12. Gödel’s Incompleteness Theorem
At the risk of losing my audience, I wanted to cover this topic because I feel it underlies my justification for trying to cure my MS in an irrational way. If you start to haze over reading it, please just skip to the next chapter. While I try to explain it in a way that anyone can understand, I’m not sure how good a job I’ve done. I’m actually not sure that a good job can be done…
Gödel’s Incompleteness Theorem is the granddaddy of them all, since it applies to mathematics which lies at the very core of all science. One could safely call mathematics the ultimate Aristotelian “First Philosophy” because it is basic to all science before one adds the particular details of any one science.
Gödel showed that within a rigidly logical system, propositions can be formulated that are undecidable or indemonstrable within the axioms of the system. That is, within the system, there exist certain clearcut statements that can neither be proved nor disproved.
Hence one cannot, using the usual methods, be certain that the axioms of arithmetic will not lead to contradictions … It appears to foredoom hope of mathematical certitude through use of the obvious methods.
Perhaps doomed also, as a result, is the ideal of science – to devise a set of axioms from which all phenomena of the external world can be deduced.
Thus, Rationalism is by nature selflimited and unable to explain everything that happens to us in the world.
The bottom line is that Gödel’s incompleteness theorem gives me a rational basis to abandon Rationalism as my only source to seek a cure for this multiple sclerosis.
Why does this matter to me? It matters because of the subtitle of this book, “A Rationalist Seeks a Miracle Cure”. While that might appear to be selfcontradictory at first, Gödel gives it meaning again.
I remain a rationalist, even though I acknowledge that Rationalism is selflimiting. Rationalism is still the best system ever devised for finding truth. It simply is incomplete, i.e. some truths must be found outside it.
Here’s Gödel’s proof in plain English:
 Suppose we have a COMPUTER supposedly capable of correctly answering any question.
 Now consider the following proposition:
“The COMPUTER will never say that this sentence is true.”
 Now, what happens when we ask the COMPUTER whether that proposition is true?
 If COMPUTER says it is true, then “COMPUTER will never say this sentence is true” is false.
 If “COMPUTER will never say that this sentence is true” is false, then the proposition is false (since proposition = “COMPUTER will never say G is true“).
 So if COMPUTER says the proposition is true, then the proposition is in fact false, and COMPUTER has made a false statement.
 So COMPUTER will never say that the proposition is true, since COMPUTER makes only true statements.
 We have established that COMPUTER will never say the proposition is true.
 So “COMPUTER will never say the proposition is true” is in fact true.
 So the proposition is true (since the proposition = “COMPUTER will never say that this sentence is true”).
 We have thus produced a true statement which COMPUTER cannot make.
Therefore…
That ayahuasca may cure my MS, could well be a truth which Rationalism cannot support. However, what matters ultimately, is the truth. Not the method by which we arrive at it.
Bob thinks I have a neurotic and incorrect view of the meaning of Rationalism.
While I may indeed be neurotic, I think I understand rationalism about as well as it can be understood. Warts and all, it’s still the best system we’ve got. It’s just that it has failed me in this particular case. Gödel makes it possible for me to accept this.
11. Footprints of God
Over the last ten years or so, I have been involved in reading just about every science book I could get my hands on. It began with a book called The Arrow of Time. I remember, at the time, being blown away by how little science really could tell us about time. What it really is and why it is unidirectional. Apparently, all the formulas that science uses regarding time can be run in the opposite direction as well, and there’s great dispute over why, in reality, they can only be run forward.
I mean, if the passage of time isn’t understood, what is? So I picked up a copy of The Cosmic Code by Pagels. Another revelation. Quantum physics remains the most impossible to understand truth that we seemed to have discovered. This laid the groundwork for what was to follow.
Physics, biology, genetics, chaos, information theory, complexity, emergence… The list goes on and on. I would read each book and have a wonderful feeling afterwards that I understood more.
I came to the conclusion that what I had been looking for all these years or at least what had been motivating me was a sense that science seems to run into walls no matter which direction is chosen. Ultimately, all our measurements seem to turn into Cantor Dust when we take them out to their logical extreme. No ultimate answers. In any direction. Ever.
I might as well try to define Cantor Dust as I believe it is extremely useful in demonstrating what it is that I am trying to describe overall.
Here’s a quick rundown on Cantor Dust….
“For the Cantor dust example, we start with a large segment (the initiator), divide it in three equal smaller segments, and take out the middle one. This process (the generator) repeats indefinitely, producing the cantor dust.” ^{[1]} The “dust” consists of an infinite number of segments whose total length amounts to ZERO.
Thus was born the working title for a book I thought of writing, Footprints of God. The idea is that “God” (used here as a shorthand for the indefinable) has left its footprints behind on reality.
These footprints manifest as impenetrable barriers to the scientific explanation and understanding of reality. When I say impenetrable, I mean as defined by our best current theories of science. In other words, our science recognizes these barriers and is the source of their definition.
Quantum Physics
Of course the most obvious examples lie in Quantum Physics. Often described as one of, if not the most tested and validated theory in the history of science, quantum physics uses mathematical formulas to predict statistical outcomes of subatomic particle events. It works. Always.
The problem is in translating the math into concepts we can grasp. We can’t. All the various interpretations lead to conclusions that simply make no sense to us. Particles are both particle and waves. Or one or the other, depending upon which test we run.
Bell’s theorem shows that fasterthanlight information can be transmitted unlimited distance. A particle linked to another particle then moved to the other side of the galaxy will cause the other particle to set its spin direction when its spin is measured.
Classic monstrosities like Schrödinger’s Cat remain unanswered. The more we know about a particles location, the less we can know about its direction. And what is the meaning of “measurement” anyway. Doe’s this involve human consciousness in the actual creation of reality? Lots of people believe it does… It goes on and on like this.
Relativity
Einstein didn’t like the “dice throwing” involved with quantum physics, though he was one of its central creators. He is much better known for giving us relativity, both Special and General. E=mc2 is actually his way of telling us that matter, i.e. stuff is actually energy. A whole hell of a lot of it! Mass multiplied by the speed of light squared. (Approximately 300,000 kilometers per second!) Fine.
Except that his relativity theories left us with all sorts of things we can’t really comprehend as well. It predicted black holes… singularities where the laws of physics as we understand them cannot apply. What does apply in their place? By definition we can’t know.
And guess what? Hubble telescope has been turning up all sorts of evidence of black holes out there. So according to Einstein, our immutable laws of physics apply only to part of the universe.
Perhaps the most famous wall we can attribute to Einstein is the speed of light itself. According to the theory, matter cannot move faster than the speed of light. The universe has a speed limit. What happens is that the closer and closer matter moves to the speed of light, the more and more mass it acquires, (the more it weighs) until at the end point, matter moving at the speed of light will have infinite mass. That’s not possible, right?
Or is it? Black holes have infinite mass, by the same theory. Would moving matter at the speed of light just create another kind of singularity?
Life
We’ve been celebrating the decoding of the human genome for the last few years. Amazing piece of work! We’re engineering rats that glow green and goats that produce spider web material in their milk. Only a question of time till we get to the bottom of this problem and start creating life forms from scratch, right? Nope.
Putting aside the issue of the thousands of proteins created by each of the thousands of genes, we’re really no closer to understanding what makes things alive than we were in biblical times. Hard to believe, but there it is. We see how life is made up of chemical combinations of molecules. We have no idea whatsoever what it is that causes these molecular combinations to live.
Anyone who tries to identify what it is ends up creating a “black box” with some madeup term.
Perhaps the most famous of these black boxes is Vitalism which has been loudly put down by all reasonable scientists, but which remains the only modern attempt to explain life.
Complexity and Emergence
The newest “black box” to emerge, (heh!) is emergence. This is the word used to describe the fact that in nature, the sum is often more than the parts. Break the human body down into its chemical components and you’ll get an idea what that means.
The notion is that once a certain level of complexity is reached in a system, new structures, unrelated to the structures of the components, “emerge” out of the sum of the components.
The problem is that by their very nature, complex systems cannot be predicted. The very best anyone hopes for once this “science” matures is to be able to predict possibilities.
Although I am unaware at this point of any scientific theory that proves we can never penetrate this mystery, all indications are and have been, that it is indeed impenetrable. Another footprint.
All these “footprints” show us the limits of Rationalism as a method of finding truth. But the ultimate proof of the limits of Rationalism is known as Gödel’s Incompleteness Theorem.

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