Epictetus

Let's say I wanted to solve my dating issues. I present the following approaches:

1. 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.

2. 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.

W... (read more)

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.... (read more)

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... (read more)

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

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... (read more)

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 suppress... (read more)

Naive calorie restriction is just regular calorie restriction with a negative name. Good eating habits entail calorie control. That's not naive. It's basic.

By "naive" I just mean calorie restriction without any other consideration. For example, a diet where one replaces a large pizza, a 2-Liter bottle of Coca-Cola, and a slice of chocolate cake with half a large pizza,1 Liter of Coca-Cola, and a smaller slice of chocolate cake is what I'd consider naive calorie restriction. I don't know that anyone would seriously argue that the restricted ver... (read more)

The very idea that 1 may be not-quite-certain is more than a little baffling, and I suspect is the heart of the issue.

If 1 isn't quite certain then neither is 0 (if something happens with probability 1, then the probability of it not happening is 0). It's one of those things that pops up when dealing with infinity.

It's best illustrated with an example. Let's say we play a game where we flip a coin and I pay you $1 if it's heads and you pay me $1 if it's tails. With probability 1, one of us will eventually go broke (see Gambler's ruin). It's easy think o... (read more)

The reason low carb diets lead to weight loss is because they restrict calories. I'm aware of many dieting tricks that can assist, but a calorie deficit must be created in order for weight to be lost.

No one in this thread is disputing that you need a calorie deficit to lose weight. My contention is that this is merely the beginning, not the end. Let's refer to the following passage from the linked article:

Translation of our results to real-world weight-loss diets for treatment of obesity is limited since the experimental design and model simulations r

Hunger is the big diet killer. It's very hard to maintain a diet if you walk around hungry all day and eat meals that fail to sate your appetite. Losing weight is a lot easier once you find a way to manage your hunger. One of the strengths of the low-carb diet is that fat and protein are a lot better than carbs at curbing hunger.

So how to solve the problem of scientific misconduct? I don't have any good answers. I can think of things like "Stop awarding people for mere number of publications" and "Gauge the actual impact of science rather than empty metrics like number of citations or impact factor." But I can't think of any good way to do these things. Some alternatives - like using, for instance, social media to gauge the importance of a scientific discovery - would almost certainly lead to a worse situation than we have now.

If you go up the administration... (read more)

Situations where an event will definitely or definitely not occur doesn't seem to be consistent with the idea of randomness which I've understood probability to revolve around.

"Event" is a very broad notion. Let's say, for example, that I roll two dice. The sample space is just a collection of pairs (a, b) where "a" is what die 1 shows and "b" is what die 2 shows. An event is any sub-collection of the sample space. So, the event that the numbers sum to 7 is the collection of all such pairs where a + b = 7. The probability o... (read more)

Would I pay $24k to play a game where I had a 33/34 probability of winning an extra $3k? Let's consult our good friend the Kelly Criterion.

We have a bet that pays 1/8:1 with a 33/34 probability of winning, so Kelly suggests staking ~73.5% of my bankroll on the bet. This means I'd have to have an extra ~$8.7k I'm willing to gamble with in order to choose 1b. If I'm risk-averse and prefer a fractional Kelly scheme, I'd need to start with ~$20k for a three-fourths Kelly bet and ~$41k for a one-half Kelly bet. Since I don't have that kind of money lying aroun... (read more)

(3) Having agreed to do something silly (like wearing a uniform) may put you in a frame of mind where you're more likely to agree to other silly things the leader of the group asks you to do later.

Why are uniforms necessarily silly? Let's take military dress uniforms. In the US, you can tell a military member's rank and branch of service, and even get an idea of their service record, just by looking at their dress uniform. To insiders, this can be rapidly gleaned looking at someone from across a room. With millions of members, individuals cannot possibly be expected to know everybody else and so the uniform serves a useful function.

Recently came across Valiant's A Theory of the Learnable. Basically, it covers a method of machine learning in the following way: if there's a collection of objects which either possess some property P or do not, then you can teach a machine to recognize this with arbitrarily small error simply by presenting it with randomly selected objects and saying whether they possess P. The learner may give false positives, but will not give a false negative. Perhaps the following passage best illustrates the concept:

Consider a world containing robots and elephants

High fructose corn syrup and its ilk have been rather devastating.