, that always hold true, but for which there is no proof that it is so.

His proof centred on creating a self-referencial statement. The mathematical equivalent of the coaster that has, “the statement on the other side of this coaster is false”, on one side and “the statement on the other side of this coaster is true”, on the other.

With the arrival of computers, Gödel’s work scotched the plan of some magical algorithm to test the truth of any conjecture.

Mathematicians were back in business, ironically because they may be working on things that were impossible to prove, yet also impossible to disprove. A doomed quest of eternal hope, never finding a counter-example.

How many people about the world are intrigued by truths that cannot be proven?

How many are working on problems that have already been solved elsewhere?

Or are lacking some key bit of knowledge someone else has?

Working with some incorrect assumption in their model of the universe.

Perhaps something undecidable in our world?

Gödel also studied Einstein’s equations of general relativity.

These equations are difficult to solve, they are inherently self-referential, which can pose lots of problems, most notably issues of causality, since time is involved in the whole equation.

Minor details like this were unlikely to discourage Gödel. He came up with a solution based on the assumption of a giant rotating mass of dust.

Time rotates too in this solution and at a certain, Gödel, distance it starts to go backwards in time.

In a Gödel universe, things can go round in circles forever.

Perhaps there are symmetries where the time reversal part of the path just unwinds the history, so that when it arrives back at its origin, it is in exactly the same state as it left. No information is transferred in this process.

Are the only paths that go backwards in time those that are always, locally, travelling at the speed of light?

Did Gödel suspect that these matters might lay in the realm of the unprovable, due to the self-referential nature of Einstein’s equations?

I have found as I explore ideas here in blume land not to worry greatly about whether what I am trying to do is actually possible.

The spirit of blume is not to be overly concerned by whether something is possible or not, so long as it is possible for some reasonable proportional of the time.

It can result an a little going round in circles, whilst I decide which of the competing constraints really matters. Usually, during this process, the constraints change as other possibilities are considered.

blume has been an experiment in learning the python asynchronous world. It has taken a while to learn some new patterns of working.

As I have got more comfortable with the ideas, it has allowed me to think about problems from a different perspective. New language features such as await open up a whole different way of looking at problems.

This approach extends into the cosmology, asking the question of what would a universe look like, if it worked as Gödel proposed?

I believe, Gödel’s solution does not exhibit expansion, so would have been a Hoyle universe.

Now if we see this through de Sitter lenses, we get the appearance of expansion.

Based on the aggregate rotation of the matter in the universe. Twisting in on itself, whilst staying in place.

But this is just a feature of geodesics in de Sitter space, with a Gödel twist.

Which reminds me, I really need to get blume.dss working.

Oh and I see a blume.magic.Spell on the horizon.