"And where did you learn about physics, Neo?"

"..... In the Matrix...."

(It works very poorly for this, and I speak from recent personal experience)

If we let t be time in seconds, and f be frequency in Hz, the sine wave formula is y = sin(2pitf). The 2pi is the periodicity of the sine function. If f is 1, we sweep through 2pi once per second. If we let f be 2, then it sweeps through two times per second, and so on.

So, you can think of the lookup index as being the tf part, but with t counting in integer fractions of a second, with the caveat that you'll want to perform some interpolation between values.

If the waveform were more complex than a sine wave, then in the general case this "skipping agead" could cause distortion. A sine wave is one of a couple special cases (square wave being another, and arguably it's "cheating") where you're not skipping "too far" to cause distortion. (That relates to the Nyquist sampling theorem and low-pass filtering, as kens mentions)

Myself, I hope for more for my own two children than just that they have children of their own some day, just as my parents didn't have me only in order that they might someday have great-great-grandkids they'll never meet

Culture and ideas transmit through channels parallel to heredity. Celibate monastic orders are one obvious example.

I want to live in a diverse culture for a reason analogous to why I'm wary of agricultural monocultures: All it takes is the right virus to come along, and all of a sudden we don't have any bananas anymore. There are some tragic failure modes associated with strong, cohesive, anti-"diverse" cultures.

(And I understand it they did this knowing the effect it would have. It wasn't some accident.)

If land--but specifically not improvements to that land--is taxed then there's relatively more incentive to make productive use of the land. $1 of investment to improve the productivity of land by building housing or whatever is tax advantaged over $1 of investment to try to hold onto appreciating land in hopes it goes up.

For a thermal kill you have to deliver some number of Joules of energy into the target. You can use a lower powered laser over a longer period of time, up to a point. You have roughly 25 milliseconds of thermal confinement time before the mosquito starts to cool off. Longer exposures can work, but the total energy dose needed goes up. Longer exposures also require keeping the laser aimed at the target for a longer time.

Power needed also depends on how closely you can track the target. If you make the spot small enough that the target catches all of it then you minimize power requirements, but that increases the complexity of the optics. If you use a spot size larger than the target then the optical and tracking complexity go down, but you're no longer sending all of your Joules into the target.

If they'd said "determined new constraints on a hypothetical 5th force" or something I would have gotten a correct impression.

`.[]` takes a list and turns it into a sequence consisting of each element of that list.

`| x` applies the filter `x` to that sequence, turning it into a new sequence.

The outermost `[ ]` builds a list from that new sequence.

(Whether they were trying to be funny or not I couldn't tell you.)