I feel like that notion of different clustering algorithms should be included in the Human Guide to Words sequence. Love it!
rnollet
Karma: 25
Bentham’s Bulldog recently posted an attempted takedown of Functional Decision Theory on LessWrong.
Here, if you want to read it first.
the true prior probability was 100%
Not sure what you mean by that.
It sounds a lot like the typical mind-projection fallacy Jaynes warns against.
(Do you see what I mean?)
I expect you already know some of these, but for anyone interested:
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Asaf Karagila’s Anti-anti Banach–Tarski arguments. A short blog post whose main point is that “The axiom of choice is not at fault here. The axiom of infinity is.” As an illustration, he shows that if, instead of the axiom of choice, one assumes dependent choice and that all sets of reals are Lebesgue measurable, then there is a partition of the real line into strictly more parts than elements.
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By the same author: Zornian Functional Analysis, or: How I Learned to Stop Worrying and Love the Axiom of Choice. A 30-page article discussing some of the (often counterintuitive) consequences of rejecting the axiom of choice.
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ZF(C) is not the only way to axiomatize set theory as a first-order theory. Lawvere’s Elementary Theory of the Category of Sets (ETCS) is a reasonable alternative. I find it interesting that in ETCS the axiom of choice is built in without much hesitation, whereas the axiom of replacement is not part of the core theory (though it can be added to recover equivalence with ZFC). While the set theorists I have spoken to tend to regard replacement as a major axiom, I do not often see arguments that it should be rejected in order to avoid paradoxes. (For a short introduction to ETCS, I personally recommend Tom Leinster’s Rethinking set theory, an 8-page article navigating between intuitions and formalism.)
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On the Banach–Tarski paradox, Vsauce’s Michael Stevens has made a video that gives a clear explanation and helpful visualisation: link.
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A Possible Way To Achieve All Your Goals
No link here?
If you had time for writing a bit about the pros and cons of a few books, I would be very interested.
Thank you for this detailed answer.
Some more questions:
notice if it’s something that calls to you
I am not sure exactly what you mean here. From what I am reading, it is very difficult to know what it is without having experienced it. So how am I supposed to know? Do you have examples of motivations that would not be right?
(I would say that I personally feel very curious as to what it looks like, and that I would be significantly sad to learn that I can’t even try to get there.)
I highly recommend practicing as part of an organized community. […] You’re also looking for a teacher who can be your mentor in all this.
I expected that. Then:
What are the standard keywords I should look for? What I mean is that I know quite nothing about the surrounding culture. Would I be looking for a “Buddhist church”? A “Zen temple”? — Are those the same? — A “meditation school”? Something else entirely?
What if there is no such community in my city? Is there a next best thing that still permits me to start that journey, or is your advice to not try that without a local community?
So, what if I want to get started on my own path toward enlightenment? What should I do? What should I avoid?
Oh, it looks exactly like the kind of reference that everyone here seems to be aware of and I am not. ^^ I will be reading that. Thanks a lot.
Ok. Thanks. So:
p(bus has number ≤ 1546 | city has 2992 buses) = 0.5
implies
p(city has < 2992 buses | bus has number 1546) = 0.5
?
If that is your reasoning, I do not see how you go from the former to the latter.
Is it a general fact that:
p(bus has number ≤ n | city has N buses) = p(city has < N buses | bus has number n)
or does it work only for 0.5?
In that case, probability is n/N, and if we look for 0.5 probability, we get 0.5 = 1546/N which gives us N = 2992 with 0.5 probability.
Again, I am confused.
From what you write I understand this :
p(bus has number ≤ n | city has N buses) = n/N
so p(bus has number ≤ 1546 | city has N buses) = 0.5 iff. N = 2992
therefore p(city has 2992 buses | bus has number 1546) = 0.5
But from your other comment, it looks like that last step and conclusion is not what you mean. Can you confirm that?
Or do you mean :
therefore p(city has ≤ 2992 buses | bus has number 1546) = 0.5 ?
Or something else entirely?
Thank you. It is clearer that way. ^^ I feel like it would be less confusing (more true?) to write “below 30” rather than “30” in the sentence I quoted. ;-)
I looked at my clock and it was 15:14. It gives a 50 percent probability that the total number of hours in a day is 30
I am curious how you got that number.
It seems to me that, for any reasonnable prior, it it more probable that there is 16 hours in a day rather than 30.
Maybe I am misunderstanding your “50 percent probability”?
As a wise man once said
This link is dead.
For anyone interested, if I understand correctly, this was supposed to point to a review by E.Y. of Shadows of the Mind by Roger Penrose. A copy of that review can be found here : https://whatshouldiread.fandom.com/wiki/Shadows_of_the_Mind.
Tread cautiously when you hear someone arguing against “realism”
This link appears to be dead.
I guess that it was supposed to point to this text :
https://www.yudkowsky.net/rational/the-simple-truth(or : https://www.lesswrong.com/posts/X3HpE8tMXz4m4w6Rz/the-simple-truth )
This link is dead.
To the best of my understanding, this is a working link to the same comic strip:
https://dresdencodak.com/2005/06/14/lil-werner/
But this is not the narrator speaking. It is written on a picket sign by a protester. ;-) I think that a lot of english-speaking people would make that kind of mistake, which makes that picket sign quite believable, in my opinion.
It looks like this link is dead.
Do you have a correct link? Or the title of the video?
I would be very interested in watching it (if I have not already).
I remember reading that Tolkien once observed what a beautiful sound the phrase “cellar door” makes; and that this is the kind of awareness it takes to use language like Tolkien. ;-)
Before reading further, here is my tentative answer.
The law of conservation of momentum that this machine would violate can be proved from Newton’s laws of motion.
If Mr L. calculations are based entirely on Newton’s laws, then what he has found is a contradiction in mathematics.
If they are based on different, incompatible laws of motion, then why should we trust those new laws?