Wednesday, October 19, 2016

[iyuepsrr] Ultimate Lorem Ipsum

Provide a random excerpt of the original Cicero text (De Finibus), looping back to the start if necessary.  This should be easy.

[esvcmzuy] Hemispherical jigsaw puzzle

Start with a hemisphere with a picture on it.  Partition it into regions, then make pyramids (with bases with spherical caps) by extruding (intruding) the regions to the center.  If the pieces are designed to fit together in only one way, then it can be a jigsaw puzzle, even having shapes that stay together if correctly matched (e.g., dovetail).

Two hemispherical puzzles (the pieces of both jumbled together) could, after both being solved, be joined together into a sphere.

All the pieces could be shaped the same, but this is much harder for a hemisphere than for a sphere.  Maybe a special base, though that will give away most of the challenge of figuring out how the pieces are supposed to fit.

Trim off or round off the tips of the pyramids to make the pieces less dangerous to accidentally step on.

[yidzlgbu] Isohedral pyramids

Any convex polyhedron can be decomposed into a collection of pyramids (pyramid base = polygon face, pyramid apex = polygon interior point).  For an isohedron with apex at center, all the pyramids are congruent.

Might make for a nice puzzle, easy to construct because all the pieces are identical.  Maybe round off the tips to make it less dangerous to accidentally step on.

[cjvvgoqf] Music player filesystem

Simplest is 1 "program", a bunch of songs in order.  Possible UI actions: play program in order from the beginning, go forward/backward one song, repeat program, repeat one song, shuffle program.

This was the model for the iPod shuffle that did not have a display.  It is similar to physical media formats: tape, records, CDs (though the latter 2 do have rudimentary random access).

Next is multiple programs: play the default (first) program, go forward/backward one program, repeat all programs, repeat one program, repeat one song.  The same song could be included on multiple programs; the device should deduplicate.  A program could be an album or playlist.

Is two levels or hierarchy too complicated to navigate without a display?  More levels?

Filesystem features required: symbolic links for deduplication, ordering of files and directories, metadata.

Inspiration was the lack of a standardized interface to play a music library stored on an external device on a car stereo, using an interface built into the car.

Tuesday, October 18, 2016

[umqmxbar] Numbers whose factorial is just less than a power of 2

3 5 22 28 48 63 64 90 536 548 557 2689 6627 35053 49692 55139 2418263 9519742 18582322 19015320 43430008 43578373 45601897 103481702 455189228 760006976 1855572486

s=0; m=0; for(i=1, 10^100, s+=log(i)/log(2); q=s; f=q-floor(q); if(f>m, m=f; printf(" %d",i))); print("")

64 was artificially inserted into the sequence; it is the same as 63.  64! = 0.9966 * 2^296 = 0.9966 * 256^37.

If one only has a uniform random bit generator, permutations of this many items can be generated easily, with high probability (low probability with rejection sampling).  In fact, looking at the high order bits when they come out are enough to (usually) quickly know to reject.

Going the other direction: 3 6 7 11 15 20 24 62 65. Stopping at 81 because it's hard to imagine someone with a good random permutation generator larger than shuffling a deck of 81 Set cards.

How can the above record sequences be computed (extended) quickly?  There seem to be many algorithmic tricks possible.

Monday, October 17, 2016

[seuezdxy] My Little Inferno

Create an alternate ending to the My Little Inferno video game which makes the point that the player just burnt away a chunk of their life playing the game.  Inspired by the Yogscast playthrough commentary.

[piurrvti] Zeta calculator

In this video, the interviewer asks "If I were to enter into a calculator, 1 plus 2 plus 3 plus 4 and so on out to infinity, and then hit equals, would I get the answer minus 1 twelfth?"  The answer is of course, what does it means to do that "out to infinity?"

An interesting alternative valid question is, "If I were to enter -1 into a calculator, and then hit the zeta function button, would I get the answer -1/12?"  The answer is, what kind of calculator provides the zeta function?  The zeta function is a little bit more complicated to compute than, say, sine, but not too bad.  It's not considered useful enough to provide, though perhaps if it were, it would stimulate more interest in analytic number theory.

[esojjvln] Single elimination blitz

To make a chess tournament attractive to many people entering (as an alternative to segregating by class or rating), do things that increase variance -- increase the probability that a low-rated player can win or do well in the tournament.  Single games of blitz has higher variance.  Single-elimination tournaments have high variance.  Chess has draws, so not exactly suited for single-elimination; perhaps Swiss permitting repeated encounters until a decisive result occurs.  Tournaments with only a small number of rounds have high variance.

Inspired by poker and bridge, which have variance built into the game by being a game of incomplete information.

No matter what the structure, monetary prizes have to be carefully structured, or else there will be incentives for people to pay people off to throw games.  Every game must be zero-sum in terms of prizes or expected prizes (though this will induce many draws due to risk averseness).  For a single large grand prize, those still in contention for the grand prize must only play each other: there might be some byes due to draws causing an odd number of people to be in the money.

[ndvgnkvu] Porn blocker as history and cache blacklist

Repurpose the list of sites in a porn blocker or other parental control software as a blacklist of sites not to cache or store in browser history.  Because the list of sites is public -- included in the publicly available porn blocker -- the user can plausibly deny even knowing about the sites, which could not be done if the user had to hand-create a blacklist.

[wbcjkvuu] Look to zoom

How pleasant a UI is it to show a large image in a virtual reality environment, then use head tracking to choose where to zoom?  The zoom center probably slowly drifts toward the center so the user does not have to keep head cocked constantly, but that means the head has to track this drift.

Anything that requires pointing is equivalent to mouse on a regular display.

[houaffqc] Chess960 hiding 1 move

Modify Chess960 very slightly so that the initial position is not revealed to black until after white's first move.

White's clock starts running as soon as white sees the initial position.

[rmosscuf] Human CA

Create a demonstration with a large number of people, each doing a very simple task, resulting in very complicated global behavior.  Famous is cellular automata, though it would be nicer to have something more robust to people making mistakes.

[bdqrodel] Crazyhouse limited drops

Variations on the drop rule for crazyhouse chess (or shogi):

Pieces may only be dropped on the original position (two possible places for rook, knight, bishop, 1 place for queen, 8 for pawn).

Pieces may only be dropped on their original rank (1st or 2nd rank).  Further possibility: some (maybe all) pieces start in hand, to be dropped on their original rank whenever the player feels it fit to do so.

Pieces may only be dropped on squares not attacked by the opponent.

Pieces may only be dropped on squares controlled (attacked) by the player.  (Previously explored.)  Further possibility: pieces may be dropped directly onto an opponent's piece, capturing it.

[uitadwod] Stackage

Stackage for Haskell packages has the curious behavior that packages can disappear from it even though they were perfectly fine.  The cause of such a disappearance of say a package B is as follows: package B was originally pulled in as a dependency of another package A, and the maintainer of package A quit, so package A and all its dependencies, including package B, are candidates to be removed from Stackage.  Package B survives only if it has a direct maintainer in Stackage or is a dependency of another maintained package.

Inspired by the many packages that got dropped when lambdabot got removed from Stackage nightly, e.g., brainfuck.

Although the stated goal of Stackage is a curated collection of Haskell packages, each with an explicit maintainer willing to fix bugs and compilation problems (e.g., with new versions of GHC), I have found that a side feature is more useful: the identification of a large mutually compatible collection of packages without version dependency problems.  Such a side feature -- such a collection -- could be computed automatically without having to have a direct or indirect maintainer for each package in the collection.  I wish such a larger collection existed.

Start with, say, Stackage Nightly and expand it to include every package in Hackage that compiles cleanly and is compatible with Stackage Nightly and with every other package in the expanded collection.  There may be tricky cases of mutually incompatible packages in a potential expanded set which will need to be resolved, e.g., the newest version of A requires an old version of B, and the newest version of B requires an old version of A.  Perhaps resolve such conflicts in favor of the choice which causes the expanded set to be as large as possible.

Tangentially, how can one safely build a package (to test whether it compiles cleanly) if one is not sure whether a package's build script is evil?  Probably some kind of operating system container or sandbox.  Identify packages which use simple, presumably safe, build mechanisms, probably pure Haskell, versus packages which do something unusual, e.g., call a Makefile, which ought to be scrutinized before building.  (Inspired by a build script of software, I think maxima computer algebra, which creepily attempted to send email back to the author every time it was compiled.)

Can compiling a carefully crafted source file with GHC allow the author of the source file to perform arbitrary user-level actions within the operating system?

Friday, October 14, 2016

[cqvfuwdi] Decisive Swiss

Modify Swiss pairing for chess tournaments so that two players who have played already can meet again if all their previous meetings were draws.  Helps later when using head-to-head result as a tiebreaker.

Thursday, October 13, 2016

[cozkvurf] Unabomber math

Tell a story of the Unabomber sitting in prison working on proving the Riemann Hypothesis.  Not too unrealistic: his Ph.D. was in analysis.  The story is, this was always his endgame: he knew he might be spending the last few decades of his life in prison, and he knew he could do something productive and satisfying with his time there.

Tell a story of someone else, not yet in prison but considering embarking on a project very likely to result in a long prison sentence, studying up on math beforehand -- maybe the Clay Millennium problems -- to prepare for eventually doing time.

It would be politically uneasy if a prisoner, especially an especially bad one such as the Unabomber, were to achieve positive renown for doing something like proving the Riemann Hypothesis while imprisoned.  Therefore, we expect prisons to be set up to make such work difficult: what are those things?  Ends up being a roundabout restriction on speech.  Study whether such roundabout restrictions on speech also occur outside of prisons.

A vindictive society wants to make sure people in prison suffer, not be able to do anything pleasant, even if thinking and writing about math should be pleasant.  Should vindictive society get its way?

[dmvmqfvo] Change from within and without

Attempting to cause change from within: working within the system.

Attempting to cause change from without: disrupting the system, e.g., protests.

Which succeeds when (if ever)?  Why?

When does both being done simultaneously synergistically help each other?  When does both being done simultaneously impede each other?  What causes the difference?

Probably matters: zero-sum versus positive-sum.

Pessimistic hypothesis: change from without never succeeds, always impedes.  We almost suspect conspiracy-theory-style social manipulation for the social forces that cause it to be attempted (often) despite it being counterproductive.  Inspired by identity politics driving wedges, causing groups to want to or be willing to hurt each other more.

[pgmjypdp] Lens Flare The Force Awakens

Create versions of JJ Abrams Star Wars movies adding egregious lens flares everywhere.

Wednesday, October 12, 2016

[yvxbdfoi] VR flashcards

An evolution of technology, for example, for learning foreign language vocubulary.

Foreign word - English word
Foreign word - picture
Foreign word - animation or movie
Foreign word - 3D still scene or 3D movie

E.g., learning names of vegetables: get a sense of scale, turn it around to see it from different angles.

Maybe gross anatomy medical education.

[gwpxocih] More apostrophes

Take a string of letters with apostrophes, substitute the regular expression [a-z]+ for each apostrophe.  If there is a unique English word that matches that pattern, then let the contracted form with apostrophes be a valid contraction of that word.  Currently existing contractions are grandfathered in, despite violating this rule.  Maybe we need an alternate character that is not an apostrophe.

(Tangentially, there seem to be very few current cases where leaving out an apostrophe leaves a valid sentence or fragment with a different meaning.  Maybe apostrophe-s versus s-apostrophe versus s-alone for possessive singular versus possessive plural versus adjective (maybe name) ending with an s.  It is ironic that apostrophes are what people are sticklers about; they are almost purely decorative -- vestigial.)

(Another tangent: there is ambiguity between apostrophe-s meaning "is" or possession: Bob's back.)

Perhaps forbid apostrophes in the first or last position.

What contractions will exist?  List them in order of word frequency (and probably stop before the words become too obscure: trying to figure out an obscure word with missing letters is too hard.)

Finding these contractions seems computationally difficult.

[gxpgqixq] Notes on higher dimensional mazes

Consider two different types of 2D mazes on a grid of squares:

Some of the squares are black (indicating blocked); other squares are white (indicating passage).  Call this type of maze a "maze of blocks".

All the squares are white, but there are infinitesimally thin walls preventing passage between certain adjacent squares.  Call this type of maze a "maze of walls".

Depicting a 3D maze of blocks in 2D is fairly easy: just show slices.

A 4D maze of blocks is similarly easy.  A MxNxPxQ maze could be depicted as a PxQ array of MxN slices.  It could also be depicted as a MxN array of PxQ slices.  These different depictions are interesting when two of the dimensions are small, 2 or 3.

Consider a MxNx3x3 maze of blocks.  First, depict it as a 3x3 array of MxN mazes.  One can determine whether one can move along the 3rd or 4th dimension by looking at the corresponding square on an adjacent MxN maze.  This can be annoying or time consuming if the MxN maze is large.  Add annotations to each square in the MxN maze showing which 3rd and 4th dimension steps are possible: thin colored rectangles.  The ultimate goal is to provide enough information so that a person can form a model of the maze (or local parts of it) in their heads (interestingly, a 4-dimensional model) and solve chunks of it in their heads.

I have seen a 3D maze of walls depicted in slices, with certain squares in each slice marked with a small black square indicating a hole down or a larger thin ring indicating passageway up the ceiling.  Could be generalized to 4D with the same per-square annotations described above.


The simplest maze structure is a tree: there exists a unique path between any pair of nodes.  Make the maze a little bit harder (or easier, depending on the point of view) by adding loops.  The obvious starting idea is just one loop, and lots of trees hanging off of it.  What next?

In 3 dimensions and more, there are no constraints on graphs that can be embedded in a maze: there are no problems with paths needing to cross like in 2D.  Other loopy graphs: tetrahedron and higher simplices (equivalently complete graphs), torus grid of 2 or more dimensions, hypercubes, cross polytopes.  Cubic graphs, including snarks, are neat.  Cross polytopes and simplices have very small diameter.  Which loopy graphs are interesting for mazes?


Consider a maze of blocks of N dimensions, where N is quite large, but the maze has width 2 in all dimensions.  (Maze total volume is 2^N.)  Is it difficult?  How can one depict it to aid solving?

For a GUI, N switches denoting the coordinates, a light above each switch signifying whether changing that coordinate is permitted (not a solid block).  Maybe not just a light but the name of the room (block).

What interesting loopy graphs above can be embedded in a 2^N maze of blocks?  If not 2^N, then maybe 3^N offers enough space.

A 2^N maze of walls might lose most its geometric aspect; it might as well be an abstract graph.

[whsrvxdi] Spiral around a sphere

Draw a spiral from pole to pole on a sphere, then place points uniformly along the spiral.  This is one quick and dirty way to scatter points on a sphere avoiding points close to each other.  The best spiral probably has the latitude spacing between turns equal to the distance between adjacent points on the spiral.  Some messy details still need to be worked out.

[qgbcnfov] up dn ambigram

Lowercase up and dn (abbreviation for "down") can be flipped to read the other word.  Also arrow pointing up.

[ugawzrcp] Entropy loss in repeated hashing

How much entropy is lost when iterating a hash function?  We expand on this answer:

The probability a given bucket is occupied (gets hit), or equivalently the proportion of buckets occupied, when there are n buckets and f[i]*n trials is

f[i+1] = 1- (1 - 1/n)^(f[i] *n)
= 1 - z^f[i]
where z = (1 - 1/n)^n
n = 2^b where b is the width of the hash, e.g., b=128 for MD5.
f[0] = 1

The quantity z could be approximated as exp(-1) for large n, and the whole expression could be approximated as f[i+1] = 1-exp(-f[i]), but we do not have to make these approximations.  Evaluate z directly with arbitrary precision arithmetic to avoid round-off error.

Similarly, the recurrence could be approximately solved as a closed-form function of its index, but we do not have to approximate.  Instead, explicitly iterate the recurrence however many times you were planning to iterate the hash function.  This computation will take roughly the same amount of time that the iterated hash function iterations would have taken.  The recurrence computation can be done with double-precision floating point, or with arbitrary precision arithmetic if you are worried about round-off error.

(Aside: the first iteration loses approximately 0.6617 bits of entropy.  If we naively assume the amount of entropy lost each iteration is the same, then SHA-512 would converge to a fixed point after 774 iterations.  This intuition is false, because as the number of trials decreases, we are less likely to lose filled buckets due to collisions.)

Finally, evaluate the bits of entropy lost as -log(f[i])/log(2).  It may be instructive to choose the number of iterations to be a power of 2: i = 2^j.  Experimentally, I confirm that the answer about j-1 bits.

Note well, this is still an approximation because the it does not account for the hash function being the same each iteration, so that values can go in a loop.

Aside: run Floyd's cycle-finding algorithm on various hash functions and other cryptographic primitives to see if short cycles can be found.

Tuesday, October 11, 2016

[ssgyfepw] Tree digit separators

Insert different separators recursively (like a binary tree) between digits of a long digit string to make it easier to read.  Here we demonstrate one possible collection of separators on the SHA-512 hash of the empty string.

cf 83.e1 35:7e ef.b8 bd ** f1 54.28 50:d6 6d.80 07
d6 20.e4 05:0b 57.15 dc ** 83 f4.a9 21:d3 6c.e9 ce

47 d0.d1 3c:5d 85.f2 b0 ** ff 83.18 d2:87 2f
63 b9.31 bd:47 41.7a 81 ** a5 38.32 7a:f9 27.da 3e

The separators get fancier further up the tree. "nothing", space, period, colon, double-asterisk, line break, paragraph break, (to be used later) line of dashes, line of equal signs in its own paragraph.

Alternatively, we could repeat the smaller separators each time, building up a little pyramid.  This time we avoid newline separators but add some different ones: cf 83 . e1 35 .,. 7e ef . b8 bd .,:,. f1 54 . 28 50 .,. d6 6d . 80 07 .,:':,. d6 20 . e4 05 .,. 0b 57 . 15 dc .,:,. 83 f4 . a9 21 .,. d3 6c . e9 ce .,:'**':,. 47 d0 . d1 3c .,. 5d 85 . f2 b0 .,:,. ff 83 . 18 d2 .,. 87 7e . ec 2f .,:':,. 63 b9 . 31 bd .,. 47 41 . 7a 81 .,:,. a5 38 . 32 7a .,. f9 27 . da 3e

With groupings of 3 digits instead of 2, this is isomorphic to "extremely long scale".  Below is a 768-digit number between a "septillion" and an "octillion".

123 456.789 012:345 678.901 234 ** 567 890.123 456:789 012.345 678
901 234.567 890:123 456.789 012 ** 345 678.901 234:567 890.123 456

789 012.345 678:901 234.567 890 ** 123 456.789 012:345 678.901 234
567 890.123 456:789 012.345 678 ** 901 234.567 890:123 456.789 012
345 678.901 234:567 890.123 456 ** 789 012.345 678:901 234.567 890
123 456.789 012:345 678.901 234 ** 567 890.123 456:789 012.345 678

901 234.567 890:123 456.789 012 ** 345 678.901 234:567 890.123 456
789 012.345 678:901 234.567 890 ** 123 456.789 012:345 678.901 234


567 890.123 456:789 012.345 678 ** 901 234.567 890:123 456.789 012
345 678.901 234:567 890.123 456 ** 789 012.345 678:901 234.567 890

123 456.789 012:345 678.901 234 ** 567 890.123 456:789 012.345 678
901 234.567 890:123 456.789 012 ** 345 678.901 234:567 890.123 456
789 012.345 678:901 234.567 890 ** 123 456.789 012:345 678.901 234
567 890.123 456:789 012.345 678 ** 901 234.567 890:123 456.789 012

345 678.901 234:567 890.123 456 ** 789 012.345 678:901 234.567 890
123 456.789 012:345 678.901 234 ** 567 890.123 456:789 012.345 678

We can also experiment with a ternary tree where each separator, including "nothing", is used up to twice in a row.  (We again change up the sequence of separators.)  Here is a 243-digit number: 123 456 789 . 012 345 678 . 901 234 567 .:. 890 123 456 . 789 012 345 . 678 901 234 .:. 567 890 123 . 456 789 012 . 345 678 901 .:*:. 234 567 890 . 123 456 789 . 012 345 678 .:. 901 234 567 . 890 123 456 . 789 012 345 .:. 678 901 234 . 567 890 123 . 456 789 012 .:*:. 345 678 901 . 234 567 890 . 123 456 789 .:. 012 345 678 . 901 234 567 . 890 123 456 .:. 789 012 345 . 678 901 234 . 567 890 123

Not specified is what to do if the binary or ternary tree is not full.

Sunday, October 09, 2016

[hmnfenka] Dreams

Hypothesize that one of the reasons humans dream during sleep is to stabilize mental health: the brain generates happy dreams that seem real, for sad people.  The temporary happy "reality" causes hormonal and other beneficial physiological effects.

[fyvtfvvq] Some distributed technologies

Some of these are also sometimes labeled "federated".

RSS, PubSubHubbub

[fliglzph] Making sex unenjoyable

Sexual assault and rape sometimes cause long-term trauma which makes having sex unpleasant.  People who find sex unpleasant are less likely to do it, and consequently less likely to have children.  Assuming controlling sex is one of the most important functions of society, we would expect to see sexual assault and rape institutionally deployed to accomplish this function (kind of horrifying).

Military victory is often followed by the invading army raping the conquered locals.  This might be purposeful to decrease the population growth rate of the conquered, allowing to conquerors to gain a population advantage, especially useful if the conflict lasts generations.

Are there other instances of this happening?

Sexual assault causes long-term trauma only sometimes, only under certain conditions (though we have not yet exactly identified those conditions).  A society or subculture might be engineered so that people deemed less desirable to breed encounter those trauma-inducing conditions more frequently, and then a background rate of sexual assault, causing trauma in some but not in others, causes the differential rate of having sex and consequently having children.  For example (perhaps this is more general than just an example): sexual assault might cause trauma only in people lacking a strong social support network.  A strong social support network is granted only to those who abide by the rules and membership requirements of the society or subculture; those who do not are shunned and live as lonely outcasts and suffer traumatic consequences.

[kuqjbyhj] Desirable features for a shell

Features of bash I use.  (Browsing through the manpage of bash.)  Motivation was thoughts of creating a better command-line shell, perhaps with a more regular syntax or more features, but a better one will have to retain old useful features.

^Z & bg fg wait "time wait" $! jobs
readline, history
redirection noclobber >|
interpolation (backquotes)
environment variables for child processes
subshells (parentheses) usually then piped
completion (tab)
glob expansion
cd pushd popd dirs pwd CDPATH
set -e -x "-o pipefail" -u
programming: control flow, local variables, functions
exit status && ||
prompt customization

[qmxwfkbd] Bullying the different

The common, perhaps universal, pattern of bullying is that "the different" are targeted.  Three possible evolutionary mechanisms, attempting to answer a previously asked question.

1. Bullying tests whether someone is in the tribe, to discover whether they can be trusted.  How would one pass the test?  This could be taught.

2. Someone has already been identified as not part of the tribe, someone who has allegiances elsewhere so cannot be trusted.  Bullying serves to expel them from activities and benefits of this tribe.

3. Bullying may serve as incentive to abandon their old tribe and maintain allegiance to the new one.

Attempts to regulate bullying seem doomed to fail, as they seem to be trying to regulate human nature.

People are different in many ways.  Which differences are selected for bullying, and which are not?  Why?  Assuming correct #2 above, it would be the differences, especially behavior, that signify tribe membership, whether someone can be trusted.  These behaviors might be subtle, and may only happen to correlate with the popularly believed reasons for bullying (e.g., race, gender, body shape, sexual orientation).

If someone is selected for bullying, how accurate are the bullies' determination that they are not part of the tribe, someone who cannot be trusted because they have allegiances elsewhere?  I suspect it is frighteningly accurate, but if not, this could be taught to be more accurate, though such teaching is politically incorrect.

[uakrhrvm] Questions about Rat Park

Why aren't there more replications?  Maybe negative results aren't getting published.

Are there political difficulties in getting funding to attempt a replication?  Political difficulties in publishing a confirmation (positive result)?

Is it a particularly difficult experiment to perform?  Perhaps needing to obtain and handle a controlled substance.

I suspect there are (or will be) some positive and some negative results in replications.  What determines the outcome?  Are some rat stimuli more effective than others at preventing or breaking addiction?  What neurological mechanisms are involved in the rat that cause the positive and negative results?

I suspect experimenter bias has a strong effect on the outcome.

Saturday, October 08, 2016

[myfnohif] Infinite cross bridges

Draw a square.  Divide it into thirds horizontally.  Take the middle rectangle and divide it into thirds vertically, yielding a small square in the center 1/9 the area of the original.  Recursively repeat infinitely on this center square.  Place electrical resistors on all segments and calculate the resistance between two corners of the original square.

Draw a square.  Draw a smaller square inside it.  Connect the corresponding vertices of the two squares.  Repeat.

Latter is equivalent to a prism with a square grid of resistors on its surface.  We can imagine other infinitely long thin geometric shapes: stack of octahedra.

[exgbexzz] Adversarial truth discovery

An adversarial framework seems like it should work well for discovering truth: each side challenges the other's version of the truth, causing lies and manipulation to be revealed.

We see this model in science, in the justice system, in political campaigns in democracies, in journalism.  However, these examples cynically or pessimistically demonstrate that reality is almost diametrically the opposite of theory.  It sometimes works in science (but often not: "cargo-cult science"), and both the justice and political systems are about who can bullshit better.  Journalism, motivated by advertising revenue, publishes the entertaining version of the story, not necessarily the true one.  In all these fields, effort seems better spent trying to take advantage of fallibility in human reasoning than to actually discover truth.

We imagine an alternate universe in which adversarial truth discovery does work well in all these fields.  It would have an interesting side effect: transcripts of jury trials and propaganda from a political campaign would be extremely good educational resources afterward.  Suppose unemployment were an important political issue between two parties.  As the sides debate and try to convince voters, both sides need voters to understand how the labor market functions and how domestic and macroeconomics work so that voters can evaluate propsed policy differences between the two parties.  Therefore, both sides will produce very good, easy to understand, educational material on these topics.  If the educational material is bad, confusing, the voter might come to the wrong conclusion and vote for the opponent, so there is tremendous incentive for the educational material to be good, and for the parties to attack opponent's bad educational material.  Compare this to the incentives (or disincentives) to create good educational material in the traditional education system.

Perhaps someday computers can help.

[odunhugu] Inclusive counting in music

Inclusive counting, not typically used in (American) English, is still present in musical terminology.  An interval of 7 notes higher than the base note of a scale is called an octave.  1 note higher is called a (major or minor) second.  6 octaves has nothing to do with the number 6*8 = 48; instead 6 octaves is 42 notes.

[ycnkrkrd] Replicate Riemann's zeta calculation

Replicate Riemann's 1859 hand calculation of the first few nontrivial zeros of the zeta function.  This seems formidable.  Feel free to use log tables and any other resources Riemann might have had at the time.

[jiekvsvp] Frobeniusly strong Lucas pseudoprimes

We compute composites (pseudoprimes) which pass the strong Lucas primality test with P and Q chosen by Selfridge Method A, and additionally satisfy the Frobenius-like criterion V[n+1] = 2Q (mod n) mentioned in Baillie's original paper, which can be tested almost for free.

There are 304 such pseudoprimes less than 10^9, and 757 less than 10^10.  The corresponding numbers for the strong Lucas pseudoprime test without the above Frobenius-like criterion are 1415 and 3622, so this almost-free test improves things significantly. (See OEIS A217255 and These Frobeniusly strong Lucas pseudoprimes are a subset of the strong Lucas pseudoprimes.

Below are the 304 pseudoprimes less than 10^9.  Further pseudoprimes here.  Source code will be posted later.

5777 10877 75077 100127 113573 161027 162133 231703 430127 635627 851927 1033997 1106327 1256293 1388903 1697183 2263127 2435423 2662277 3175883 3399527 3452147 3774377 3900797 4109363 4226777 4403027 4828277 4870847 5208377 5942627 6003923 7353917 8518127 9401893 9713027 9793313 9922337 10054043 11637583 13277423 13455077 13695947 14015843 14985833 15754007 16485493 16685003 17497127 19168477 19347173 20018627 22361327 23307377 24157817 25948187 27854147 29395277 29604893 30299333 31622993 31673333 32702723 33816593 34134407 34175777 36061997 39240233 39247393 39850127 40928627 41177993 42389027 42525773 47297543 49219673 49476377 50075027 51931333 53697953 57464207 59268827 62133377 64610027 67081607 67237883 69244097 70894277 73295777 73780877 74580767 75239513 75245777 75983627 83241013 83963177 85015493 85903277 86023943 87471017 89746073 90686777 91418543 93400277 98385377 100981997 104943827 106728053 110734667 116853827 117772877 122879063 124477513 131017577 131990627 136579127 139904627 140782823 142593827 143221993 144967877 146278373 148472347 150204577 153256277 154308527 156715343 157132127 158197577 163578827 166850777 168018353 171579883 177991277 179295443 184135673 185504633 186003827 192227027 196754513 202368143 207023087 210089303 211099877 213361937 226525883 229206347 231437957 247030877 247882963 253755053 254194877 257339503 257815277 259179527 264250367 264689963 276795217 277932113 280075277 284828777 290256947 293485877 306219377 311387693 312189697 316701527 320234777 320297657 334046627 344107133 347522647 347547437 360783793 370020797 375578683 376682627 384646597 386628527 387009737 400091327 400657277 401790377 403675973 409245563 420717527 429992597 432988877 437118527 438894377 439744397 440964593 443146057 443969063 448504697 450825377 455039027 456780193 461700077 461807147 461819483 464407883 465523103 465964127 467486627 468245207 469721647 475167377 480053573 480891143 481033907 485326403 495101777 500337713 504097397 523827527 540136277 543893783 544339637 546540347 552576653 558030527 562046627 563601257 570122027 574181327 577647017 582182327 582934477 583031693 584238563 590901317 595402877 598147577 598364773 623709217 628919117 634888253 638227127 640151777 649354103 657333797 657665777 659936423 664939277 667595897 670042903 670786877 672810497 686258627 688773443 691455077 691593047 692726473 704907377 706840573 709706567 713971187 721652587 727615877 729645563 731349233 734498627 747587777 756310507 768614027 771325967 772719947 773515133 780421277 788342777 797102627 798790787 799500077 800484227 807775547 811541327 812957903 825393997 831065633 838472417 839350363 847053323 847887823 856901267 863097377 869420473 873933527 878330573 922483693 923962577 930039743 940801877 947756267 957697997 961095923 961931213 969210377 978920627 979805777 983720077 985125077 986079553 988367813

[wdgqdnby] Riemann zeta sound

In "Prime Number Races" by Andrew Granville and Greg Martin is an interesting formula involving the Riemann zeta function, reexpressed below in Haskell-style notation for mathematics:

\x -> 1 + 2 * (sum $ do { s <- rootOf zeta ; guard $ real_part s == 0.5 ; let { gamma = imag_part s} ; guard $ gamma > 0 ; return $ sin (gamma * log x) / gamma})

It is the sum of sine functions, like a Fourier transform.  This suggests synthesizing a sound using the same coefficients, the imaginary part of the roots of zeta along the critical line.  The first root is at 14.13, so we scale down every root by that factor yielding the sequence 1, 1.49, 1.77, 2.15,...  Then, take logarithms base 2^(1/12) to express the frequency ratios of the higher harmonics in musical semitones.  Here are the first 100 intervals in semitones:

0 6.87 9.88 13.27 14.64 16.93 18.40 19.39 21.17 21.79 22.87 23.97 24.84 25.27 26.44 26.96 27.58 28.20 29.05 29.38 29.87 30.63 31.00 31.55 31.82 32.52 32.92 33.14 33.67 34.10 34.51 34.79 35.07 35.68 35.81 36.19 36.48 36.85 37.23 37.45 37.63 38.08 38.36 38.56 38.87 39.04 39.46 39.66 39.84 40.08 40.42 40.59 40.90 41.00 41.24 41.58 41.75 41.88 42.14 42.33 42.60 42.77 42.97 43.05 43.40 43.54 43.70 43.89 44.04 44.26 44.51 44.58 44.73 44.93 45.17 45.26 45.46 45.60 45.70 45.98 46.09 46.23 46.33 46.54 46.68 46.86 46.99 47.09 47.22 47.45 47.58 47.63 47.83 47.91 48.10 48.24 48.39 48.44 48.57 48.78

Two potential issues:

The amplitude of each harmonic properly should be scaled by the reciprocal of gamma, as in the formula above.  However, the human ear is has variable sensitivity across the frequency spectrum, so it might be better to allow the listener to individually control the amplitude of each harmonic to explore different aspects of the music of the primes.  Let the listener also control the fundamental frequency and apply a band-pass filter, in order to hear different segments of harmonics.

The harmonics get more and more densely packed the higher one goes, in contrast to regular Fourier transforms, in which the harmonics are equally spaced in frequency.  For example, there are 5888 harmonics at 147 semitones above the fundamental (rounded to the nearest semitone), corresponding to the 88075th through 93962nd zeros.  (We used this table of Riemann zeta zeros.)

One idea is not to worry and synthesize the sound anyway.  Harmonics get somewhat densely packed even for regular Fourier transforms when viewed in the logarithmic semitone scale: there are 281 harmonics at 147 semitones above the fundamental, corresponding to the 4733rd through 5013th harmonics.

Another idea is to rescale the coefficients (roots) so that they are roughly equally spaced in frequency.  The spacing of the zeros along the critical line is related to Gram points and the Riemann-Siegel theta function.

Previous work on the sound of the Riemann zeta function.

Friday, October 07, 2016

[abymulnr] Primes in the neighborhood of powers of two

Prime numbers in the vicinity of "nice" powers of two.  The exponent is itself of the form 2^n, 3*2^n, or 5*2^n.  The larger primes were discovered with Pari/GP.  The gap between 2^65536-5627 and 2^65536-99267 took about 2.8 days.  2^65536 = 2^2^2^2^2.

Primes were verified additionally with 20 iterations of Miller-Rabin, with randomly chosen bases.

Search ranges: 2^2^15 -149000 +227000, 2^2^16 -154000 +163000.  For others, the search stopped at the last number.

Related OEIS: A058220 A058221 A129786.

Previously: Smaller numbers, Twin primes

2^1 +0 +1 +3 +5 +9 +11 +15 +17 +21 +27

2^2 -1 -2

2^2 +1 +3 +7 +9 +13 +15 +19 +25 +27 +33

2^3 -1 -3 -5 -6

2^3 +3 +5 +9 +11 +15 +21 +23 +29 +33 +35

2^4 -3 -5 -9 -11 -13 -14

2^4 +1 +3 +7 +13 +15 +21 +25 +27 +31 +37

2^5 -1 -3 -9 -13 -15 -19 -21 -25 -27 -29

2^5 +5 +9 +11 +15 +21 +27 +29 +35 +39 +41

2^6 -3 -5 -11 -17 -21 -23 -27 -33 -35 -41

2^6 +3 +7 +9 +15 +19 +25 +33 +37 +39 +43

2^8 -5 -15 -17 -23 -27 -29 -33 -45 -57 -59

2^8 +1 +7 +13 +15 +21 +25 +27 +37 +51 +55

2^10 -3 -5 -11 -15 -27 -33 -41 -47 -53 -57

2^10 +7 +9 +15 +25 +27 +37 +39 +45 +63 +67

2^12 -3 -5 -17 -23 -39 -45 -47 -69 -75 -77

2^12 +3 +15 +31 +33 +37 +43 +57 +61 +63 +81

2^16 -15 -17 -39 -57 -87 -89 -99 -113 -117 -123

2^16 +1 +3 +7 +15 +21 +27 +43 +45 +51 +63

2^20 -3 -5 -17 -27 -59 -69 -129 -143 -153 -185

2^20 +7 +13 +25 +33 +37 +51 +57 +85 +105 +127

2^24 -3 -17 -33 -63 -75 -77 -89 -95 -117 -167

2^24 +43 +73 +75 +115 +117 +121 +165 +205 +225 +231

2^32 -5 -17 -65 -99 -107 -135 -153 -185 -209 -267

2^32 +15 +61 +75 +81 +91 +93 +163 +181 +201 +217

2^40 -87 -167 -195 -203 -213 -285 -293 -299 -389 -437

2^40 +15 +27 +55 +97 +115 +141 +157 +177 +253 +277

2^48 -59 -65 -89 -93 -147 -165 -189 -233 -243 -257

2^48 +21 +61 +75 +91 +235 +241 +243 +253 +297 +315

2^64 -59 -83 -95 -179 -189 -257 -279 -323 -353 -363

2^64 +13 +37 +51 +81 +93 +141 +307 +331 +393 +493

2^80 -65 -93 -117 -143 -285 -317 -549 -645 -765 -933

2^80 +13 +85 +235 +253 +343 +435 +457 +555 +597 +753

2^96 -17 -87 -93 -147 -165 -189 -237 -243 -315 -347

2^96 +61 +81 +121 +151 +253 +403 +423 +627 +633 +765

2^128 -159 -173 -233 -237 -275 -357 -675 -713 -797 -1193

2^128 +51 +81 +165 +273 +385 +421 +463 +573 +625 +757

2^160 -47 -57 -75 -189 -285 -383 -465 -543 -659 -843

2^160 +7 +291 +357 +421 +471 +501 +643 +685 +861 +921

2^192 -237 -333 -399 -489 -527 -663 -915 -945 -1059 -1143

2^192 +133 +453 +511 +565 +813 +1005 +1045 +1113 +1131 +1423

2^256 -189 -357 -435 -587 -617 -923 -1053 -1299 -1539 -1883

2^256 +297 +301 +357 +487 +583 +757 +795 +807 +847 +931

2^320 -197 -743 -825 -843 -873 -1007 -1017 -1217 -1815 -2955

2^320 +27 +261 +391 +525 +561 +793 +931 +1413 +1857 +1981

2^384 -317 -1437 -1557 -1617 -2147 -2319 -2729 -3087 -3093 -3273

2^384 +231 +331 +417 +535 +735 +817 +823 +835 +933 +1015

2^512 -569 -629 -875 -975 -1695 -1827 -2529 -2807 -2967 -3143

2^512 +75 +145 +285 +727 +1105 +1147 +1273 +2743 +3177 +3913

2^640 -305 -503 -735 -995 -1019 -1215 -1593 -2015 -2033 -2805

2^640 +115 +303 +391 +757 +1287 +1485 +2943 +3627 +3711 +3861

2^768 -825 -1385 -1815 -1845 -2069 -2277 -2825 -3209 -6953 -9189

2^768 +183 +241 +427 +955 +1423 +1723 +1831 +2161 +2851 +3225

2^1024 -105 -179 -1397 -3177 -5025 -5409 -6083 -6369 -6615 -7137

2^1024 +643 +1081 +2113 +2715 +3711 +5335 +5793 +5947 +7015 +7447

2^1280 -1175 -1665 -3149 -5907 -7079 -7607 -7703 -8865 -10043 -10277

2^1280 +1815 +2251 +2553 +3217 +4075 +4405 +4435 +7081 +7405 +9087

2^1536 -3453 -4977 -7769 -8333 -9923 -10859 -11429 -11795 -11843 -11877

2^1536 +75 +1381 +1605 +2487 +4903 +6333 +6637 +7191 +7597 +7681

2^2048 -1557 -2543 -7437 -8507 -9443 -9509 -11339 -11837 -12459 -12855

2^2048 +981 +1617 +3063 +3211 +4143 +7405 +9843 +10665 +10725 +11097

2^2560 -75 -1347 -2745 -6599 -7245 -10205 -12659 -17417 -18413 -20159

2^2560 +903 +4077 +4125 +4363 +5025 +10593 +12153 +13581 +13891 +14767

2^3072 -47 -2165 -4737 -6117 -6489 -7625 -9617 -15269 -23993 -24279

2^3072 +813 +877 +3427 +5131 +9133 +12367 +12433 +13435 +16003 +17245

2^4096 -2549 -8067 -8627 -8799 -9443 -14477 -16859 -17555 -18365 -20655

2^4096 +1761 +7227 +7423 +10093 +10473 +13965 +17335 +17355 +19891 +22803

2^5120 -7097 -7779 -11619 -12689 -15435 -20799 -26745 -28727 -30527 -31955

2^5120 +5467 +6741 +20847 +25135 +26611 +29335 +30147 +33237 +33567 +40791

2^6144 -5157 -6369 -6639 -13773 -13785 -22437 -22923 -27029 -39879 -41895

2^6144 +375 +1275 +2853 +3901 +5545 +11877 +11953 +13171 +14875 +15481

2^8192 -2439 -5619 -9345 -9515 -19085 -19733 -21713 -45933 -46643 -51453

2^8192 +897 +9543 +10813 +13371 +14931 +14985 +15505 +15763 +16305 +19423

2^10240 -323 -10119 -27353 -34179 -40253 -44975 -47195 -66917 -76307 -82187

2^10240 +2601 +15295 +25011 +35671 +46123 +53697 +54387 +58843 +65215 +67963

2^12288 -27803 -30519 -39213 -41045 -43197 -60465 -65055 -72195 -73853 -78515

2^12288 +11293 +17437 +25951 +40413 +40803 +41965 +42775 +46555 +56623 +66175

2^16384 -13797 -29027 -62747 -99125 -101543 -107609 -115673 -118119 -134357 -134705

2^16384 +2775 +36333 +42027 +47025 +55933 +80391 +91395 +95665 +98581 +104565

2^20480 -479 -9159 -21203 -32885 -86435 -88767 -100073 -102509 -104097 -124599

2^20480 +8367 +24201 +28173 +32787 +36061 +46051 +52323 +70725 +72163 +81187

2^24576 -1875 -32507 -37217 -61373 -66905 -67475 -97023 -98079 -103815 -119235

2^24576 +241 +22461 +35193 +80967 +130677 +130965 +145611

2^32768 -25353 -38783 -53373 -61725 -67553 -79613 -112985

2^32768 +118113 +143905 +145027 +160771 +162873 +182005 +187861

2^40960 -48069 -70803

2^40960 +59815 +74031

2^49152 -34689 -37923

2^49152 +1605 +11923

2^65536 -5627 -99267 -123563

2^65536 +44061 +44181 +58227 +106417 +116193 +119031

Thursday, October 06, 2016

[oobhikls] Unsatisfying P != NP

Someday, it may be proven that P < NP; however, the proof might be disappointing or unsatisfying.  It might be proven that one (obscure) NP problem is not in P, but it unfortunately provides no insight as to whether another NP problem, a problem that you care about, perhaps integer factorization, is not in P.  It could be, or it could not be (assume the proof technique does not generalize).  Or it might be proven that in the worst-case, a problem cannot be solved in polynomial time, but this isn't helpful if your particular instance of the problem isn't in that worst-case class.  For example, it might be proven that factoring requires super-polynomial time for a set (infinite sequence) of very rare, very difficult to construct integers, but this doesn't help for cryptography because practically all RSA numbers will not be in that class.

If it is proven that P = NP by showing a polynomial time algorithm for an NP-complete problem, then things will be very exciting (or practically, perhaps not, if the exponent is huge): by reduction it will provide a polynomial-time algorithm for every problem in NP.  Is it possible that P = NP might be proven not going through the NP-complete route and yield a similarly disappointing or unsatisfying proof?  Perhaps a non-constructive proof: there exists some deterministic Turing machine equivalent to a nondeterministic Turing machine...

[sxbpxqpu] Splitting the primes by 3, 4, 6

All prime numbers except 2 are of the form 4k+1 or 4k+3.  (Actually, all odd numbers.)  This distinction is made famous in Fermat's Sum of Squares theorem and quadratic reciprocity.

All prime numbers except 3 are of the form 3k+1 or 3k+2.

All prime numbers except 2 and 3 are of the form 6k+1 or 6k+5.

Each of the residue classes contains roughly half the prime numbers.  (Nice article: "Prime Number Races" by Granville and Martin.)  I don't think there are other moduli which result in two classes of equal size.  (All prime numbers (all numbers) are of the form 2k+0 or 2k+1, but former contains only prime element, namely 2.)

The remainders for each of these can also be written +1 and -1.  Therefore, each prime can be annotated with 3 signs, moduli 3, 4, and 6.

The annotation for currently largest known Mersenne Prime M74207281 is +-+ (plus minus plus).  The annotation for the exponent is +++ (plus plus plus).

[vnluuail] 4D virtual reality

A good use of 3D virtual reality might be to depict 4-dimensional objects, kind of an analogy to how 2D displays are frequently used these days to depict 3-dimensional objects, especially in games.

There still remains the issue that what the eye sees is a 2-dimensional image projected on the retina.

[fuusnzvv] Prime enough

You come across a composite number that resists factorization, so you call it prime and use it accordingly.  Under what conditions or applications is this a bad idea?  Under what conditions is it fine (so long as no one discovers a factor)?

Probably a bad idea if you don't know the factorization but someone else (secretly) does, though I have no concrete examples of how things go wrong.  Any other cases?

Previously, if you can't factor N, then factor N-1.

Monday, October 03, 2016

[cmpuuxwa] Good teachers are bad for society

If school, not just business school and college, but even primary school, is intended to separate students destined to become high productivity workers from low, then good teachers, who help keep in school those students destined to become low productivity workers, and who help students destined to become low productivity workers pass tests intended to distinguish low productivity from high, these good teachers are interfering with the system, making it difficult for the rest of society to distinguish between low productivity people from high by looking at their education, a signaling mechanism in an imperfect (asymmetric) information game.

This model assumes that a person's productivity is exogenous: you don't actually learn anything in school, equivalently, nothing a teacher teaches ultimately affects productivity.  Productivity might be entirely determined by the social support structure around a person.

Does this model explain teacher salaries?  Society needs incompetent people, and only incompetent people, to be teachers.  Promotion and firing have to be geared toward retaining and rewarding the incompetent.  What mechanisms in the workplace and school system can accomplish this?  Kind of a kakistocracy.

Education as a signaling mechanism has most famously been analyzed for labor and employment, but it probably gets used in other fields, too, like courtship.  Good teachers might be indirectly affecting -- helping students subvert -- those fields, too.  Flaws in the courtship process cause at best a waste of time, at worst, sexual and domestic violence between people incompatible with each other.

[yxnisako] Base 26 checksum

Create an error correcting code or check digit for base 26, detecting mistakes that humans tend to do, like swapping adjacent letters, like the Verhoeff check sum for numbers.  Maybe adapt Verhoeff's idea for the dihedral group of order 5 to order 13.

Better might be taking input in base 27, allowing one escape character, and emitting a base 26 check letter or letters.

[huxoeaub] Bypassing SIM activation on Verizon Motorola Droid 4

The "touch 4 corners in succession" method works to bypass "A SIM card is needed to operate this phone" when initializing a factory-reset Droid 4.  It succeeded in portrait mode; I see other reports it also works in landscape mode.

What is the history of this circumvention?  Was it originally revealed by Motorola?  If not, how could anyone discover it?

Friday, September 30, 2016

[kumkhtsj] Large type augmented reality

One potentially useful application of augmented reality is to deliver information to people with less vision, e.g., who need large type.  The goggles could read distant or small text (perhaps it is encoded also as a bar code to aid the goggles) then redisplay it as (probably scrolling) large type in front of the user.

[kwqpymmm] Marshall simul

Find a strong chess player who plays the Marshall Attack and have them give a simultaneous exhibition, playing black, unconventional for a simul.  Many beginners play the Ruy Lopez as white, so will likely easily be led into the Marshall.

Maybe host the event at the Marshall Chess Club.

Could also be done with Berlin Defense.

[yfeiupcb] Unrefrigerated meat

Meat is difficult for off-grid cooking because it needs to be kept refrigerated.  Unless it is still alive.  How many people does it take to eat a cow in one meal?  How difficult is off-grid slaughter?

[olhemvjt] Draws broken by time remaining

Consider resolving chess draws by whoever has more time remaining on their clock.

Maybe black gets a slight time advantage to start because white has more ability to control the opening.

Maybe a long Bronstein delay before each move, so players can (if they wish) play without using any time at all.  Maybe time deducted in quantized chunks, e.g., minute.  Inspired by traditional time controls in go 囲碁.

[zirjsqzg] Segregation by weight

If body shape, including obesity, is correlated with social class, then we will expect to see things that cause segregation or discrimination by body shape for the purpose of accomplishing segregation or discrimination by class: keep the wrong people out.

Fat people will be uncomfortable with physical activity, especially activity in warm environments, because of the square-cube law.

Conversely, thin people will be uncomfortable in cold environments.  This might be be occurring in highly air conditioned work environments.

[hpwxmcmo] Blame culture

Something bad happens, and you look for a person to blame.  This psychological need to blame a person, not, say, a process or an institution, is a strong characteristic of some cultures but not others.  Examine how this custom develops, and is passed on to each new generation.

Finding the person to blame is usually followed by punishing the person.  Vindictive, vengeful society.  Probably a fractured society has lots of Us versus Them and willingness to see Them suffer.

Is it correlated with the importance of giving credit, the dual of blame?  The importance of attaching a person's name, maybe your name to a good deed.  Influences things like copyright.

[utjnmonw] Self-power free

Squarefree numbers lack factors of the form n^2.  This could be generalized to cubefree and so forth.  It could be further generalized to numbers lacking factors of the form n^n.

Any interesting properties of such numbers?

[wgigwrzi] Ulam spiral squares

For each diagonal segment in the Ulam spiral of primes, replace it with a square that has that diagonal.  What will the image look like zoomed out a lot?

In the original Ulam spiral, the image will just look gray in the center fading to white further away as the density of primes decrease.  Replacing diagonal streaks with squares increases density.

[pislnyhv] KRPKR endgame

Is underpromotion ever necessary in the KRPKR chess endgame?  There are probably situations in which promoting to KQRKR is stalemate but KRRKR is a win.

When can the defender force conversion to a difficult KQKR endgame?, where difficult is defined as more than N moves away from an easily won position, e.g., checkmate, Philidor.

[qgjwwzhs] Suicide taboo making things worse

The suicide taboo probably extends to the still-living: people tend to shun and distance themselves from the suicidal.  This of course makes things worse, pushing people to suicide.

Assuming the taboo could be reversed, we would have friends supporting suicidal friends, even in supporting their desires for suicide.  Probably need to decriminalize assisted suicide even by nonprofessional friends.  Enemies would of course also support a person's suicide, but assume a suicidal person can easily distinguish between the two, because friends do other things than help you suicide ("Friends help you move...").  (Hopefully the court system can distinguish also.)  Amidst all this, the suicidal tendency (and rate) counterintuitively decreases because a person continues to have their support network rather than being shunned.

[imlbinkm] Many computers as one

A distributed system simulating a single system with lots of cores is (probably) a nice abstraction for the programmer, vaguely similar to distributed memory simulating shared memory.

OpenMosix and successors (LinuxPMI) seem mostly dead.

Maybe Linux LXC.  Probably need live migration.

Design an operating system to make this kind of stuff doable.

[jbtgxnlw] Capitalization

Capitalization is used in English for many purposes, e.g., sentence separator, emphasis.  Create a NLP tool to automatically classify them.

Proposed usage is when translating to a medium which has a different convention for emphasis, e.g., boldface.

[wcetdpyo] Battling gravity

The Yuuzhan Vong invasion of the Star Wars galaxy began with the destruction of the planet Sernpidal using the Yo'gand's Core technique of crashing a moon into it.

Tell a story of it ending in equally epic fashion, a force battle between a Jedi and a dovin basal, each trying to move a moon in opposing directions.

Yoda: size matters not.

Tuesday, September 27, 2016

[fuiynihj] Two games on a checkerboard

Checkers (draughts) uses only half the squares on the board, begging some way to make the other half useful.  Vladimir Vigman proposes two independent games.  Similar ideas:

Two independent games of different sizes, one 10x10 and one 8x8, to prevent mirror strategy.

Two independent games played by two pairs of opponents (4 people total) cross ways.  The appeal/difficulty is dealing with the distraction of another game going on on the same board.  Fast time controls would add a physical challenge of needing to avoid hands colliding.

Something like bughouse chess were captures on one half-board can be transfered to the other half-board.

A way for online spectators to watch two independent games simultaneously making efficient use of screen area.  Online could easily also provide it as a way to simultaneously play two different opponents.

[doxvmyhv] Fishtail skirt

I suspect that the fishtail blues move and other hip-centric juke-joint blues moves were invented while wearing a "swishy" style short skirt or dress.

[bubtfjda] Sequestered correspondence chess

People cheat at chess by using computers.  In correspondence chess, this is no longer even considered cheating: it is a battle of how well you can wield your engine.

People go on vacation and deliberately cut themselves off from communication and computers, perhaps remote locations.

Kill two birds with one stone: a chess vacation at a spot which strictly enforces a monastery-like environment with no computers, where you can play chess, perhaps correspondence chess so you are not constantly tied to the board, against others in similar environments.

[yrwkbxjr] Key stretching in Python

A demonstration of how to increase the number of rounds of password hashing for generating a crypt(3)-style password hash (e.g., /etc/passwd or /etc/shadow), similar to the mkpasswd utility.

# python3

import crypt
# defaults to SHA-512
# 10 million rounds takes 9 seconds on my computer
salt=salt[0:3] + "rounds=10000000$" + salt[3:19]

[ntcvdfzp] Human binary arithmetic

How accurately and rapidly can humans do binary arithmetic?

When doing a large decimal calculation by hand (especially multiplication) e.g., calculating pi, perhaps it is more efficient to do radix conversion at the beginning and end.

[baqwuqso] Monsters in Lake Baikal

Large lakes are sometimes inhabited with cryptozoological monsters (Loch Ness Monster, Champ, Ogopogo).  (Also similarly of course, the ocean.)  Invent such a monster for Lake Baikal, which currently doesn't have one: as a very large, very deep, very old, fairly remote lake with a similar long thin shape as Loch Ness, there is plenty of room for imagination: it surfaces only once every million years to feed.

Currently only exists folklore of how the nerpa got there, so far from the ocean.

[dhukumsa] Stridin'

Modify blues struttin' to travel a lot, if the dance were invented in a venue with lots of space.  Key differences from foxtrot, one-step, etc.: close embrace, low level maintaining some blues aesthetic.

[ybzqupva] Marshall Attack

Is the Marshall Attack (of Ruy Lopez) the only popular chess opening named "attack" in which Black is doing the attacking?  (Cf. King's Indian Attack vs. King's Indian Defense)  Pedants might call it Marshall Counterattack or Marshall Countergambit.

[gxtbdznp] Carcinogens in cigarettes

Smoking causes lung cancer, but exactly which compounds cause what amount of cancer?

Identifying the most carcinogenic could help produce cigarettes that are less dangerous.  Or mass produce just the most carcinogenic compounds to use as a chemical weapon.  (Not sure how useful it would be as a weapon which takes years to kill, maybe a surreptitious murder.)

Intriguing is the possibility that polonium, highly radioactive, accounting for only a trace of the mass of cigarette smoke, accounts for a large portion of cancer caused.

[jucahlag] Polonide

The chalcogens get smellier as you go down down the periodic table: oxygen, sulfur, selenium, tellurium.

Tell a fictional story of the Marie and Pierre Curie being the first mortals to smell a polonium compound (organopolonide), then, as they vomit for (say) months due to the odor, regretting every decision they've ever made in life, especially taking up chemistry.  "You think it's a chacogen? (retch)"  "Yeah, I'm pretty sure it's a chalcogen. (retch)"

In reality, smelling polonium would have killed them due to its intense radioactivity.

[qoqbetqt] Forested virtual reality

One of the most dramatic impacts humanity has had on the planet is deforestation.  Simulate in virtual reality or augmented reality what your area, your terrain, would have looked like before people, likely heavily forested.  Which kind of trees (requires science to answer)?  Computer graphics of sun and sky filtering through lots of little leaves is difficult.  Bark texture may also be difficult.

[tmgjbmah] GMP mpz_urandomm nonuniform

The GNU MP function mpz_urandomm tries rejection sampling up to 80 times (MAX_URANDOMM_ITER) to find a random number which fits within the user-specified range.  Each attempt I think fails with probability at most 1/2, so the probability of 80 consecutive failures is around 0.5^80, an extremely small number.

After 80 failures, it silently uses mod to bring the too large number into range, which destroys the uniformity.  I think it should instead abort, because 80 consecutive failures means something deeper is going wrong, perhaps a faulty random number generator which only emits '111...'.

[fpnlixqu] Peace and War

Is military might the only way long term peace has occurred in history?  Is it the only way it can occur?  Within a country, military might translates to a fascist government.

[dqttfhkg] Best worst ranking

For a competitive event in which competitors compete in several sub-events, let the "all-around" ranking be the ranking in the competitor's worst event.

Who is the best chess and go 囲碁 player?

[txdialwv] Delendum effect

Does the phenomenon of a person's compassion toward someone else dropping suddenly to zero have a name?

Referencing "Carthago delendum est".

[ptzvyvue] Proven media decoders

It would be nice if a web browser handled every possible media type under the sun; however, this increases the work required for the maintainers, and increases the attack surface of security vulnerabilities for malformed images.  (Ostensibly, these were the reasons given by Mozilla for removing support for MNG; there was probably political component of wanting kill off image formats they did not like.)

For security vulnerabilities, one could add back any media decoder formally proven free of security defects.  Thry could also have proven resource usage (memory, CPU) characteristics.  Less ambitiously, they could be run in a runtime sandbox that blocks faulty decoders from doing harm as well as enforce constraints of memory and CPU usage.

Continuing along the formal path, the decoder could be proven to correctly decode a specification of an image format (or other media format), at which point the user can download and substitute any other implementation which also is proven follows the spec.  This could provide a mechanism for additional media formats to be introduced aside the browser: an image gives its type, implicitly or explicitly a specification of how it is to be decoded, and the user (user agent) goes out and finds a decoder that is proven to meet the spec (as well as other guarantees).  There remains (among other things) the challenge of a bug-free specification.

[vnztnsqt] Lakey McLakeface

Loch Lochy seems like a similar fictional Scottish-sounding construction, or perhaps Lake McLakeyface.  There's also a Loch Loch (Cairngorms National Park), a loch so nice they named it twice.

[wgbcueip] Deep endgames

Train a neural network to classify chess endgames, then (this is the hard part) extract knowledge from the nets that is useful for humans to play the endgame.

Perhaps classify not just whether a position is won, lost, or drawn but also whether a move is making progress.

[uzgrzkla] Countdown

Cheap digital wristwatches usually have alarms and stopwatches but rarely countdown timers.

To time how long it takes to do something, but for which one may be too distracted at the end to stop a stopwatch or note the time, set a countdown timer with the estimated time at the beginning.  The accurate interval time may be found by bisection, updating the estimated time each iteration.  This takes many trials.

Monday, September 26, 2016

[rotqywrk] foldl foldr

foldl: (x * y) * z

foldr: x * (y * z)

Also a nice reference:'

Wednesday, September 21, 2016

[djipuhos] One quadrillion dead

If the realistic estimates of the population of an ecumenopolis like Coruscant, almost completely covered in skyscrapers miles high, are to believed (as opposed to the officially published figure which seems way too low), then perhaps a quadrillion people died in the destruction of Hosnian Prime, a similarly urbanized planet: 100000 to 200000 times the current earth population.

Alderaan seems similar to earth now, so much much fewer were killed by the Death Star.

Tell a realistic story of galactic war in which death tolls in the quadrillions, even a daily death toll in the quadrillions, is par for the course.  Before the planet busting weapons, maybe Base Delta Zero against an ecumenopolis.

Incidentally, Starkiller Base illustrates the weakness of Saddam Hussein's unmoveable supergun: fire it just once and its location will be revealed to the enemy, who will come and destroy it.  The Death Star, being mobile, was a much better design.

[icplkeor] Founders versus Gases

The Founders (of the Star Trek DS9 universe) encounter a species of gaseous life forms.  The gases treat the liquids with tremendous hostility and contempt, seeking to to destroy or subjugate all liquids.  The Founders of course recognize that this parallels how they see and treat solids, and then... the story remains to be written.

[ospzwams] Faster light

How would the universe be different if the speed of light were faster, perhaps much faster?

Probably magnetic fields are weaker, or electric fields are stronger.  Other subatomic effects probably wreak havoc compared to the current universe.  (The "tuning" theorists might say the speed of light is exactly the right speed for intelligent life to observe it and ponder it.)

Inspiration is hard science fiction in an alternate universe in which high speed travel around (say) the galaxy is possible without having to invoke machinations such as hyperspeed or wormholes, or to worry about time dilation.

(Alternatively, the characters could just live longer.)

[zonmerbp] Fermat test

The worst case failure rate over bases for the Fermat test of primality approaches 100% in the case of Carmichael numbers.  However what is its average failure rate, say, over all 8192-bit numbers, if the base is chosen randomly (or even deterministically, e.g., 2)?  This should be easy to measure exhaustively for small numbers, then extrapolate.

(As comparison, the worst case failure rate for the Miller-Rabin test is bounded above by 25% over all bases, so even if you happen to hit one of those worst case numbers, repeated tests with different bases will drive 0.25^n to zero.  I do not know the average failure rate of Miller-Rabin, though it is probably very low.)

If one is randomly sampling large numbers in search of a prime, then, at some size, the probability of accidentally selecting a Carmichael number becomes lower than the probability of machine error over some number of repeated Fermat tests.  What size is the the break even, after which it is not worth the additional programming effort to implement Miller-Rabin?  (This is not for the case when there might be an adversary who might deliberately feed you Carmichael numbers.)

[crnsbmxl] Generating random big integers

Given a source of uniform random unsigned integers over a range (not necessarily a power of two), generate a uniform random large integer.  This is probably not too hard.  Use a previous subroutine as a last step.

Inspiration was the Miller-Rabin probabilistic primality test, whose failure rate 1/4 requires that the bases be chosen uniformly randomly all the way up to the number being tested, typically a large number.  I'm guessing very few implementations of Miller-Rabin do this sampling correctly.  Arnault (August 1995). "Constructing Carmichael Numbers Which Are Strong Pseudoprimes to Several Bases" has constructed large composite numbers which pass the Miller-Rabin test for all small bases, and it seems likely that one can construct such a pseudoprime for any given deterministic collection of bases.

If one were to attempt to construct a random large integer from just one double precision random deviate, then only about 2^52 bases are possible, and it's only a little preposterous to imagine constructing a pseudoprime that passes the test for all these bases.

[wlpwaeor] Computer generated porn

How soon will computer-generated pornography constitute the majority of porn consumed?  It might be soon, as porn requires less acting ability so might be easier for a computer to synthesize.  Computer graphics can deliver photorealism already.  Or it might take a very long time, as people might be very sensitive to notice when it isn't right.  It might also take a very long time because computers are and will always be expensive compared to an amateur with a cam.

It'll be a gradual process, because even with computers, there will still be required (for a while) human models to provide features and starting points for computer-generated models, motion capture performers, and imaginative and creative people to imagine and create the porn in/with a computer instead of live.  Popular camgirls that week might serve as inspiration for computer generated copycats.

The sex work industry will change, though it is constantly changing due to technology.

Society will probably change in its views about child pornography when any child pornography that can be imagined can be generated in a computer without harming any child and be photographically indistinguishable from the real thing.

[vpywtggp] Communicating via chess moves

To avoid prearranged draws, consider structuring a tournament with random pairings each round and players sequestered from each other so they cannot see whom they are playing.  How difficult would it be for players still to communicate with each other, confirming each other's identity then agreeing to a draw, through their moves, perhaps opening moves?

Do things become easier or harder if players are permitted to see the other games in progress, without the players' labeled of course?  On one hand, it might make it possible for a player to determine who other players are by observing style and opening selection, and determine who the player is playing by a process of elimination.  On the other hand, visible games could help a player pretend to be another player trying to take advantage of draw prearrangements between other players.  Maybe the visible other games are delayed.

Chess960 would probably make it more difficult to communicate via opening choice.

Having a few weak players in the tournament might decrease the tendency of prearranged or short draws.  The strong players cannot know for sure whether they are playing a weak player against whom it would be a shame to give up a draw.

[npvraiac] GUI command line

Create a widget for a desktop environment which is a one-line command line, with which one can launch GUI applications or even run sequences of commands all in one line e.g., separated by semicolons in bash syntax.

If clicked on, the widget can expand to display a full terminal window complete with any console output the GUI commands may have emitted.  The widget probably runs a virtual terminal, e.g., screen or tmux, to be able to nicely redisplay output at any desired window size.

Typically GUI applications should be started and backgrounded, i.e., &.  Provide a feature that backgrounds commands by default, so the widget remains available to accept more commands.  Perhaps it backgrounds after a delay or user activity in the just opened GUI window.  Maybe also some way of distinguishing console output of different backgrounded applications.  Perhaps each application runs in a separate "screen" window, though that thwarts things like cd.

This should be easy.

[npvraiac] Guillotine

A curious bit of trivia begins the story: 1977 was the last time the guillotine was used in France, surprisingly recent.  But 1977 is in fact the last time anyone was executed in France, because as a civilized country, France abolished the death penalty after that.

Who was the last person person executed in France?  Can you guess characteristics about the person and about the crime?  Answer: an Arab man convicted of kidnapping, rape, and murder of a young white French woman.  And well duh, you could have guessed that: in a country with popular sentiment on the cusp of abolishing capital punishment, it's the lower class committing a sex crime against the upper class that incites the blood lust for revenge; similar to lynchings for (perceived) sex crimes in American history.

Who was the last person executed in Western Europe, before all of Western Europe abolished the death penalty?  The answer is, again, this case -- France was the last to abolish the death penalty -- and again, duh, you could have guessed it given how high social tensions are between Arab and white in France.  (Though if the answer were instead the English executing an Irishman, the Germans executing a Turk, or anyone executing a Romani, that would not be too surprising.)  France probably is the closest to reenacting the death penalty for exactly this continued social tension (terror attacks), though one wonders what method of execution they will use.

Once again, a lesson for America: the continued existence of the death penalty reflects the social tension and discord in the country.  If the death penalty is abolished too quickly, we'll probably see lynchings again.

Japan also still has a death penalty.

[ykvgtzld] Nonuniform shared memory

Having a distributed memory system simulate shared memory, i.e., cache coherent non uniform memory access, is a very convenient abstraction for programmers.  However, what other features could be provided to make it possible for a dedicated programmer to optimize things, breaking the abstraction?

The OS moves blocks of memory closer to the processor using it.  A program can declare in advance that it plans to frequently access (or write) a block of memory.  Or the program could explicitly request a block of memory be moved closer.  Conversely the program could prevent the OS from automatically moving a block of memory if it knows it will be a bad idea.

Alternatively, some way of migrating a process to the processor close to the memory that the process will accessed.  Perhaps automatic, perhaps explicitly yes or explicitly disable automatic.

A program could issue a bunch of memory requests, wait for the first few to respond, then cancel the remaining requests.  The remaining requests, if they arrive back, should not displace elements in the cache.

[sufdptlv] Disablable convenience features

Consider a feature (e.g., in software) to make things more convenient to users.  Can the feature be disabled by the user?

Often the convenience feature makes the common case easy, but needs to be disabled to make the less common case possible.

[rwewgwkn] Failure of strong and weak governments

If government is too weak, organized crime takes over.  If government is too strong -- fascist -- it itself, or its agents, fearing no repercussion,  become the perpetrator of crimes.

Worse still, in between them is an unstable equilibrium: organized crime will leverage its organization to weaken government further, while a fascist government will leverage its power to snuff out opposition and maintain power.

How can these bad outcomes be avoided?

[kpzuqkgz] Fist fight versus cat fight

In the movies, the trope is, a fistfight breaks out among men, a catfight breaks out among women.  Subvert this trope.

Which is the superior fighting form, perhaps for people who have no fight training?  On one hand, a fist fight seems to have rules, e.g., no kicking, while a catfight has none.  On the other hand, kicking might be difficult (especially balance-wise) for someone without training.

Monday, September 19, 2016

[sfhjvcgz] USA chess Olympiad asterisks

The previous two American chess Olympiad team gold medals have (silly IMHO) asterisks next to them: Soviet Union did not participate, and Soviet Union did not exist yet.

The recent gold medal could also have a silly asterisk: Armenia did not participate, and Vassily Ivanchuk (of Ukraine, whom USA tied in match points) was out playing checkers (draughts).  Armenia and Ukraine have dominated gold medals in previous recent Olympiads.

[yjjuwafv] Carlsen Olympiad

With Norway's (seeded 12th) surprise high finish (5th) in the recent chess Olympiad, it's fun to speculate how it could have done even better if GM Magnus Carlsen had won more games, not that he played especially poorly.  Because he is undisputed world champion and the highest rated player (2857), we can always argue Carlsen should have won more games.

The games in which Carlsen could have done half a game point better (he had no losses) and the half point would have mattered for Norway's match points were

Round 3 draw with black against GM Constantin Lupulescu (2618) of Romania

Round 6 draw with white against GM Julio Catalino Sadorra (2560) of Philippines, arguably one of the bigger upsets of the event

Round 11 draw with black against GM P. Harikrishna (2752) of India.

Norway finished tied with India in match points, but worse in tiebreaks.  One more match point in any of these games would have vaulted them over India to 4th place.  Two more match points would have tied them in match points with Russia (3rd place) with unknown tiebreaks.

Of course, a different result in any of the rounds would have affected the Swiss pairings of subsequent rounds.

Of course, speculations about how Carlsen could have played better improving Norway's finish ought to be paired with how all the other players could have played worse.

The Chess Results website, despite choosing the language to be English, still uses German abbreviation for colors: s (schwarz = black) and w (weiss = white), which happen to common surnames.

Monday, September 12, 2016

[hpjgrskw] Art and politics

There have certainly been artists like Nina Simone and Dante Alighieri for whom their art was a expressly political statement.  But there have also existed artists who were expressly apolitical: they endeavored to create art that transcended political and social boundaries, art that captured a universal aspect of the human condition.  Sure, their art may reflect the sounds, language, movement, etc., of the culture they were born into, but those are the tools they had to work with, and not an endorsement of, or even participation in, a political position.  To ascribe politics to their art is profoundly disrepectful, akin to declaring that they are failures as artists, failures in their artistic quest to create something that rose above the foibles and quibbles of human politics.  Therefore, when discussing politics as it relates to an art form, e.g., dance, be mindful that adding politics to where there wasn't intended to be by the artist can be just as disrepectful as removing politics from where there was intended to be, depending on each artist.

In the context of politics of race, and dance.

[erewaocu] Publicly funded journalism

Journalism is a public good, so suffers from tragedy of commons: a private business has difficulty making a profit from it (unless it resorts to journalism as entertainment, which we see happening: politics as NASCAR).

The standard solution for inducing the optimal production of public goods is public funding, but publicly funded journalism tends to go terribly, e.g., Pravda.

Is there a solution?  Perhaps somehow the public or agents of the public enforcing accountability in accuracy and completeness of the journalism, maybe something adversarial.

[rjejcxti] Overlapping leagues

On odd years, leagues of (say) 16 formed by ranking all the players ranked in order (perhaps by Elo from chess) and choosing segments of 16.  Play round robin within each league.

On even years, the top league is 8 and does double round robin offering more rigorous competition among the very top, perhaps establishing who is the best.  The lower leagues remain 16, so the boundaries are staggered compared to odd years.

One could do promotion and relegation, or simply rerank all players at the end of each season (Elo), and reassign to leagues.

How much cooperation and Elo manipulation can occur to game the system?  Fischer criticized round robin tournaments.

[shgifulx] De Bruijn sphere

Draw a pattern onto a sphere so that every small localized segment of the pattern is unique.  Probably subdivisions of an icosahedron (triangles) or dual (pentagons and hexagons).  You get to choose what is meant by "small localized segment".

Inspired by the De Bruijn torus, but we do not require every subpattern appear, only that every subpattern be different from the rest.

[vgbuolje] Prime frieze

This picture, illustrating the distribution of primes, is neat.  Its width is 3 * 5 * 7 * 11 = 1155, so exhibits stripes.

Find dimensions, products of small primes, which fit neatly onto one screen, illustrating the logarithmic decrease in density.  1155 is just a little bit too wide for 1080 HD.  OK to scale down by a small integer factor, yielding grayscale.

Perhaps simply omit multiples of 2 (already done) 3 5 7 11, splicing out white columns.

Are there dimensions which yield prominent diagonal stripes as well as vertical?

[xcrwyhfw] Bluetooth broadcast

Create a device which can broadcast the same music to many different Bluetooth audio players simultaneously.  (Perhaps a typical computer can already do this: it can certainly handle a few Bluetooth devices simultaneously, e.g., mouse and keyboard.)

Goal is for a DJ to broadcast a silent dance party.

[uthxtenp] Language for speed reading

Create a language, in particular an orthography, designed for speed reading.

It will probably incorporate color, because the eye is sensitive to that.  It will probably be more two dimensional, like Chinese or Korean, rather than linear like Latin scripts: chunks of meaning cover a more compact area rather than spread out over a long thin line, though this could be mitigated with narrow columns of text.  It might look more like pictures and diagrams, because 1000 words.

[jtdrvpoi] Pursue your dream

Tell a story which juxtaposes the seemingly noble principle that one should and should be able to pursue one's dreams, with the reality that the dreams that the characters pursue are terrible: selfish, destructive to society, etc.

Perhaps exploration on what social forces, perhaps sinister forces, cause people to have the dreams they have.

[jqwinvkz] More Chaconne

Bach's Chaconne, or any chaconne, being variations on a short harmonic theme, invites composition or improvisation of further variations on the theme, like jazz.

Bach's Chaconne also certainly invites orchestration and arrangement for other instruments and ensembles, which have been done and should be continued.  There are moments which sound like, "this is where the full orchestra comes in".

[zeuzurcz] Multiplication table up to 20

One only needs to memorize the multiplication table up to 5*5 in order to be able to multiply up to 10*10.  For digits larger than 5, substitute (10-x) and use the distributive rule (FOIL).

However, having sunk the cost of memorizing up to 10*10, one can apply the same principle to multiply up to 20*20.  Recursively go further, i.e., 40, though that might be more work than the traditional tableau.

Flash cards app showing partial sums.

[fnngupvi] Chess960 knight handicap

Consider a human versus computer chess tournament with the human getting an advantage of a knight.

Rybka vs. Meyer seemed to prove that a knight is too much of a handicap, but I still feel there is more that computers could do to learn to swindle.

To decrease the human's advantage, let it be initial position be chosen randomly among the Chess960 opening positions.  A human can no longer deeply prepare a single low-risk or anti-computer opening from the orthodox opening position.  Meanwhile, the computer, being not constrained by memory, can deeply prepare 960 openings (or 1920 if we randomize which knight is removed) designed to lead the human into tricky waters.

[sgnuxiuo] Multiplication table in various bases

Omitting multipliers 0 and 1 because they are trivial (which makes the entire base 2 multiplication table trivial).  Source code in Perl.  Heavy lifting is done by "bc".

There are some patterns visible between bases.

Base 3


Base 4


Base 5


Base 6


Base 7


Base 8


Base 9


Base 10


Base 11


Base 12


Base 13


Base 14


Base 15


Base 16