tromp

My favorite is the (partly analog) PRW-7000FC-1JF, as seen on https://cdn11.bigcommerce.com/s-e31c8/images/stencil/1280x12...

A language that was designed to make Kolmogorov complexity concrete is Binary Lambda Calculus, a self interpreter of which takes only 168 bits (21 bytes). Unlike the Lisp self interpreter in the article, it operates on a bitstream and thus has to include a parser.

> Overall, I built a Graph Reduction engine

I did the same for my performant implementation of pure functional programming language BLC/BLC2, which in 400+ lines contains a graph reduction engine for combinatory logic, to which the lambda calculus programs are converted by Kiselyov's bracket abstraction algorithm.

[1] https://github.com/tromp/AIT/blob/master/uni.c

I'm more interested in the converse question: how well does an LLM perform as a compressor, compared to gzip (ignoring its insanely lower speed)?

Not every bitcoin tx output.

With taproot (P2TR), scripts are optional, and outputs can be based solely on Schnorr signatures.

When code is a maze describes my 1988 IOCCC entry [1]

    char*M,A,Z,E=40,J[40],T[40];main(C){for(*J=A=scanf(M="%d",&C);
    --            E;             J[              E]             =T
    [E   ]=  E)   printf("._");  for(;(A-=Z=!Z)  ||  (printf("\n|"
    )    ,   A    =              39              ,C             --
    )    ;   Z    ||    printf   (M   ))M[Z]=Z[A-(E   =A[J-Z])&&!C
    &    A   ==             T[                                  A]
    |6<<27<rand()||!C&!Z?J[T[E]=T[A]]=E,J[T[A]=A-Z]=A,"_.":" |"];}

[1] https://tromp.github.io/pearls.html#maze

> Volkswagen just build the world's most aerodynamic road car ever.

A drag coefficient of 0.158 is not quite setting a record. Aptera's road-legal car has a coefficient of only 0.13, while Hyundai achieved a drag coefficient of 0.144 with the Aero Challenge concept car [1] (but it's not clear whether that vehicle is road-legal, or even what it looks like).

[1] https://www.azernews.az/region/245135.html

No, that would be https://en.wikipedia.org/wiki/Renaissance_Technologies

> I still keep in a drawer an old OnePlus 5 I bought in 2017 with a pristine Android system.

How pristine is that when the last supported Android version is 10?

> This phone is sometimes necessary. Like when a known bug in /e/OS prevented my banking app from working for several months.

This surprises me. Until very recently I was using a phone I bought in 2017, which similarly supports no Android beyond version 10.

Since early this year, my bank app started insisting that I upgrade my Android to 11 or higher, and hence stopped working.

More recently, Gmail also started insisting I upgrade Android. As a result I had to get a new phone, which in many ways is worse than my old phone (still 7.2" but worse aspect ratio, no more full fingerprint sensor and much worse battery life).

So the idea of keeping an old phone around in order to bank seems rather odd to me.

Make that 44...

You may have missed this part:

> What this does not show

> The attack above depends on conditions that ordinary Bitcoin keys do not meet.

> Ordinary Bitcoin keys are not affected by any of this

> A properly generated private key is spread across roughly 2 to the power of 256 possibilities. The square root of that is 2 to the power of 128, which is not attackable by anyone, with any budget, ever.

That also sounds like a good french name for Binary Lamda Calculus.

Note that this is not an extension of the pure λ-calculus.

Abstraction (λx.e) and application (f a) are missing, although the let construct "let x = e1 in e2" is equivalent to their combination ((λx.e2) e1).

The paper has few details on the higher-level specification language in which users specify desired behaviour:

> Specification Language. Specifications are written as relations between input and output ports, expressed using linear expressions. On their own, specifications are not λ _λ programs. It is the job of the synthesizer to find λ _λ programs that realize a given specification. For example, a simple switching behavior can be specified as output[i] = input[j], while a 2x2 AllReduce operation can be written as output[1] = (input[1] + input[2])/sqrt(2) and output[2]= (input[1] - input[2])/sqrt(2).

The second λ is subscripted. As footnote 1 in the paper says:

> Pronounced “lambda lambda”. One λ refers to the λ-calculus and the other refers to an optical wavelength.

> So in 2018, an international team of scientists created a BEC out of strontium atoms, and hit one of those atoms with a carefully tuned laser, exciting its outermost electron and turning it into a Rydberg atom. Several other atoms from the BEC were caught within between that outer electron’s inflated orbital.

This is not so much putting 170 atoms in one, but inflating one beyond the size of its 170-atom neighbourhood.

The hard part being to cool the neighbourhood to such an extremely low temperature that the inflated atom doesn't ionize.

You may find this area on google maps at https://www.google.com/maps/@52.1792241,5.0288801,516m

> Binface received 26.9% of the vote

> That's why Count Binface has been able to stand in so many high-profile elections. He has, however, lost his £500 every time, after failing to meet the minimum 5% of votes cast in order for his deposit to be returned.

It would seem he didn't lose his £500 this time...

TREE(3) is also unimaginably tiny compared to the normal form size of (λa.aaa(λbλcλdλe.ebbbcde)aaaa)(λfλx.f(fx)) [1].

[1] https://wiki.bbchallenge.org/wiki/Lambda_Calculus#Champions

His dyneema driven drum is eerily similar to the dyneema driven drum (called "snek") https://rowingbike.com/nl/model/thys-222-revolver#content-7 on the Thys rowingbike https://rowingbike.com/nl/model/thys-222-revolver

> You can easily demonstrate it [half an inch] as the ratio between one inch and two feet, compared to the reference ratio between one inch and one foot.

You seem to have your units confused. Half an inch is a distance, while ratios, or comparisons of ratios, are all dimensionless scalars.

> Sodium Ion can go to 10,000 cycles (27 years) with a 70% capacity reduction at that life.

The article claims much better:

> the company’s GS1.1 [Sodium Ion] system will store energy for 20 years, over roughly 20,000 cycles, and still retain 80 percent of its capacity. For LFP, a basic durability benchmark pegs them at 70 percent capacity after 8,000 cycles.

> When asked, "do you need any special programs or software to make ASCII Art?", the great ASCII artist Joan G. Stark said: "All you need is a text editor with a fixed-width font."

You can find her impressive ASCII art archived at

https://web.archive.org/web/20091028031724/http://www.geocit...

It can be solved if the memory is bounded. But unbounded memory comes with undecidable problems.

This is like Proof-of-Work, but for an extremely small amount of work, that would already overwhelm human effort, like computing a single SHA256.

Every single cryptocurrency (except one or two) concentrates wealth on the founders and early adopters.

> In France, Germany, Austria, Switzerland, the Low Countries, Ireland and Scandinavia, however

What are the Low Countries? Is that a mis-translation of the Netherlands?

Meanwhile, a single human cell's DNA stretches for about 2 meter, one human's DNA stretches for about 2 x 5.4 trillion meter, and all living human DNA for a whopping 8.6 x 10^22 meters, nearly a thousand times longer than the fungi networks...

[1] https://www.reddit.com/r/theydidthemath/comments/1gfq6k2/how...

Shor doesn't solve an NP hard problem. It's even possible that factoring and discrete log are in P, while P != NP.

The paper builds on the results of "Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems" by Abrams and Loyd [1], from which I quote:

> The last qubit now contains all the information that we need; however, for small s, a measurement of the last qubit will almost always return |0>, yielding no information. > We wish to distinguish between the cases s=0 and s>0.

> Step 4. Repeatedly apply the nonlinear operation to drive the states representing these two cases apart at an exponential rate: eventually, at a time determined by a polynomial function of the number of qubits n, the number of solutions s, and the rate of spreading (Lyapunov exponent) λ, the two cases will become macroscopically distinguishable.

[1] https://arxiv.org/abs/quant-ph/9801041