But your citation gives both statements:

“In fact, the monkey would almost surely type every possible finite text an infinite number of times.”

and

“The theorem can be generalized to state that any sequence of events that has a non-zero probability of happening will almost certainly occur an infinite number of times, given an infinite amount of time or a universe that is infinite in size.”

So when you say the number of times is “unknowable” the actual answer is “almost surely an infinite number of times” no ? Since the probability of that can be calculated as 100%. The mindfuck part is that it is still possible that no monkey at all will type a particular text, even though the probability of that is 0.

The probability that only 2 monkeys will type the text is also still 0, same as 3 monkeys, 4 monkeys, etc. - in fact the probability of any specific finite number of monkeys only typing out the text is still 0 - only the probability of an infinite number of monkeys typing it out is 100% (the probabilities of all possible outcomes, even when infinite, have to sum up to 1 after all)

We just know that it will almost surely happen, but that doesn’t mean it will happen an infinite amount of occurrences.

Basically, if we know “it will almost surely happen” then we also know just as surely (p=1) that it will also happen an infinite number of times (but it might also never happen, although with p=0)

Ok, this is interesting, so thanks for pointing me to it. I think it’s still safe to say “almost surely an infinite number of monkeys” as opposed to “almost surely at least one”, since the probability of both cases is still 100% (can their probability even be quantitatively compared ? is one 100% more likely than another 100% in this case ?)

The idea that something with probability of 0 can happen in an infinite set is still a bit of a mindfuck - although I understand why this is necessary (e.g. picking a random marble from an infinite set of marbles where 1 is blue and all others red for example - the probability of picking the blue marble is 0, but it is obviously still possible)

That’s the thing though, infinity isn’t “large” - that is the wrong way to think about it, large implies a size or bounds - infinity is boundless. An infinity can contain an infinite number of other infinities within itself.

Mathematically, if the monkeys are generating truly random sequences of letters, then an infinite number (and not just “at least one”) of them will by definition immediately start typing out Hamlet, and the probability of that is 100% (not “almost surely” edit: I was wrong on this part, 100% here does actually mean “almost surely”, see below). At the same time, every possible finite combination of letters will begin to be typed out as well, including every possible work of literature ever written, past, present or future, and each of those will begin to be typed out each by an infinite number of other monkeys, with 100% probability.

But it also works with infinite number of monkeys, one will almost surely start typing Hamlet right away.

Wouldn’t it even be not just one, but an infinite number of them that would start typing out Hamlet right away ?

The Threnody is definitely his most famous, but he has used that technique in some of his solo compositions for cello as well - example

He’s playing Penderecki

Expat is short for expatriate, not ex-patriot. Both expatriate and patriot do come from the same Latin root (patria, fatherland) via French.

But yes, expatriate means someone who lives outside (ex) of their fatherland (patria) - can be used for both immigrant or emigrant, depending on context.

The word average is often used to mean mean, however it can be used less specifically - median is a type of average as well.

From Merriam-Webster definition of average:

1a) a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values

Also, things like testosterone levels in a population usually follow a normal distribution, where both mean and median are the same, so the distinction is often meaningless for practical purposes

The only fuel you can make from water is hydrogen. The RS-25 engines used on the SLS core stage and the Space Shuttle used liquid hydrogen, as did the J-2 engines on the second and third stage of the Saturn V (but not the first stage, which used RP-1 (kerosene) burning F-1 engine)

Starship’s Raptor engines use liquid methane however. There are a bunch of tradeoffs between the different fuels, but generally liquid hydrogen is more difficult and expensive to deal with. With low cost reusability being one of the primary objectives of Starship, liquid methane was chosen as the best option. The fact that it can also be manufactured on Mars was also considered, since CO2 is abundant in Martian atmosphere.

LOX is liquid oxygen, which is not a fuel, but an oxidizer. Starship is fueled by liquid methane. Methane can not be made from just water, you need a source of carbon. On Mars for example methane could be produced from CO2 in the atmosphere and water from ice.

YouTube video ads can’t be blocked with just DNS blocking unfortunately, they are served from the same hosts as YouTube videos.

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Chinese is also not right - 正确的 (zhèngquè de) means “proper”

Left and Right as the sides are 左 (zuǒ) and 右 (yòu) - you can also add 邊 (biān) to each which means “side” to be more explicit, but they are also used separately in many contexts where the left/right meaning is needed.

The Chinese characters for 左 and 右 actually originated as pictograms of the left and right hand in the early forms of Chinese writing, but later forms both contain general “hand” component (𠂇) with components 工 and 口 added for differentiation

The kids always adapt though.

There is a strong survivorship bias in this though. Some kids do adapt, maybe even most, but many still are harmed, and have been by unhealthy exposure to radio, television, videogames, etc. in the past. Social media is even wreaking havoc in the older generations right now.

It’s easy to point at the survivors and the success stories and say see, there is nothing to worry about - but that’s also a bit like pointing at the lifelong smokers who do not get lung cancer as an argument against promoting non-smoking.

The history of Taiwan is quite a bit more complex than that, but the PRC (current government in mainland China) has never controlled Taiwan - it was never theirs.

Taiwan was a Japanese colony from 1894 until 1945 when Japan was forced to hand it over to the ROC (the successor government to the Qing dynasty, which was the last time you could argue China controlled the island - the Qing managed to almost fully colonize it before losing it to the Japanese, although a lot of the mountainous parts of Taiwan were still mostly autonomous at that time and inhabited by aboriginal Taiwanese who continued to resist the Qing rule)

The ROC takeover of the island is also seen as another colonization by many Taiwanese as well - the descendants of the Qing era colonists who were mostly Hokkien speakers from Fujian, while the ROC migration in 1949 was mostly Mandarin speakers from wider China, who fairly brutally imposed their rule over the island (see 4 decades of martial law, etc.)

ROC managed to reform itself over time, and Taiwan is now a vibrant democratic country which is forging its new national identity where most people would prefer to be left alone to control their own affairs.