I did overlook the definition of H. Apologies.
The point is that the behavior of H is paradoxical. We can prove that it can't return true or false without contradiction. But if that's provable, that also creates a contradiction, since H can prove it to.
More precisely, H will encounter a proof that the question is undecidable. It then runs into the following two if statements:
if check_if_proof_proves_x_halts(proof, x, i)
if check_if_proof_proves_x_doesnt_halt(proof, x, i)
Both return "false", so H moves into the next iteration of the while loop. H will generate undecidability proofs, but as implemented it will merely discard them and continue searching. Since such proofs do not cause H to halt, and since there are no proofs that the program halts or does not, then H will run forever.
Why can't I be unsure about the truth value of something just because it's a logical impossibility?
If you're using logic to determine truth values, then a logical impossibility is false. The reason is that if something is logically impossible, then its existence would create a contradiction and so violate the Law of Noncontradiction.
From the link:
That means that we can’t actually prove that a proof doesn’t exist, or it creates a paradox. But we did prove it! And the reasoning is sound! Either H returns true, or false, or loops forever. The first two options can’t be true, on pain of paradox. Leaving only the last possibility. But if we can prove that, so can H. And that itself creates a paradox.
H proves that it can't decide the question one way or the other. The assumption that H can only return TRUE or FALSE is flawed: if a proof exists that something is undecidable, then H would need to be able to return "undecidable".
This example seems to verify the halting problem: you came up with an algorithm that tries to decide whether a program halts, and then came up with an input for which the algorithm can't decide one way or another.
Isn't the obvious answer, "because, assuming your life isn't unbearably bad, living the next 1,000 years has higher expected utility than not living the next 1,000 years?"
We don't have accurate predictions about what the next 1,000 years are going to look like. Any probability calculation we make will be mostly influenced by our priors; in other words, an optimist would compute a good expected utility while a pessimist would reach the opposite result.
Responses like yours confuse me because they seem to confidently imply that the future will be incredibly boring or something.
I'm saying that if there's nothing impressive about my life in the present or the past, then I'm not one to expect much more out of the future. Some people have a cause or goal and would like to live long enough to see it through--good for them, I say.
I harbor no such vision myself. It's possible that something comes up at a later time and, over the course of 1,000 years (say), it seems rather likely that at some point I'd encounter that feeling. It's equally likely that something unavoidably bad comes up. On balance, I'm indifferent.
Honestly, I don't even find the prospect of living another decade all that exciting. If it's anything like its predecessor, my expectations are low. If I were to suddenly die in that time I wouldn't think it a big loss (albeit my family might not like it so much), but if I'm alive I'll probably manage to find some way to pass the time.
If you asked me whether I'd like to live another thousand years (assuming no physical or mental degradation), I'd ask myself "Why would I want to live 1,000 years?" and, failing to find an answer, decline. If I were told that I was going to live that long whether I liked it or not, I'd treat it more as a thing to be endured than as an exciting opportunity. The best I'd expect is to spend the time reasonably content.
Needless to say, I wouldn't make any great sacrifice today for that kind of longevity. If I avoid wanton hedonism, it's because that lifestyle can lead to accelerated degradation and the associated problems. Concern about longevity hardly enters into my calculations.
Confidence is based on your perception of yourself. When someone tells you to be more confident, it's probably because they believe your perception of yourself is worse than reality. Excessively low confidence is no less of a delusion than excessively high confidence.
Of course. I seem to have overlooked that.
Used rot13 to avoid spoilers:
K unf qrafvgl N rkc(-k^2 / 32) jurer N = 1/(4 fdeg(2*cv))
L unf qrafvgl O rkc(-l^2 / 2) jurer O = 1/fdeg(2cv)
Fvapr gurl'er vaqrcraqrag gur wbvag qrafvgl vf gur cebqhpg bs gur vaqvivqhny qrafvgvrf, anzryl NO * rkc(-k^2 / 32 - l^2 / 2). Urapr, gur pbagbhe yvarf fngvfsl -k^2 / 32 - l^2 / 2 = pbafgnag. Nofbeovat gur artngvir vagb gur pbafgnag, jr trg k^2 / 32 + l^2 / 2 = pbafgnag, juvpu vf na ryyvcfr jvgu nkrf cnenyyry gb gur pbbeqvangr nkrf.
Guvf vf gnatrag gb gur yvar K = 4 ng gur cbvag (4,0). Fhofgvghgvat vagb gur rdhngvba sbe gur ryyvcfr, jr svaq gung gur pbafgnag vf 1/2, fb k^2 / 32 + l^2 / 2 = 1/2. Frggvat k = 0 naq fbyivat sbe l, jr svaq gung l = 1.
You're conflating weight loss and nutrition throughout.
Short term, the body is resilient enough that you can go on a crash diet to quickly drop a few pounds without worrying about nutrition. On the other hand, nutrition is an essential consideration in any weight-loss plan that's going to last many months. That's why I associate the two.
But, again, it isn't the aim that a diet should involve no hunger when compared to your current meal plan. That is just plain silly and irrational.
Certain approaches purport to do this very thing by means of suppressing the appetite so that one naturally eats less. Consider, for example, the Shangri-La diet.
I will grant that if one wants to lose 2+ pounds a week over a long period of time, then the pangs of hunger are unavoidable.
There seems to be this idea floating around that you can diet, lose lots of weight, and not have it consume some bandwidth in your life. BS.
Agreed. This is especially true if there's a psychological component to the initial weight gain. For example, stress eaters will have to either avoid stress or figure out a new coping mechanism if they want to lose weight and maintain the weight loss.
Let's say I wanted to solve my dating issues. I present the following approaches:
I endeavor to solve the general problem of human sexual attraction, plug myself into the parameters to figure out what I'd be most attracted to, determine the probabilities that individuals I'd be attracted to would also be attracted to me, then devise a strategy for finding someone with maximal compatibility.
I take an iterative approach: I devise a model this afternoon, test it this evening, then analyze the results tomorrow morning and make the necessary adjustments.
Which approach is more rational? Given sufficient time, Approach 1 will yield the optimal solution. Approach 2 has to deal with the problem of local maxima and in the long run is likely to end up worse than Approach 1. An immortal living in an eternal universe would probably say that Approach 1 is vastly superior. Humans, on the other hand, will die well before Approach 1 bears fruit.
While rationality can lead to faster improvement using Approach 2, a rationalist might try Approach 1, whereas a non-rationalist is unlikely to use Approach 1 at all.
Simple amendments to the general problem such as "find the best way to get the best date for next Saturday" will likely lead to solutions making heavy use of deception. If you want to exclude the Dark Arts from the solution space, then that's going to limit what you can accomplish. The short-term drawbacks of insisting on truth and honesty are well-documented.