Reality, Part 4 – Impossible Things

“…sometimes I've believed as many as six impossible things before breakfast.” – Lewis Carroll, The White Queen to Alice.

With Planck’s Quantum Theory, Einstein’s Theories of Relativity, Heisenberg’s Uncertainty Principle, and others, the first half of the 20th century presented us a lot of impossible things to believe. Of all of them, the one that is still the most unprocessed intellectually started with Kurt Gödel, a colleague of Einstein’s at Princeton. In the 1930’s he formulated his Incompleteness Theorem.

He more or less proved that logic can’t tell us everything that is true about our world. The “more or less” part is partly because the logic he used to prove this is the same logic he proves can’t tell us everything. If that makes your head spin, you’re in good company.

It has a relationship with undecidable or independent statements. A common example is, “This statement is false.” Is that true or false? Think about that for a few seconds—not too long! It’s called independent, because it’s independent of the true-false dichotomy. It simply doesn’t have a truth value. Like pairs governed by the Uncertainty Principle, if you try to pin it down on one side, it vanishes.

Gödel discovered that any useful line of rational thought will eventually encounter some statement that cannot be proved either true or false within that line of logic. It may be obviously true or false from another approach, but that other approach will also encounter a similar problem eventually, and so on. To be precise, Gödel’s proof was about statements in arithmetic, but if you can’t be sure about arithmetic, it’s hard to see how other lines of logic would be any better off.

What this means to us and our reality is still very much under discussion, but it’s clear that having to change our logical system constantly and forever in order to understand our world puts all our rational conclusions on shaky ground.

This kind of thinking led later to Alan Turing’s discovery of the impossibility of solving the halting problem. He showed that there is no possibility of knowing beforehand that given premises will lead to any conclusions at all, no matter what logical approach you take. Bottom line from all this: it isn’t just faulty logic that causes problems in our understanding, logic itself has built in problems.

In addition to the problems of logic you also have the problem of the premises themselves. Logic doesn’t start from nothing. It must have something that “everyone knows” without proof or question. In addition to what I’ve already said about that, let’s look at the fundamental elements of our physical world.

In one of my first series of posts, “Time and the Origin of the Universe”, I identified space, time, motion, and mass as being completely interrelated and inseparable. They always appear together in the concept of momentum. You can’t have any one of the four without the other three and measuring any one of them depends on an ability to measure the others. That’s a non-starter because you can’t measure any of them independently.

You can find my complete discussion in “Time and the Origin…”, but think just of time. Everyone knows how long a minute is, right? Well, we agree on it when referencing a clock, but that isn’t the same thing. In order to measure something, you must have something outside it to compare with it. One minute is how long it takes a given clock to move a certain distance or oscillate a certain number of times. We find consistency in how different clocks measure time. (As long as the clocks are together, and we don’t ask for TOO much accuracy!) but clocks are not outside of time. If the rate of the flow of time were changing, all the clocks would change with it. Just being consistent in their measurement doesn’t mean that what they are measuring is stable.

We know how long a meter is because there is an international standard meter of length that we compare all our rulers to. We know how long a minute is, because there is an international standard clock that we compare all our clocks to. But if time slowed down, so would that international standard along with all our clocks. They would still match, and we would never notice a change.

I’m not talking about the effect of relative motion and gravity on time as described by special relativity. I mean here and now, wherever you are, in an inertial reference frame with no relativistic effects. Time could be changing its rate of flow and you would never know it, because everything about your life would change with it: your heart rate, your blood flow, the neurons firing in your brain, the speed of light, and, of course, your clocks, including your fitbit. Everything derived from measuring time would adjust also, and that’s, well, everything we measure.

How long a minute is objectively is unknown and unknowable. We can’t measure time itself. If we can’t measure time, we can’t measure anything.

None of this makes science stop working, because absolute measurements don’t matter to us if our relative measurements are consistent within our existing theories, but it does further undermine the logical foundations that we assign to science. Once again, we are left with a priesthood preaching a reality to us, and I suggest our faith in what they tell us is the source of the tenets of the reality they preach. If we all believed something else, we would find priests and priestesses to preach it to us, and it would be just as true for us as science is now.

I am very pro-science. I believe that science is the best interpretation of reality we have, and we need to hang onto it. I want us to understand that science is fundamentally threatened today. If we want to preserve it, we have to understand its weaknesses. Gödel, Turing, and others have posted warning signs that we should heed. The worst defense you can make for anything is to claim something about it that isn’t true. Science is not absolute, even ideally.

We have time. There is a great deal of conceptual inertia in billions of shared perceptions, and “water runs downhill” is one of the few things on which we have a pretty solid human consensus, so the perceived permanence of scientific reality is persistent. But maybe it wasn’t so persistent when humans were fewer and lived in more isolated groups. This viewpoint sheds a very different light on early human culture. It also gives us pause when considering where the collective human perception may be headed next.

Hugh Moffatt

Waltham, Massachusetts

September 7, 2019