Most of the notes in my copy are about “The Leap to Universality” .
He’s taken with the theory of the Turing machine as universal computer, and expanded it to other kinds of universality.. indeed he thinks there is a completely general kind of universality, a universal universality.
A universal Turing machine is universal in the sense that it can emulate any finite Turing machine. It pulls the trick off by having an infinite memory, in which any finite TM can be represented as a programme. A computer with an infinite memory cannot be built, so a UTM is an abstraction: it doesn’t exist in the real world. Reality didn’t make a jump to universality when digital computation was invented, because for every real digital computer there is an infinite number of programmes which can’t fit into it.
Deutsch also gives the example of number systems. There are ways of writing numerals that don’t allow you to write arbitrarily large numerals, and ways that do. So the ways that do are universal … in a sense. They don’t require actual infinities , like a UTM. On the other hand, the argument only demonstrates universality in a limited sense: a number system that can write any integer , cannot necessarily write fractions or complex numbers, or whatever. So what is the ultimately universal system? No one knows. Integers have been extended to real numbers, surreal numbers, and so on. No one knows where the outer limit is.
Deutsch toys with the idea that DNA is also universal, but it is not at all clear whether DNA as we know it can build any living organism, or what life in the most generic sense is. Deutsch seems to think that digitality and error correction, both of which DNA has, are necessary components of universality. This is, as ever based, on analogy with the UTM, the universal digital computer , but it seems plausible that digitality and error correction are necessary components of digital computation, not universality.
So there are two problems: the lack of a single concept of universality; and one of the major constituent concepts of universality isn’t realisable. There’s no jump to universality because there is no jump to infinity.
“Not only can all problems be solved, but all people can solve problems. People have universality. As Deutsch says: “there can be only one type of person: universal explainers”. Universal explainers can create explanatory knowledge.
This falls out of the Church-Turing Thesis where anything is computable if it can be performed by a Turing machine”
Are human minds actually analogous to Turing Machines? No, because, the truly universal TM has infinite memory and is infinitely programmable—neither is true of humans. In addition, We can’t completely wipe and reload our brains, so we might be forever constrained by some fundamental hardcoding , something like Chomskyan innate linguistic structures , or Kantian perceptual categories. And having quantitative limitations puts a ceiling on which concepts and theories we can entertain. Which is effectively a qualitative limit. Being able to rewrite out genetic code does not entirely avoid the problem: if we have a blind spot that we are not even aware of, we cannot overcome it.
Deutsch believes there is no limit to explanation. That’s like the claim that there is no highest number: it’s theoretically true , but in practice there is a limit to the numbers you can think about. So he doesn’t just need the claim about the limits of explanation, in the abstract, he needs a claim about the limitations, or lack thereof of the human mind.
And he has one, which is the conjecture that humans are universal explainers. This is argued by analogy with Turing machines, which immediately runs into the problem of finite memory. Whatever algorithm generates any possible explanation needs to fit in a human brain...and merely having the capacity is no guarantee of having the algorithm.
It also runs into the problem that’s it’s an argument by analogy. Argument by analogy isn’t logically valid. Worse still, computation and explanation aren’t entirely analogous. A universal computer can run any programme given to it by an external.agency, but a human explainer must be able to create explanations.
For Deutsch, the ability to explain is all-or-nothing...so that if you are an explainer, you can generate any explanation, and if you aren’t ,you can’t generate any. Why? Surely a limited, imperfect explanation-generator is conceivable. That’s an unrefuted conjecture, too.
And there’s plenty of evidence that the ability to create and understand explanations lies along a spectrum. Newtons and Einsteins arise barely once a century,..and the less gifted are often unable to grasp their explanations, let alone recreate them.
Deutsch seems to think that non human animals aren’t universal explainers, and therefore aren’t explainers at all, but, again, there is an observed spectrum of abilities ..a dog isn’t as smart as a human , but is a lot smarter than a worm.Or maybe the line is somewhere beneath really smart humans, like physics PhDs. But the 99% who aren’t physics PhDs aren’t hopeless at explanations. The all-or-nothing theory would predict that the large number of people who aren’t quite as smart as physics or professors, can’t come up with explanations at all. The non physicists clearly can come up with explanations, But they clearly can’t come up with any explanation, since they can’t understand any explanation...If someone can’t understand relativity when it is explained to them, how can they have the power to recreate it?
But just because the physics PhDs are better explained doesn’t mean they are universal explainers. Why shouldn’t the universal explainers be some alien species with an average IQ of 1000?
Deutsch is in favour of explanation in the abstract but seems oddly uninterested in explaining well attested facts about variations in cognitive ability.
Most of the notes in my copy are about “The Leap to Universality” .
He’s taken with the theory of the Turing machine as universal computer, and expanded it to other kinds of universality.. indeed he thinks there is a completely general kind of universality, a universal universality.
A universal Turing machine is universal in the sense that it can emulate any finite Turing machine. It pulls the trick off by having an infinite memory, in which any finite TM can be represented as a programme. A computer with an infinite memory cannot be built, so a UTM is an abstraction: it doesn’t exist in the real world. Reality didn’t make a jump to universality when digital computation was invented, because for every real digital computer there is an infinite number of programmes which can’t fit into it.
Deutsch also gives the example of number systems. There are ways of writing numerals that don’t allow you to write arbitrarily large numerals, and ways that do. So the ways that do are universal … in a sense. They don’t require actual infinities , like a UTM. On the other hand, the argument only demonstrates universality in a limited sense: a number system that can write any integer , cannot necessarily write fractions or complex numbers, or whatever. So what is the ultimately universal system? No one knows. Integers have been extended to real numbers, surreal numbers, and so on. No one knows where the outer limit is.
Deutsch toys with the idea that DNA is also universal, but it is not at all clear whether DNA as we know it can build any living organism, or what life in the most generic sense is. Deutsch seems to think that digitality and error correction, both of which DNA has, are necessary components of universality. This is, as ever based, on analogy with the UTM, the universal digital computer , but it seems plausible that digitality and error correction are necessary components of digital computation, not universality.
So there are two problems: the lack of a single concept of universality; and one of the major constituent concepts of universality isn’t realisable. There’s no jump to universality because there is no jump to infinity.
“Not only can all problems be solved, but all people can solve problems. People have universality. As Deutsch says: “there can be only one type of person: universal explainers”. Universal explainers can create explanatory knowledge.
This falls out of the Church-Turing Thesis where anything is computable if it can be performed by a Turing machine”
Are human minds actually analogous to Turing Machines? No, because, the truly universal TM has infinite memory and is infinitely programmable—neither is true of humans. In addition, We can’t completely wipe and reload our brains, so we might be forever constrained by some fundamental hardcoding , something like Chomskyan innate linguistic structures , or Kantian perceptual categories. And having quantitative limitations puts a ceiling on which concepts and theories we can entertain. Which is effectively a qualitative limit. Being able to rewrite out genetic code does not entirely avoid the problem: if we have a blind spot that we are not even aware of, we cannot overcome it.
Deutsch believes there is no limit to explanation. That’s like the claim that there is no highest number: it’s theoretically true , but in practice there is a limit to the numbers you can think about. So he doesn’t just need the claim about the limits of explanation, in the abstract, he needs a claim about the limitations, or lack thereof of the human mind.
And he has one, which is the conjecture that humans are universal explainers. This is argued by analogy with Turing machines, which immediately runs into the problem of finite memory. Whatever algorithm generates any possible explanation needs to fit in a human brain...and merely having the capacity is no guarantee of having the algorithm. It also runs into the problem that’s it’s an argument by analogy. Argument by analogy isn’t logically valid. Worse still, computation and explanation aren’t entirely analogous. A universal computer can run any programme given to it by an external.agency, but a human explainer must be able to create explanations.
For Deutsch, the ability to explain is all-or-nothing...so that if you are an explainer, you can generate any explanation, and if you aren’t ,you can’t generate any. Why? Surely a limited, imperfect explanation-generator is conceivable. That’s an unrefuted conjecture, too.
And there’s plenty of evidence that the ability to create and understand explanations lies along a spectrum. Newtons and Einsteins arise barely once a century,..and the less gifted are often unable to grasp their explanations, let alone recreate them. Deutsch seems to think that non human animals aren’t universal explainers, and therefore aren’t explainers at all, but, again, there is an observed spectrum of abilities ..a dog isn’t as smart as a human , but is a lot smarter than a worm.Or maybe the line is somewhere beneath really smart humans, like physics PhDs. But the 99% who aren’t physics PhDs aren’t hopeless at explanations. The all-or-nothing theory would predict that the large number of people who aren’t quite as smart as physics or professors, can’t come up with explanations at all. The non physicists clearly can come up with explanations, But they clearly can’t come up with any explanation, since they can’t understand any explanation...If someone can’t understand relativity when it is explained to them, how can they have the power to recreate it?
But just because the physics PhDs are better explained doesn’t mean they are universal explainers. Why shouldn’t the universal explainers be some alien species with an average IQ of 1000?
Deutsch is in favour of explanation in the abstract but seems oddly uninterested in explaining well attested facts about variations in cognitive ability.