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Cake day: July 6th, 2023

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  • I used to think like this, but then I discovered the sequel song which would be utterly unnecessary if the devil actually won the first time. Technically the song is by a different artist, but Charlie Daniels played on the track and I’m going to count that as canon.

    It’s been ten long years since the devil laid his fiddle at Johnny’s feet

    And it burned inside his mind the way he suffered that defeat

    Lyrics



  • Yeah exactly, it’s not like websites turned out to be totally useless or anything: the bubble was that tons people were making websites for everything in the hopes that they would get investment and maybe figure out a purpose down the line if they felt like it. Values got inflated and then popped. Clearly though we still use websites for lots of things because they are a good way to exchange information and interact with users.

    The AI bubble is the same. It’s garnering huge investment at the moment, its value is inflated, and eventually the market will pop. That doesn’t mean we won’t be using generative AI in the future or that it doesn’t have value at all. Some companies will survive, the sector will start to grow again more gradually and our fridges will have AI in them that does something actually useful.




  • I have always been a fan of stable time loops so I guess option 2 is the best one for me.

    One trope I’d like to see more of is loops which are not stable themselves, but are stable as a group. Eg a 2-loop has loop A in which someone goes back in time and changes history leading to a new timeline loop B. Someone in loop B later goes back in time and changes history in a way that turns the timeline back into loop A.

    My headcanon is that your option 3 is basically an n-loop that we only see the first few loops of.


  • Yeah I think I was overcomplicating it in my head, I kept getting caught in the hows and whys of squaring everything in Pythagoras’ theorem, that maybe it could get around the problems of some being irrational and some not.

    Ultimately I think you’re right that the scaling itself is the problem: scaling irrational numbers to be whole numbers generally won’t work outside of those specific cases.


  • Can there exist Pythagorean triples in which the leg lengths are not coprime with each other but both are coprime with the hypotenuse?

    I don’t think so. Using the theorem, (an)² + (bn)² = c² … Algebra… c = n(root(a² + b²))

    If c is a whole number, then the root must give a whole number, and therefore n divides c

    If any of the values in (leg1: leg2: hypotenuse) are irrational, that does indeed mean the values cannot scale to be whole numbers?

    Hypothetically I can see it working from the algebra. We can construct some trivial cases like taking 3:4:5 and dividing all those lengths by root(2). All lengths are now irrational and could be made whole by multiplying them all by root(2). We can also do it with different roots in a way that is hard to type on mobile but essentially involves breaking up, say, root(30) into component roots and having different pairs of components between the top and bottom of the fraction line but that is essentially the same thing as dividing them all by the same root. I can’t see a general way of doing it if they are not all irrational in the same way, though I am just a maths teacher not a proper researcher.