was watching some gaming vids, fell asleep with autoplay on and woke up to this
@Zero_Contradictions
Жыл бұрын
This must've been an awesome video to wake up too.
@ParthKohli
2 жыл бұрын
Incredibly fascinating! Probably the best course I have seen on this channel.
@eugut
Ай бұрын
as reference to self reproduction part see Douglas Hofstadter's Godel Escher Bach( self-reference, self-reproduction)
@tmp544
2 жыл бұрын
1:14:50 i have been thinking about this question for days which is related to pset2 #4 [projection of decidable iff T-recognizable].How can we be sure that proofs itself doesn't cause looping.In the sense of projection problem How can i be sure that recognizable T is trying new inputs and not wasting its time with a pointless circles in specific pair of (x,y)
@dtung2008
9 ай бұрын
This is a lecture with many confusing proofs. To prove SELF, we can use a standard programming language to open its own source code and print it. So using the lemma, Pw = "Print w on the tape and halt". I claim P_ is a SELF program. This is almost the same as later recursive proofs that defines TM R = "Get own description then print ". I was confused that why the size of MIN_{TM} is infinite necessary means there is an arbitrary length TM. But I think the reason is the number of any finite length TM is finite, so infinite number of MIN_{TM) must include any length TM. But then the gap will be why MIN_{TM} is infinite? It probably is easy to create a minimum TM of any length such as print a sequence of random numbers, but any better argument? Overall with R = "Get own description , ... " recursive proof become easier to construct. So to facilitate easier construction of proofs one probably is worthwhile to study what are allowed (macro) actions inside a Turing machine, such as "get own description", "run", "enumerate", "print"?
@Vikingofriz
6 ай бұрын
You can’t just read a program’s source, that’s basically cheating as now you ask the OS to give you that code. The whole point of all this is that a program can self replicate without relying on any other external mechanisms, just by itself, only having the ability to write something. You can read a wiki article about quines which explores this topic.
@ahbarahad3203
10 ай бұрын
Binging this shit like its Netflix Aint got enough braincells to nail it Gotta keep going to stay off the streets
@Zero_Contradictions
Жыл бұрын
Are there true statements that cannot be proven, but we can reason that they are true anyway, without using the Recursion Theorem?
@kannix386
Жыл бұрын
i think all of those unprovable, but true statements are non-constructive, meaning they will never be of any relevance for what we humans use maths for.
@ahbarahad3203
10 ай бұрын
Isn't that like the Godels Incompleteness Theorem
@bkling123
Жыл бұрын
I'm confused by the proof of the fixed-point theorem. What happens if f is the identity transformation? Then, R will go into an infinite loop. Or, what if f adds the line "print 'hello'" or adds 1 to whatever R computes? The proof doesn't seem to cover that possibility either.
@dtung2008
9 ай бұрын
If f is an identity transformation, that only means every points are fixed points. You can pick any f, but you can not specify R. R has to be specific as shown in the proof. Simulate and simulate (S, w) in the proof did give the same result. But I agree, if you want to implement the same thing on a standard computer, it will be very confusing. So it probably is fair to ask what does such theorem really mean?
@muhammadhelmy5575
2 жыл бұрын
31:25
@esepecesito
2 жыл бұрын
Companion of this lecture, could be this video: kzitem.info/news/bejne/l5essHyXfGV0ZYo
Пікірлер: 15