I was confused about Solomonoff induction a while ago. Since code from any part of whatever program is running could produce whatever string is observed, why would shorter programs be more likely to have produced the observed string? My understanding of the answer I received was that, since the Turing machine would produce its output linearly starting from the beginning of the program, a program with extra code before the piece that produced the observed string would have produced a different string. This made sense at the time, but since then I've thought of a variant of the problem involving not knowing the full length of the string, and I don't think that answer addresses it.

Since the code that produces the string can be arbitrarily long, and when trying to apply the principles of Solomonoff induction as a general means of induction outside of computer science we often can't observe the full string that whatever the code producing our observed string may have produced (for example, trying to find laws of physics, or the source of some event that happened in an uncontained / low-surveillance environment), why is a shorter program more likely? The program's length could be a billion times that of the shortest program to produce the string and be producing a ton of unobserved effects. I could wave my hands, say something about Occam's razor, and move on, but I thought Solomonoff induction was supposed to explain Occam's razor.

Harry should be screaming at Dumbledore to use his time-turner. There are a lot of options, constrained mostly by the necessity of seeing a Hermione-looking-thing die.

"I've already used it six times today, Harry..."

"So," Harry said, "you know those really simple Artificial Intelligence programs like ELIZA that are programmed to use words in syntactic English sentences only they don't contain any understanding of what the words mean?"

"Of course," said the witch. "I have a dozen of them in my trunk."

Did she mean that she had muggle computer programs? Or did she mean some magical artifacts that work in the same way, or was this just a simple misunderstanding?

Better suited to the open thread.

There is no search for a program inside a huge string of bits. The probability of a program is the probability that random string of bits begins with it, which is 2^-len . The programs are self delimited, i.e. the program could be a string like 011011... , the ... being a string of random bits that aren't read or which we decide not to consider to be a program (e.g. if the program simply sets up copying of input tape onto output tape). There's also no search for data inside the huge string of output, it has to begin with data. The 'search' has to be done if you want to find this probability - you have to try every input string.

Re exercise: Good point, but I'd emphasize making a strong habit over doing it a lot. Spending a lot of time is easier during summer, but harder to carry over. Sure, do that, but also make sure you have a 15 minute routine, say, that you do every morning. Even a five minute routine isn't to be sneezed at, if you're doing bodyweight exercises like pushups.

Doing a stretch and 5 minutes of exercise during study breaks is worth a try. Could help avoid some of the physical problems with long hours of computer use. (Press down with your whole hand during pushups - strong fingers, hands and arms will help avoid RSI.)

A little more information (if you have it) would help with some of this. Computer Science is a huge field, so getting a sense of what you're interested in, why you're doing it, and what background you already have would probably help with recommendations.

What skills do you already have?

if people were following my calculations starting from partway through they would arrive at the same answers

If this is motivated by desire for trustworthiness, linking to the source of the life expectancy figures should have higher priority. (Also, how did you calculate the average? Weighed by overall population of those countries, population under ten, number of AMF clients, simply averaging the four numbers, ... ?)

I'll edit the post to use life expectancy figures from ten years ago.

If you used the ten years old data, you would most probably obtain lower expected age at death for today's ten-years olds* than for today's newborns. But it should be higher. The problem is not that the life expectancy changes during the time. The problem is that the life expectancy at birth is average of life times of all people born, while the life expectancy at age of ten is average of life times* of all people that survived until this age. The latter is higher than the former, since all children who died before their tenth birthday (and who lower the former average) are excluded from the statistics. In e.g. Zambia, about 11% of children die before age of five, so you can imagine how this influences the discussed difference. (I was unable to quickly find data for this to illustrate the difference explicitly.)

* Note that life expectancy at age x usually means the expected remaining time of life, not the expected age of death (which obviously is obtained from the former by adding x).

(Edited.)

~38.81755

What's the point of keeping seven-digit precision? Especially in spite of the fact that your calculation includes a disproportionately rough guess of "an average age of ten", another fact that the life expectancy estimates from different sources can differ up to 10% from each other and the problematic assumption that if you save a ten-year old child, his or her expected survival time is equal to the country's life expectancy minus ten? (The data of life expectancy are usually given at birth. Poor countries have usually relatively high child mortality; if you survive until the age of ten, your life expectancy is much higher than the listed figure.)

your recreation time would need to be ~931 times as valuable as an equivalent amount of time in a third world person's life

It is even more valuable for me.