
God's Number Is 20 (2010) - weinzierl
https://cube20.org/
======
trentlott
A small note - is anyone else frustrated that the video can't be played in
both directions?

Watching someone disorder a solved cube is not particularly interesting or
satisfying. I'm sure it does serve the text, but boy it irks me.

~~~
rlue
You can always click-and-drag the progress slider backwards.

I think I'm more annoyed that the step-backwards and step-forwards buttons
skip the animation and just flash to the cube's next state.

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_petronius
Comparing the quarter-turn metric and the "standard" metric is very
interesting.

I'm fascinated that for both, the number of positions above a certain distance
starts to reduce again (which is much more pronounced in the quarter-turn
table). Intuitively, it isn't obvious to me why this would be so, but it's
nerd sniped me into thinking about how combinations work in general and the
geometry of the Rubik's cube particularly.

Off to Wikipedia!

~~~
kevinventullo
Here's an analogy: take a point on the sphere and consider the set of points
on the sphere that are distance _d_ from that point. The size of that set
increases as _d_ goes from 0 to 1/4 * circumference, then decreases as d goes
to 1/2 * circumference, and you end up with just the antipodal point.

There's probably some general argument that you'll always see this with any
sufficiently nice compact metric space.

~~~
rocqua
Feels to me like this is required of any 'lattice' (partial ordered set with a
unique supremum and infinum for every sub-set).

Notably, given any 'cross-section' of a lattice (a set A such that given an x
in A, and any x > y then y in A) has a 'surface' (the set of all points x in z
such that for all y in A we NOT z > x). That cross section needs to start (1
element) at the cross section containing only the 'infinum' of the entire
lattice. Similarly, the surface needs to end small (1 element again) at the
cross-section that is the entire lattice.

In between, it will generally by larger. I think there might be some
'convexity' results that can be proven about the surfaces of increasing
sequences of cross-sections. Given specific kinds of lattices.

It feels to me like a cartesian-lattice would always have this convexity
porperty. (By convexity I mean that the surface starts of increasing, might be
constant for a while, and then must continue decreasing.)

Cool subject, makes me wish I was doing a PhD in mathematics.

~~~
JadeNB
For reference, what you call a 'cross section' is sometimes called an ideal or
a downset. I can't quite make out your definition of 'surface', but, if it is
meant to read "the set of all points x in A such that for all y in A we have
not y > x", then it is the set of maximal elements of A. I'm not an expert on
posets, but, if I've got the terminology right, your notion of convexity
sounds like you want to deal with a ranked poset with unimodal h-vector.

------
mrcactu5
Here's some notes from Harvard on how to count Rubik's Cube positions with
Group Theory

The number is: 2^(12) _3^8_ 8!*12!

[http://www.math.harvard.edu/~jjchen/docs/Group%20Theory%20an...](http://www.math.harvard.edu/~jjchen/docs/Group%20Theory%20and%20the%20Rubik's%20Cube.pdf)

~~~
skrebbel
I know mathematicians hate interpunction with a passion but that one's pretty
extreme! I have no idea where the timeses and the parentheses are supposed to
go..

~~~
LeifCarrotson
It's not helped by the fact than HN markup is interpreting asterisks as
requests for italics and backslashes as escape sequences...

~~~
simias
The fact that HN still doesn't have a proper way to display code or
mathematical formulas after all these years is a bit ridiculous. I guess by
now it's part of the website's culture...

~~~
yjftsjthsd-h
I'd prefer real markdown, but iirc 4 spaces of indentation does it?

    
    
        Foo*bar

~~~
saagarjha
Two:
[https://news.ycombinator.com/formatdoc](https://news.ycombinator.com/formatdoc)

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ErotemeObelus
I thought this was the successor to Time Cube at first.

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crististm
So 35 years can be compressed into, say 6 weeks, using only about 300
computers. I'm impressed what we can do with the computers of today.

~~~
rntksi
Divide and conquer

~~~
yitchelle
If you have 43,252,003,274,489,856,000 computers, it could solve in
milliseconds!

~~~
peterwwillis
Then you'd have to have 43 quintillion network operations. That would probably
take a couple hundred years.

~~~
vectorEQ
not with 43 quintillion mbps :O

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andybak
Can skilled players usually solve a random position in 20 moves? If not -
what's the usual human target for an arbitrary position?

~~~
hmate9
No. Humans memorise algorithms for different patterns and then apply them.
Humans don’t solve a rubic’s cube by trying to find the least moves.

~~~
aeorgnoieang
According to sibling comments of your own, you're wrong. Humans _deliberately_
solve cubes with the least number of moves and even compete to do so.
Generally tho, you're probably correct.

~~~
rimliu
And even in speed solves sometimes a different algorithm (which may be a bit
longer/not as convenient to execute) is applied if the solver knows that it
will lead to the more favourable position afterwards. E.g. OLL/PLL skips.

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tazeg95
God move for pocket cube is 14, how to generate all positions and solve the
cube : [https://en.jeffprod.com/blog/2017/solving-a-rubik-s-
pocket-c...](https://en.jeffprod.com/blog/2017/solving-a-rubik-s-pocket-cube-
with-a-graph-database/)

------
ktpsns
Just to put the statement "35 CPU-years of idle computer time donated by
Google" into relation: One year is ~8640 hours. This means 302.400 CPU hours.
That's nothing compared to a single research proposal (we count in multiples
of millions of CPU hours). Any explanation of this number?

~~~
_hl_
I guess that's just all they needed until they were done?

~~~
ktpsns
The worth of a single CPUh on a cluster is roughly 0,1€. That's a 30k€
donation from google. Weird that they put this number at the front.

My guess is that they run on a large number of CPU cores. On 1000 cores, it's
already 300 million CPUh. Really, to put this into relationship, on many
clusters you get 100k CPUh for free when you apply for getting access, just to
test your code. That's why 300k CPUh is not much.

~~~
_hl_
So you're saying the donation is insignificant in comparison to other
applications? I'd say 30k€ is pretty significant, and it makes sense to thank
them by mentioning it right at the front.

~~~
ktpsns
Every donation is significant. It's just uncommon in science to mention
donations in the first sentence at all. As a reader, this suggests something
exceptional. My point is only that this number isn't.

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Vagantem
So there is 43,252,003,274,489,856,000 positions of a Rubik's Cube? Pretty
mind blowing.

~~~
sjcsjc
And there are
80658175170943878571660636856403766975289505440883277824000000000000 possible
shuffles of a pack of cards which is also mind blowing but really just an
excuse for me to wheel out this excellent link again
[https://czep.net/weblog/52cards.html](https://czep.net/weblog/52cards.html)

~~~
Dylan16807
Or in the typical way of measuring entropy, about 2^225. So you can make a
connection through these impossibly big numbers into levels of security for
cryptography, and see how this particular amount of impossible is right in the
middle of typical use. It's also interesting to think about how a deck of
cards is both elegant and unwieldy as a way to store a key.

~~~
alex_stoddard
[https://en.wikipedia.org/wiki/Solitaire_(cipher)](https://en.wikipedia.org/wiki/Solitaire_\(cipher\))

    
    
      "The Solitaire cryptographic algorithm was designed by Bruce
      Schneier at the request of Neal Stephenson for use by field
      agents in his novel Cryptonomicon, enabling them to
      communicate securely without having to rely on electronics or
      having to carry incriminating tools, It was designed to be a
      manual cryptosystem calculated with an ordinary deck of
      playing cards. In Cryptonomicon, this algorithm was
      originally called Pontifex to hide the fact that it involved
      playing cards."

------
yonatron
26 actually is G-d's number in Kabbala. (G-d's name Y-HVH has the the gematria
(Jewish numerology) equivalent of 26 - an important number in kabbala and
gematria.) I conclude therefore that the quarter-turn metric is the correct
one! :)

~~~
mirimir
Yeah, that's what I thought TFA would be about.

OK so this is totally off the wall.

Back in the late 80s, I recall an Apple video which claimed that all of the
Hebrew characters are 2D projections of some 3D shape. And then [something
about creation, the structure of reality, etc]. I also remember something
about a lawsuit by some guy in California, claiming that the video producer
had stolen his work.

I think that I even had a videotape. But it's all gone, or maybe packed in a
box that I've lost track of. And it was so pre-Internet that there's no trace
that I've managed to find. It was very trippy stuff.

Anyway, had to ask :)

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Causality1
For a second I worried that someone had managed to post that TimeCube lunatic
to HN.

~~~
namuol
I think this site is making an homage/reference to it.

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megaremote
Is there a position you could get the cube into, maybe by having to take it
apart, that can not be solved?

~~~
poizan42
Yes by taking it apart, just rotate a single corner, flip a single edge or
swap two edges.

------
drinane
Its definitely 42 folks.
[https://en.wikipedia.org/wiki/42_(number)#The_Hitchhiker's_G...](https://en.wikipedia.org/wiki/42_\(number\)#The_Hitchhiker's_Guide_to_the_Galaxy)

~~~
paulddraper
To point out the obvious, that's the answer to the Life, the Universe, and
Everything, not God's Number.

~~~
magduf
Well isn't that kinda the same thing? If God is everywhere and in everything,
you're talking about the same thing, so 42 is definitely the true number of
God!

