5 ms·

I get a kick out of these kinds of pure math problems where there's such a large gap between what is provable and what might be the best answer. "We can prove

I get a kick out of these kinds of pure math problems where there's such a large gap between what is provable and what might be the best answer. "We can prove it can be done with 10^200 pieces, but it can probably be done with less than 20". Close enough.

cyberbanjo 5y ago
In terms of all the choices, it's a pretty small sliver
gilleain 5y ago
A great example of such a range of bounds is the problem that Graham's number was an upper bound for : https://en.wikipedia.org/wiki/Graham%27s_number https://en.wikipedia.org/wiki/Graham%27s_number "Thus, the best known bounds for N* are 13 ≤ N* ≤ N''." Where N'' is ... really hard to type, it's so large!
- tromp 5y ago
  It's not hard to type in lambda calculus [1]: (λ (λ 2 1 (λ 1 (λ λ 1 2 (λ 1)) (λ λ 5 (2 1)) 3) 1) (λ λ 2 (3 2 1))) (λ λ 2 (2 (2 1))) [1] https://mindsarentmagic.org/2012/11/22/lambda-graham https://mindsarentmagic.org/2012/11/22/lambda-graham
  - dmonitor 5y ago
    it is when your keyboard doesn't have a lambda key
    - richardfey 5y ago
      It's just an ALT + 955 away!
      - voldacar 5y ago
        alt 955 gives me ╗
        richardfey 5y ago
        That should be 187: https://theasciicode.com.ar/extended-ascii-code/box-drawing-character-double-line-upper-right-corner-ascii-code-187.html https://theasciicode.com.ar/extended-ascii-code/box-drawing-...
        voldacar 5y ago
        both 955 and 187 give me that character. I wonder if it has to do with the keyboard I'm using because 955 mod 256 = 187 and I'm using an old keyboard with a usb adapter, so it might be truncating to 8 bits for some reason
  - alanbernstein 5y ago
    Of all the discussion of lambda calculus I've seen, this may be the most interesting bit. I've never really understood the purpose, not how to read it. This might actually encourage me to understand.
    - lisper 5y ago
      You might like this: https://flownet.com/ron/lambda-calculus.html https://flownet.com/ron/lambda-calculus.html Or the movie version: https://www.youtube.com/watch?v=8qC1iZN5ozw https://www.youtube.com/watch?v=8qC1iZN5ozw
  - speed_spread 5y ago
    Now I just wanna play Half-Life
- zimpenfish 5y ago
  The best thing about Graham's Number, apart from it being unrepresentable in the universe(!) because it's just THAT BIG, is that they know the last few digits (7262464195387).

cyberbanjo 5y ago

In terms of all the choices, it's a pretty small sliver

gilleain 5y ago

A great example of such a range of bounds is the problem that Graham's number was an upper bound for : https://en.wikipedia.org/wiki/Graham%27s_number https://en.wikipedia.org/wiki/Graham%27s_number "Thus, the best known bounds for N* are 13 ≤ N* ≤ N''." Where N'' is ... really hard to type, it's so large!

tromp 5y ago
It's not hard to type in lambda calculus [1]: (λ (λ 2 1 (λ 1 (λ λ 1 2 (λ 1)) (λ λ 5 (2 1)) 3) 1) (λ λ 2 (3 2 1))) (λ λ 2 (2 (2 1))) [1] https://mindsarentmagic.org/2012/11/22/lambda-graham https://mindsarentmagic.org/2012/11/22/lambda-graham
- dmonitor 5y ago
  it is when your keyboard doesn't have a lambda key
  - richardfey 5y ago
    It's just an ALT + 955 away!
    - voldacar 5y ago
      alt 955 gives me ╗
      - richardfey 5y ago
        That should be 187: https://theasciicode.com.ar/extended-ascii-code/box-drawing-character-double-line-upper-right-corner-ascii-code-187.html https://theasciicode.com.ar/extended-ascii-code/box-drawing-...
        voldacar 5y ago
        both 955 and 187 give me that character. I wonder if it has to do with the keyboard I'm using because 955 mod 256 = 187 and I'm using an old keyboard with a usb adapter, so it might be truncating to 8 bits for some reason
- alanbernstein 5y ago
  Of all the discussion of lambda calculus I've seen, this may be the most interesting bit. I've never really understood the purpose, not how to read it. This might actually encourage me to understand.
  - lisper 5y ago
    You might like this: https://flownet.com/ron/lambda-calculus.html https://flownet.com/ron/lambda-calculus.html Or the movie version: https://www.youtube.com/watch?v=8qC1iZN5ozw https://www.youtube.com/watch?v=8qC1iZN5ozw
- speed_spread 5y ago
  Now I just wanna play Half-Life
zimpenfish 5y ago
The best thing about Graham's Number, apart from it being unrepresentable in the universe(!) because it's just THAT BIG, is that they know the last few digits (7262464195387).