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Why I Don't Love Gödel, Escher, Bach

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Re: Why I Don't Love Gödel, Escher, Bach

#221

Post by chriswarbo »

lisper wrote: post #165
vignesh_m wrote: post #150

Earlier quoted context omitted.

I think op's problem is different than the one normally studied - he wants to design a halting program and find the class of programs for which it works. This is typically not very popular as these statements depend a lot on the program, and the representations of programs unlike the halting problem computability statement.

Yes, I understand that. And what I'm saying is: you can't do that. The halting problem is formally equivalent to proving arbitrary mathematical theorems. For every program, there is a corresponding theorem which is true IFF the program halts, and for every theorem there is a corresponding program that halts IFF the theorem is true. So the question: for what programs can the halting problem be decided? is formally equ…

>> he wants to design a halting program and find the class of programs for which it works.

> Yes, I understand that. And what I'm saying is: you can't do that.

Not sure if it's relevant, but it's certainly possible to define an approximate halting-problem-decider, then figure out what it does and doesn't work for.

For example, a trivial implementation which checks if the given program is equal to `42`, outputs "halts" if it is, outputs "don't know" if it isn't. The space of programs it works for is { `42` }, the space of programs it doesn't work for is `remove(42, enumerateAllPrograms)`

Re: Why I Don't Love Gödel, Escher, Bach

#222

Post by ggm »

It is not obligatory to like it. Few grand works are truly flawless. The ideas underneath are entertaining, and informing, and made me think (I got to read a pre-publication proof copy in the UK on the brink of University Computer Science degree)

Sure, it could have been shorter. I bet if you cut any bit, somebody out there would complain it was missing.

Re: Why I Don't Love Gödel, Escher, Bach

#223

Post by beaconstudios »

chriswarbo wrote: post #221
lisper wrote: post #165

Earlier quoted context omitted.

Yes, I understand that. And what I'm saying is: you can't do that. The halting problem is formally equivalent to proving arbitrary mathematical theorems. For every program, there is a corresponding theorem which is true IFF the program halts, and for every theorem there is a corresponding program that halts IFF the theorem is true. So the question: for what programs can the halting problem be decided? is formally equ…

>> he wants to design a halting program and find the class of programs for which it works. > Yes, I understand that. And what I'm saying is: you can't do that. Not sure if it's relevant, but it's certainly possible to define an approximate halting-problem-decider, then figure out what it does and doesn't work for. For example, a trivial implementation which checks if the given program is equal to `42`, outputs "halts…

Thank you, this is the space I'm wanting to work in - maximising the number of programs that can be decided. I'm just not sure what kind of logic I could use for such a system.

Re: Why I Don't Love Gödel, Escher, Bach

#224

Post by beaconstudios »

lisper wrote: post #214
beaconstudios wrote: post #197

Earlier quoted context omitted.

you're right, my phrasing wasn't ideal there. I'll try to clarify: what I want to do is to create a static analyser based on a set of axioms/deductions that can determine which of the "always halts/does not always halt/don't know" categories a program fits into. (I'm rephrasing the categories because a program like "(x: int) => x == 1 ? halt : loop" fits into the second category). What I'm wanting to figure out is th…

> you could clearly change "x is even" to any "x is wholly divisible by " Or... "x is a prime number" "x is a counterexample to the Goldbach conjecture" "x is an encoding of a planar map that cannot be four-colored" "x is the encoding of an algorithm that solves the traveling salesman problem in polynomial time" "x is the encoding of a formal proof of the Riemann hypothesis"

For which the answer from the program is "I don't know".

Re: Why I Don't Love Gödel, Escher, Bach

#225

Post by muro »

lolc wrote: post #28
muro wrote: post #5

tl;dr. Excellent first few chapters (which deserve the high praise and possibly are the cause of all the hype), gets less and less interesting. At some point, I dreaded returning to it and gave up.

Did you sum up your experience reading the book? Or did you try to sum up the critique we're discussing here? If it's the latter you failed.

The book.

Apologies, you are right, should have been clearer. I think the other comments at the time were also about the book, not the article.

Re: Why I Don't Love Gödel, Escher, Bach

#226

Post by nmca »

core-questions wrote: post #208
schoen wrote: post #195

Earlier quoted context omitted.

David Benatar is the most famous exponent of the opposing view: https://en.wikipedia.org/wiki/David_Benatar https://en.wikipedia.org/wiki/Antinatalism Edit: though several weaker views are more common in animal rights advocacy, for instance that being born in order to be raised for food is not a benefit to an animal, that being born in order to be raised for food in a factory farm is not a benefit to an animal, or th…

This is such a patently ridiculous, self-defeating viewpoint. Simple teleology defeats it, in the sense that everyone who holds this view will probably die childless, and will not be very successful at spreading their views generationally. As for the animals - hey, I said I want them treated decently. I don't extend them the same courtesies as I extend to humans because they're not human, and I don't shed a tear for…

> Simple teleology defeats it, in the sense that everyone who holds this view will probably die childless, and will not be very successful at spreading their views generationally.

This is very silly, it plainly conflates truth and popularity.

> As for the animals - hey, I said I want them treated decently.

Suggests "decent" treatment of animals is preferable to "indecent" treatment; this is broadly accepted.

> I don't extend them the same courtesies as I extend to humans because they're not human

Suggests animals/animal suffering are/is of less moral importance than humans/human suffering. This is also broadly accepted.

> I don't shed a tear for their deaths because to do so is to anthropomorphize them, a quintessentially childish way of viewing the world.

Suggests anthropomorphisation of animals is undesirable because it is stereotypically childish; childishness is bad. Seems like quite a silly argument, kids are also fond of breathing etc.

> Said animal wouldn't exist otherwise, and could not benefit from not existing, so the potential for benefit is always higher on the existence side, even if the probability is very low - it's still higher than a guaranteed 0.

You care about the expectation, not the "potential for benefit".

In any case, the way in which you've presented these ideas suggests that you're a consequentialist maximiser (eg think that it's the outcomes of actions/choices/rules that matter, and that there exists some partial order of the desirability of possible worlds). I'd suggest that if you keep thinking about animal welfare and how to balance the lives and living conditions of animals against your own social and dietary needs, you may well decide that you want to reduce your meat intake. Peter Singer's "Animal Liberation" is fairly classic, "The Possibility of an Ongoing Moral Catastrophe "[0] is much more general but pretty great.

[0] https://link.springer.com/article/10.1007/s10677-015-9567-7

Re: Why I Don't Love Gödel, Escher, Bach

#227

Post by ummonk »

dmd wrote: post #153

There's a discussion in GEB about mystery/detective novels, and how the physical fact of seeing that you're near the end of the book leaks information about the state of the plot to you. He muses - what if you inserted some number of blank pages at the end, so you weren't sure where the end was? But no, that's too easy - you might flip through and see them. What about Lorem Ipsum text? Well, that's better, but still…

>There's a discussion in GEB about mystery/detective novels, and how the physical fact of seeing that you're near the end of the book leaks information about the state of the plot to you.

I noticed this when watching mystery tv shows. When I find myself wondering "wait is this the real culprit?" I just look at how much time is left till the ending...

Re: Why I Don't Love Gödel, Escher, Bach

#228

Post by lisper »

beaconstudios wrote: post #224
lisper wrote: post #214

Earlier quoted context omitted.

> you could clearly change "x is even" to any "x is wholly divisible by " Or... "x is a prime number" "x is a counterexample to the Goldbach conjecture" "x is an encoding of a planar map that cannot be four-colored" "x is the encoding of an algorithm that solves the traveling salesman problem in polynomial time" "x is the encoding of a formal proof of the Riemann hypothesis"

For which the answer from the program is "I don't know".

Really? Even for "x is a prime number"?

Re: Why I Don't Love Gödel, Escher, Bach

#229

Post by softawre »

dmd wrote: post #153

There's a discussion in GEB about mystery/detective novels, and how the physical fact of seeing that you're near the end of the book leaks information about the state of the plot to you. He muses - what if you inserted some number of blank pages at the end, so you weren't sure where the end was? But no, that's too easy - you might flip through and see them. What about Lorem Ipsum text? Well, that's better, but still…

YouTube videos do this sometimes. I've seen it in the StarCraft space.

Re: Why I Don't Love Gödel, Escher, Bach

#230

Post by dang »

greggarious wrote: post #128
js2 wrote: post #80

Earlier quoted context omitted.

https://news.ycombinator.com/user?id=greggarious has your upvoted and favorited comments and stories. (Your favorites are public, your votes private.)

Thanks, that is useful but I upvote lots of stuff so a separate saved list can also be useful :) For now, I have a bookmarks folder for stuff like this.

The 'favorites' feature is a saved list. It's not widely used. Maybe we should promote it, or maybe get rid of it.
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