Dennis Hackethal’s Blog
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Mysticism and the Mathematicians’ Misconception
Somebody asked on the Objectivism Subreddit:
What is the Objectivist answer to the nonduality philosophies?
In other words, I talk to religious people who claim that they can meditate into a state of pure consciousness where all is one, and that subject object duality is an illusion, etc. They sometimes ostensibly rope in science and such, too.
As I understand it, this is incompatible with objectivism, and I am seeking a good argument against this position.
Here’s part of my answer:
As far as we know, consciousness (and with it, the existence of a subject) is a property of certain kinds of information processing. Information processing is always a physical process. There is no such thing as purely abstract information processing (David Deutsch), so consciousness requires a physical substrate which instantiates it.
Therefore, physical objects always precede consciousness. Consciousness cannot exist without a physical reality. […]
I realize this is not an objectivist answer, but hopefully a physicsbased answer still helps.
That information processing, aka computation, is always physical, is, again, an insight by physicist David Deutsch. He built on Alan Turing’s work on computational universality:^{1}
[T]he model of computation [Turing] used was physical. Strips of paper divided into squares with symbols and a finite set of discrete operations on them. The universal Turing machine. And when he conjectured that this machine was universal for proofs, the phrase he used, was that it could compute anything which “[c]ould naturally be regarded as computable”. At the time, the word ‘computer’ meant a human being. […] Someone whose job was to manipulate symbols on sheets of paper. And the manipulators obeying the rules, human beings[,] are physical objects too. So, by ‘anything that [c]ould naturally be regarded as computable’, Turing meant: computable in nature – by physical objects. And by ‘provable’, he meant provable by physical objects.
Skipping a bit, Deutsch then calls the denial that information processing is always physical the Mathematicians’ Misconception:
But I soon found out that not everyone saw it that way. [Some] insisted that Turing’s phrase “[c]ould naturally be regarded as computable” referred to mathematical naturalness – mathematical intuition – not nature. And so [to them] what I had proved wasn’t Turing’s conjecture. It was about physics. So I asked some mathematicians what mathematical intuition is. Turned out, it was as much of a mystery to them as to me. Some of them said it was metamathematical intuition. Fair enough, but they couldn’t tell me what that was either. Some kind of mathematical mysticism, I think. But one thing they were all adamant about nevertheless, was that Turing’s conjecture was about whether his mathematical model of proof matched – not the physical world – but something else. Like mathematical intuition or something.
Now, Turing’s basic insight, was that proof is computation, and computation is physical, and hence proof is physical. That it isn’t physical – seemed to me a philosophical absurdity. But it was an absurdity that all the mathematicians I asked insisted on. And most (not all) – most nonmathematicians who’d thought about computation, didn’t. So I called it the Mathematicians’ Misconception. (The denial that proof is physical – is one way of putting it.)
After I wrote my answer, the one I quoted at the beginning of this article, I wondered: the people OP describes on the one hand, and the mathematicians who have the misconception Deutsch describes on the other… do they make the same underlying mistake?
They do. The answer is in what Deutsch calls “mathematical mysticism”. Both are mystics. And more: by denying that physical reality necessarily precedes consciousness, those mystics who meditate also share the Mathematicians’ Misconception in particular, albeit unknowingly.
A difference between them is that mathematicians do seek truth; they are conscientious, at least when it comes to math. But their Misconception is a clear example of how mysticism can ruin even careful thought processes in otherwise rational endeavors. This mysticism has caused smart people to advocate silly notions like ‘the universe is a big computer’. As Deutsch explains, such claims are arbitrary:
[T]he answer to Eugene Wigner’s famous question about why mathematics is ‘unreasonably effective in science’, is not that the physical world is actually being computed, on a vast computer – belonging to God. Or to supernormal aliens – Snailiens. Because there’s no reason, other than the Misconception, why the Snailiens’ computer should itself generate that particular tiny piece of mathematics we call ‘computable’.
In other words, once you succumb to the Mathematicians’ Misconception, all bets are off – you might as well claim there’s a god or mysterious aliens who run everything.
Some 25 years after Deutsch identified the Mathematicians’ Misconception, he published his book The Beginning of Infinity. He writes:
[W]e live in a society in which people can spend their days conscientiously using laser technology to count cells in blood samples, and their evenings sitting crosslegged and chanting to draw supernatural energy out of the Earth.
Clearly, being conscientious on the job is not enough: you need conscientiousness in philosophy first and foremost because your philosophy influences all your other thinking. If you’re conscientious only while doing math or biology but not while thinking in general, or while evaluating your thoughts, you can easily succumb to the “philosophical absurdity” Deutsch identified. That’s because, unlike Deutsch, you will lack the skill to identify it as an absurdity. And that’s a philosophical skill, not a mathematical one.
Philosopher Ayn Rand defines mysticism:
[M]ysticism is the claim to some […] nonrational, nondefinable, supernatural means of knowledge.
[It is] the belief that […] man must be guided by some irrational “instinct” or feeling or intuition […].
That’s exactly what those mathematicians phrased pseudoscientifically as metamathematical intuition. Since, as Rand discovered, there can be no compromise in matters of truth and rationality, such mysticism has the potential to ruin entire fields if it takes up even an inch of thought. (This is the logic behind how god sneaks into the minds of otherwise atheistic mathematicians who think the universe is one big computer.) Conversely, it was in part because Deutsch rejected such mysticism as a “philosophical absurdity” that he was able to make huge progress in computation theory (by coming up with the concept of quantum computation).
Deutsch succinctly explains the allornothing character of reason:
A bubble of sense within endless senselessness does not make sense.
Either everything makes sense or nothing does. You can’t just decide to use reason in one domain and mysticism in another.
As OP points out, mysticism leads some to embrace nonduality philosophies “where all is one”. (I think it’s best to speak of a plurality rather than just duality but that’s for another blog post.) It’s not just mysticism generally, but the same mysticism underlying the Mathematicians’ Misconception, that causes meditation mystics to make essentially the same mistake: to claim that computation need not be physical.
It’s worth pointing out another mistake, one many rational people make when it comes to mysticism.
Deutsch reasonably concluded that Turing was referring to something physical, not some mystical intuition – Turing was a scientist, after all. Deutsch’s mistake was to assume others would go about it as rationally as he and Turing had. Rational people often think others are just as rational. This is a mistake the protagonist of Ayn Rand’s novel Atlas Shrugged, Dagny Taggart, makes repeatedly. Leonard Peikoff quotes one of Rand’s journal entries (brackets mine):
[One of Dagny’s errors] is overoptimism […] in that she thinks men are better than they are, she doesn’t really understand them and is generous about it.
This mistake we could call the Creators’ Misconception. To be clear, this mistake is not a kind of mysticism – it’s a mistaken projection or extrapolation of one’s own virtues onto others. Rand elaborates (second ellipsis is Peikoff’s):
[…] Dagny is committing an important (but excusable and understandable) error in thinking, the kind of error individualists and creators often make. It is an error proceeding from the best in their nature and from a proper principle, but this principle is misapplied. . . .
The error is this: it is proper for a creator to be optimistic, in the deepest, most basic sense, since the creator believes in a benevolent universe and functions on that premise. But it is an error to extend that optimism to other specific men.
From what Deutsch describes, like Dagny, he thought others were more rational than they really were. He ascribed rationality (correctly, I think) to Turing but also to people who are actually mystics. Dagny learns the hard way that most people are not as good as she thinks they are, and I think Deutsch learned it, too.
Dagny’s next mistake was to think she can change people and inspire them, that “she can teach them and persuade them, [that] she is so able that they’ll catch it from her”, as Rand writes in the same journal entry. Rand calls this overconfidence. Deutsch’s next mistake, on the other hand, seems to have been a kind of resignation: to compromise on some of his views by hiding them, presumably to accommodate some of his readers. As Rand explains, such compromises cannot work.
In conclusion, there are two important mistakes. First, even people in rational pursuits often succumb to mysticism, such as mathematicians with their Misconception. One has to be careful and take vigorous steps to protect oneself against mysticism. The best protection is conscientiousness of thought in general and an unwillingness to compromise on truth; surfacelevel rationality isn’t enough. Second, rational people – creators, innovators – often think others are just as rational and as good as they are. This is the Creator’s Misconception. For example, creators underestimate just how widespread mysticism is.

I have learned that Deutsch misquoted Turing. It should be ‘could naturally be regarded’, not ‘would’. I have updated the above quotes accordingly. Also, Turing does not speak of anything being regarded as computable but of numbers. But I can’t update quotes to fix that mistake without making additional changes and guessing what Deutsch might have meant. Dear reader, don’t repeat those mistakes. ↩
References
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What people are saying
There remains the question if the currently discussed world models of physics (e.g. some variant of quantum mechanics plus general relativity) already covers all of physical reality  apart from the problem that those theories are still awaiting a unification. This is a serious philosophical debate (mind/body problem, "hard problem of consciousness"), and the stance "consciousness can be fully explained by the underlying physics as we know it" is of course possible, but there are others (see D. Chalmers e.a. for full coverage of the topic). What do you think about this?
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Not a physicist but I doubt they cover all of physical reality in the sense that they’re some ‘ultimate’ explanation. Even our best theories are always going to have shortcomings. That includes theories we come up with after the unification you mention. There’s never a guarantee that tomorrow we won’t find some new aspect of physical reality which our best theories do not yet cover.
Consciousness is always the result of a physical process. But that in itself doesn’t explain consciousness. Any viable explanation of consciousness will let us program it on a computer.
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