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Joined 6 months ago
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Cake day: June 1st, 2024

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  • I don’t think that’s why kids hate it. Rather, teachers fail to explain the underlying motivations, the reasoning and the purpose which makes math feel like arbitrary decisions.

    I’d argue math is much more uncertain than other subjects. What’s the purpose of the endoplasmic reticulum in your cells? Just memorize the textbook. Find all X such that [statement] is true? You better have some creativity! Or a lot, depending on the problem.

    Some accompanying evidence for uncertainty: https://xkcd.com/2117/



  • I’ve found a proper approximation after some time and some searching.

    Since the binomial distribution has a very large n, we can use the central limit theorem and treat it as a normal distribution. The mean would be obviously 500 billion, the standard deviation is √(n * p * (1-p)) which results in 500,000.

    You still cannot plug that into WA unfortunately so we have to use a workaround.

    You would calculate it manually through:

    Φ(b) - Φ(a), with
    b = (510 billion - mean) / (standard deviation) = 20,000
    and
    a = (490 billion - mean) / (standard deviation) = -20,000
    and
    Φ(x) = 0.5 * (1 + erf(x/√2))
    

    erf(x) is the error function which has the neat property: erf(-x) = -erf(x)

    You could replace erf(x) with an integral but this would be illegible without LaTeX.

    Therefore:

    Φ(20,000) - Φ(-20,000)
    = 0.5 * [ erf(20,000/√2) - erf(-20,000/2) ]
    = erf(20,000/√2)
     erf(14,142)
    

    WolframAlpha will unfortunately not calculate this either.

    However, according to Wikipedia an approximation exists which shows that:

    1 - erf(x) ≈ [(1 - e^(-Ax))e^(-x²)] / (Bx√π)
    

    And apparently A = 1.98 and B = 1.135 give good approximations for all x≥0.

    After failing to get a proper approximation from WA again and having to calculate every part by itself, the result is very roughly around 1 - 10^(-86,857,234).

    So it is very safe to assume you will lose between 49% and 51% of your gut bacteria. For a more realistic 10 trillion you should replace a and b above with around ±63,200 but I don’t want to bother calculating the rest and having WolframAlpha tell me my intermediary steps are equal to zero.



  • I’m a cis guy, so feel free to ignore everything I said. Though I do want to comment because I have experienced something similar (except not in regards to gender.)

    My strategy to cope with it is to take a break from whatever I was watching the instant I start experiencing this and just allow myself to feel sad for some time. I don’t think ignoring these emotions helps, so I’ll bury myself under a mountain of plushies until the negative feelings pass. Once I feel better I usually don’t have any issues with continuing the video/movie/series and actually start enjoying it again. After all, I actually want to watch them. Also, after feeling like I’m capable of rational thought again it helps to question myself why I felt upset and to think of “counterarguments” that contradict the negative thoughts.

    Your mileage may vary but it can’t hurt (except momentarily) to give it a try.