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Cake day: June 14th, 2023

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  • I am a bit late to this party, but I thought I’d piggy back on your comment to halfway address it using math.

    We want to run data centers cool. This means keeping the center itself as close to 20°C as possible.

    If we lose our convection and conduction then our satellite can only radiate away heat. The formula governing a black body radiator is P = σAT^4. We will neglect radiation received, though this is not actually a negligible amount.

    If we set T = 20°C = 294K. Then we have the relationship of P/A = 423.6 W/m^2

    According to an article I found on the Register from this April:

    According to Google, the larger of the two offered pods will consume roughly 10 megawatts under full load.

    This would imply a surface area of at minimum 23600 m^2 or 5.8 acres of radiator.

    I don’t know how large, physically, such a pod would be. But looking at the satellite view of a google data center in Ohio that I could find, the total footprint area of one of the large building of their data centers is ballpark in that range. I don’t know how many “pods” that building contains.

    So it’s not completely outside of the realm of possibility. It’s probably something that can be engineered with some care, despite my earlier misgivings. But putting things in orbit is very expensive, and latency is also a big factor. I can’t think of any particular practical advantages to putting this stuff into orbit other than getting them out of the jurisdiction of governments. (Not counting the hype and stock song and dance from simply announcing you’re going to set a few billion dollars on fire to put AI into space.)

















  • A problem that only affects newbies huh?

    Let’s say that you are writing code intended to be deployed headless in the field, and it should not be allowed to exit in an uncontrolled fashion because there are communications that need to happen with hardware to safely shut them down. You’re making a autonomous robot or something.

    Using python for this task isn’t too out of left field, because one of the major languages of ROS is python, and it’s the most common one.

    Which of the following python standard library functions can throw, and what do they throw?

    bytes, hasattr, len, super, zip


  • Oh, I’ll try to describe Euler’s formula in a way that is intuitive, and maybe you could have come up with it too.

    So one way to think about complex numbers, and perhaps an intuitive one, is as a generalization of “positiveness” and “negativeness” from a binary to a continuous thing. Notice that if we multiply -1 with -1 we get 1, so we might think that maybe we don’t have a straight line of positiveness and negativeness, but perhaps it is periodic in some manner.

    We can envision that perhaps the imaginary unit, i, is “halfway between” positive and negative, because if we think about what √(-1) could possibly be, the only thing that makes sense is it’s some form of 1 where you have to use it twice to make something negative instead of just once. Then it stands to reason that √i is “halfway between” i and 1 in this scale of positive and negative.

    If we figure out what number √i we get √2/2 + √2/2 i

    (We can find this by saying (a + bi)^(2) = i, which gives us (a^(2) - b^(2) = 0 and 2ab = 1) we get a = b from the first, and a^(2) = 1/2)

    The keen eyed observer might notice that this value is also equal to sin(45°) and we start to get some ideas about how all of the complex numbers with radius 1 might be somewhat special and carry their own amount of “positiveness” or “negativeness” that is somehow unique to it.

    So let’s represent these values with R ∠ θ where the θ represents the amount of positiveness or negativeness in some way.

    Since we’ve observed that √i is located at the point 45° from the positive real axis, and i is on the imaginary axis, 90° from the positive real axis, and -1 is 180° from the positive real axis, and if we examine each of these we find that if we use cos to represent the real axis and sin to represent the imaginary axis. That’s really neat. It means we can represent any complex number as R ∠ θ = cos θ + i sin θ.

    What happens if we multiply two complex numbers in this form? Well, it turns out if you remember your trigonometry, you exactly get the angle addition formulas for sin and cos. So R ∠ θ * S ∠ φ = RS ∠ θ + φ. But wait a second. That’s turning multiplication into an addition? Where have we seen something like this before? Exponent rules.

    We have a^(n) * a^(m) = a^(n+m) what if, somehow, this angle formula is also an exponent in disguise?

    Then you’re learning calculus and you come across Taylor Series and you learn a funny thing, the Taylor series of e^x looks a lot like the Taylor series of sine and cosine.

    And actually, if we look at the Taylor series for e^(ix) is exactly matches the Taylor series for cos x + i sin x. So our supposition was correct, it was an exponent in disguise. How wild. Finally we get:

    R ∠ θ = Re^(iθ) = cos θ + i sin θ