tromp

50 ms·

781.
by tromp 2y ago
https://archive.is/zf9vO
782.
by tromp 2y ago
> there are more possible positions on a Go board (10 with more than 100 zeros after it, by many mathematical estimates) than there are atoms in the universe. Why mention estimates when we know the exact number of legal positions [1] ?
783.
by tromp 2y ago
https://archive.is/5eW9D
784.
Kurzweil: We are going to expand intelligence a millionfold by 2045(theguardian.com)
10 points by tromp 2y ago|11 comments
785.
The Fastest Data in the World(bbc.com)
1 points by tromp 2y ago|0 comments
786.
by tromp 2y ago
> To make it unambiguous we must make sure that no code word is a prefix of another code word. Technically, this is not quite correct. The class of so-called uniquely decodable codes is unambigous, and a superset of the prefix codes. One
787.
by tromp 2y ago
While the official formula [1] is (4(n+1))^(2n) , if one ignores the symbol written and head movement for transitions to halt, then this becomes (4n+1)^(2n), which is ~ 17 trillion for n=5. [1] https://oeis.org/A052200
788.
by tromp 2y ago
> the 2-color 4-state case? You mean the 2-state 4-color case...
789.
by tromp 2y ago
The article touches on that: > But just four days ago, mxdys and another contributor known as Racheline discovered a barrier for BB(6) that seems insurmountable: a six-rule machine whose halting problem resembles a famously intractable m
790.
by tromp 2y ago
> There are many variants of the original busy beaver problem, and some Busy Beaver Challenge contributors plan to keep working on these. One such variant is a functional busy beaver defined in terms of the lambda calculus [1]. Since it
791.
by tromp 2y ago
Chaitin has pointed out an important difference between such questions [1] : > In our approach to incompleteness, we shall ask whether or not a program produces an infinite amount of output rather than asking whether it produces any; thi
792.
by tromp 2y ago
> to show that if a machine is non-circular, then it is possible to produce an equivalent machine by using a halting state which is entered after the machine prints its final "symbol of the first kind". This looks rather imposs
793.
by tromp 2y ago
> Showing that these questions are equivalent is an elementary exercise. Do you mean that there's a simple computable mapping f from TMs as Turing defined them to TMs which can halt such that machine m prints finitely many 0s/1
794.
by tromp 2y ago
It's interesting indeed that Turing's machines as he defined them can never halt: > he does not discuss the halting of his machines at all, and makes no provision for the computational processes undertaken by his machines ever
795.
by tromp 2y ago
I'm really curious about the drag coefficient of this smooth wedge shape.
796.
by tromp 2y ago
Not all exercise sucks. When the weather is good and I ride my recumbent through the beautiful Dutch landscape, I'm getting both exercise and joy.
797.
by tromp 2y ago
Curiously, in the pure lambda calculus with Church numerals, the factorial function doesn't need recursion, since Church numerals already act like iterators: fac = λn.λf.n(λf.λn.n(f(λf.λx.n f(f x))))(λx.f)(λx.x) or as a lambda diagram:
798.
by tromp 2y ago
https://archive.is/wwZ1k
799.
by tromp 2y ago
> Encodings built up within lambda calculus are not known to lambda calculus itself, and are ambiguous. Which is why it's strange for trealira to single out Church encoded booleans and numbers.
800.
by tromp 2y ago
> run on the equivalent of 24 Watts of power per hour. In comparison GPT-4 hardware requires SWATHES of data-centre space and an estimated 7.5 MW per hour. power per hour makes no sense, since power is already energy (in Joule) per unit
801.
by tromp 2y ago
> The original Lisp was based on mutable singly linked lists. Lambda calculus has no lists, except for Church-encoded ones (just like lambda calculus only has Church encoded booleans and numbers). While Lambda calculus only has 1 argumen
802.
by tromp 2y ago
As far as incremental games go, I find Antimatter Dimensions [1] to be one of the most extensive and polished ones. [1] https://ivark.github.io/AntimatterDimensions/
803.
by tromp 2y ago
Arcade game play + some ports: https://www.youtube.com/watch?v=plS_BH2ecS0
804.
by tromp 2y ago
> The resources needed to produce solar cells and plant them on solar farms are silicon-rich sand, sunny places and human ingenuity, all three of which are abundant. The last one reminds me of a quote attributed to Einstein [1]: > Two
805.
by tromp 2y ago
Money buys some happiness. It buys freedom from financial worries. Which by itself is a large source of happiness. But there are many other forms of happiness. Freedom from health worries is another major one. Mastering skills, achieving go
806.
by tromp 2y ago
Much more of such beautiful imagery can be found at Nikon's Small World Competition that's been running for 50 years [1]. [1] https://www.nikonsmallworld.com/galleries/photomicrography-c...
807.
by tromp 2y ago
It's usually 6 transistors, 4 of which form 2 cross-coupled inverters [1]. [1] https://en.wikipedia.org/wiki/Static_random-access_memory#De...
808.
by tromp 2y ago
> Yu said the perovskite modules cost about CNY 1.4 ($0.19)/W. He said perovskites could be manufactured more affordably than this, and claimed that once the company's 1 GW commercial line is fully operational, costs could fall
809.
by tromp 2y ago
> No one else is even close. Not remotely close. No production car is close. But prototypes certainly are. Mercedes-Benz demonstrated 8.3 kWh/100 km [1], which translates to 7.5 miles/KwH, while Aptera claims 10 miles/KwH
810.
by tromp 2y ago
I would say the combinator \x\y\z.x z (y (\t.z)) is more poetic than Y, since it forms a basis for combinatory logic all by itself. Not only can you make Y from it, but every other combinator as well. And it's the smallest term with th

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