Sunday, December 24, 2006

Motion Sensor UI

Why aren't Virtual Reality headset/goggles mainstream yet? The weight (though not the mass) can be counteracted by helium (or if living dangerously, hydrogen) pockets, and the head position can use the same sensor bar/micromechanical accelerometer combination that the Nintendo Wii uses.

Imagine wearing a motion-sensor bracelets while sitting at your computer. They can be used as human user interface devices. Stick your left arm out to browse backward to the previous webpage. Make a rolly motion with your hands to scroll down (basketball traveling violation). Switch to different applications by punching different areas in space.

Easy Sudoku

_4
3_
_1
__
__
__
_4
__

Friday, December 22, 2006

Minimum wage

A minimum wage causes well known deadweight loss in the labor market. Is there a way to avoid it but still achieve socially beneficial income redistribution? Perhaps handouts to employees who earn less than a threshold. How can we avoid employers sending low wages to zero?

It would have to be a lump sum handout to everyone in the population per hour worked, but perhaps implementable as an income tax deduction for high wage earners.

This still has the problem where zero is a minimum wage, preventing negative wages.

English Huffman 1

In the same style as Ken's blog: English Huffman 0 except order-1, the preorder Huffman compression tree for the next character given a current character. + is a low-probability escape character, _ is whitespace. The distribution following the escape character is uniform.

+::::yz:wx:::qr:op::uv:st::::ij:gh::mn:kl:::ab:+_::ef:cd
_:::i:c:::::::+_xzqkun:a::lro:::w:::jvyf::dp:hm:t:s::geb
a:::_l:r:::u:fhm:bv::::i:k:w::z:ea::j::+oqx:dyt::::pgcsn
b::::y::b:j::::h:::+xkqd::z:fgnv_a:lo:::i:::t::m:pwcsrue
c::o::li:k:ur::he:a:::c:y:s:n::p:bm:d::f:::+xw:jz:q:vg_t
d:_::o:a:s:::::::k:::+xzqptwvgn:e:::r:ld:u:y:::bf::jhcmi
e:::n::y:fo::p::qh:b:k:::+jzu:ix:::mea:d:c::gwv::r::lts_
f::o::uai:::f:t::::c::m::::::+qzjxvhds:::gb:w:p:nkyl:re_
g:_::he::::lnuo::::g:y:t:::cb:w:::vz:k:::+xqjd::fpmsa:ir
h:e::i_:::t::uy:r:::l::p::zgvb::::f::::+jxkqcd:wh::snmoa
i:::::v::::u::h::+yw:jq:ixzkos:::mr:fe:c:g::pba:n:t::dl_
j::o:e:a::h::cp:::bv::njm:ts:_:::f:w:l:k:g:q:::+zxy:rdiu
k:_:e:i:::::r:gbo:::wh:p::c:::::+zqxvjkl:a:y:u::md:tf:sn
l:::a::u::v:cw::r:b:::h:::+qx:jzngf:s::k:mpt:yi:::dol:e_
m:::i:::::tl:::gvdc:n::f::w::x::+qz:kjhrsp:o::bm:uy:e:a_
n::::s:y::::::q::+xzbhmf:u:::wp:rjvt:d::aio:_:g::c:k:lne
o::::w::kc:b::y::::+qzjxg:m:p:iv:::sltr::u::o:d:e:ahf:_n
p::e:al::o:p:::y:::::::::+zxjqv:wkg:cb:m::nfdsu:r:_:i:ht
q:::i:a::s:we::::::::+kgh:jqf::n::yzxo:lm:::pct:r::vdb_u
r::_::ts:::::fbvkd:y:mn:e::ao:::ur::::h::::+xq:zjwpl:cgi
s:_:::iot:::a:c:::::::::+zxvjgb:qfyn:hu::s:p::k::rdw:mle
t:::e::u::cwy:sr:o:::::::f:gp:vb:::z:d:x:::+qjknmltai:h_
u::::p:i::::zx::v::w::+qjuk:ho:fyn:lr::::am:ecs:t:_::bdg
v::i:a:::::pd::u::wvlt:s:y:::::k:q::+jzgn::hxm:c::bfr_oe
w::h:::r:::::gpm::u:c:z::::+qxjvb:y:ft:w::dkl:sno::i_:ea
x::p:i::::h::f:r::::+jqg::kzd:s:nw:y:m:l:bv:u:oxe:_:t:ca
y::o::s:::cr:a:::g::k:v:::+jqxzdn:b:mw::i:t::l:u:h:yfpe_
z:e::ai:::y::w:hglo:_:z::u:::d:r:x:::+jqfmb:s:::t:vk:ncp

Wednesday, December 20, 2006

Building a pyramid out of bricks

Suppose you are constructing a pyramid out of blocks like the ancient Egyptians did. Each new block is placed centered over the point where the corners of four blocks of the level below meet. What is the ultimate shape of the pyramid as a function of the dimensions of the bricks of which it is composed?

Let the length along the edge from base to apex be called the side length. If cubes are used, the ratio of the side length to the base length is sqrt(6):2., which is taller than an equilateral square pyramid. If flatter blocks are used, with height sqrt(0.5) times width or length, then each face is an equilateral triangle. If one builds an upside-down pyramid beneath it as a foundation, then it's a half-buried regular octahedron.

If the Egyptians made equilateral triangle faces, then they must have known the Pythagorean Theorem, as well as a practical method of extracting square roots.

There is one more interesting square pyramid: the one formed by connecting the corners of a face of a cube to the center. It has side length sqrt(3)/2 and is related to the rhombic dodecahedron. It may be constructed by stacking half-cubes.

What material should it be constructed out of to stand the test of time? Poured concrete, perhaps reinforced, is the choice in this day and age (forget blocks: just pour each layer directly) but it would be very cool to see one constructed of giant blocks of clear artificial quartz. Diamond may catch fire, maybe sapphire would also work: is it aluminum oxide? There might not be enough aluminum.

Beautiful Programming

Let there be a few things implemented by beautiful code.

--
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Tuesday, December 19, 2006

Boolean Gadgets for Binary Multiplication

in conjunctive normal form

X=(A+B+C)mod 2 = Parity3

(A+B+C+!X) (!A+!B+!C+X) (A+B+!C+X) (A+!B+C+X) (!A+B+C+X) (A+!B+!C+!X) (!A+B+!C+!X) (!A+!B+C+!X)

X=carry(A+B+C)

(A+B+!X) (B+C+!X) (A+C+!X) (!A+!B+X) (!A+!C+X) (!B+!C+X)

F=X*Y

(F+!X+!Y) (!F+X) (!F+Y)

F=(A+B) mod 2 = xor = Parity2

(A+B+!F) (!A+!B+!F) (A+!B+F) (!A+B+F)

C=Carry(A+B)

(A+!C) (B+!C) (!A+!B+C)

X=Y

(X+!Y) (!X+Y)

Distribution

(A+BC) = (A+B) (A+C)

Computer programming contest

Consider an optimization contest whose prize is disbursed in proportion to the length of time a candidate remains the optimal so far. It may be funded by an annuity or perpetuity depending on whether the contest is open-ended in length.

Friday, December 15, 2006

Supermassive black hole merger

What does the merger of two galactic black holes look like? It is the most massive but compact event in the universe. Is it observable safely and within human time scales? What if they each have accretion disks and jets? How fast is the final mutual rotation--is it quite slow because of the wide escape horizon? Does the show end abruptly when one singularity enters the other's event horizon?

Computer vs. The World Chess Match

Deep Fritz has defeated Kramnik 4-2 in Bonn. Let the next man versus machine contest be Computer versus The World.
But instead of playing a linear series of games, the computer program plays a game tree against humanity. Two websites support the challenge. The first stores every move made so far, publically viewable so that the humans may explore the tree so far. From any human move in the tree, a human may branch off a new variation which the computer calculates a response.

With many humans simultaneously exploring many branches of the game tree, one might expect a computer program to get bogged down. However, computer programs may be replicated, and if we don't insist on strict time controls, we can make the program always play deterministically with respect to the board configuration, irregardless of what physical processor is computing the move. Thus, on one side we have humanity exploring the game tree, and on the other a SETI@Home-style distributed computing project calculating the computer response to each new leaf.

Suppose a winning line is discovered. Humanity may celebrate that it collectively was able to defeat The Machine. But if this contest has actual prizes, we have a problem. The winning line will almost certainly be the product of many people's contributions: how do we divide the prize? The solution is to make this not a contest for the win, but an artistic one: judges award prizes according to how spectacularly embarrassingly poorly the computer is induced to play. Perhaps the programmers may weigh in on the judging, encouraging prizes for uncovering weaknesses that will be fixed in the next version of the program. Judging is the point of the second website, a forum for discussion about the artistic merit of various moves.

When the point is not necessarily to win but to demonstrate the computer playing poorly, some of those demonstrations may occur on drawn or losing lines. We wish for a mechanism to prove the computer erred, drawing or losing a line it could have won or drawn. At a drawn- or lost-by-the-computer leaf of the tree, every computer move back to the root is marked as a potential bad move. At any potential bad move, the human can switch sides, in essence claiming "I can play better from this position than you have." Care needs to be taken to avoid the computer playing against itself, and consequently positions achieved by transposition.

One interesting artistic challenge is to beat the computer once, take the line, switch sides buy some point and show that the computer could have won by beating it again as the opposite color. This will produces another lost-by-computer line, within which is another opportunity to switch sides and show how the computer could have won. The process may be repeated, and the end result is a line where the computer has given up multiple opportunities for a win, as demonstrated in the side variations.

A small variation of this grand scheme is to let "The World" consist of just one person, perhaps the human world champion. This itself is like the idea of a match that the human needs only to win one game, or prove a drawn game could have been won, to win the match.

I wonder if this could be set up as a human-computer simul, with one human and many replicates or the computer program, under the constraint that the program must play the same move in identical game states.

Tuesday, December 12, 2006

Go to Sun

If you wanted to fly into the Sun, but were OK with taking a long time getting there, how would you do it? Some kind of solar powered or solar wind contraption?

Monday, December 11, 2006

Cell Fractal

Is the Cell BE and the Playstation 3 particularly suited for fractal computation? Especially arbitrary precision deep zooms.

Square Root Pyramid

A pyramid of the first N-squared digits, in base N, of the square root of N, for N from 0 to 16. (Zero is the invisible tip of the pyramid.)

1

10
11

120
120
212

2000
0000
0000
0000

21042
23240
11324
10400
13441

224103
122055
214532
500432
040411
055205

2434330
6654246
0332333
2613624
6615662
3042200
2313525

26501171
46376357
14441054
57542331
56522537
23707267
54056504
47352046

300000000
000000000
000000000
000000000
000000000
000000000
000000000
000000000
000000000

3162277660
1683793319
9889354443
2718533719
5551393252
1682685750
4852792594
4386392382
2134424810
8379300295

33534781483
717A7320678
4A648721160
78472490883
50711AAA317
71131198955
78303107503
840A8013430
0673437A404
62566345368
2625A487045

3569B73BB715
20982A77945A
A3BB17635011
92060BB2B865
653562BB160B
2A5895A91201
04455152A928
267A19329301
B385BB7A27BA
A83137645955
A11453342438
1592370B2862

37B451C466C91
C692520276B60
1158204643121
B597312B9A462
685019B818044
9C69977518B63
4AA094637945A
607987B0A8895
A04895559325C
694CC113CC18C
10C13613A4678
780810436A304
C444929321751

3A55171DC9B9AB
C1505DB61C58B9
4A85C4983087BC
89495129278B43
D760C5C74281C4
D24ABC31C9BBD7
3298AC74AC9987
886106165C940B
5588686149DDA4
9B5C372CA5610A
52B2DCB73CB9B1
A95331B3766098
D8319B46873B82
41B128748029D5

3D164BADDB995E9
84D12CE1AB17076
8D2CC6C049774D5
6418C514860B587
83766A469782CA4
86677E93768D36C
71BEA7D17AACCDE
3C1C1DBAE161659
56168CCB271D74A
30A9006CB721246
3E9966E37C64E4C
EAB820D20E30106
2E740319C33E715
799EBA7188333DC
9192126A5127B79

4000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000

echo 'scale=1000;for(i=2;i<=16;i++){obase=i;sqrt(i)}' | bc | perl -pwe 's/\\\n//;s/\.//' |
#!perl -nw
$l=$.+1; for($i=0;$i<$l*$l;$i+=$l){ print "",(substr$_,$i,$l),"\n" } print "\n";

Sunday, December 10, 2006

Alien cosmic rays

What if ultra high energy cosmic rays are signals from an alien intelligence? If aliens want to communicate, they should use a signal that will not be confused with a natural source. Photons are the obvious first choice, but there so many natural photons out there that it's hard to be heard above the din. Cosmic rays, protons, are different. The fact that they carry so much energy and have no easy natural explanation immediately calls attention to them. Two open questions remain: Even if we allow artificial methods, how are they produced and survive the journey through space? And how can we decode information contained in them? Just how much information, if any, can one encode in a proton?

Saturday, December 09, 2006

Send your corpse to Mars!

Getting to Mars is a lot easier if it's a one-way trip.

Getting to Mars is a lot easier if you don't need a controlled landing.

Getting to Mars is a lot easier if you don't need life support.

So, if you want to "technically" be the first person on Mars, you can arrange to have your dead body sent and "buried" on Mars. The technical challenges of sending a ~100 kg payload to Mars have already been solved, especially if it's also acceptable if the landing is botched and you your corpse is eternally preserved in the cold vacuum of space. Or you land on the Sun.

Sir Richard Branson, are you listening? Make it a service of Virgin Galactic.