tromp

12 ms·

1. 181.▲
   by tromp 10mo ago

   The initial long comment starts with the [ command and ends with the ] command so it forms a loop that is executed while the current cell is nonzero. But initially, all tape cells are zero, so the whole loop is in fact skipped. Readability
2. 182.▲
   by tromp 10mo ago

   The initial state of Shor's algorithm just has the n-bit number to be factored. From there it creates the superposition in the next n steps. Forget the talk about amplitudes. What I find hard to believe is that nature will let us compu
3. 183.▲
   by tromp 10mo ago

   Any implementation of Shor will need vanishingly small amplitudes, as it forms a superposition of 2^256 classical states.
4. 184.▲
   by tromp 10mo ago

   Using Brave on MacOS, I cannot scroll the page to see the entire text. On Firefox, it scrolls fine.
5. 185.▲
   by tromp 10mo ago

   I realize this is a minority opinion, and goes against all theories of how quantum computing works, but I just cannot believe that nature will allow us to reliably compute with amplitudes as small as 2^-256. I still suspect something will b
6. 186.▲
   by tromp 10mo ago

   https://archive.is/RWHYY
7. 187.▲
   by tromp 10mo ago

   > better privacy, or easier scaling You can get both [1] without trading away anything except trusting Pedersen commitments to actually commit to their values (i.e. no-one ever able to compute one particular EC discrete log). > they o
8. 188.▲
   by tromp 10mo ago

   It turns out that Rush Hour becomes much harder if we shrink the cars from size 2x1 to size 1x1, while maintaining their direction to be either horizontal or vertical [1]. While the hardest 6x6 Rush Hour puzzle takes 51 moves, the hardest U
9. 189.▲
   by tromp 10mo ago

   You can only have one URL for each scheme though, else your compiler will report something like error: redefinition of label 'https'
10. 190.▲
    by tromp 11mo ago

    If coding is the purest form of art, then lambda calculus may be the purest form of code. Its graphical representation [1] also looks somewhat artistic. [1] https://tromp.github.io/cl/diagrams.html
11. 191.▲
    by tromp 11mo ago

    It's far from accurate, since ((1+sqrt(5))/2)^-7 ~ 0.03444
12. 192.▲
    by tromp 11mo ago

    I think it's a little preposterous to conjecture that the inverse of the fine structure constant is "governed" by the expression N^2+C^2 + ((1+sqrt(5))/2)^(N-C) with N=11 and C=4. You can probably find hundreds more appr
13. 193.▲
    by tromp 11mo ago

    https://archive.is/YUXoT
14. 194.▲
    by tromp 11mo ago

    I just see a generic Google Drive page saying I need to request access. You may need to set public access...
15. 195.▲
    by tromp 11mo ago

    I linked to the paper in a recent comment [1]. The author has been active in the Higher Order Community Discord channel for quite a while. The Higher Order Company [2] is developing HVM (Higher Order Virtual Machine), a high performance imp
16. 196.▲
    by tromp 11mo ago

    https://archive.is/E84zn
17. 197.▲
    by tromp 11mo ago

    https://archive.is/g9n8i
18. 198.▲
    by tromp 11mo ago

    > there's an easy way to translate LC to IN While easy, it sadly doesn't preserve semantics. Specifically, when you duplicate a term that ends up duplicating itself, results will diverge. There exist more involved semantics pre
19. 199.▲
    by tromp 11mo ago

    https://archive.is/1OTNW#selection-1177.0-1177.49
20. 200.▲
    Ukraine survives another crisis with Donald Trump(economist.com)

    6 points by tromp 11mo ago|6 comments
21. 201.▲
    by tromp 11mo ago

    You can enter (λn.n(λc.λa.λb.cb(λf.λx.f(afx)))Fn0)7 to compute the function Col' from [1] to 7, resulting in (3*7+1)/2 = 11. Unfortunately, this visualization is much less insightful than showing the 7 successive succ&swap ope
22. 202.▲
    by tromp 11mo ago

    Since the Collatz conjecture is not (known to be) finitely refutable, we cannot encode it as a program whose termination decides the conjecture. If the existence of diverging orbits were disproven though, then we could.
23. 203.▲
    by tromp 11mo ago

    Yes; the Col' function trivially terminates for all n, since Col n' is just (if odd n then 3*n+1 else n) `div` 2
24. 204.▲
    by tromp 11mo ago

    If that were true, then every number would lead to a cycle (possibly a different one from 1-4-2). It would make the decision problem (whether a given initial number leads to 1) decidable, and the Collatz conjecture finitely refutable.
25. 205.▲
    by tromp 11mo ago

    The closely related function Col' which also divides 3n+1 by 2 in the odd case, is concisely represented by the 65-bit lambda calculus term λ1(λλλ31(λλ2(421)))(λλ1)1(λλ1) operating on Church numerals [1]. It starts from the pair of num
26. 206.▲
    by tromp 11mo ago

    https://archive.is/NOnfx
27. 207.▲
    by tromp 11mo ago

    I like this closely related and slightly more subtle problem: Which unique square (up to symmetry) must be left if you cover the 64 squares of a chess board with 21 3x1 trominoes?
28. 208.▲
    by tromp 11mo ago

    https://archive.is/YHMSL
29. 209.▲
    by tromp 11mo ago

    The intended use case is for remote execution where the user (data owner) pays a service provider to run services on their hardware. It could still work if the user somehow prepares the chip herself and ships it to the service provider to b
30. 210.▲
    by tromp 11mo ago

    This should not (so much) be compared with Fully Homomorphic Encryption (FHE) but with a Trusted Execution Environment (TEE). It is a very elegant and minimal way to implement TEEs, but suffers from the same drawbacks: a data owner has to t