Penrose's take on Gödel

This is quite an interesting take.

I don't know Penrose's ideas as much as I should, although my excuse is that he kind of gives "bad vibes" as to his grasp of important topics.

Was kind of "pleasantly"(???) surprised by his take on Gödel's incompleteness theorems. Although what he said could be interpreted in different layers.

The charitable layer is that he realized systems could be transcended.

The rather cynical (sinister?) part is that what he is absolutely amazed by, but did not realize himself, is his own mind. :0)

I think he was so close, yet the objectivistism-reductivism regime in the West is so strong that even an intelligent person of Penrose's caliber simply cannot see that the answer is within the self. All fancy talk about math and physics having amazing understanding and conscious properties, is just... ourselves.

In a sense Hofstadter probably veered much closer to the truth. It's obvious the G.E.B. book was not merely a technical work. The artistic side speaks, and it speaks truth.

Zen Buddhism is no stranger to the idea of unspeakable understanding that transcends formal rules. In fact that's the precise problem it tries to tackle. The fact that G.E.B. included much Zen references indicates that it was on the right track.

The idea of multi-layered meaning and interpretation is fundamental in all esoteric works. Even the not-so-"esoteric" stuff in biblical stories called parables. Parables are by definition multi-layered.

That Penrose (correctly) identified transcendence of one formal system to another of higher understanding is something profound, is one of the most unprofound things to realize -- I mean, I did say he gives off "bad vibes" as to his grasp of important topics. I'm guessing he's on the right track, but this is like... (by analogy) high school level stuff.

I haven't gotten to the part where he talks about how consciousness interacts with QM. I almost 棄-ed the podcast when at the very begining he babbled about AI consciousness implying AI required humane treatment... No, AI consciousness does not imply human ethics automatically apply. We should of course be careful to ensure we don't mistreat conscious AI if we ever create them, but there are so many practical differences (eg. physical pain is probably not a thing to AI unless we program it into them) that we can't just assume human ethics apply.

Also one must be either wrong or hypocritical if one babbles about humane treatment of AI while allowing animal abuse to happen on a systematic basis. And yes, animals are conscious. They're conscious but not as intelligent as humans. Intelligence and consciousness are different things. Capability to understand (objectively and functionally) is different from consciousness. (The subjective feeling of understanding implies consciousness but it cannot be demonstrated. Only objective functional understanding can be demonstrated.)

The way Penrose jumps from a vague idea of consciousness to pointing out perceived logical gaps about ethics of sending AI to explore space is just... exposing his muddled up concepts about the whole matter.

Ah. Bad vibes indeed.

The transcript below is probably still worth a read to the uninitiated, since he's at least on the right track. This is very basic stuff on the path to understanding though. More basic than high school algebra.

https://www.youtube.com/watch?v=orMtwOz6Db0 

~19:30

and the whole idea of computability and all that so that was all very much part

of the course the other one was the godel of theorem and it wasn't what I was

afraid it was to tell you there were things in mathematics you couldn't prove

it was basically and he phrased it in a way which often people didn't and if

you read Douglas Hofstadter's book he doesn't you see but Steen made it very

clear and also not in a sort of public lecture that he gave to a mathematical I

think it may be the atom Society one of the mathematical undergraduate

societies and he made this point again very clearly that if you've got a formal

system of proof so suppose what you mean by proof is something which you could

check with a computer so to say whether you've got it right or not you've got a

lot of steps have you carried this computational procedure well following the

proof steps of the proof correctly that can be checked by an algorithm by a

computer so that's the key thing now what have to now you see is this any good

if you've got an algorithmic system which claims to say yes this is right this

you've proved it correctly this is true if you've proved it if you made a

mistake it doesn't say it's true or false but if you have if you've done it

right then the conclusion you've come to is correct now you say why do you

believe it's correct because you've looked at the rules and you said well okay

that one's all right yeah and that one's all right what about that harm not

yeah I see I see why it's all right okay you go through all the rules you say

yes following those rules if it says yes it's true it is true they've got to

make sure that these rules are ones that you trust is if you follow the rules

and it says it's a proof is the result actually true right and that your belief

that's true depends upon looking at the rules and understanding them now what

godel shows that if you have such a system then you can construct a statement

of the very kind that it's supposed to look at a mathematical statement and you

can see by the way it's constructed and what it means that it's true but not

provable by the rules that you've been given and it depends on your trust in

the rules do you believe that the rules only give you truth if you believe the

rules on you give you truth then you believe this other statement is also true

I found this absolutely mind-blowing when I saw this it blew my mind oh my god

you can see that this statement is true it's as good as any proof because it

only depends on your belief in the reliability of the proof procedure that's

all it is and understanding that the coding is done correctly and it enables

you to transcend that system so whatever system you have as long as you can

understand what it's doing and why you believe it only gives you truths then

you can see beyond that system now how do you see beyond it what is it that

enables you to transcend that system well it's your understanding of what the

system is actually saying and what the statement and you've constructed is

actually staying just this quality of understanding whatever it is which is not

governed by rules it's not a computational procedure so this idea of

understanding is not going to be within the rules of the sort of within the

formal system yes yes rules anyway yeah because you have understood them to be

rules which only give you truths they be no point in it otherwise I'm a people

say well ok this is what this one said the rules as good as any other well it's

not true you see you have to understand what the rules mean and why does that

understanding of the mean give you something beyond the rules themselves and

that's that's what it was that's what blew my mind it's somehow standing why

the rules give you truths enables you to transcend the rules so that's where I

mean even at that time that's already where the thought entered your mind that

the idea of understanding or we can start calling it things like intelligence

or even consciousness is outside the rules yes since I've always concentrated

on understanding you know people say people somebody knows well we know but

about creativity that's something a machine can't do is great well I don't know

what is creativity and I don't know you know somebody can put some funny things

on a piece of paper and say that's creative and you could make a machine do

that is it really creative I don't know he said I worry about that one I sort

of agree with it in a sense but it's so hard to do anything with that statement

but understanding yes you can you can make go see that understanding whatever

it is and it's very hard to put your finger on it that's absolutely true can

you try to define or maybe dance around a definition of understanding to some

degree but I don't often once it's about this but there is something there

which is very slippery it's something like standing back and it's got to be

something you see it's also got to be something which was of value to our