yaakov34

This has become insufferable. I work in a medicine-adjacent field, but nobody in their right mind could possibly take what I do to be in any way related to some kind of bioweapon or whatever the hell they're pretending to be saving us from. The dumb Fable guardrails made me stay with Opus, now that this is coming there, we'll be saying goodbye.

The Z3 was not a general purpose computer; it was a calculator that performed a predetermined sequence of operations that was written to its tape. It was remarkable for being all-binary in an era when differential gears and cams were very common in computing devices, and had some other advanced features. But the 1990s article that declared it Turing-complete is just silly. It would apply to every four-function calculator that supports rounding, and programming a computer like that is not just "impractical" - both the tape and execution time would grow exponentially in number of branches - but it is not the model that Turing proposed. The whole point of Turing's (theoretical) device is that a short program using the abilities of that device could perform unlimited computations; if you make the program length unlimited instead, that's a much less interesting model of computation.

The problem is that anything that gets into Wikipedia becomes ingrained in the Internet's collective mind, which then can't be changed.

The claim that the Z3 computer was Turing-complete is not true. There is a paper arguing for it, but a detailed reading of it shows that this is an extremely far-fetched and somewhat disingenuous stretch. (The disingenuous part is because any fixed-function calculator could then be claimed to be "Turing-complete", not just the Z3). The central point of the Church-Turing thesis is that a finite set of instructions, given an unlimited memory to work with, can perform any calculation we can imagine (where the "can imagine" part makes the thesis philosophical). The "finite set of instructions" is indispensable, however, since if the instructions are unlimited, you can simply encode any answer you want into them. The "Turing" mode of Z3, which was of course never used, involves a program which essentially scales in length with the total number of calculations it will perform - or even the exponential of that number, if there are many branches - which is not a good model of a Turing machine.

Of course, no computer is a true Turing machine, since the memory is always limited, but our computers are a useful physical approximation of a Turing machine because a small program can compute using a large memory. The Z3 is not that type of a device at all.

That's how this plane worked - the inflation pressure in flight was supplied by the motor. I don't think heating the air was desired, but some heat will inevitably end up in the air as it is compressed.

No, you're not even close.

That doesn't say anything about Polonium being selectively taken up by the plant and used for growth. Just contamination on the sticky covering of the plants. Which doesn't make smoking tobacco good in any way, shape or form whatsoever, but it's not at all the same claim.

A quick search doesn't bring up any examples of radiophile organisms, in the sense of taking up radionuclides that are used for something. "Radiophile" bacteria exist, but that just means they are highly resistant to ionizing radiation. What are radioactive fertilizers? Potassium is radioactive to a small extent, but it doesn't seem like it's ever used for that property.

Can someone explain what we are talking about here? Something having to do with Musk's son's name?

I am not the best person to ask, since it's not my field. I heard this from the neuroscientists that I worked with. My understanding is that there are spiking and non-spiking neurons in most nervous systems, including human, but most of the ones in ours are spiking. The earliest-evolved animals, such as nematodes, do not have spiking neurons, or myelin, or some of the ion channels in neuron membranes that more evolved neurons have. Their neurons still have axons and dendrites, but the signals propagate much more slowly and in different ways. I am not sure how well they are understood.

As I said, this is possibly out-of-date information. If there is someone here from the neuroscience field, they can probably make a better comment.

Ralph's main work was on neural impulses in the visual cortex, and on measurements of various potentials in the living brain. He published a memoir called "Another Day in the Monkey's Brain". I believe he had potential medical applications in mind, but I don't think anything that was close by. Unfortunately, he died of an illness in 2011.

I explained above what happens when the dimension grows - spheres and cones do indeed take up a smaller and smaller portion of their unit cube, eventually having negligible volume. This is important in the context of high-dimensional statistics and so on.

If you want to actually have infinite-dimensional volumes, you can't just assign finite values to them in a simple way, or you will have contradictions such as a certain volume being completely covered by a union of things which have 0 volume. In infinite dimensions, you instead have various measures like the Gaussian measure. Feynman's path integrals are a kind of way to assign a value - called amplitude - to an infinite-dimensional manifold (a kind of "volume") of paths. But that takes us well to the side of the idea of the ratio between cube and inscribed figure volumes.

Actually, you have that exactly right, and it's a very important fact in mathematics and statistics. A unit sphere takes up a smaller and smaller part of a unit cube as the dimension grows (and a unit cone is similar). In other words, a unit circle fills up most of the unit square (~3.14 out of 4), a unit sphere fills a little over half of the unit cube (~4.2 out of 8), and as the dimension grows, the fraction becomes negligible.

Imagine that you have something which depends on many variables (hundreds), and you're trying to predict its behavior based on your previous experience. There is a high chance that the next combination of variable values that you see will be in one of the corners of the many-dimensional cube, because that's where the volume is (the central part of the cube has negligible volume, as we said above). This means that every measurement is in effect an outlier along several dimensions, making predictions very difficult. This is part of the "curse of dimensionality" in statistics. I have seen some people with excellent understanding of mathematics trip themselves up in this area.

Sure, have fun:

"Workers of the Soviet Union! Let us consolidate ourselves even more around the Communist Party and the Soviet Government, mobilize our forces and our creative energy for the great work of building a Communist society in our country! Long live the unbreakable union between Party, Government, and People!"

The closest thing to a universal approach would be a Kalman filter. It's usually where you start when you have noisy measurements coming in, and you need to maintain state such as value and derivative.

Since the original question was about computing the velocity of a car, and since I work in the automotive field, let's take a real example: you want to know the approximate position, acceleration, and velocity (linear and angular) of your car. Your inputs are driven wheel speed (noisy, affected by wheelspin), non-driven wheel speed (noisy), accelerometer output (inaccurate, only present for some axes), GPS position (updated occasionally, has errors), and steering angle (pretty accurate, can be put into a chassis dynamics model). Almost certainly, you would use a Kalman filter to estimate the state of the car. Naive approaches such as subtracting two wheel speed values to obtain acceleration will not work well.

My point is that we should remember that numerical algorithms are a developed field with a lot of knowledge, and we should take advantage of the proven approaches. Sometimes, programmers who are not specifically from the physics or numerical fields, and who need to perform some computation, reach for a very simple approach such as the rectangle-rule integrals, and get bad results.