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What are the most mindblowing things in mathematics?
  • Just after going through a few examples in my head, the difficulty becomes somewhat more apparent. let's start with 3. This is odd, so 3(3)+1 = 10. 10 is even so we have 10/2=5.

    By this point my intuition tells me that we don't have a very obvious pattern that we can use to decide whether the function will output 4, 2, or 1 by recursively applying the function to its own output, other than the fact that every other number that we try appears to result in this pattern. We could possibly reduce the problem to whether we can guess that the function will eventually output a power of 2, but that doesn't sound to me like it makes things much easier.

    If I had no idea whether a proof existed, I would guess that it may, but that it is non-trivial. Or at least my college math courses did not prepare me to find one. Since it looks like plenty of professional mathematicians have struggled with it, I have no doubt that if a proof exists it is non-trivial.

  • People Aren’t Facing Up to the Horrors a New Trump Term Would Bring | G’bye, NATO. G’bye, “Don’t Ask, Don’t Tell” repeal. G’bye, democracy. He’s telling us plain as day. Why aren’t people listening?
  • Yeah, I hear you. Lots of things get said, but little gets done-- I can't argue with that. But I'm looking for concrete examples because most of the goals and results people are expecting, from my perspective, are things that only get accomplished through legislation. Democrats have recently been focusing on voting rights. A solid voting rights bill would be a solid step toward tackling the issues you mentioned, but in June the most recent bill was voted against by all 50 Republican senators.

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  • ALBUQUERQUE, N.M. —

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  • PPP fraud is ‘worst in history’: $200B stolen and blown on Lamborghinis, beach houses and bling
  • experts say crooks created fake businesses or lied about their numbers of employees to get access to more free cash

    If you were creative and unscrupulous, you probably could have come up with something. Forged documents or the like.

    Finley faces up to 30 years in prison, and paying more than $3.2 million in restitution, plus a $1.25 million fine.

    But then there's that.

  • The world's most-powerful AI model suddenly got 'lazier' and 'dumber.' A radical redesign of OpenAI's GPT-4 could be behind the decline in performance.
  • Might be right but in my experience a lack of skill in conversing with AI is a much greater factor in determining it's usefulness. It's almost always going to defer to the user. It's like when someone is dealing with tech support and they tell them to try turning it off and on again. If that really is the solution, and the user insists that it is not, CGPT is going to make something up just to appease the user's request.

    Users have to know that CGPT isn't magic. How they behave affects how it behaves. Kind of like talking to actual people, which is what it's essentially trying to simulate.

  • InitialsDiceBearhttps://github.com/dicebear/dicebearhttps://creativecommons.org/publicdomain/zero/1.0/„Initials” (https://github.com/dicebear/dicebear) by „DiceBear”, licensed under „CC0 1.0” (https://creativecommons.org/publicdomain/zero/1.0/)JE
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