Thursday, April 28, 2016

[ubhjfyxs] Words for the hyperoperation hierarchy

enneate ennate (merging consecutive vowels) nonate (Latin creeps in, as with polygons: John Conway "Naming Polygons" in newsgroup geometry.pre-college)
hendecate undecate
dodecate duodecate
tridecate triskaidecate
3 = triate trate
2 = biate bate duate diate date
1 = monoate monate unuate uniate unate

These are the most silly ways of saying add, multiply, and raise to a power.

enneation ennation nonation
hendecation undecation
dodecation duodecation
tridecation triskaidecation
3 = triation tration
2 = biation bation duation diation dation
1 = monoation monation unuation uniation unation

Tetration = tetra + iteration, yielding tetraration, but substituting rar = r because it is awkward for the special case of tetra only.

ennearation ennaration nonaration
hendecaration undecaration
dodecaration duodecaration
tridecaration triskaidecaration
3 = triration
2 = biration duration diration
1 = monoration monaration unuration uniration unaration

Of course, tetration is enough.

[jiabppsm] Epsilon nought and tetration

It is curious that Cantor Normal Form for ordinal numbers seems to arbitrarily stop at exponentiation in the hyperoperation hierarchy and not include tetration or beyond.  The choice causes epsilon-nought to be the first ordinal not expressible with exponentiation.  However, if tetration were permitted, then

epsilon nought = (tetrate omega omega)

Does including tetration induce weird holes or duplications, perhaps around (tetrate (omega+1) omega) or (tetrate omega (omega+1))?  This could be similar to the difficulty of defining tetration for real second arguments.

Epsilon nought is supposedly useful for proofs using induction, so there is something deeper going on in the arbitrary choice to stop at exponentiation.

After including all operations hyperoperation hierarchy, one could define the first ordinal not accessible by an expression consisting of those operations.  More precisely, one could define an ordinal that is the limit of (hyper1 omega omega) (hyper2 omega omega) (hyper3 omega omega) (hyper4 omega omega) (hyper5 omega omega) ..., so the omega-th member of the hyperoperation hierarchy.

[jryeuysy] Mersenne tower

One rarely gets to write a "real" number as a tower of powers (as opposed to large numbers constructed solely for the sake of being large), so let us write the recently discovered Mersenne prime 2^74207281-1 as a short tower of 2s:

2^(74207281-very small)

Or (tetrate 2 5.21467299217592807307) using tetration extended to real numbers by "linear" approximation.

Or, as a tower of 10s:

(tetrate 10 2.8662315739486796570)

Each of those decimal numbers could be computed to millions of digits. There's a Procrustean feeling to this: Mersenne numbers are inherently related to powers of 2, but we are forcing this one to be a power of 10.

Given a number N, solve for X in N = (tetrate X X).  Analogous problem for self-exponentiation.

[cqejnfvs] A note about the Goldstein Theorem

The mapping from a number in hereditary base notation to an ordinal number with omegas always results in an expression for an ordinal number with terms joined by plus signs only (addition), never minus signs (subtraction), because hereditary base notation by construction only has pluses.  A sequence of such plus-sign-only expressions that is strictly decreasing will converge to zero in a finite number of steps (this was the meat of the proof of the theorem).

If minus signs were permitted, then the following sequence

omega, omega-1, omega-2, omega-3...

is strictly decreasing but would not reach zero in a finite number of steps.  Arguably "omega-1" is not even defined for ordinal numbers, though such an expression could have been formed by substitution starting from something other than hereditary representation:

Given a positive integer N, prove that the sequence

N, N-1, N-2, N-3...

will reach zero in a finite number of steps.

Wednesday, April 27, 2016

[mzihtlnd] Tetration is enough

Addition, multiplication, exponentiation, tetration:  The applications get sparser the further up one goes, so beyond tetration seems mostly unnecessary, except for specialized fields dealing with large numbers for the sake of being large.

[hzvqnqfc] Hereditary Mersenne

Write Mersenne prime numbers in hereditary base 2 notation (hereditary representation), because why not.  Creates a wavy line of exponentiation.

[uewlvzdn] Binder with plastic sleeves

A 3-ring binder with each paper page encased in a clear plastic sleeve seems to be a sturdy method of book binding, not requiring special tools or equipment.  (In contrast, putting three-hole punched paper directly into a binder is extremely fragile: almost analogous to the humorous write-only memory or write-many read-once memory.)

Of course, very expensive per page.

How long-lasting is it?  Potential issues: ink from the page transferring to the plastic sleeve.  Degradation of plastic sleeve.  Plastic becoming not clear.  Cracking or tearing around the binding holes on each sleeve.

Not available in sizes other than letter paper.

Tuesday, April 26, 2016

[qfvmgvos] Extremely long scale numbers

Recursive construction of large numbers:

A0 = nine hundred ninety nine = 999
A0+1 = thousand = 10^3 = 10^(3*1) = 10^(3*2^0)
A1 = A0 thousand A0 = nine hundred ninety nine thousand nine hundred ninety nine = 999,999
A1+1 = million = 10^6 =  10^(3*2) = 10^(3*2^1)
A2 = A1 million A1 = nine hundred ninety nine thousand nine hundred ninety nine million nine hundred ninety nine thousand nine hundred ninety nine = 999,999,999,999
A2+1 = billion = 10^12 = 10^(3*4) = 10^(3*2^2)
A3 = A2 billion A2 = 999 thousand 999 million 999 thousand 999 billion 999 thousand 999 million 999 thousand 999 = 999,999,999,999,999,999,999,999
A3+1 = trillion = 10^24 = 10^(3*8) = 10^(3*2^3)
A4 = A3 trillion A3
A4+1 = quadrillion = 10^48 = 10^(3*16) = 10^(3*2^4)
A5 = A4 quadrillion A4
A5+1 = quintillion = 10^96 = 10^(3*32) = 10^(3*2^5)
sextillion = 10^192 = 10^(3*64) = 10^(3*2^6)
septillion = 10^384 = 10^(3*128) = 10^(3*2^7)
octillion = 10^768 = 10^(3*256) = 10^(3*2^8)
nonillion = 10^1536 = 10^(3*512) = 10^(3*2^9)
decillion = 10^3072 = 10^(3*1024) = 10^(3*2^10)
vigintillion = 10^3145728 = = 10^(3*1048576) = 10^(3*2^20)

Coincides with American short scale up to 999 million 999 thousand 999 = 10^9-1.  Coincides with British long scale up to 999 thousand 999 billion 999 thousand 999 million 999 thousand 999 = 10^18-1.

I was tempted to introduce a made up suffix like -zillion, e.g., mizillion, bazillion, trizillion..., to avoid redefining existing words, but since there already exists confusion between the American and British scales, I felt there was no harm in adding more.

The key feature is that very large numbers can be expressed while introducing new vocabulary much slower, logarithmically slower, than the traditional method.  The Latin prefixes conveniently line up with the exponent of the power of 2, inspired by the British scale.  (It was also possible to have a construction building from 99 hundred 99 + 1 = thousand, but it does not line up with Latin so well.)

Create a program to convert to and from words and values.  It might be necessary to use the word "zero" as a placeholder to avoid ambiguity.  (Or, prove that such placeholders are not necessary.)  Try the program on some large Mersenne primes.

There's a sort of middle-endian feeling to it, as the most important word that determines the size of the number is embedded somewhere in the middle.

Because of the tree like structure, it might be the basis for steganographically encoding large numbers, e.g., cryptographic keys, as parse trees of sentences with word substitution.  Perhaps use a base other than 10, maybe mixed radix.

Also consider Japanese numerals.

Monday, April 25, 2016

[yjogsatv] Japanese days of the week

The Japanese abbreviations for the days of the week, 月 火 水 木 金 土 日, are more compact than their English counterparts, Mon Tue Wed Thu Fri Sat Sun.

The Unicode code points (in decimal) are 26376 28779 27700 26408 37329 22303 26085.

Are their any languages for which the first letters of the names of the days of the week are distinct?

[qqzihsax] Half turn Rubik's

A Rubik's cube limited only to half turns is entertainingly difficult.

[rxvquuuu] Monochromatic supercube

Consider a Rubik's cube with all white faces, but with arrows drawn on each face, with all arrows facing the same direction on each face, so a supercube.  How difficult is this to solve?  It might depend on the pattern of arrow directions between the faces.  How many distinct ways are there to draw an edge-aligned arrow on each of the six faces of a cube?

[fzgcaugq] Noncyclic De Bruijn

The traditional De Bruijn sequence is cyclic: certain combinations span the break between the end and the beginning.  The standard method to construct a non-cyclic De Bruijn sequence is to copy and append the first few digits from the beginnning onto the end (usually some zeroes).  Can this be improved?  Are their shorter sequences that cover all combinations, not allowing cycling from the end to the beginning?

Also De Bruijn torus: can we improve over copying the entire left and top sides to the right and bottom?

[cvejwwrf] Immune from invasion

In the olden days, if one country thought another country was weak, they would invade (and possibly genocide).  (Inspired by Lebensraum.)  This created incentive for countries to maintain some sort of a reasonably functioning, economically productive state.  (Unlike the collapse of the western Roman empire.)

Nowadays, if a country can field a nuclear arsenal, they can retaliate against invasion with such devastating force that no one will dare invade.  Therefore, there is no longer as much incentive to maintain a reasonably functioning state.

Is this logic true?  Are nuclear weapons unique and unprecedented in the history of military warfare in their ability to provide immunity from invasion?

Maintaining a nuclear arsenal does require a reasonably functioning state.

If a state is functioning poorly, even without invasion it may fall to internal forces of regime change, so the incentive to maintain a reasonably functioning state still exists even in a nuclear armed power.  (E.g., regime change in Soviet Union.)  Civil war could have external countries supporting the rebels.  Is an external country supporting and winning a rebellion functionally equivalent to invasion?  One could imagine the installed puppet government committing acts like genocide to benefit that external country that supported the rebellion.

If a nuclear armed government is facing a rebellion supported by an external country, will they use their nuclear weapons against the external country?  Should they?

Is the incentive to maintain a reasonably functioning state even good?  One could imagine a state using its nuclear umbrella to allow its citizenry to live peaceful and happy, albeit technologically backward and less economically productive, lives.  In contrast, in the past, a "reasonably functioning state" probably meant exactly one thing, "able to field an army", which is not necessarily good for the country or for human civilization as a whole.

Military alliances between nuclear and non-nuclear armed powers also cause weird effects.  The non-nuclear ally must accede to the desires of the nuclear ally or risk being expelled from the alliance.  Meanwhile, the non-nuclear ally gains the immunity from invasion accorded to nuclear armed powers.

[ijxatmmn] Women attracted to money

Stereotypically, women are attracted to rich men.  Women also have less earning power than men (modulo the difficulties of exactly comparing earning power).

The traditional narrative has the causality in this direction: because women face institutional barriers in earning lots of money, they must seek out men with money.

However, we could hypothesize a different mechanism: in a hypothetical society in which women do not face barriers in earning lots of money, they have less incentive to seek out men.  This will result in less couples, less children, population decline, and the society will implode on itself, resulting in either extinction or change in society.  Therefore, only societies that place barriers on women from making money (or more broadly, create incentives for coupling) will survive: kind of a social Darwinist argument applied to societies competing against each other instead of individuals.  This hypothesis does seem to be supported by data that increasing education for women (and thus increasing their earning power) correlates with a declining birth rate, and more egalitarian societies having lower birth rates.

There are some leaps of logic in the argument:

The biological imperative to procreate is pretty powerful.  We have not described any force powerful enough to override the imperative to explain declining birth rates.

Regardless of their own earning power, women could still continue to be attracted to rich men, because, all other things being equal, more money is more better.  Therefore, whatever psychological mechanisms that program a woman's ideas of what she finds attractive could still continue to operate in more egalitarian societies, and still drive women to couple.  We have not described what those mechanisms are and why they should stop operating.

We revisit another aspect of this model.  If men's attractiveness in the eyes of women is determined by their wealth, then the biological imperative to procreate will incentivize men to earn more money, so to be more economically productive.  A more productive society will again win Darwinistically over one which is less productive.  Do more egalitarian societies see less productivity in men?  Is the loss of their productivity offset by the increased productivity in women?

I strongly suspect there is still much more going on, including game theory.

[idydqxzf] Rubik's cube steganography

A 3x3 Rubik's cube provides a way of encoding 65 bits, though the problem of mapping cube states to numbers, especially of mapping them one-to-one, is left unsolved.  Like shuffling a deck of cards, it provides a convenient way of generating 65 bits of entropy, assuming hand scrambles can be trusted.

It is not too suspicious to be found carrying a scrambled Rubik's cube.  Carrying two identically scrambled Rubik's cube (a backup key) might be suspicious, but the nature of the backup could be concealed by (say) applying an easily reversed checkerboard algorithm to it.  (Creating two identically scrambled cubes is analogous to solving a cube.)  Store the cubes in boxes so they do not get accidentally turned.

A supercube (picture cube) provides exactly 11 bits more, or 76 bits.

4x4 cube 152 bits. 5x5 cube 247 bits. 6x6 cube 385 bits (but almost 386).

Megaminx 225 bits. Gigaminx 875 bits. Teraminx 1903 bits. Petaminx 3310 bits.

Previously, code for computing the number of combinations.

[vcppbmdn] Rubik's cube combinations

We implement in Haskell the formulae at to compute the number of combinations of a NxN Rubik's cube, as well as a supercube (for which center facet orientation matters) and a super-supercube (also called a "real" cube, for which inner cubie orientations also matter) variations.

import Math.Combinatorics.Exact.Factorial(factorial);

div_exact :: Integer -> Integer -> Integer;
div_exact x y = case divMod x y of {
(q,0) -> q;
_ -> error "division had a remainder";

common :: Integer -> Integer -> Integer -> Integer;
common i den_base n = let {
e1 :: Integer;
e1 = div (n*n - 2*n) 4;
e2 :: Integer;
e2 = div ((n-2)^2) 4;
numerator :: Integer;
numerator = (24 * 2^i * factorial 12)^(mod n 2) * factorial 7 * 3^6 * (factorial 24)^e1;
denominator :: Integer;
denominator = den_base ^ e2;
} in div_exact numerator denominator;

cube :: Integer -> Integer;
cube = common 10 ((factorial 4)^6);

supercube :: Integer -> Integer;
supercube = common 21 2;

super_supercube :: Integer -> Integer;
super_supercube n = let {
e1 :: Integer;
e1 = div_exact (n^3-4*n+(mod n 2)*(12 - 9*n)) 24;
e2 :: Integer;
e2 = div (n-2) 2 + mod n 2;
e4 :: Integer;
e4 = mod n 2 * div n 2;
} in (div_exact (factorial 24) 2)^e1 * 24^e2 * (factorial 7 * 3^6)^(div n 2) * (factorial 12 * 2^21)^e4;

Incidentally, the output numbers factor easily. The largest prime factor in them is 23. One could do the calculations over a factor base of primes from 2 to 23 to get the output directly in compact factored form.

Next, we consider the Megaminx, and higher odd-order variants (so not Flowerminx / Kilominx):

-- n=1 megaminx; n=2 gigaminx; etc.
megaminx :: Integer -> Integer;
megaminx n = div_exact (factorial 30 * factorial 20 * (factorial 60)^(n^2-1) * (factorial 5)^(12*n) * 2^28 * 3^19) ((factorial 5)^(12*n^2) * 2^n);

Full Haskell source code.

Wednesday, April 20, 2016

[wwsnjkib] Asshole

"Asshole" describes a relationship, not a person.  The relationship between the describer and the described, probably contempt.

[nujwkgbz] X street in X

Enumerate instances of where there is a street that has the same name as the city in which it is located.  More interestingly, trace the history of why that street got the very special name.  Sometimes, perhaps often, it is not the main street of the city.

[iiucvwtg] Two knights versus promoted pawn

Make the two knights versus pawn chess endgame more difficult by requiring that, at checkmate, the pawn must have promoted.

[tcbskdhn] How not to

"How to" is important to document, but also important is to document failures, providing bounds on how far one can deviate from the instructions.  Anecdotes of failures can be crowd sourced.

[bgdnnpfy] Twisted and evil

Some alternate version of Star Wars in which the complex nature of good and evil are explored:

Luke: But you said Darth Vader was twisted and evil!
Obi-wan: Many of the truths we cling to depend greatly on our point of view.
Luke: Fuck you, Ben.

[ogcqfppx] Easy access to paraboloids

When making any bowl-shaped object, e.g., tableware, choose a paraboloid (likely truncated by a plane) as the shape unless there is a good reason otherwise.

Easy access shapes able to concentrate or emit parallel rays might be useful for education and tinkering.

Maybe there's a danger of shiny objects catching the sun a just the right angle and setting things on fire.  A nanny state might ban paraboloids for this reason, though the conspiracy theorists would theorize that the government doesn't want to make it easy for the populace to build radio dishes.

[wkqkumle] De Bruijn style music

Create a song which has within it all (say) 4 note songs.  A De Bruijn sequence doesn't quite work because scale transpositions can be considered equivalent.  Cyclic is OK: the song repeats.

Simplifications / constraints: Limit to two octaves of a small scale, e.g., pentatonic.  We don't care about covering 4 note songs with a range greater than an octave, or jumps larger than a fifth, or tritone jumps.  Limit rhythm in some way, the most obvious being only quarter notes, though that might be too boring.

Inspired by change ringing .

[ppzkvtnw] The Shitshow

A TV show about the dysfunctional behind-the-scenes production of a TV show.  Inspired by stories of dysfunction behind the scenes of real TV shows.

Same idea as 30 Rock.

[czcebacy] Bending the body variously

People try many different chairs, even standing desks, but all fail due to the fact that the body does not like to maintain any one position for an extended period of time.  Even lying down becomes uncomfortable after a while.

Create a motorized chair-ish device that continually moves the body to different configurations and orientations, perhaps from lying to standing.  If it is for working at say a computer, the screen and input devices also need to move.  Mouse must be magnetically attached to mousepad, or use a trackball.  Because the arms may move around, the keyboard needs to be split.

[tqyvaumr] Reflecting CPU instructions

Provide a system call or library function which gives the number of CPU instructions this thread has executed, independent of CPU time or wall clock time.

Perhaps (probably) approximate: maybe the OS tracks CPU time per thread and returns that number multiplied by a factor.

Get a heterogenous collection of computers to all do the same amount of work, perhaps for benchmarking.

[pcpzbfob] Lexicographic numbers

Given a set of numbers, strictly speaking, digit sequences because 01 and 1 are distinct, sort them lexicographically.  Unfortunately, in certain places, one cannot insert a new number.

It is impossible to insert anything before 0.  It is impossible to insert anything between 1 and 10.

We assume these numbers are keys to a map-like data structure, and we would always like to be able to insert anywhere.  Real numbers would work, except concrete implementations like IEEE 754 do have values which are minimum and also have pairs of numbers with nothing in between.

Fix this by considering digit sequences contrained to end in 5.

Decreasing sequence: 5 > 25 > 15 > 05 > 025 > 015 > 005 ...
Increasing sequence: 5 < 85 < 95 < 985 < 995 < 9985 ...

Equivalently, assume that every number invisibly has a 5 appended to it.  We can easily insert things before 0:  000 < 001 < 002 < 00 < 01 < 02 < 0.  This part resembles women's clothing sizes, or machined part sizes, with longer strings of zeroes meaning smaller.

Confusingly, 10 < 1.  Numbers sort like this: 10, 11, 12, 13, 14, 1, 15, 16.  One can see there are plenty of things that can be inserted between 10 and 1.  In the close neighborhood of 1 is 14 < 145 < 149 < 1 < 1502 < 150 < 152 < 15.  We can also insert things before 10.  0 < 05 < 06 < 09 < 100 < 104 < 10.

The empty string curiously sorts between 4 and 5, though perhaps it should be forbidden.

The invisible 5 at the end sometimes acts like a digit whose value is in between 4 and 5, because X4999999... < X < X5000000...

Compute the shortest number between two given numbers, or smaller or larger than a given number.  If there are many such shortest numbers, determine the middle one.  1 "" 7 8 9 97 98 99 997 998 999 ...  But when counting up, it makes more sense to compute the least shortest number: 1 "" 5 6 7 8 9 95 96 97 98 99 995 996 997 998 999 ...

I had a few false starts before discovering this scheme and am not completely convinced the scheme doesn't have problems.

The idea could be extended to sorting words with letters, even compound words with spaces in which the space character lexicographically sorts before a.  Let M be the invisibly appended letter, analogous to 5.

For binary, we need at least two invisible appended digits, 01 or 10.  For balanced ternary, I think the invisible digit could elegantly be 0.

For the purpose of creating numbers which always have another number in between, and larger, and smaller, arbitrary precision real numbers, including negative numbers and arbitrary precision after the decimal point, would work just as well and be less confusing.  Though sorting seems harder, needing to first locate the decimal point.

[fqmwiugx] Email address

Typing an email address, for whatever reason, is awkward, requiring an interface with lots of buttons, or some other awkwardness like T9 input (with symbols).  Onscreen keyboards and handwriting recognition (by human or by machine) are similarly awkward.

Instead of typing it in, let an interface be able to accept it by scanning a QR code or reading NFC.  This of course requires the user to carry a physical token.  Maybe tattoo.  Cameras are more compact than keyboards.

The at sign @ annoyingly is not one of the 45 special alphanumeric characters that QR encodes efficiently, though it is not that big of a deal to encode 1 character with a byte encoding.  Perhaps modify email clients (or more ambitiously, the email standard, or even more ambitiously, create a new standard entirely) that permits one of the 9 other punctuation marks as a separator.  I advocate Space.

A physical token can deliver more data than a human can easily memorize, so can also usefully provide things like a public key or public key fingerprint.

[tqucxexi] Creating people with something to lose

A welfare state provides assistance to the poor.  This potentially gives the provider of the assistance, namely the government, tremendous power to control people through the threat of withholding that assistance, and such absolute power will corrupt absolutely.

Certain forms of assistance, for example, minimum wage laws, are difficult for the government to withhold to particular individuals.  Other forms of assistance, for example, the government directly providing money, cause less distortion in the economy than minimum wage laws, but are easy for the government to withhold.

One possible workaround for the government having too much power: Instead of the government providing money directly, let it be some heterogenous collection of independent assistance providers.  If one provider corruptly refuses assistance to someone, they can turn to another provider.  There's the tricky problem of people taking from multiple providers, which if the government were the sole provider, they can ban multiple identities.  Instead of efficiently providing money as assistance, they can provide material assistance of things it does not make sense to take more than one of, e.g., food.

If this heterogenous collection of providers gets is funds from private donations, then the model precisely captures the privatized welfare system favored by conservatives.  It has flaws, most basically people want to donate to help One Of Us, and not One Of Them.

The original inspiration was crimes committed by people at the bottom of the social pyramid who have nothing to lose.  Welfare policies are often directed at decreasing such crime.  On one hand, it seems sinister to be altering behavior by threatening to withhold welfare assistance, treating people like puppets.  On the other hand, will welfare assistance with guarantees it cannot be withheld be effective in changing behavior, or will it continue to perpetuate a class of people with nothing to lose?

More generally, when does "good" monoculture happen?  "Good" meaning people don't see others as One Of Them (and then committing crimes against them).

[kwntcebt] Cube mate in 3

A Rubik's cube that is a small number of moves, say 3, from solved makes for a nice puzzle.  The player is challenged to find the optimal solution rather than applying a generic solving method.  Similar in spirit to chess mate in N problems.

Ideas on how to set up the puzzle:  The obvious method, make 3 random moves while looking, fails because it is too easy to remember the scramble you did.

Scramble 3 moves behind your back, turning the cube a lot between turns.

Have a friend do it where you can't see.

Build a machine to do it, concealed behind a screen.

Computer algorithm to get to the puzzle state by a roundabout way: first find a short sequence to a random state (utilizing God's Number), then solve for a short sequence (via Kociemba algorithm or similar iterative deepening) from that random state to the target 3-move-scrambled state.  Hopefully the short sequence does not go through 0- 1- or 2-move scrambled states.

Rubik's Touch (if it could be modified) could offer such puzzles.  It has the advantage of being easily able to be reset to the puzzle start state.

Deep cut puzzles change a lot even in a single move, so would provide challenging short puzzles.

[fvjoblmc] Robotic pets

On one hand, with computers getting more powerful, it seems like soon (if not already) we can create robots which can handle all the complexities of the real world in a reasonable if someone stupid way.

On the other hand, mechanical engineering has not advanced as fast as computer science (though this is a comparison between apples and oranges).

Can a human learn to love a machine as they would a biological pet?  Perhaps we still need some more advances in fluffy and squishy mechanical engineering.

Robotic pets of course have advantages over biological ones.

From there, it seems only a short hop (possibly over the uncanny valley) to robotic children as depicted in Spielberg's A.I. Artificial Intelligence.

Robotic versions of really stupid animals, e.g., fish, turtle, insects, seem doable now.  Perhaps put the computer outside the robot and control it wirelessly.  Though we still need to program the effect of the pet learning to trust its owner, which provides the great pleasure of owning a pet.

[kxjcihjt] What is real?

Reality is merely the model which provides the best predictions, though "best" is fuzzy: most accurate and most precise.

Inspired by the question, are fields (in physics, e.g., electric field and magnetic field) real, or are they merely mathematical tools to calculate more real effects like motion?  By this definition, they are definitely real.

[zsiutopq] Most expensive bridge

Divide the inflation adjusted cost of a bridge by the number of crossings per day.  What are some expensive, rarely used bridges?

Of course, this is not a fair statistic because we want the opportunity cost of the next best crossing.

Inspired by the Mackinac Bridge which does not seem to connect any major metropolises.

[vnuugcwh] Human chromatography

Gather a bunch of humans.  Apply some sort of stress.  Watch them separate out by... something.

Tuesday, April 19, 2016

[vjqzxiau] Change ringing

Change ringing with the bells ringing in sequence (as is traditionally done) is inefficient: a De Bruijn sequence can accomplish all permutations faster.

Instead of one bell at a time, ringing them as chords allows hearing every possible mixing.  Every possible n-chord sequence also seems doable for small n.

Neither of these work so well with the physical constraints on how often a single bell can be rung.  Both long gaps and rapid succession are bad.

[zsrwafja] My God it's full of lies

Parody of the line from the novelization of 2001: A Space Odyssey.

[otuodiyg] Adjusting the number of failed password attempts

For authentication systems that do something drastic after a number of consecutive failed password attempts (e.g., iPhone wipes the device), let the threshold number be adjustable higher by the user.  It could also be automatically adjusted based on the length of the password.  Should the threshold number be linear or exponential in the length?

Inspired by needing to type a long password on an flaky input device which often dropped keystrokes.

[zrkjrxzb] Quality by not quality

An environment which does not put emphasis on creating high quality may paradoxically create higher quality than one which does, by the mechanism that the lack of emphasis on quality creates a safe environment to make mistakes, and then people learn and improve through making mistakes.

Monday, April 18, 2016

[gkszsqre] Standard Model

Chapter 1: some pretty charts organizing the quarks, leptons, neutrinos, and force carriers.

Chapter 2: Multi page formula of the Standard Model Lagrangian.

It's a little steep between chapters 1 and 2.

T-shirt: What part of (insert equation from, compiled from Diagrammatica by Veltman ) do you not understand?  Or, find the sign error.

[okaremlt] Always count in base 100

When numbering things on a computer, e.g. files, always start at 00 or 01 and not 0 or 1 so that things can easily be lexicographically sorted until 99.  "Usually" you don't have over 99 things, but you often have over 9.

Alternatively, 8 is followed by 900.

[jprwidsh] Wishful thinking software ecosystem

All the software bundled with a computer system is perfect and bug-free, so there is no need for a software update mechanism.

The bundled software provides everything a user could ever want to do with the system, so there is no need for a mechanism for distribution of additional software, e.g., app store.

On one hand, these are silly, mocking deficiencies of many old platforms.

On the other hand, they are within the realm of imagination.  Software engineering might someday produce perfect software.  The bundled software could provide enough components for a user to easily build anything further wanted.

[hencdqdu] Abusing a biometric database

Given access to a large biometric database, it becomes a lot easier to find people who look alike, where "look" means the features stored in the database, which could include appearance but other features too.  This capability can almost certainly be abused, which is worrying, because only large powerful organizations can field or have access to large biometric databases.

Hire someone who looks like someone else to commit a crime, to thwart eyewitness identification.

[bliqpkxk] 8 to the bar

Hypothesize that in the phrase "eight to the bar", the "bar" is a dance bar of 8 beats, and not a musical bar of typically 4 beats.  (The 8 counts to a bar is why dancers count off 5 6 7 8 at the beginning while musicians count off 1 2 3 4, or "ah 1, ah 2, ah 1 2 3 4".)

If a dancer asks for 8 to the bar, e.g., "Beat me daddy, eight to the bar" (Andrews Sisters), then the dancer is asking for 8 strong beats to the dance bar, so a strong beat on every quarter note.  This contrasts to just 4 strong beats in a dance bar, a strong beat on every half note.  This distinction is the same as the "4 feel" and "2 feel" known to jazz drummers and rhythm sections.

A 4 feel is famously the style of swing music, with the bassist playing a note on every beat, often a walking bass line.  A 2 feel is famously the style of blues and rock 'n' roll.  (There are of course, many exceptions.)  A dancer asking for 8 to the means asking for a swing song as opposed to a blues or rock song.

This YouTube video, at 2'25", illustrates the difference between 2 feel and 4 feel.

[nmrjialj] Shoe throwing

Create a sport, perhaps similar in style to a shooting range, in which the goal is to throw your shoe to hit a target.  Inspired by the Bush shoeing incident.  A populace that is good at this is kind of like the sword of Damocles, in a symbolic way.

Some sort of large conveyor belt that returns your thrown shoe back to you.

[arhfweaq] Standardized cookie formats

For the common use cases of cookies, create standards of cookie data formats the websites can conform to (and announce their conformance) so that users can examine and interpret their cookies.

[pygitqnl] Density of containered foods

Foods sold in a watertight container, e.g., bottle, can have their mass easily measured (weight of container before and after emptying) and their volume easily measured (after emptying, refill with water).  Calculate and publish densities (because it's fun?).

Requires a kitchen scale and a graduated cylinder.

[cjkhaezz] Kyu dan threshold

Kyu and dan rankings in go 囲碁 almost act like negative and positive numbers.  If it were exactly like numbers, then calculating the stone handicap by subtraction would be easy.

In order for them to exactly act like numbers, there would have to be a 0 kyu rank that is equivalent to a 0 dan rank.  1 kyu and 1 dan would be separated by 2 ranks.  This would not be too strange: an extra large barrier between kyu and dan ranks, signifying advancement from student to master.

The way it currently works (I think) is that 1 kyu is followed by 1 dan; there is no 0.  Equivalently; 0 kyu = 1 dan and 0 dan = 1 kyu.  The crossover occurs at 0.5 kyu = 0.5 dan, if fractional ranks existed.

Another way it could work (but doesn't) is for 1 kyu = 1 dan, essentially zero being "spelled" 1.

[cfsleqpw] Resolving EPR with wormholes

Special relativity forbids information traveling faster than the speed of light.  General relativity does not.  Therefore, resolve the Einstein-Podolsky-Rosen paradox by stringing a wormhole between two entangled particles, allowing them to communicate as fast as they need.  The size of the wormhole is smaller than we can currently observe.

It is unsettling to think of space as like swiss cheese filled with lots of tiny holes connecting different points superluminally, or of space being crisscrossed by lots of tiny wormhole tunnels, but everything else in quantum mechanics -- and general relativity -- is unsettling also.  Most wormholes will be short: entangled particles can't travel very far before hitting something that observes one of them, at which point communication happens through the wormhole, and the wormhole becomes no longer necessary, so we assume it dissipates by some unknown mechanism.  Or, if there are entangled particles flying around for long distances in a nearly perfect vacuum, then, because it is a vacuum, there's nothing in the region that will "care" that there's a long wormhole in the area.

How small can wormholes be?  Is there a relationship between the size of a wormhole and how much, or how quickly, information may be transmitted through it?  What interaction would such tiny wormholes have with surrounding matter?  Currently there exists no theory of quantum gravity, but in the future, there may be an experimentally supported one, which in turn could disprove this theory.

Holding the mouth of a wormhole open requires negative matter.  Future subatomic particle experiments may disprove whether entangleable particles are composed in part of negative matter, in a way similar to how mesons are composed of both matter and antimatter.

Inspired by the Conway Kochen Free Will Theorem, which makes the assumption of no superluminal communication between particles.

[ajkaflia] Compress recursive text

Consider using mathematically generated text as (one of) the test cases for data compression methods.  For example:

Look and say sequence: 1 11 21 1211 111221 312211 13112221 1113213211 ...
Dragon curve: RRLRRLLRRRLLRLL...

The sequences have a lot of repetition, but do not repeat in any obvious periodic way, which is often a characteristic of data one wants to compress.

A quick test on 1 GB of Dragon Curve found that bzip2 compressed much better than gzip or xz but was also much slower.

Also human genome.

Sunday, April 17, 2016

[sqnzlbyw] Three button laser mouse

Missing in the market landscape is a simple corded laser mouse.  We prefer corded (a.k.a. wired, so not wireless) to not have to worry about running out of battery, and to decrease weight.  Laser to avoid the bright red LED.  Simple 2-button or 2-button-with-scroll-wheel to avoid accidentally hitting one of possibly many side buttons causing unintended effects.  Laser mice seem to be targeted at gamers and have a zillion extra buttons.  Also, one reason for using an (infrared) laser mouse instead of a bright red optical LED mouse is to avoid casting distracting light from the mouse to the surroundings when using it in a dark environment.  Gaming mice often also have a zillion lights on the top side, negating the benefit of avoiding the LED.

[hoskxrso] Menger building

The Menger sponge seemingly cries out to be built as a building: courtyards, windows overlooking courtyards, vertical shafts to permit natural light to get to internal areas.

[slmywigd] Wikipedia history report

On a subject that interests you, examine the full history of all edits to the article.  Is there an interesting narrative, perhaps of the article being systematically and persistently made worse?

The opposite of a report in which one is forbidden from citing Wikipedia: one can only cite Wikipedia.

[iqzzgvod] How is an icosahedron like an even permutation?

Create a geometric demonstration of how the rotations of an icosahedron or dodecahedron align with the even permutations of 5 objects, in particular the group action.

My guess is there is no good demonstration: that the two groups are isomorphic is just coincidence, vaguely an instance of the Strong Law of Small Numbers: there are not enough small finite groups to meet the demands made of them.  The icosahedral group had to factor into some collection of small finite simple groups, and A5 is where it just happened to land.

Why is a raven like a writing desk?  Lewis Carroll was a mathematician.

[csclnykm] Beans Don't Talk

By Conway, based on Beanstalk by Isbell, is an elegant game.  Two moves: 3n+1 and 3n-1, then automatically dividing by 2 until it is odd.  Getting to 1 wins.  The major open question is whether there are starting numbers from which neither player can force a win.

How far out has it been verified?  What is the longest known win?  What are some strategies that don't involve a giant look up table?  Probably factorization.

Reminiscent of Collatz conjecture.

[evlqigce] Konane

When playing konane on a checkerboard, place the light pieces in the dark squares and vice versa so that they have good contrast.

An odd by odd board starts with more pieces for one player.

What happens if all the pieces are identical?  Impartial konane, not a partizan game.  Both players may move any of the pieces.  Resembles peg solitaire.

Easily generalizable to more dimensions or other graphs with a notion of three nodes in a straight line.

[ymtwwbli] Online chess opening research

As you play someone in online chess, let the UI make available both yours and the opponent's previous games and moves played from the current position, perhaps annotated with computer analysis.

Both players can see both players' past games, so there is no advantage in information.  You know, they know you know, you know they know you know, etc. (common knowledge).

Amateurs can mimic the opening preparation done by professionals, though not have to memorize it.

[sjegcxoq] Avatars for online chess

Being able to design an avatar for online chess might be enjoyable for some players, even though it seems silly or extraneous.  The UI will probably keep it possible to turn off having to view your opponent's avatar, but a player might benefit from being able to see his or her own avatar play the moves, a way of fantastically being someone else.

More ambitious is for one's computer to do motion capture to animate one's avatar at the virtual board.

[yokhizjo] Chess960 opening selector

Let an online Chess960 interface preferentially choose initial positions that both players have not played, or played least frequently.  There remains a tricky detail of balancing the two players concerns: probably minimize the maximum of the two frequencies.

A player could game the system by being able to predict in advance what initial position will be chosen and prepare for it, negating the benefit of Chess960.  Need to have some randomness so that the optimal initial position is not always chosen.

Offer special recognition to players who have played every initial position with both colors, and have won from every initial position.

[uhgfhmup] Solar powered buoy

Intriguing is a computer mounted in a buoy floating in international waters (terra nullius), so not subject to the laws of any country on what it may compute, most famously laws about copyright.  As computers get more powerful, it may begin to resemble a person not subject to any laws.

Use solar power.  Or maybe wind or wave or tide.

How can it communicate with land, especially if it needs to do so surreptitiously?

How can it defend itself from being discovered and destroyed?  It might begin to resemble an autonomous submarine.

Of course, nature makes the ocean already a harsh place to try to survive, e.g., storms.

Previously, a satellite.  Space is also terra nullius.

[nhmbkbcx] Chaotically moving dance floor

Create a floor subdivided into many intersecting discs.  Each disc turns sometimes and stops sometimes to allow other discs to turn.  Cuts in one disc will need to line up properly to allow an intersecting disc to turn.

The Geranium Puzzle illustrates the concept.

Inspired by a club with a slowly rotating dance floor, a single disc.  Multiple slowly rotating discs might make more mixing happen.  Of course, stuff getting caught in the cracks will be a problem.

[gboweiiv] Cave of the crystals and Climate change

Exploring the Cave of the Crystals required a special refrigerated suit, as humans cannot survive in high humidity and high (but not melting or burning) temperatures.

Global warming is predicting to bring about conditions requiring similar suits in certain parts of the world (Pal and Eltahir, "Future temperature in southwest Asia projected to exceed a threshold for human adaptability").

[zhnknjpl] Visible premove

Create an online chess interface in which premove is permitted, but the opponent can see the premove that you are planning to make.

Making visible more information, having less hidden information, will hopefully yield higher quality games.

[vwysedoo] Dubbing

A technology that I am surprised that doesn't exist yet is altering one person's voice to match another's.  Both people read the same calibration text, or even different texts which both cover most of the phonemes, and then it seems a simple matter to map over the phonemes.

Dub the audio track of a movie from one language to another, preserving the original actor's voice.  The intermediate steps (not done automatically) include translation, then a stand-in voice actor speaking the translation, then the audio of the translation being adjusted from the voice of voice actor to the original actor.

Of course, such technology makes it difficult to trust that an audio recording is authentic.

Famous calibration texts:

Stackexchange question

The North Wind and the Sun

These may be problematic if the target language includes sounds that do not occur in English, though interpolation or extrapolation may be sufficient.

[tgeaiqgh] 1958 Tybee Island B-47 crash

According to Wikipedia, it is unknown to this day whether the lost bomb (a Broken Arrow incident) had a plutonium capsule or the plutonium capsule had been removed and replaced with a lead one for training purposes.  This seems like a catastrophic failure of record keeping, separate from the catastrophic airplane accident: the government lost track of a large quantity (150 lb?) of plutonium.  If the plutonium capsule had been removed, where did it end up?

[vzirowdx] Rust game and free software

The Rust video game, in attempting social commentary by assigning players to an unchangeable race and gender, unintentionally clearly illustrated the issue that free software has been advocating all along: users should have control over their software.

The unhappiness that some players feel is not strictly because they are unhappy with the character to which they have been assigned, but because they do not get to exercise control over it.  They are locked in.

Tangentially, although the media would like to play the story up as male gamers feeling emasculated, I have heard anecdotes of heterosexual male gamers preferring a female avatar (in games in which one can choose one's character's appearance) for rational reasons, for example, if that's the character one is going to be looking at all the time, it might as well be pleasant to look at.

[fccsfygy] Spider playing a violin or guitar

Does a spider walking over the strings of a violin cause it to make enough noise as to be heard by a person in the same room?

Originally reported on a internet picture meme.

If it doesn't, then do it Mythbusters style: highly amplified electric guitar.

[brsrmbrz] Hydrogen times phi

To avoid harmonics, aliens (or humans) should broadcast (or listen) at the frequency of the hydrogen line times the golden ratio, not "hydrogen times pi" has mentioned in the movie Contact.  Phi is the most irrational number.  In contrast, pi is unusually close to harmonics at 22/7 and 355/113.  The frequencies of hydrogen times phi are, depending on whether one multiplies or divides, 2298.264784206 MHz and 877.8590324196 MHz, falling in the UHF band of microwave radio.

For frequencies more at human scale, divide by some high power of phi.  Phi^44 yields 1.1 seconds.

Or divide the Planck frequency by some high power of phi.  Planck time multiplied by phi^207 yields 0.98 seconds.

Or, broadcast gravitational waves.  It is vaguely possible that some natural process causes harmonic coupling between EM radiation and gravitational radiation.

[wuekezop] Hyperfine structure of ground state cesium

Neutral (i.e., non-ionized) cesium (caesium, cæsium) has 55 electrons, including a single electron in its outermost shell (valence shell).  Having a single outermost electron is characteristic of alkali metals, and hydrogen.

In the ground state, this outermost electron occupies the 6s orbital.  There is (exactly) one hyperfine transition possible for this 6s ground state electron: between spin up and spin down.  There is no hyperfine structure for the electrons in the inner shells because they are all paired (1 spin up pairing with 1 spin down) in completely filled shells.  Therefore, there is exactly one hyperfine transition for ground state cesium.  (The motivation for this post was, cesium atomic clocks are said to be regulated by the hyperfine transition of ground state cesium; however, which hyperfine transition?)

For ground state cesuim, the total electron angular momentum J has magnitude 1/2.  The total nuclear angular momentum I has magnitude 7/2.  The total atomic angular momentum F can take magnitudes F = 3 and F = 4.  Transitioning between these two F states (equivalently J = 1/2 and J = -1/2) induces the hyperfine structure.  F = 4 is the higher energy state.  The difference in the two energy levels corresponds to radiation with frequency exactly 9192631770 Hz, providing the definition of the second.

The speed of light is also an exact number by definition, so the wavelength (lambda = c/f) can be expressed as an exact rational number: 21413747/656616555 meters.  This might be the only wavelength that makes sense to be expressed as an exact rational number.  The frequency factors as 2 * 3 * 3 * 5 * 7 * 7 * 47 * 44351.  The speed of light (in m/s) factors as 2 * 7 * 73 * 293339.  The greatest common factor is 14.  Had humanity settled on different base units for time and length many years ago, these numbers would be different.

The wavelength happens to be a human-scale length: about 3 cm or 1.25 inches.

Incidentally, starting from the ground state with its electron in the 6s orbital, the most common excited state pushes the electron to the 6p orbital, yielding the high intensity spectral cesium D lines.  The 4f and 5d orbitals (and others) are harder to get to.  There are two possible excited 6p states, corresponding to J = 1/2 and J = 3/2 (yielding 2 D lines).  In the latter, F can be 2, 3, 4, or 5 so there are many hyperfine transitions between them.

References from which this post was written:

Cesium D Line Data, Daniel Steck

[soblhbbm] Computers playing go 囲碁 endgames

Monte Carlo go 囲碁 programs currently play "slack" moves if they are sure they are going to win, or lose, which is aesthetically not pleasing.  This could easily be fixed by adjusting komi when it starts doing that (which can be detected when the evaluation is near 0 or 1).  Evaluate the position for a range of komi.  This of course is computationally more expensive, maybe doable for analysis.

Just how strongly can Monte Carlo go 囲碁 programs play endgames?  As well as a human pro?  Better?  Can they handle combinatorial game theory as described in Mathematical Go?

[alazzrkk] Encoding data in Korean

One can convert a number to base 11172 then express it using the Precomposed Hangul syllables Unicode block (starting at code point 44032 decimal).

The large block itself is actually form of mixed radix notation, with the multipliers being, from big-endian to units, 19, 21, and 28.  This is useful for visually looking up the code point of a character.  There remains the problem that some jamo are visually very similar, so vulnerable to noise.

[hrpyultg] 21 cm toys

Create toys and trinkets featuring the length 21.10611405413 cm, the wavelength of the astronomical hydrogen line.  One of the most important lengths in the universe happens to be human-scale.  Usually things are much smaller or much larger.

Most interesting would be an antenna whose resonant frequency is 1420 MHz.

Incidentally, how can the value 21 cm be derived from quantum first principles?  It must have originally been done so to make the astronomical prediction, because the spontaneous transition is too rare to be observed in a laboratory, and hydrogen masers had not been invented yet.

[mpzjfeyb] Text contrasting margin

The color of text should be the opposite of the color of the margin area that is inaccessible to printing.  For most screens, that color is black, so text should be a light color.  Paper is white, so text should be black.

When using a glowing screen in a dark environment, the inaccessible area beyond the edge of the screen is of course black.

Text can go all the way to the edge of the printable area but still have contrast against the background of the margin.  Inspired by the failure of black text on a white background with text extended to the very edge of the screen.  The first letters of each line merged into the black margin, especially left side vertical strokes B b D E F H h I i K k l L M m N n P p R r U u.

[rvkxatlh] Role model

Under what conditions will a person, famously a child, emulate someone else's behavior and be convinced not to think critically about their emulation?

Of course, inspired by the politics around role models, including censorship of media depicting bad role models and punishment of public figures deemed bad role models.

The typical argument is that someone will assume causality from the bad behavior to high status.  But the causality is often kind of a stretch, so requires deliberately ignoring the instinct to think critically about the "stretch".  When do people not think critically?  What incentives cause not thinking critically?  Perhaps bad role models are dangerous only in environments which also have incentives to destroy critical thinking, for example, parents requiring of their children not to think but obey.  Placing the resulting blame for the emulation on the role model seems wrong in that case.

Create fiction subverting the trope: a character surrounded by seemingly terrible role models but chooses not to emulate them.  Or, surrounded by good role models but the character turns out bad.

[tkihzbvq] Managing incognito cookies

A more paranoid mode of incognito mode found in browsers:

Cookies are not shared between tabs or windows.

Open link in new tab does not transfer cookies to the new tab.  This might be a little confusing for users: a new tab may seem to log out of a site, but they will easily be able to learn and understand this simple model.

Also avoid setting HTTP Referer when opening a link in a new tab.

Websites that open new windows or tabs might break, but those are not really nice websites anyways.

Alternatively, have some UI way of depicting that one tab is a child of another tab, so share the same cookie jar.  Maybe each window has its own cookie jar.

Clicking on a link that exits the current website also creates an empty cookie jar for the new website, preventing cross site cookies.  Pressing "back" restores the old cookie jar.  Pressing "forward" restores the new cookie jar.

Also consider not setting HTTP Referer when following a link that exits the website.  So HTTP Referer would only be set for internal links and embedded content (e.g., images).

Perhaps the UI always opens a new window when exiting a website to make it more clear that it is a new cookie jar.  User configurable.

UI for user to manually specify transferring over cookies to another tab.

Also, things other than cookies that act like cookies, e.g., beacon images.

[xomqwiod] Freenet specification

Things not documented very well, yet, except as source code:

Disk file format of cache, store, etc.

Wire data format of peers communicating with each other, assuming knowledge of relevant cryptographic keys.

The lack of documentation is probably due to laziness (lack of resources), but possibly security by obscurity.  The above two might make life easier for attackers.

The Freenet Client Protocol is documented.

[krhenuna] Just a calculator

First, an evolution of mechanical devices for calculating:

Adding and subtracting in unary.
Adding and subtracting in decimal (abacus).
Multiplication and division.
Roots, powers.
Logarithm and exponential.
Special functions.
Abstract algebra.

At what point does a calculator have so many features -- too many features -- that it becomes something more than just a calculator?

Consider drawing the line at, the features that are built in to the calculator are limited to things that have mathematical purity, a timeless unchanging quality to them.  Near the border: the conversion rate between inches and centimeters is included, but the conversion rate between dollars and yen is not (requiring network to keep up with the changing world).  Similarly, time zone conversions are not included.  The speed of light is included (defined to be a constant value), but the fine structure constant is not: it can still change due to better scientific measurement.

Things that are not mathematically pure are required to be user input.

An algorithm to compute something (e.g., a graph algorithm) is included, even though in the future better algorithms to compute the same thing might be developed.  The algorithm as a mathematical function from input to output remains unchanged.

Probably make an exception for built-in "help" text documenting itself, even though documentation can be improved over time.

[jxgfbqmx] Daddy

Investigate the etymology of the word "daddy" meaning male object of affection, often erotic affection.

Incest is supposedly a taboo in all cultures.

[smgzmobb] Horror is not safe

Anything described as "safe", especially "feeling safe", can be turned on its head to be a template for horror fiction.

Inspired by the political controversy around "safe space": writing horror subverting it seems very easy.  Is there such a thing as politically incorrect horror?

[xomvdqgt] Words of random lengths

Given a corpus, construct a trie annotated with counts or probabilities.  Implicitly or explicitly include the probability of the end of a word.  What features does this trie have, in particular features of the probability distribution of children of a node?

Synthesize a similar trie for an artificial language, seeing to emulate the "shape" of words of a natural language, for example, the distribution of word lengths.

Original goal was to create a red herring: text that looks like natural language that has been coded by a substitution cipher, having structures resembling natural language, but which is actually randomness.  (Kind of the opposite of cryptography: cryptography is things that look random which aren't; this is things that don't look random but which are.)

Common roots and suffixes are probably too difficult for a trie; we would need a directed graph, with words generated as a Markov chain.  Maybe cheat and assume that all roots have been compressed down to one character in the artificial language.

Easiest might be a trie whose probability of the end-of-word symbol increases by depth.  The non-end-of-word children of a node have some skewed probability distribution.  Generate this trie on the fly while generating random text, expanding (and remembering) nodes only as needed.

[fufxfanw] Circular symbols

Create a writing system or data encoding system that can pack arbitrary amounts of data into a circular region (disc), of course, requiring finer resolution at high density.

Most obvious is concentric circular segments.  The radial width of the segments decreases as the density increases.  How many angular segments per circle should there be, for a given radius (radial distance / radial width)?

Inspired by go 囲碁 kifu with numbers from 1 through (usually) 200ish written inside circular pieces.  Three digit numbers are the wrong shape for a circular region.

Spherical barcodes (future post).  We could also consider packing data inside a sphere.

[uxdaxoii] Hexagon and hypercube

The length of the space diagonal of a 4-dimensional unit hypercube is 2, not an irrational number like for 2 and 3 dimensions.

The length of the longest diagonal of a regular hexagon with side length 1 is also 2.

This might be why the 24-cell honeycomb and the hexagon tessellation are considered related.

[dmuwqriz] Keep the protons together

Compute the strength of the electromagnetic repulsive force between protons in the atomic nucleus, probably strength per unit mass, and realize just how powerful the strong nuclear force is.  The strong nuclear force does not merely balance electromagnetic repulsion of protons: for small nuclei it's very hard to induce fission or radioactive decay by perturbing them with particle collisions.  (Larger nuclei are another matter, often easily willing to give up positive charges by alpha or positron emission.)  Similarly, it's amazing that small nuclei get more stable (so release energy) by stuffing more protons into a small region through fusion.

[fojwzpbc] Japanese numbers

Japanese numerals, Unicode code points in decimal, and some alternate forms.  They are scattered through the CJK block, in contrast to the digits 0-9, which are clustered in order.

柒 or 漆
1229522769243362144232902202373852026578 or 284222542029590

陌 or 佰阡 or 仟
2534238476 or 2033638433 or 2019133836

The alternate forms that are commonly used are 0 (not an accounting character), 1, 2, 3, 10.  However, it also seems possible to alter the following characters by adding or erasing strokes: (5,9) (5,10) (5,1000) (5,10000) (6,8) (6,10000^4) (7,10) (7,10000^3) (8,10000^3) (9,10000)

秭 or 𥝱
2074020806201402241931213 or 153457


Even larger numbers are no longer single kanji.

[rvkxkkwz] Iroha table

The ordering of the characters in the Japanese Iroha poem (いろは), often used as ordinal numbers in Japanese.


Transliteration of the character according the the primary Unicode name. It is not always how the character is normally pronounced.
Ordinal number
Ordinal number in Japanese
Hira decimal
Unicode code point of hiragana character in decimal.  These values are 96 less than the corresponding katakana code point value.
Hira hex
Unicode code point of hiragana character in hexadecimal
Kata decimal
Unicode code point of the katakana character in decimal.  The values are (for easy cutting and pasting) 12452 12525 12495 12491 12507 12504 12488 12481 12522 12492 12523 12530 12527 12459 12520 12479 12524 12477 12484 12493 12490 12521 12512 12454 12528 12494 12458 12463 12516 12510 12465 12501 12467 12456 12486 12450 12469 12461 12518 12513 12511 12471 12529 12498 12514 12475 12473.
Kata hex
Unicode code point of the katakana character in hexadecimal
Coordinate on a go 囲碁 board (omits I)
Index counting from zero, possibly useful for base 47

IrohaNumJnumHiraHira decimalHira hexKataKata decimalKata hexGoZero

The obsolete characters are 25 and 43.

Here is the same table with the rows permuted to gojuon order.  Gojuon is the same order as Unicode for hiragana and katakana.

IrohaNumJnumHiraHira decimalHira hexKataKata decimalKata hexGoZero

ん (12435 U+3093) ン (12531 U+3043) N does not appear.

Reading the Go column vertically yields the cryptic pangram (omitting i) AY O SQHT GVDKU C FE X PWJLRBNZ M.

Thursday, April 14, 2016

[rzicybcp] Preserve email with linked images

Given an email message that includes external images that you choose to view, store a copy of the images in your mail archive.

Somewhat related, let one's mail server immediately fetch the images upon receipt of the email, rather than the mail user agent upon opening the message.  This will thwart beacon images.

[zlsrxuop] Bring your B game

Set up a scenario where that is part of a motivational speech (in contrast to A game).

[jkgfdxox] Proportion of provable

Given Godel's Incompleteness Theorem, what percentage of true mathematical statements are provable?  Of the unprovable, what proportion are provably unprovable?

These questions can be made precise for example by placing limits on the length of the statement expressed in some specified mathematical notation, e.g., first-order logic.

Is it even possible to know the answers to these questions?

We wonder if the answer might be similar to that of real numbers: most -- almost all -- real numbers are uncomputable; perhaps most true statements are unprovable.

[xwdoqekw] Fit

Many people ask, "Where do I fit?"  (Pippin, Corner of the Sky)

Fewer ask, "Why do I fit?" (or not fit).  What are the forces that shaped you and others so that you get along with them, and you feel fulfilled?

Even fewer ask, "Why do few people ask, 'Why do I fit?'?"

[nrkgykge] Second Coming of Athena

The goddess returns to find a world dominated by science and knowledge, her thing.

Athena versus Watson versus Google: the machines score 0.

Athena chats with brilliant scientists, giving them answers to questions that have stumped their fields for generations.  (What should be asked?)

[ivslzbie] Encrypted data storage

Both local storage encrypted with full disk encryption and cloud storage encrypted with a password known only to the user are very possible, though no one seems to have made the whole stack convenient and easy yet.

[gockoxjc] Squawk box

A small device with buttons that makes sound seems generically interesting, encompassing everything from musical instruments to iPod shuffle.

Create a generic computer with no display.  Of course, sound output could be an internal speaker or headphone output or Bluetooth.

Many previous posts on what an ergonomic small collection of buttons should be.

[emzojvoq] One slice of bread

A single slice of bread is something someone might reasonably buy with cash, costing about a penny.  This is an argument against eliminating the penny.  (Inspired by a discounted loaf of day-old bread being sold for 10 cents at a supermarket.)

What other things might people buy, with cash, costing about a penny?  Condiments, cooking ingredients (e.g., teaspoon of salt), bags.

It probably needs to be a special situation in which the labor cost of the transaction does not dominate the cost of the good being bought or sold.  Maybe honor system of payment.

Wednesday, April 13, 2016

[ceucjhmw] Getting the iPhone password out of a dead guy

The FBI's legal collision with Apple regarding getting data out of an encrypted iPhone curiously occurred for the first time in a case where the owner (Syed Rizwan Farook, technically not the owner but the person who knew its password) of the iPhone was (shot) dead, and not in a case of a living prisoner or arrestee stoically refusing to divulge the password or PIN.

Does this mean that, until now, whenever the FBI wanted to know the contents of an encrypted iPhone, it has always been able to coerce the password out of a living person, perhaps through harsh or devious interrogation?  Exactly what techniques do law enforcement agencies use to coerce revealing a password?  Just how effective, quantitatively, is their rubber-hose cryptanalysis?  It is frightening if the answer is "nearly 100%".

Alternatively, maybe this was the first time the FBI thought it could win such a legal case, riding on anti-Muslim public opinion and TERRORISM TERRORISM TERRORISM, hoping Apple would comply without a fight.

[saxordhd] When do the ends justify the means?

Instead of trying to answer this age-old philosophical question correctly once and for all, pick a policy to be used to make decisions related to that question, and stick with it until one officially modifies the policy.

We need a language for specifying such policies, perhaps a way of quantifying the cost of the means, and the benefit of the ends.

We also need to record instances of the policy being exercised.

This way, policies and their effects can be compared and hopefully improved over time.

[ghunzstp] Reducing image size

Some notes for reducing the data size of an image, inspired by people sending giant email attachments.

Crop.  Tools: gimp, pnmcut, jpegtran, exiftran

Reduce the resolution to what is necessary for what is being communicated.  Do you need to communicate roughly what a person looks like, or the exact layout of pores and hair follicles on their skin?  Tools: pnmscale

For JPEG (jpg), similarly reduce the compression quality to capture only the necessary detail.  Tools: cjpeg -q

Is color necessary or is grayscale good enough?  Tools: jpegtran -grayscale, ppmtopgm

For PNG: pngcrush -brute optimizes the image with no loss.

pnmdepth reduces the color depth.

Choose the best image format.  JPEG is good for real world photographs.  PNG is good for computer generated artwork, e.g., text and figures.  Djvu offers good compression of black-and-white text.

JPEG 2000 (jp2) offers even better compression than JPEG, especially at low bitrates, including the intriguing Region Of Interest (ROI) feature for higher quality for only part of an image.  Tools: JJ2000 jasper.

Other image formats: BPG, WebP, JPEG XR

Computer generated figures that started out as vector graphics format (Adobe Illustrator, Visio, Dia) will probably take up less space exported as compressed svg than to a raster image format like PNG.  Other vector formats: Postscript (ps), PDF.  Plus, vector provides infinite resolution!  Tools for lossless data compression: gzip bzip2 xz.

A picture of text takes up much more space than, say, HTML with CSS.

A vector image exported to an antialiased raster compresses worse with PNG than without antialiasing, though omitting antialiasing might be ugly.

[vksdztpo] Tablet as thin client

Create a tablet that has low CPU power and memory.  All the computation is done on a remote server (perhaps a personal server) which hosts the session to which the tablet communicates wirelessly: VNC RDP etc.

Special apps for displaying video and audio.  Maybe also phone.

Sun Ray

[fclnywau] Do people change?

Do people change?  Can people change?  Or is change an illusion of people developing into whom they were destined to develop?

Define change either as movement along a predestined path toward a predestined destination or goal (in which case, yes, people obviously change), or movement of the path or goal itself.  The latter definition is weirder but more interesting, so is the subject of this post.

Of course, this question has shades of the philosophical question of free will.

"Path" is a fuzzy concept, probably needing to encompass the multitude of possibilities due to external stimuli or effects from the environment yet to occur.

If people have free will, then they can change.  If they do not, then the person they are, encoded in a snapshot in time, serves as a perfect predictor of their entire future behavior, so there is a constancy -- a lack of change -- in the person that they are, as they progress into their future.

The fuzziness of question can be sharpened by invoking the concept of prediction.  If people can change, predicting their future behavior for a given contingency is difficult; they might have changed between now and then; predictions are inaccurate.  If not, predictions can be accurate.  Note well, the future contingency has to occur to know whether the prediction given the contingency is accurate.

What if predictions are accurate not because people can't change, but because social forces external to a person are too powerful?  Though it continues to be a tricky question because social forces could be the thing forcing someone not to change.

One of the powerful psychological mechanisms preventing change is identity.

Inspired by ideas that you can tell how a person will turn out from a relatively young age: their identity has solidified by (say) their teenage years.  (Assuming future conditions are known, e.g., assumed similar enough to today.)

[anggchml] Network filesystem inspired by git

Network filesystems are awkward beasts, having to deal with many failure modes and often full of bugs in doing so.

Network connectivity down.  Fileserver malfunctioning.  Race conditions of multiple clients editing the same file.

Instead of trying to make life easy for the client by providing the illusion of the "perfect" behavior of a single-user single-threaded local filesystem, expose some of the difficulties to the user/client, and let the client figure out how to proceed.

File was written to local cache.  File was transmitted to server.  Merge conflict happened (inspired by git).  For network filesystems backed by distributed storage, signal to the user that consistency has happened (eventual consistency): all backend servers now have the same copy -- your copy -- of the file.

Prefetch a file into the local cache.  Is the locally cached file out of date?

[hxyfuzsw] Kifu

A kifu of a go 囲碁 game is a very compact method of describing a game: all the stones played with a number on each stone.  It is a little bit unwieldy because one has to search for the next move, but that is the price of compactness.

It does require some annotations to side, e.g., dealing with captured stones.  What is the complete set of conventions for such annotations?  I think the first stone played at an intersection is given on the board; later stones are given as annotations.  There might be another one involving play which repeatedly captures and plays on the same spot: ko fights.

Incidentally, there is some ambiguity of exactly what "kifu" means.  It could mean the specific format of publishing a game (famously in newspapers) described above.  This is meaning being used in this post.

It could also mean generically any game record, in any format, e.g., SGF is a type of kifu.  Or any presentation of a recorded game, e.g., Javascript game player playing out a specific game.

It could also mean specifically the handwritten game record done by the game recorder during a live game, analogous to scoresheets in chess.

Given only a kifu, provide commentary to the game, for example, especially good or bad moves.  This is a challenge intended only for high-level players, needing to mentally erase the stones that haven't been played yet (or have been captured), vaguely similar to blindfold chess or commentating just given a listing of chess moves.