Tag: Godel

Reason is a limited process and can never explain everything objectively

Reason is a limited process because it arises from consciousness, which observes the universe via filters. The mind has physiological filters (ex, wavelengths of light you can perceive, frequencies of sound you are limited to), chemical filters (the specific biochemistry of your brain, your mood and emotion, etc), and mental filters (pre-existing ideas and biases, fidelity of your metal models and assumptions, simple lack of knowledge). These are all best understood of as filters between you and the “objective” truth of reality. The universe as you observe it and understand it is vastly more complex than you can understand. The process of reason happens only with information you can process at the end of that chain of filters, so you are always operating on an insufficient dataset.

The brain is actually evolved to extrapolate and infer information based on filtered input. The brain often fills in the gaps and makes us see what we expect to see rather than what is actually there. Simple examples are optical illusions and the way the brain can still make sense of the following sentence:

Arinocdcg to rencet rseaerch, the hmuan brian is plrectfey albe to raed colmpex pasasges of txet caiinontng wdors in whcih the lrettes hvae been jmblued, pvioedrd the frsit and lsat leetrts rmeian in teihr crcerot piiotsons.

As a result, there are not only filters on what we perceive but also active transformations of imagination and extrapolation going on that actively modify what we perceive. These filters and transformations all happen “upstream” from the rational process and therefore reason can never operate on an untainted, objective reality. Despite the filters and transformations, the mind does a pretty good job, especially in the context of human interactions on the planet earth (which is what our minds and their filters and transformations are optimized for, after all). However, the farther up the metaphysica ladder we go, the more we deviate from that optimal scenario for which we are evolved (or created, or created to have evolved, or whatever. I’ve not said anything to this point that most atheists and theists need disagree on).

A good analogy is that Newton’s mechanics were a fantastic model for classical mechanics, but do not suffice for clock timing of GPS satellites in earth orbit. This is because Newton did not have the tools available to be aware of general relativity. Yes, we did eventually figure it out, but Newton could not have ever done so (for one thing, his civilization lacked the mathematical and scientific expertise to formulate the experiments that created the questions that Einstein eventually answered).

Godel’s theorem makes this more rigorous by demonstrating that there will always be statements that can neither be proved nor disproved by reason. In other words, as Douglas Hoftstadter put it, Godel proved that provability is a weaker notion than truth, no matter what axiom system is involved. That applies for math and it applies to philosophy, it applies to physics and it applies to the theism/atheism debate.

Related – more detailed explanation of Godel’s Theorem and implications on reason.

cargo cult quantum physics

From time to time I encounter people online who are enamoured of quantum physics in a dilettante sense, obsessed with the implications upon macroscopic reality, and the broader philosophical questions about what is real anyway. I’ve come to think of their arguments as “cargo cult physics” because in a way, they simply snowball the debate with terminology, quote papers, etc and basically obfuscate beyond the capability of anyone to really follow what they are saying.

Here’s an example from a particularly painful (for this, and other reasons) thread at Talk Islam.

aziz 3:03 pm on January 26, 2011 Permalink | Edit
Keid, you take the extremist position that there is no reality – and then you insist that reality is only empirical. There’s a fundamental tension that not even Godel can save you from here.

I welcome your intellectual pity, and i reciprocate.

THE 6:56 pm on January 26, 2011 Permalink | Edit
OK deconstruct. I am not saying there is no reality. (How could I possibly know that?). I am saying reality is for us a theory.

Now it’s very possible that it is a true theory. It certainly agrees with all the empirical evidence, in the information flows we have access to, that there is an external causal reality. That external stuff also seems to form our physical substrate.

But we try to make theories now about the nature of that external & substrate-level reality. We start to understand that although it obeys rules that seemed to be mechanical when we first started to study it, the deeper we go into the structure, the more it becomes abstract and information-like.

Particles become quanta become qubit states in a information-bearing field?

Also very important this: The whole notion of a continuous space with continuous fields, breaks down as you get to the Planckian level, 10^-35 meters. So we need a new paradigm.

So now we postulate: Is there a supportive subPlanckian substrate to the entire world? Presumably it could be even more information-like, more abstract. Could it be pure information?

How could this work?

Well there are clues. Number one IMHO is the holographic conjecture. We can reinterpret the quantum fields that make up the universe as a isomorphic to fields in an outgoing 2 dimensional surface at the edge of the universe. The area of that surface has to be quantized into planck-sized areas. Could it be a cellular lattice of some kind? In some, as yet unknown, geometry?

Then the information could be qubits being exchanged between cells in that geometry.

Understand that lattices can arise naturally, e.g Crystals. Geometry just has to have the right symmetry, thats all, to form repeating cells capable of computation.

I know this is vague and impressionistic, but I’m not a real physicist and I’m out of my depth here.

As you can imagine, I’m paying a lot of attention to current attempts to confirm Hogan’s noise.

THE 8:12 pm on January 26, 2011 Permalink | Edit
I found Paola Zizzi’s paper thought provoking.

How to respond to this? Well of course, reality is a theory. But it’s a damn good one. The entire point of theory is to approximate reality in a useful way. Invoking crystals and quantum cubits and whatnot is just adding noise. Unlike Hogan’s noise, this noise is well confirmed.

Anyway I am not trying to pick on my interlocutor here, just frustrated with the way these sorts of debates turn out. Basically it’s all a condescending attempt to wave big words around at me to intimidate me because I have spiritual faith. Pointing out I have a PhD in physics is kind of pointless here. I believe in God, so I must be an idiot on some fundamental way, and here’s the proof: [insert gibberish].

You see the same sort of thing with people who believe in Singularity – but I’m a Singularity skeptic.

proving Gödel

The implications of Gödel’s Theorem are profound. A full understanding of its implications is not restricted to math professionals, however – there are numerous books that have addressed Gödel, aimed at a layman audience. Of these the most famous is Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas R. Hofstadter. That’s a book that every geek needs to have on their bookshelf. However, there are many more, and short excerpts from many of these books on the topic of Gödel have been compiled in one place.

The most powerful explanation of Gödel is to simply restate its proof in general terms. That proof, originally published in Infinity and the Mind by Rudy Rucker, is reproduced below (courtesy of Miskatonic.org).

1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
3. Smiling a little, Gödel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G for Gödel. Note that G is equivalent to: “UTM will never say G is true.”
4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.
5. If UTM says G is true, then “UTM will never say G is true” is false. If “UTM will never say G is true” is false, then G is false (since G = “UTM will never say G is true”). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
6. We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”).
7. “I know a truth that UTM can never utter,” Gödel says. “I know that G is true. UTM is not truly universal.”

As Rucker says, think about that a bit. It grows on you. Rucker goes on to explain,

With his great mathematical and logical genius, Gödel was able to find a way (for any given P(UTM)) actually to write down a complicated polynomial equation that has a solution if and only if G is true. So G is not at all some vague or non-mathematical sentence. G is a specific mathematical problem that we know the answer to, even though UTM does not! So UTM does not, and cannot, embody a best and final theory of mathematics …

Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth … But, paradoxically, to understand Gödel’s proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Gödel’s name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it.

The castle to which he refers is Reason itself.

Or, as The Hoft put it:

Gödel showed that provability is a weaker notion than truth, no matter what axiom system is involved.

(for more on the limitations of reason, and the false promise of what Hofstadter called “super-rationality”, see Super-Rational blog.)

The Tao of Scientism

Daniel Dare is one of those web personalities you come across who you might initially think is a crank, but after integrating over time you see that they have a subtle depth. He’s largely hostile to belief and subscribes to the Dawkins ultra-rationalist condescension of spiritualism. I haven’t asked him directly but I suspect he would strenously disagree with the inconvenient truth that rationality itself is flawed. At any rate, he’s got a blog and it’s worth subscribing to on RSS.

I think he’d be one of the most interesting people in Twitter if he were to get the Zen. In the meantime, I’ll settle for his Tao.

Douglas Adams and God

What is especially striking about the Hitchhiker’s Guide to eth Galaxy is how insightful it can be on matters of religion, given that DNA was(inhis own words) a militant atheist.

I had the privelege of asking Douglas Adams a question about religion directly, at his own blog some years ago. The full exchange went:

Continue reading “Douglas Adams and God”