tromp

9 ms·

121.
by tromp 8mo ago
> Equihash (200,9) for PoW – memory-hard, ASIC-resistant As demonstrated by ZCash, the parameters (200,9) are not a great choice for ASIC-resistance, with (144,5) requiring much more memory, while also having much shorter solution witnes
122.
by tromp 8mo ago
https://archive.is/ZZouR
123.
by tromp 8mo ago
https://archive.is/hrBxU
124.
by tromp 8mo ago
https://archive.is/rz84W
125.
by tromp 8mo ago
> If you don’t want people to rewrite history, you have to be wasting tons and tons of resources 24/7, 365. And that’s why Bitcoin burns as much power as a significant country. No, Bitcoin burns that much power because it has become
126.
by tromp 8mo ago
Another comment asked for the smallest unrepresented number with 64 bit programs. While I cannot give a definite answer there, and one may never be found, here we see that the first unrepresented normal form size for programs up to 33 bits
127.
by tromp 8mo ago
A Rube Goldberg machine is one intentionally designed to perform a simple task in a comically overcomplicated way, usually consisting of a series of simple unrelated devices. Programs like Melo and w128 are the opposite, performing a hard t
128.
by tromp 8mo ago
> Line comments are declared with // and all content from the starting position to the end of the line is considered a comment. > Range comments are used to comment a certain range. /* is used to start a range comment a
129.
by tromp 8mo ago
> the fast growing hierarchy is both constructive Only the part for which we have well-defined fundamental sequences is constructive. As far as I know, there is no such system of FS defined up to PTO(Z_2), the Proof Theoretic Ordinal of
130.
by tromp 8mo ago
In terms of the Fast Growing Hierarchy, it's about f_62(9) or what the article would denote as [62] 9. It's way smaller than Graham's Number, which involves 64 iterations of mapping n to 3 ↑↑↑... {n uparrows) 3, whereas this
131.
by tromp 8mo ago
If it were about coding fast growing functions, then it would have had to mention the incredible 47-bit lambda calculus term λn. n n (λe λx. x e x) (λm. m (λe. m e m)) that achieves f_ε₀ growth. But it expects its argument to be a so-called
132.
by tromp 8mo ago
Yes, I studied theoretical computer science in University, but I believe the article should be accessible to anyone with a willingness to learn some of the background material. E.g. there are many good introductory texts on the lambda calcu
133.
by tromp 8mo ago
Let me go ahead and compute that for all halting lambda terms of length at most 33 bits. The output I got from a modified BB.lhs is (giving the normal form size and the number of terms with that normal form size): 4x208506 6x203638 7x93072
134.
by tromp 8mo ago
BLC can output any literal 60 bit string x as the 64-bit (delimited) program 0010 x, so in that sense it would be some 61 bit number. But if ask about just lambda calculus terms without the binary input, then I think it would be some small
135.
by tromp 8mo ago
> that headline doesn't even include "program" (or "compute"). Neither does Scott's article titled "Who Can Name the Bigger Number?" [1] The title is just a way to invite the reader to find out why
136.
by tromp 8mo ago
> If I give you 64 bits, you can't tell me what number those bits represent You have to tell me the (non-cheating) programming language that the 64 bit program is written in as well. > And you're asking, what is the largest
137.
by tromp 8mo ago
Turing Machines and Lambda Calculus can only output insanely large numbers by building those numbers from scratch using their Turing completeness. So while lambda calculus can output something exceeding Loader's Number, it needs well o
138.
by tromp 8mo ago
Please no more comments to the extent of "i can define a much larger number in only 1 bit". What makes my blog post (hopefully) interesting is that I consider tiny programs for computing huge numbers in non-cheating languages, tha
139.
by tromp 8mo ago
As I've replies several times before, we don't allow arbitrary mappings. We allow computable mappings but consider only obviously non-cheating languages like Turing machines or lambda calculus or Linux's bc or any existing pr
140.
by tromp 8mo ago
To find the largest number that is computable by a program of at most 64 bits in a non-cheating language; i.e. one that's not geared toward producing large numbers.
141.
by tromp 8mo ago
Following BLC8's bytewise encoding convention of [1], w218's binary encoding 0100 0101 1010 1000 0110 0110 0000 0001 0101 1011 1011 0000 0011 1001 1101 0 gets padded with 3 arbitrary least significant bits, say 000, and becomes 4
142.
by tromp 8mo ago
The post addresses this very issue: > Precisely because the Turing machine model is so ancient and fixed, whatever emergent behavior we find in the Busy Beaver game, there can be no suspicion that we “cheated” by changing the model until
143.
by tromp 8mo ago
> Precisely because the Turing machine model is so ancient and fixed, whatever emergent behavior we find in the Busy Beaver game, there can be no suspicion that we “cheated” by changing the model until we got the results we wanted. Sorry
144.
The largest number representable in 64 bits(tromp.github.io)
121 points by tromp 8mo ago|85 comments
145.
by tromp 8mo ago
Next year: One solution for too many A+'s? Harvard considers giving A++ grades. Here in the Netherland's "energy label" home insulating rankings, we're up to A++++ [1] [1] https://nieuwbouw.nl/begrij
146.
by tromp 8mo ago
https://archive.is/bFbbx
147.
by tromp 8mo ago
From FSD to Full Self Destruct ...
148.
by tromp 9mo ago
There is more coverage if you read HN in active mode at https://news.ycombinator.com/active which leaves flagged posts more visible too.
149.
by tromp 9mo ago
> That’s over ten times as many games as estimated. That's still a pretty good estimate of an exponentially large quantity; the exponent being off by only 1. With these estimates you cannot hope to do better than estimating the expo
150.
by tromp 9mo ago
I think that the average chess game played between humans contributes between 20 and 40 new positions (note that a 30 move chess games has 60 plies).

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