Saturday, June 24, 2017

[otuvylgr] Music for phone speakers

Compose music optimized for "performance" on cell phone speakers, typically unable to play low frequencies (bass), nor play very loud.  Might have other limitations too.  Similarly laptop speakers.

This is a form of constrained music, something that composers have dealt with forever.

[tkqkkadl] Advertisers and entertainers

Hypothesize that advertisers and entertainers understand human psychology and sociology far better than than science does, because they have significant money riding on it.  Data mine advertising and entertainment for scientific insight in these fields.

Any particular advertiser or entertainer might not be able to express what they understand about psychology or sociology; they just stumbled upon something that works and will keep doing it so long as it does.  We need to combine many inputs.

There are of course many, many failed advertising campaigns and entertainment attempts.

Science cares about causality: what caused a person or a group of people to be who they are?  Advertising and entertainment might not care so much: they take who people are as a given and try to make as much money as possible off of them.  Maybe causality provides an underlying model for things like, people who like this will also like that, or won't dislike that, etc., and advertisers and entertainers do care about that.

[lorvoqjf] Thematic move

Create a computer program to find "thematic" moves in chess, a vaguely defined term seen in chess problems, opening theory, and possibly others.  There are many examples of the label, so perhaps this is a good task for machine learning.

Thematic might mean, leading to an important idea, a mechanism, a theme, seen in many variations (including variations not starting with this thematic move).  It is not necessarily the strongest move.  There is often a strong element of pedagogy in thematic moves.

Discovering and extracting the commonalities between different but related things is an important task in many fields.

[kcmkycqt] Private cell service

How easy is it for a private individual to set up a cell tower and distribute SIM cards that work for routing phone calls only between those who connect to that tower?  Maybe a small networked collection of towers.

The use case is a group of people in an area are collaborating, communicating with each other with cell phones.  The authorities try to disrupt the group by shutting off their cell service.  The group then sets up and switches over to their own private cell tower.

Probably much easier would be to use smartphones, Wifi access points, local servers, and software for communication over wifi.

[ustpplud] Cartoon physics on/off

Create a cartoon which has as a plot device some mechanism by which cartoon physics (and biology, etc.) can get turned on and off.  When cartoon physics is off, characters suffer devastating and likely horrifying physical injuries.

[hrkyphaf] Zerg rush pressure

Simulate a large number of simple autonomous agents attacking a defensive fortification or line.  They behave as a whole kind of like a corrosive liquid, searching and streaming though holes where they are found or made.  What behavior rules in the agents induce this kind of behavior?  When a hole is found, the information needs to be communicated over long distances so that everyone knows to head for it.  If there are multiple holes of different sizes, send the right amount through each hole to maximize flow.  Best might be encoding and transmitting information about pressure, which is normally not done when simulating particles.

[vprcouyu] One man versus an army

Consider highly unbalanced variants of chess in which one player's (the player with the weaker set of pieces, the defender) goal is simply to survive as long as possible.  For example, full set of pieces on the attacker's side versus lone king, or lone king and a piece or two.

Might want variants in which pawns do not promote, because once the attacker has several queens, mating quickly becomes trivial.  What happens to pawns on the eighth rank?  Staying a useless pawn is probably the most critical, getting in the way of the attacker's other pieces.  Other possibilities: disappears immediately, or the defender can spend a move causing a pawn to disappear, or pawns not permitted to advance beyond (say) 4th rank.

Monday, June 19, 2017

[msekkqtq] Oil wealth social upheaval

To what extent can all the turmoil in the Middle East be attributed to one simple cause, the automobile?

Cars require gasoline; gasoline comes from oil; the Middle East has oil.  Exporting oil resulted in vast wealth, and wealth caused changes in social and power structures.  Hypothesize that these changes caused turmoil through a variety of mechanisms, yet to be enumerated.

Unlike in the United States in which oil caused an outsider of the political establishment, Rockefeller, to gain wealth and power, it seems at first glance that in the Middle East those who already had power benefitted the most from the oil export income.  Nevertheless, we hypothesize that this still induced turmoil.

Trouble always follows money.  Enumerate how.

[duxsarjz] Words for power or truth

Speech can be used to search for truth, or to try to acquire power (usually at the expense of whoever currently has power).  It is difficult to distinguish between them, and there is often a lot of overlap, e.g., speech to expose the lies perpetuated by those in power.

The purpose of censorship is often (probably always) about the power side of the issue.  It has this double edged sword effect of also inhibiting the search for truth.

For speech trying to acquire power, you might support free speech or support censorship depending on where your political preferences lie regarding who is currently in power and who is trying to acquire power with the speech.  Moreover, you should rationally support free speech or censorship accordingly (on a case by case basis), because speech does seem to be effective for acquiring power, and who's in power will affect your well-being.

Possibly we should work on decreasing the effectiveness of speech to acquire power.

[kikpukyi] Digraphs expected

Fancy keyboards, especially virtual keyboards, have the ability to send multiple sequential key presses to the application, for example digraphs and polygraphs.  However, such digraphs are only useful in certain modes, most commonly typing text, and may be actively harmful in other modes, e.g., a keystroke driven command mode like for vi.  For example, often we want to provide the feature of undoing the last keystroke.  Thus, an application needs to communicate with the keyboard what features it should provide at the moment.  This seems messy.  Alternatively, the user can put the keyboard in various modes manually, but that requires more keystrokes.

[bqngzmqz] Death of James Hodgkinson

Exactly what were the circumstances of the death of James Hodgkinson, the shooter at the Congressional baseball game practice?

This was a premeditated political act, so presumably Hodgkinson worked out beforehand the political calculus regarding what he should do to maximize his political impact.  It seems that surviving, being arrested, then having his day in court ought to have been a high priority.  With large swaths of the country vehemently opposed to Trump and the Republican Congress, and especially the DC metro area heavily leaning liberal, it seems likely that at least one juror in 12 selected from that region might be willing to exercise jury nullification, refusing to convict (hanging the jury), agreeing with Hodgkinson's politics and the need for drastic political action to right the rapidly sinking ship of state.  In the event of such a judicial outcome (perhaps after multiple such mistrials), it would become open season on Republicans in Washington, inspiring many copycats, thereby greatly magnifying Hodgkinson's political impact.  This calculation Hodgkinson could have worked out beforehand, or should have.  It was not necessary to kill as many Republicans as possible; even just maiming (he could have seen that Steve Scalise was injured), even missing entirely could have set the ball rolling toward "open season", so long as he survived to trial (and mistrial).

It is possible Hodgkinson did not know about the concept and possibility of jury nullification.  It is possible Hodgkinson knew about it but believed it to be extremely unlikely, perhaps not attuned to the political climate of the DC metro area, or of the country.  What he knew and believed can likely be discovered with research.

It is possible Hodgkinson disliked the idea of prison so much that he intended for this to be a suicide mission from the outset and so kept shooting until he got shot.  Perhaps he calculated (wrongly, IMHO) he would have more political impact as a martyr.  Again, whether any of this is true can also be discovered with research.  A suicide mission might have left a suicide note.

The most sinister possible scenario is that Hodgkinson did in fact intend to survive, tried to surrender peacefully, but was then shot in cold blood by Capitol Police, who made the same political calculation as given here and judged that under no condition should the shooter be allowed to live because of the potentially dangerous political repercussions.  Perhaps the Capitol Police have standing orders to this effect, or training to act this way without having to think.  Actually, the revenge instinct is innate; it takes training not to act that way.

NB: Capitol Police is a police force that protects the Capitol and members of Congress.  This is a separate organization from the Washington, DC police.

Sunday, June 18, 2017

[nkzwtvoy] Chaconne arrangements

Bach's Chaconne works quite well on guitar (e.g., Segovia), especially the thick chords and arpeggiated sections.  It does not work as well as violin for sustained notes and scales.  The obvious idea is to arrange it as a guitar and violin duet to get the best of both instruments.  However, in general, those two instruments seem rarely paired in duets.  Why?

Consider playing it on electric guitar.  Electric guitar can sustain notes, and effects pedals can create many different timbres.  Play it in the style of Jimi Hendrix's Star Spangled Banner: the song might work well with transitions between dark and stormy, and light and pretty.  Inspired surprisingly by solo violin by Ivry Gitly, who treats it roughly.

Eastman Saxophone Project (arr. Matthew Evans) is very nice, though could be improved toward the end.  Call and response by the instruments of different timbres works really well.  Arpeggiated sections do not work so well on wind instruments.

Busoni is mostly very nice, though he made some radical changes, which ought to be made optional.  Kissin omits an ossia at 13:00, and it sounds closer to the original, and better.

Trifonov plays the Brahams arrangement slowly, which captures better how a chaconne is a baroque dance form, so needs to match the capability of natural human movement.

[zjnjvvrc] Video with orientation sensor track

Add to video data storage format a data track recording the camera's orientation sensor, angles and compass direction.  This information is often available in smartphone cameras.

Provide tools to view and edit the track, probably cleaning up noise.  Maybe correlate with changes in visual field.  Project the video onto a sphere, similar to Steadicam.

[mladwfub] New Hogwarts astronomy professor

A running plot driver in Harry Potter is that there is a new Defense Against the Dark Arts teacher every year.  Tell a very different story in which there is a new Astronomy professor each year.  The battle is not between light and dark, but between the earth and heavens.

[waehfxjm] Privacy and freedom charismatic leader

The technology and groundwork exists for goods and services which protect users' freedoms (e.g., no DRM) and privacy.  All we need now is for consumers to demand it.  One way to induce demand might be charismatic leaders.

It's interesting that none have emerged already.  Why not?

Saturday, June 17, 2017

[xwaezvvv] Draw a large binary tree

What is the largest full binary tree that has ever been physically drawn?  Maybe wall sized with leaves requiring a magnifying glass or microscope to examine.  What interesting could be written at the leaves?  Maybe a single random or pseudorandom bit, providing a data expander, though not very robust because there is exactly one copy of any leaf.  Or a significant amount of data per leaf, probably as a 1D barcode, because leaves need to be very thin.

Consider drawing the inner nodes as light or dark regions, inspired by Gray code wheels, rather than stalks as trees are typically drawn.

Thursday, June 15, 2017

[kaoyobsz] Surrounded by wonderful people

If you find yourself at an event, venue, or in an organization a surrounded by (what you perceive as) wonderful people, look for the mechanisms which kept out those who aren't wonderful.  These are often ugly institutionalized mechanisms.

Also, reflect on your reluctance to repeal or remove those mechanisms (and you can understand how similar such mechanisms persist).

Inspiration is from quite afar: in chess, the winner is the player who made the next-to-last mistake.  Corollary: analyze your victories critically.

[jszknfox] PRNG with large seed

To create a random number generator with a large seed that depends on every bit of that seed, break the seed in to small parts, seed a separate random number generator (e.g., stream cipher) with each part then combine the outputs, for example with XOR.  If using XOR, need to make sure no two seed parts are the same, or else they cancel each other out.

Another way is to take the large seed and (lossy) compress it into a cryptographic digest (e.g., SHA) then used the digest as a key or seed for the RNG.  This technique has the advantage or disadvantage that the internal state of the generator or at least starting state, is much smaller than the large original seed.

Sunday, June 11, 2017

[bcpudyua] DoS mitigation with P2P HTTP

The Content-md5 header in HTTP, and its successors in RFC 3230 and RFC 5843, hint that it might be possible to substitute some peer-to-peer protocol for the bulk of HTTP.  Find the content with a known or given hash anywhere, e.g., in someone else's cache, not just from the original server.

This only works with static content.  Yet unspecified is how one comes to know the hash of the content you want.

What should be done if the declared hash in the header does not match the computed hash of the received content?

[ewlplvow] Point growth in other spaces

The point growth fractal (coral) in the Euclidean plane (or space) is a battle between trees, which would like to branch and grow exponentially, and space, which grows only polynomially with radius.

Make the battle more severe by growing it on a (say) horizontal strip.  Cylinder also possible.  Mouse over a point to highlight the descendants.  Pick a vertical line of pixels and it highlights the most recent common ancestor.

On the other end of the spectrum, make area or volume increase exponentially also: hyperbolic space.  Conveniently, any regular polygon (pentagon or more) tiles (some) hyperbolic plane, so can be used as a pixel.  A few possibilities for hyperbolic 3-space.

Even more extreme, grow it directly on an empty infinite binary tree.  The point wanders among empty siblings or cousins, parent, or children until it occupies node with a filled parent: there are 5 possible directions of a step.  This will likely not be interesting, because there seems to be no possibility of crowding out.

Friday, June 09, 2017

[qnnqrcqx] Making crossword puzzles harder

Some possible variations on crossword puzzles:

Multiple letters can be placed in a box.  Maybe the combination in a box makes linguistic or semantic sense.

A specified subset of the letters, in specified order, of the full answer to a clue is placed in the boxes.  For example, the letters could go in in reverse order.

[pirmitjt] Tax car width

Place a tax or toll on vehicles based on width.  This incentivizes narrow cars which coexist better with bicycles on congested roads.

A automobile shape never seen is the narrow van, capable of carrying many passengers in N rows of 2, or cargo.

[agjiszuz] Gravitational waves as sound

If gravitational waves were intense enough, could they be perceived as sound?  Either the waves make the air molecules move, or the waves directly move the structures in the ear that perceive sound.

Tuesday, June 06, 2017

[xjgxcsiq] Completion GUI for touch screen CLI

Tab completion is very useful for a command line interface.  For adapting it to a touchscreen, we would like to slightly modify it to be able to select among multiple possible completions with a tap, instead of typing the next letter.

[zwvicgaa] Sudoku input gesture

Filling in a square in a sudoku grid with 3 taps on a 3x3 grid on a touchscreen is elegant: first tap to select the larger 3x3 square, second to select individual square within the larger square, third to select a digit.  Could also be done with physical buttons, like numeric keypad.

On a touchscreen, some sequences of taps could be combined into a gesture, a swipe, though there are complications.  What should be done about multiple taps on the same square, and swipes traveling through a square that aren't relevant?

Speed contest: a single number in a grid is shown.  Do the taps or gesture to input the  number at the location as quickly as possible.

[cqhumjvi] Dating superpower

Write a story in which protagonists use a superpower to succeed in courtship, and the stated logic of why they need to use it, and why it works, is sound.  Probably commentary on conventions around courtship so deeply embedded into society than no normal power could change or circumvent them.

[rxcyhpea] Clock waves in CA

Typically in cellular automata, the clock ticks simultaneously for every cell across the universe.  This is probably difficult to build for real (at high clock frequency) because of clock skew (though we might be saved by the high degree of regularity of the grid of cells).

Consider a CA in which a clock tick is simultaneous only across a column of cells.  Neighboring cells to the left and right are ahead or behind in time.  More generally, don't fight clock skew: make it the programmer's problem (realistically, the compiler's problem).  Can Turing-complete structures still be built?

Not sure if this avoids the engineering difficulties of clock skew: different columns must be remain precisely spaced in time.

Maybe asynchronous digital logic is what we actually want, and maybe cellular automata on top of that.

[jjhossuh] Weapon prediction contest

Weapons technologies (broadly) might typically be a military's most closely guarded secrets, with wars throughout history being won by surprise unveiling of a new or radically improved technology.

(On the other hand, in order to use a technology, soldiers must be trained to use it, often many soldiers.  And it is hard to keep a secret when many people know it.)

In order to decrease the destabilizing effect of secret weapons technology, provide incentives for information to leak.  Perhaps prizes for accurate and precise predictions for weapons that haven't been publicly acknowledged or used yet.  Perhaps a market mechanism where people can put money on either side of a prediction.  Prizes awarded when the weapon is revealed.

[cgypobto] Fairy Babson task

The Babson task in chess problems could be further elaborated permitting promotion to fairy chess pieces.

[ynfztsqq] Verify 17-gon by hand

Take the expression cos(2*pi/17)+i*sin(2*pi/17), except with the trigonometric expressions written as square roots, and demonstrate raising it to the 17th power to get unity.  This will be very long and messy.  The instructive way to exponentiate is probably first repeated squarings to get to 16.  Perhaps it accompanies a piece of art with a 17 pointed star.  Also add a proof of the Gauss-Wantzel theorem.  ("A brief history of impossibility", Jeff Suzuki)

[kcxvhsoi] 3D puzzles in hyperbolic space

There are 4 compact regular honeycombs in 3D hyperbolic space: a honeycomb of dodecahedra which is its own self-dual, a honeycomb of icosahedra which is its own self-dual, a honeycomb​ of dodecahedra and a honeycomb of cubes which are duals of each other.  Investigate these for puzzles and games, almost certainly in a virtual setting.

Cubes connecting in weird ways could be a basis for a 3D maze or collection of rooms.  Incidentally this would also work for 2D hyperbolic tiling of squares.

Multiple dodecahedra or multiple icosahedra glued to each other could be a basis for monstrously complicated put-together puzzles.  Pieces based on the 3D Euclidean cubic honeycomb can be rotated in (only) 24 different ways.  Icosahedral symmetry allows 60 different orientations.

Friday, June 02, 2017

[rrchcatj] Homophobes and homosexuals

Hypothesize that the same psychological mechanisms control whether someone is homophobic (or not) and whether someone is homosexual (or not).  This is not to say they are correlated, but rather a person has just as little ability to change one aspect of their identity as to change the other aspect.  If true, there is profound irony in each side trying to force the other to act (be) different.

Previously.

Thursday, June 01, 2017

[ueajojfc] Best 17-gon star

The regular 17-gon is quite epic as a constructible figure, but it looks too similar to a circle.  A star drawn among the vertices avoids this problem and also demonstrates 17-fold symmetry.  There are many possible stars among 17 points; which one is best?

The Gauss monument in Braunschweig uses the star with narrowest possible points.

Previously.

Aesthetically attractive might be the star with nearly right angle points, probably connecting every 4th vertex.  This may highlight how 17 is 1 greater than 16, a multiple of 4.

Draw a design on the face of the star that helps quickly recognize that the star has 17 points.  This might be easy by only requiring bilateral symmetry, with one point treated differently.  Can it be illustrated that 17 is a Fermat number?

[qgfyljam] Boustrophedonic code

Write text in alternating directions on alternating lines.  Any substring in the text occupies a contiguous region.  This is not the case for conventionally wrapped text.

A contiguous region can easily be colored or surrounded with a border.  This may be useful for computer programming code, which often consists of nested text regions.

How should the Latin scripts be adapted to be written boustrophedonically?  The "backward" lines could be mirrored, upside down, or (confusingly) just written right to left.

Even more radically, also do boustrophedonic columns: alternate columns reading up and down, perhaps useful for landscape displays.

[gonctcfr] Dunkirk

Speculation on how World War II, and the rest of history, would have turned out had the Germans not halted at Dunkirk might make good speculative fiction.

The entertainment value may be aided by, history written by the victors at tends not to cover Dunkirk much, though coincidentally, there is an upcoming 2017 film.

[ckpohliq] Less nationalist Olympics

Decrease the nationalism at the Olympics (in baby steps) by allowing athletes the choice to compete not wearing uniforms representing their country, and (also perhaps optionally), broadcasters comply with their wishes.  Use the Olympic flag when a flag is needed, for example medal awards.  Broadcasters may also assign those won medals to an Olympic entity for medal counts, a journalism tradition which is inherently highly nationalist.

The underlying rules on national federations specifying limits on the number of athletes do not​ change, only appearances.

[bigpvruv] Prequel variations

Yet more alternative Star Wars prequel plots:

Ben (and Yoda) get shockingly revealed to have lied -- a lot -- to Luke in the original trilogy.  Maybe "many of the truths we cling to depend on our point of view".  The inspiration was, how did all the Jedi get killed when they are nigh invincible?  A thousand or more losing to two seems preposterous.  (How the actual prequel did it, shooting them with stormtroopers, still seems preposterous.)

One possibility: the Jedi killed each other.  Possible reasons why: over petty squabbles, the Jedi are not so noble.  Or, manipulated into doing so by mind tricks by the dark side.

Another possibility: the Jedi are not "nigh invincible".  Maybe Yoda and Ben, the survivors, represent the best of them; the rest were worse, much worse, downright incompetent.  Somewhat similar to actual prequel theme about incompetence of the Jedi as they failed to sense a Sith lord in their midst.  Covering up such incompetence could provide incentive to lie to Luke later.

Tuesday, May 30, 2017

[etjkgrvm] Dragostea din tei

"Numa Numa" is a catchy song, but it feels incomplete: perhaps missing another section or two yet to be composed, or the definitive cover has yet to be recorded.

[dlpbytpq] False flag bomb threats to Jewish synagogues

In the weeks and months following the election of Trump were a series of bomb threats called into Jewish synagogues and community centers.  At the time, these were assumed to be the work of anti-Semetic white supremacists emboldened by the election of one of their own into the White House.  However, it seems this was not the case:

"Israeli man arrested as prime suspect in string of bomb threats against Jewish community centers" (Chicago Tribune, March 2017)

From a cryptographic standpoint, the most interesting detail is that law enforcement seems to have pierced the anonymity provided by Tor to discover the suspect.  It would be nice if the suspect stands trial, so that the defense can publicly examine and challenge both the evidence against the suspect, and critically, how it was acquired and connected to the suspect, so that the public can know the extent of the state's surveillance capabilities, and so Tor can correct any vulnerabilities that the authorities exploited.  The "standard" method of defeating Tor is traffic analysis: just how much traffic metadata, and where, are authorities collecting?

Politically, there are some more interesting questions.

Both the name of the suspect and his father, also arrested, have been kept secret.  This seems unusual.  Is it by order of the Israeli Military Censor?  Had the suspect -- presumed Jewish -- been Arab or Muslim, would the names have been released (or leaked)?

Because of crimes, quite serious, committed against American institutions, it seems reasonable to extradite the suspect to stand trial, and if convicted, be punished, in America.  What is the status of the extradition?  Is it encountering diplomatic roadblocks?

Are the Jewish centers targeted in the bomb threats dropping charges now that they know "one of their own" (presumably) is the prime suspect?  Are they being diplomatically encouraged to do so?

The bomb threats appear to be a classic "false flag" operation (though other explanations are possible): it made it look, to Jews, like an enemy was attacking them, in order to galvanize them and motivate them to political (or other) action.  If so, it seems it was a very successful operation, very perceptive about the current American political climate, the media's tendency to report heavily on the bomb threats, and even to the media's disinterest in following up after the arrest.

Monday, May 29, 2017

[egxircfx] Factoring the numerators of the sum of prime reciprocals

A partial sum of the reciprocals of the prime numbers is a fraction whose denominator factors very easily (it is probably a primorial, though I have not proved it), but whose numerator is much more difficult to factor.  Below are some prime factorizations.  The three columns are an index, the nth prime, and the factorization, in the format of print(factorint) of Pari/GP.  (Not all the factorizations were computed with Pari/GP.)  The largest prime factor is elided for brevity.

1 2 matrix(0,2)
2 3 Mat([...])
3 5 Mat([...])
4 7 [13, 1; ...]
5 11 Mat([...])
6 13 Mat([...])
7 17 [19, 1; ...]
8 19 [37, 1; ...]
9 23 [43, 1; 163, 1; ...]
10 29 [269, 1; ...]
11 31 [61, 1; 4253, 1; ...]
12 37 [79, 1; 82913, 1; ...]
13 41 [2683561, 1; ...]
14 43 [47, 1; ...]
15 47 [1559, 1; ...]
16 53 [1701437, 1; ...]
17 59 [1087, 1; ...]
18 61 Mat([...])
19 67 Mat([...])
20 71 [653, 1; 24310877, 1; ...]
21 73 [79, 1; ...]
22 79 Mat([...])
23 83 [6991, 1; 17117, 1; 31727, 1; ...]
24 89 [128427649157, 1; ...]
25 97 [11887, 1; ...]
26 101 [2549, 1; ...]
27 103 [20831283974697087833, 1; ...]
28 107 [109, 1; 25013, 1; 45090757000504693, 1; ...]
29 109 [155963971, 1; ...]
30 113 [5507, 1; 67537, 1; 120585359, 1; 2153797249, 1; ...]
31 127 [4002997, 1; 164601157381, 1; ...]
32 131 [359111, 1; 2287463, 1; 901103850134867, 1; ...]
33 137 [181, 1; ...]
34 139 [1811, 1; 28393, 1; 22710555839, 1; ...]
35 149 [3923, 1; 574159, 1; 763111, 1; 24663715883, 1; ...]
36 151 [72279793, 1; 94335665844559, 1; ...]
37 157 [28547, 1; ...]
38 163 [4787, 1; 5521, 1; 72461, 1; 8380649, 1; 10408339, 1; 7832974103, 1; ...]
39 167 [278556893, 1; 3086934317, 1; ...]
40 173 [1907, 1; 10081481467, 1; ...]
41 179 [33390666307245425779, 1; ...]
42 181 [7219, 1; 220383301739, 1; 126474777435943, 1; ...]
43 191 [2382613, 1; 2446271, 1; 7448087, 1; 871590253, 1; 178268248033937558047, 1; ...]
44 193 [55721, 1; ...]
45 197 [331, 1; 75578568438239, 1; 38105656577309152682410376613803, 1; ...]
46 199 [397, 1; 1013, 1; 937077949469, 1; ...]
47 211 Mat([...])
48 223 [2882132344879945073347, 1; 45307571139926942991190133467, 1; ...]
49 227 [651126224977976987, 1; 318622749737882874703, 1; ...]
50 229 [85095942328560424348919161618392851191123181, 1; ...]
51 233 [2579, 1; 71532047297, 1; ...]
52 239 [32801, 1; 3646361, 1; 92115137111, 1; ...]
53 241 [1163, 1; 7313113087636909616856476683740381743, 1; ...]
54 251 [4457, 1; 4910826615619, 1; 1363395500165507803, 1; ...]
55 257 [339817, 1; 1513991, 1; 596996931741787, 1; 856758427621401709, 1; 2551502817340701509987573, 1; ...]
56 263 [353, 1; 27281214795174369762755731429871, 1; ...]
57 269 Mat([...])
58 271 Mat([...])
59 277 [769, 1; 17449, 1; 38853152699, 1; 25824790263806958200017, 1; ...]
60 281 [3931, 1; 4567121006246470847491526513, 1; ...]
61 283 [317, 1; 1483, 1; 1609, 1; 3083, 1; 15671, 1; 583879671521915894486003, 1; 40014655444673756284001412841, 1; ...]
62 293 [80309, 1; 43536091344561600390559851581507045347, 1; ...]
63 307 Mat([...])
64 311 [5147, 1; 358562916373373, 1; 1491945768116449, 1; ...]
65 313 [24197, 1; 180679, 1; 16666361, 1; 19487953638573362777, 1; 8677032348848311962094549, 1; ...]
66 317 [26881, 1; 1233681413, 1; 303909666003986239876228859266842827787705817105239453149, 1; ...]
67 331 ?
68 337 [4545229807, 1; 8458142681, 1; 143759487929629829, 1; ...]
69 347 [183919, 1; 2676456442899289, 1; 23977191281329122737, 1; 3403289789915363463733, 1; 141794625722542162388532383, 1; ...]
70 349 Mat([...])
71 353 [1453, 1; 831263358975239, 1; ...]
72 359 [10774822439848219544475069839689, 1; 122797736200334999541587307307277, 1; 2437316904825953681023538533923768491, 1; ...]
73 367 Mat([...])
74 373 [36637, 1; ...]
75 379 [114599, 1; 2560985953, 1; 245244287749171, 1; ...]
76 383 [24509, 1; 10904541719992241, 1; 180014284879715834547510101249288391580157, 1; ...]
77 389 [124513, 1; 3716098294674500690132872478501721045666345109541, 1; ...]
78 397 [1237, 1; 40087, 1; 193883, 1; 71681682691, 1; 8335042497553, 1; 6407545381506250342667407731823103, 1; 1632270826911851865940901782780510543, 1; ...]
79 401 [15053, 1; 39387829631, 1; 17246820026707, 1; 35482216430978507, 1; ...]
80 409 [104287094536357, 1; 315148692435993889067971, 1; ...]
81 419 [2671, 1; ...]
82 421 [1661985439636800100353810329, 1; ...]
83 431 ?
84 433 [3752943149479, 1; ...]
85 439 ?
86 443 [1049, 1; ...]
87 449 ?

Friday, May 26, 2017

[hwqfklqt] Easier 3D puzzle

3D put-together puzzles are difficult because each piece may be rotated into many different orientations, e.g., 24 for a Soma cube, which is much larger than 4 in a typical 2D jigsaw puzzle.

Make 3D puzzles easier by constraining the possible rotations.  Forcing one side to be the "top" constrains to plane rotations.

Incidentally, a 2D jigsaw puzzle based on a hexagonal tiling (6 possible orientations per piece instead of 4) seems an easy way to make a puzzle more difficult with little increase in manufacturing difficulty.

[mqdwznpq] Partial sums of reciprocals of primes

Euler proved that the infinite sum of all the reciprocals of the prime numbers diverges (but extremely slowly).

1/2 + 1/3 is the largest partial sum less than unity.  Adding the next term, 1/5, pushes it over 1.

The sum up to 1/271 is just under 2, 1/277 pushes it over.

The sum up to 1/116411 is just less than e, 1/116423 pushes it over.

Wednesday, May 24, 2017

[bjacwkze] 4 cubes

A cube with distinct faces can be rotated to 24 different orientations.  Curiously, there are also 24 permutations of 4 objects, so 4 cubes can be in 24^5 different states, about 8 million.

Vaguely similar is the isomorphism between 60 orientations of an icosahedron and the alternating group A[5].

[sicjuipl] On the beauty of things

Some people remain interested in mathematics, perhaps pursing it as a career, because they feel it is beautiful.  How is the appreciation of this beauty learned, or if it is innate, how is it unlearned in other people?  Obviously this applies to many other fields also.  Understanding this phenomenon is the key to STEM education, but I feel we are charging forward trying to increase STEM education without understanding it, so efforts may be wasted or in vain.

For a job application, can a prospective employer measure whether an applicant considers their field beautiful?  This may strongly influence employee productivity.

Tuesday, May 16, 2017

[nbdfbdlo] Not simulation

I don't think we live in a simulation, because accurate simulation of our universe is extremely difficult.  The story goes, the full quantum treatment with the Schroedinger equation of a single isolated hydrogen atom (1 electron) is relatively easy, but trying to model a helium atom, with 2 electrons, is already so difficult that numerical simulations on our most powerful computers struggle with it.  (This story might be out of date).  The universe, as even one person experiences it, is much more complicated than a single helium atom, and a full quantum treatment is necessary, because a person experiences many quantum effects, e.g., chemical reactions, not falling through the floor.

I suspect that those who speculate that we live in a simulation have never tried computational chemistry or other scientific computer simulations of the real world.  Perhaps they see video games or movies, but likely do not know of the huge amounts of simplifying assumptions made in those products when something only needs to look good enough for entertainment, not be scientifically accurate.

In order to argue we are not in a simulation, we must postulate limits on the computational capabilities of those who might be simulating us.  I suspect simulating our universe is at least NP-complete, probably at least PSPACE-complete.  Research into complexity theory, in our universe, can settle these questions.  We postulate that even in the simulators' universe, it is impossible to build computers to solve those problems in a reasonable amount of time.  Equivalently, but sounding more radical, any universe in which you can build such computers will not be able to sustain life.  (Then again, life, uh, finds a way, even in seemingly difficult environments.)

Simulating our universe is so difficult that it might be easier just to build it for real (in which case, we are again not a simulation).  This echoes one of the biggest potential uses for quantum computers being to do quantum simulations, or, not simulating a microchip in software, but emulating it with an FPGA.

[obcsqmdo] Double U

If it is necessary to sacrifice one letter of the alphabet (perhaps to fit the remainder into a 5x5 square), W seems like a good choice, being easy to substitute two U or two V.  Those digraphs occur extremely rarely in English, so there is little worry for ambiguity or collision.  Sawy vacwm.

Merging I and J, commonly done, recalling Latin, is also not too bad.

[vinlqxgw] Self winding digital watches

Create a digital wristwatch that harnesses enough power from the wearer's movement so that it does not require changing a battery, similar to self-winding mechanical watches.  It will still probably require changing its rechargeable battery due to hysteresis.  Maybe other parts will break first.

Wednesday, May 10, 2017

[ctimitkr] Sea level origin

Plot elevations of every point on earth in spherical coordinates.  The 2 angular coordinates remain the same, but make the radial coordinate the distance above or below sea level, not distance from the center of the earth.  This will cause areas below sea level, especially ocean floors, to poke through the origin and out the other side.  Maybe only do one hemisphere at a time, or omit below-sea-level points.  Let sea level be adjustable.

Inspired by spherical harmonics and electron orbitals, in which negative radii come out the other side.  (Previously.)

[sysxmawj] Mars topographic globe

Create a topographic globe of Mars with elevations magnified.  The goal is to highlight the difference between its hemispheres.  Does the Borealis Basin cause Mars to deviate significantly from a sphere or ellipsoid?

VR or 3D print.

[hoaettpp] The wanderers

Create a planetarium show in which the stars stay fixed and the planets and Sun move at accelerated speed through the fixed field of the stars.  This approximates taking a snapshot of the sky every sidereal day.  This has probably already been done.  Various options: planetary discs made bigger than reality (perhaps also scaled with distance), with tails to better see the path, the fixed background need not be the stars, it could be anything.  Perhaps recreate in virtual reality, because planetaria are expensive.  With VR, we could also magnify parallax and also depict the planets moving closer and farther away from the earth.

Consider using a modern ephemeris (e.g., JPL DE, VSOP87) to accurately model the locations of the planets.  Can the eye notice the effects of Jupiter?

If we make the approximation that all the planets lie on the same plane (ecliptic), then the location of a planet in the sky can be specified with just one number.  Plot that number versus time.

Incorporating distance essentially simulates a geocentric model of the solar system, since the observer (on simulated earth) seems not to move.

[klebiokz] Proving ellipticity

Replicate the experiments that proved that each planet moves in an elliptical orbit (as theorized by Kepler) not circular (as theorized by Copernicus).  Quite amazing is that Kepler proved his result using only naked-eye observations by Tycho Brahe and colleagues.

Replicate the experiments that proved that the shape of the earth is an ellipsoid, not a sphere.

Tuesday, May 09, 2017

[eaxgdlpg] Helium density by phase

Helium as a gas has density 0.164 kg/m^3 at room temperature and 1 atmosphere.  As a boiling liquid, its density is 125 kg/m^3 (which incidentally is much less than water, 1000 kg/m^3).

1 cup of liquid helium therefore has a mass of 0.0296 kg.  The same mass as a gas would have volume 0.180 m^3.  Approximate a party balloon as a 10.5 inch diamater sphere, so it has volume 0.01 cubic meter.  Then, 1 cup of liquid helium is enough gas to fill 18 balloons.  This assumes the pressure inside a balloon is atmospheric pressure, which is false (but might still be close enough) because the tension of the latex squeezing the gas inside would increase its pressure.

Inspiration was, how much do we have to worry about wasting highly non-renewable helium on party balloons?  I'm guessing typical cryogenic applications, e.g., MRI, use gallons of liquid helium.

Monday, May 08, 2017

[kdsvzhsd] Combination door lock

Something I'm surprised is not more prevalent (I don't know if it even exists) is a door lock that is a combination lock on the outside and a thumb turn on the inside.

Of course, combination locks generally offer less security than keyed (a tradeoff with convenience), but many people already don't care to have high security door locks (they probably have other mechanisms in place to deter or decrease breaking and entering).

Can such a lock be made with reliability on par with keyed locks?  If electronic, then power, including battery failure, is an issue.  Previously, exploring human power.

If electronic, then it could be easy to reset, assign, and revoke different combinations to different people.  Can such features be built purely mechanically?

It could be simulated with a combination lock box holding a key to a traditional keyed door lock key.  Multiple combinations could be accomplished with an OR gate.

[wlilyvep] Computing division in cyclotomic fields

Let L be a primitive root of unity, L^n=1.  Let ca=a0*L^0+a1*L^1+...+a(n-1)*L^(n-1) be an element in the cyclotomic field generated by L.  (The coefficients a0...a(n-1) are typically rational numbers in the context of the mathematical objects called Number Fields, from whence "Number Field Sieve".)  Similarly another element cb with coefficients b0...b(n-1).  We wish to divide them, to compute cb/ca.

That is, we wish to find cx such that ca*cx = cb.  Let cx have coefficients x0...x(n-1).  Expand ca*cx by the distributive law and collect by like powers of L.  For powers of L that are greater than or equal to n, reduce the power according to the rule L^n=1, that is, compute the exponent mod n.  Collect by like reduced powers.

Match up the like powers of (collected) ca*cx with like powers of cb and set them equal to each other.  This results in a system of n linear equations in the n unknown coefficients of cx.  Write the system of linear equations in matrix form Ax=b then solve for x as usual.  You probably want some matrix library that can work with exact rational numbers in order for the output coefficients of cx to be rational numbers.

The matrix A is highly structured, containing lots of cyclic permutations of the coefficients a0...a(n-1).  It might be possible to exploit this structure to compute things faster, but I don't know how.

Recall we are computing cb/ca.  If we have a constant ca but lots of different cb, then we can precompute the reciprocal of ca once (that is, divide 1/ca by the above method), then all the divisions become multiplications by the reciprocal.  However, conversely, if we have constant cb but lots of different ca, is there a way to precompute something to make it go faster?  Although the matrix A will differ each time, the pattern of the permuted coefficients remains the same, so it suggests it might be possible to precompute something.

This method can be generalized beyond cyclotomic fields.  The exponents were reduced by the rule L^n=1, so L is the generator of a cyclic group.  We can generalize to a different group structure using different reduction rules for a different group's generators.  (Groups that are not cyclic groups must have more than 1 generator.)  Note that many finite groups are very large, so we would therefore need to do very large NxN linear algebra where N is the order of the group.  We also have to be careful with collecting like powers if the group does not commute.

Pari/GP has some nice built-in functionality for computing division and reciprocal in cyclotomic fields.  We compute an example in the 7th cyclotomic field, with the 7th root of unity, the root of L^7-1=0.  Let's compute a reciprocal of (3,1,4,1,5,9,2):

? 1/Mod(3 + 1*L + 4*L^2 + 1*L^3 + 5*L^4 + 9*L^5 + 2*L^6,L^7-1)
Mod(-145932/4200025*L^6 + 97168/4200025*L^5 - 189607/4200025*L^4 + 106793/4200025*L^3 + 430943/4200025*L^2 - 128532/4200025*L - 2832/4200025, L^7 - 1)

Aside: Pari/GP can seemingly handle modulus being an arbitrary polynomial, not just L^n-1, so there is something slightly fancier going on.  Probably put the highest order term on one side: a(n)*L^n = -a(n-1)*L^(n-1) - a(n-2)*L^(n-2) - ... - a0*L^0, then define a reduction rule L^n = ... by dividing through by a(n).  Actually, just use polynomial division and remainder to reduce.

We can compute the reciprocal of (3,1,4,1,5,9,2) using the linear algebra process described above.  The coefficients come out in the reverse order as above.

? A=[3, 2, 9, 5, 1, 4, 1; 1, 3, 2, 9, 5, 1, 4; 4, 1, 3, 2, 9, 5, 1; 1, 4, 1, 3, 2, 9, 5; 5, 1, 4, 1, 3, 2, 9; 9, 5, 1, 4, 1, 3, 2; 2, 9, 5, 1, 4, 1, 3];
? (1/A)*[1;0;0;0;0;0;0]

[-2832/4200025]

[-128532/4200025]

[430943/4200025]

[106793/4200025]

[-189607/4200025]

[97168/4200025]

[-145932/4200025]

As with quadratic fields, we could also ask that if a programming library provides arithmetic on complex numbers, it could more generally provide arithmetic on arbitrary polynomial field extensions of the reals (complex numbers extend with L^2+1).  Linear algebra, solving Ax=b, is considerably hairier than complex number arithmetic, though.

Because a field extension creates a field from another field, the process can be iterated.  We can invent incredibly complicated objects which obey field axioms.

Saturday, May 06, 2017

[rhcuggst] Fast 64-bit factors

For the current ranges of the Cunningham project (August 2016), the largest number is 3^850 = 1348 bits.  For numbers of that magnitude, ECM can quickly find factors of 64 bits or less: between 5 seconds to 2 minutes depending on software, hardware, and luck.

This serves as a nice threshold for factors which do not need to be carefully preserved because they can quickly be recalculated.

[euzimeht] a^n \pm b^n

Consider numbers of the form the sum or difference of two powers (same exponent): a^n + b^n or a^n - b^n.  Integers of that form, or integer sequences indexed by n, seem interesting.  They could use a name.

Famously, Fermat's Last Theorem.

The Cunningham Project investigates b==1.  The above expression has algebraic factorizations.  Inspired by "The search for Aurifeuillian-like factorizations" and the reference to Schinzel.  We could imagine a much larger project investigating b not equal to 1.

Fibonacci numbers are almost this form, where a and b are not integers.  We need to divide through by sqrt(5).  Fibonacci also have neat algebraic properties.  We could define sequences​ r*(a^n - b^n) permitting real (maybe even complex) r a b, such that the value is integer for all non-negative integer n.

[bollcmpa] Blackjack as a speed arithmetic incentive

Play a game which has positive expected outcome for the player, so provides incentive to play it as rapidly and often as possible.  The game's mechanic could involve mental arithmetic, thereby providing incentive to learn to do mental arithmetic rapidly, so it is an educational game.

Blackjack is one possibility, except playing from the point of view of the house (the dealer).  The human dealer (representing the house) plays against one or more computer player/bettors and the card outcome of each game is shown.  The dealer has to sum the cards of each bettor's hand and decide whether to pay out.  Mistakes by the human that overpay a bettor do nothing special other than eat into the house's profits (which the human wants to maximize).  Mistakes which underpay a bettor are caught, the house must pay out, and maybe some other penalty like a time penalty which also eats into the house's profits because the house makes more money the more rounds are played.  (Even if blackjack played optimally is an exception to "the house always wins", we can still cause the house to win by having the computer bettors play less than optimally.)

[mtilcwmv] Friends who won't help you move a body

Friends help you move; real friends help you move a body.

While a social network of real friends would be potentially useful, it would probably run into legal and practical issues: How can you tell if someone is lying?  Many people don't even know themselves if they would help a friend move a body if it came to it.

Next best might be layering on an existing social network declarations that you won't help which friend move a body.  It isn't illegal to say that.  A friend then in need can then filter out those and evaluate the rest, some who might be real friends and some who might be too lazy to have answered the poll.

[ekzonzbp] Late Heavy Bombardment and Base Delta Zero

The description of LHB reads like science fiction: the earth was hit by so many asteroids that it reliquified the earth's crust.

Astroengineer such an event again.  Maybe moving Mars to plow through the asteroid belt would be enough, or maybe we have to move Jupiter again.

Or, create a story that the actual LHB was artificial (explaining why it was late).

[zlvvamaa] Distributed vs Virtual memory

Compare the speed of virtual memory on a local hard disk versus going over the network to access a remote computer's RAM.  Both are likely pretty bad, but which is worse?

The latter could be accomplished by NFS sharing a ramdisk, which is then used on the other computer to hold a swap file.  Possibly useful for a small cluster.  We would like some way of keeping the operating system on local memory, and only allow an application to use the network remote memory, so that a network or NFS fault will only crash the application and not the whole OS.

[jsqaswqe] Base 94

Base 94 seems attractive for compactly encoding data: the printing ASCII characters minus space.  Space can then function as an escape character for signifying metadata.

Byte strings (base 256 with possible leading zeroes) can be unambiguously be converted to base 94.

Curiously iroha is base 47, half of 94.

[imbnyxus] Human-powered electronic lock

Create an electronic lock (perhaps door lock) which does not require batteries or be connected to electrical mains.  Instead, power is supplied each time by the person operating it: pull a lever or turn a crank to generate electricity.  Even better, step up onto a platform which descends due to your weight, generating electricity.  6 inch * 100 lb = 68 joules = 6.8 seconds * 10 watt which seems plenty for operating a lock.

Ideally we would like reliability and ease of repairs / cost of ownership comparable or better than a fully mechanical lock.

Friday, May 05, 2017

[vssboyhp] Model organisms evolving

How much have model organisms evolved over the years to survive -- thrive -- for lab conditions, or, more likely, for the conditions during idle or storage in between experiments?

Does this affect experimental results?  Probably yes in comparing results with older results on the "same" model organism.

[hcqjiotw] Computer improving music

Train machine learning to distinguish between good and bad music.

Then (somehow) use it to improve a given piece of music.  This is different from the typical Holy Grail of a computer composing good music from scratch.

It is also similar to how humans are creative, always building on something else.

[xuzamfou] Parallel ECM

Here is a bash script to spawn several parallel instances of GMP ECM to find one factor.

command rm out.* ; nproc=4 ; for i in $(seq 1 $nproc) ; do echo The_number_to_factor  | nice -19 time -o out.time.$i ecm -c 0 -I $nproc -one 10000 > out.log.$i & done ; wait -n ; killall ecm

Notes:

Use the physical number of processors, not hyperthreaded ones.  Probably bottlenecked by ALU, not memory access.  But hyperthreading might be useful when large B2.

wait -n is a nice primitive: whoever finishes first wins.

Consider --disable-aprcl during the configure step to speed up final verification of prime factors.  It is unfortunate that this cannot be disabled at run time.

Tuesday, May 02, 2017

[shjnmftv] Dual crossword

Create a crossword puzzle with two solutions: large portions of the puzzle have two possible letters, both valid answers to the clues.

Each solution could have a theme which ties it together.

[udvieqsl] Smooth closed curve fitting

Given a set of points, fit a smooth closed curve through them.  Fairly easy and commonly done are splines, but splines are not infinitely differentiable.

Perhaps restrict it to a sum of circular harmonics around a given circle center point.

[ljtodplv] Idioms in a corpus

Given a corpus, do NLP and identify the idiomatic constructions in the language.  The most ambitious is to do this with no other information about the language, so NLP needs to guess at the meanings of words from context, then identify instances of words not being used with their normal meaning.

[mlwmffmf] Beowulf cluster

Connect a small number of computers together to create a more powerful computer.  "Small number": not needing to worry about the many possible kinds of faults, networking can be a single switch.

Because there so many ways people might want to do it, best is probably the Unix philosophy: a collection of small tools that people can hook together in many different ways.  (Bad is a walled garden.)  Many great small tools already exist, e.g., ssh, clusterssh.  What others are wanted?

[tnxlwtph] Chess board which remembers

Create a chess board / set which remembers every move played on it.  We imagine it being passed down through a family.  For example, a grandchild can review a grandparent's lifetime from first learning through mastery.

Massive challenges: very long term reliable data storage, a clock which remains accurate for the very long lifetime of the device (recorded moves are time stamped).  Maybe RAID of USB keys.

Identify and record who was playing?

Somewhat easier in cloud: is a physical chess set too antiquated?

[ogkqcild] Stupid is the new smart

T shirt idea.

[cvctzpor] 4 button sliding

Consider four buttons on a touchscreen:

ABBA
CCDD

Button A is not contiguous; it wraps around.  Unambiguous slides (gestures) are possible between any pair of regions.  3 not possible: CAD.

A tetrahedral graph also works, but it is less elegant in a rectangular region.

[ijpfyqny] Quartet covers

Why aren't there string quartet versions (covers) of many (especially modern) songs?  It seems to be a very versatile ensemble.  Hypotheses:

The era of those instruments is passed, so lack of demand for arrangements.  Piano and guitar are more popular.  Or playing recorded music.

The era of cooperation is passed.  It is hard to assemble groups of musicians willing to practice and play together.  Solo piano and solo guitar covers are more popular.

Modern music often wants both drum and bass, and a single cello cannot cover both.  A typical rock band has them separate.

The ensemble, or instruments, are not actually so versatile.  Despite seeming tremendous range of play (as seen in virtuosos), it does not cover very much all the sounds that exist in popular music, or at least, mimicking those sounds requires tremendous skill that most string players do not have.  Possible example: wind instruments can rapidly play notes with varied attacks, and dynamics within a held note.

[qruphqlk] Very narrow text figures

Consider drawing numerals extremely narrowly (in order to cram many into a small space).  Text figures will be better than numbers all of the same height because descenders and ascenders help eliminate ambiguity.

Previously similar.

[xigikele] Questions bin

Ideal is for people who understand a subject to write about it, teaching others.

Next best might be for such people to write questions about their subject, questions that are easy to answer for someone who understands the material but difficult for someone who doesn't.  Others who are experts can review the questions to verify that they have this property.

Writing questions might be less effort than writing knowledge, i.e., answers.  The latter also requires considerable skill in communicating knowledge.

Questions of course provide a directed goal for people wanting to learn material: keep learning until the questions are easy.

Unlike (say) Wikipedia, which attempts to be a compendium of knowledge, a collection of questions almost seems to be a compendium of what the reader doesn't know: a compendium of lack of knowledge.

[ovvwqpvl] Area of the earth in bits

The surface area of the earth is about 5.10e14 square meters.

It would take 48.9 bits to address a particular square meter.  68.8 bits for square millimeter.

64 bits gives regions 27.6 square millimeters, the area of a square with side 5.3 mm.

Previously, meshing the earth.

[mgihrrek] Identity by sci-fi drugs

We don't know the mechanisms by which people form and maintain their identity.  Write about a fictional world in which the mechanisms are known -- invent fictional mechanisms for it -- and the characters actively manipulate it.  Maybe they inject specific chosen drugs into children to program specific chosen identities.  Parents and others with power do the injecting.

We then see the result of the fictional manipulation resulting in people with identities familiar in our real world.

Saturday, April 29, 2017

[tenkclgv] Saved only by good intentions

Consider institutions with the power to do good or harm, and the only mechanism preventing doing harm is the moral rectitude of the people in the institution.  Are there any examples of such organizations which did not go on to do harm?  This is pretty pessimistic.

The road to Hell is a frictionless chute of good intentions.

[avkthzdj] Generalized engraving

Divide a region into a tessellation of equilateral triangles.  Divide each equilateral triangle into a grid of small equilateral triangles.  To each internal vertex of the larger triangles, assign a height value.  Vertices on the edges of the larger triangles remain at height zero, to establish boundaries between the larger triangles.  Interpolate a plane between each small triangle of vertices.  Each larger triangle represents a letter in an alphabet.

This could also be done with a small equilateral triangles dividing regular hexagons in tessellation.  The simplest size has only one internal vertex per hexagon.

Square grid requires more work in interpolating a surface between vertices of specified heights, e.g., bilinear interpolation.

3D print or mill the surface, encoding information into a physical object.

[nhemexzg] Technology to cut corners did not exist yet

Sometimes the older version of a product is higher quality than a newer version, because the technology to make at lower cost (but lower quality) did not yet exist when the old one was made.

This seems problematic: technology marches forward and things get worse.  Probably intellectual property issues preventing a different manufacturer from continuing to produce the higher quality version.

[zjutseyk] Padlock logic

A bunch of padlocks on a hasp with multiple holes functions like an AND gate: all locks must be unlocked in order for the hasp to open.  This is seen in safety lockouts.

A bunch of padlocks linked in a chain functions like an OR gate: at least one of the padlocks must be opened to break the chain.  There remains the mechanical or geometric problem of securing something (like a door) with this chain of locks.  A pin can be substituted for a padlock, and the pin can have a hole on each end, each which can take a padlock or another pin.  Other specialized hardware exists, used for granting many different parties access to land.

One can construct complicated graphs of AND and OR locks, though again there may be mechanical difficulties of fitting a padlock to connect desired nodes.  Perhaps not so bad with lengths of chain where necessary.

[zvezqqhy] Spinning the Earth faster

How much would you have to change the rotation rate of the earth for noticeable geological things (e.g., earthquakes) to start happening as the earth settles into a new oblate shape due to the change in centrifugal force?  I suspect small changes suffice: centrifugal forces will easily overpower the rigidity of the planet.  How would one change the earth's rotational speed?  Maybe launching flywheels into space.

Original thought: make launching satellites into low earth orbit easier by enhancing the speed of the equator.  Current equator speed 0.465 km/s.  Low earth orbit 7.8 km/s.  If we increased the equator speed to match Low earth orbit, the earth would break apart, though bad things would happen before that.

The Earth's orbital speed around the sun is 30 km/s, pretty fast.  But outer planets travel much more slowly.  Are there planets whose surfaces or cloud tops are sometimes traveling backwards with respect to their orbit around the sun?  Dropping something into the sun would only require escaping the planet's gravity well, not cancelling the orbital velocity.

Friday, April 28, 2017

[pqqaicol] One Ring Singularity

"And into this ring he poured all his cruelty, his malice and his will to dominate all life."

All these things that Sauron poured into his horcrux added up to considerable mass-energy packed into a very small volume.  The density was so high that the object gravitationally collapsed into a singularity.  Sauron had added rotational momentum, so it was a ring singularity, as found in a Kerr black hole.

No, you could not wear this ring on your finger.  But it could be an extremely destructive weapon.  Disappearing when wearing the ring represents leaving the universe when crossing its event horizon.

The One Ring being a singularity explains why it was so hard to destroy.  Perhaps the only way to dispose of such a thing without it causing huge damage to its surroundings is to drop it into another black hole: Mount Doom.

The Lord of the Rings: In Space!

[bvahtsov] Cunningham sculpture

Create a sculpture, probably something like a long wall, onto which the Cunningham project, maybe just base 2, is inscribed.  Leave blank spaces for unfactored cofactors.  New factors get inscribed over time: the sculpture changes.  Maybe ceremonies for new factors.

Probably separate removable panels to make easier inscribing new factors offsite and correcting errors.

What format should be inscribed?  Semi-compressed like in the Cunningham book, or full factorization to make it easily comprehensible to the general public?  Base 10 or binary?  Binary seems apt, especially for the base 2 table.  Many of the prime factors have pretty patterns when written in binary.  Previously, base 32.  Maybe barcode format (e.g., QR) for good error correction -- the sculpture serves as a (very) hard copy, more resistant to destruction than paper or electronic.    If preservation and longevity are goals, how should the sculpture be designed: what material, what styles and techniques of engraving?

QR codes can be constructed out of square tiles, and archaeology shows tiles can last a very long time.

Vaguely inspired by: Vietnam Memorial Wall, New England Holocaust Memorial (which consists of many numbers).

Previously, Mersenne.  Cunningham has an advantage over Mersenne in that Cunningham is self-certifying.  Anyone can verify that the list of factorizations (excluding blank spaces) is complete up to the maximum exponent; anyone can verify that the factorizations are correct.  In contrast, it is pretty difficult for someone to verify the primality of the large Mersenne primes, and it is very difficult for anyone to verify that a list is complete, that there are no skipped primes in the gaps.

[ucuttxtc] Mersenne sculpture

Create a collection of physical objects recording, representing, celebrating the discovered Mersenne primes so far.

Distinct objects is better than a single fixed object (e.g., a plaque allowing for new entries to be added at the end) because new Mersenne primes could be discovered in the gaps between currently known ones.

Easiest for each prime is an object with (at least) one linear dimension proportional to the log of exponent, onto which the exponent is inscribed (perhaps several times​ on different sides, backwards and forwards, for redundancy).

[ygkliadl] High precision real and modular cube roots

Computing to high precision a cube root in the field of real numbers is kind of difficult: we need special algorithms like Newton's method and out-of-core FFT-based multiple precision arithmetic.

Computing a cube root in certain fields of modular arithmetic is extremely difficult; this is the basis of the security of RSA.

Are these two difficulties related?  (Probably not.)  It would be interesting if, say, a trillion bits of real precision could be interchanged with a 100 bits of modular precision.

Wednesday, April 26, 2017

[qhxrhaqe] Attempting to destroy the One Ring

Frodo delivers the One Ring to Rivendell, and before the Council meets to go send the Fellowship into Mordor to destroy the ring, the elves try their hardest to try to destroy the ring on their own (but fail).  Depict with special effects the ring resisting all realistic and elven-magical attempts to destroy it.  Celebrimbor is dead, but perhaps they preserved his knowledge of ring-smithing, but even that was useless.

What are the mundane things the elves tried, modern and realistic future muggle technologies?  Acid, heat (yes the elves have a particle accelerator), water-jet cutter, tension and pressure, explosives (yes the elves have nuclear weapons).

(Perhaps juxtapose with how easy it was for Tom Bombadil to destroy it, or at least, make it disappear.)

[ylikmliz] Sun script

Consider a shape resembling the kanji character for sun 日 but with X's in the upper and lower rectangles.  The X's contribute 4 strokes total, and the the four sides are another 4 strokes (not the traditional convention in which the 4 sides are drawn with 3 strokes).  The middle bar adds a 9th stroke.

This also resembles a seven-segment display (with X's) except that the vertical sides are one continuous segment instead of broken into two.

Let the presence of absence of each of the 8 strokes that are not the middle bar encode 8 bits or one byte.  The middle bar is mostly optional, only necessary when the character might be confusing without it, most notably for encoding zero, which has no other strokes so would otherwise be a blank space.

[wuzostlr] Democracy for succession

Perhaps the purpose of democracy is simply to decrease the turmoil and turbulence that occurs in other forms of governments​ when a transition or transfer of power occurs.

Certainly, turbulence can and does occur in democracies, and peaceful and smooth transitions​ of power can and do occur in, for example, monarchies and dictatorships, but we hypothesize that the average rates over time differ.

Perhaps Amartya Sen's observation that democracy seems to avoid famine is only a side-effect of this.  In other forms of government, the government becomes extremely dysfunctional during power struggle turmoil (which might be occurring behind the scenes even before the current leader loses power), allowing things like famine to occur because nobody is minding the store.  (Of course, we can see dysfunction and turmoil in power struggles in a democracy also, so it remains to be identified exactly where the difference is.)

On one hand, this model suggests we ask too much of our democratic government: all we should really ask for are peaceful transitions​ of power, and not, for example, for the government to actually do good - e.g., promote the general welfare - with its power.  On the other hand, because we are avoiding turbulent power transitions and energy wasted on power struggles​, it would be nice if the government could spend its surplus energy on doing good.

[snwocelw] Cost of crisis cooperation

A crisis happens, and people who would normally not get along are forced to get along with each other.  Normally this is depicted as a good thing.  Invert the trope: cooperation came at a cost, perhaps social or psychological.  Explore or depict that cost.

Tuesday, April 25, 2017

[ymkcqmog] Polynomial through points

Given some points on the plane, fit a minimum-degree polynomial through them.  This is easy, but the resulting curve depends on the orientation (angle) of the axes, which can be arbitrarily chosen.  Which one should be chosen?  Perhaps the one which minimizes the arc length of the curve segment through the given points.

[oovttyoz] Check the reference

Given an academic paper with an inline citation to another work, create a tool which fetches the other work, does NLP on both works, and verifies that what the citer says about the cited is valid.

Also Wikipedia citations.

[mxxavtrh] Lab triple alpha

Demonstrate in a laboratory the triple-alpha fusion process, yielding carbon-12.  This seems difficult bordering on impossible.  Maybe Farnsworth fusor.

This is, anthropically, the most important nuclear reaction in the universe.

Ironically, getting the ionized helium nuclei needed as input is extremely easy: alpha particle.

Vaguely inspired by the 21 cm hydrogen line , which is very common astronomically but had never been observed in the lab and even initially seemed impossible to see in a lab because of the rarity of the "forbidden" atomic transition.  However, hydrogen masers have since replicated astronomical observations.

Monday, April 24, 2017

[vqoxpezv] Omitting named function arguments

Consider a programming language whose syntax for function calls requires naming each passed argument, but as a benefit for this extra verbosity, allows specifying the arguments in any order:

f { foo = 3, bar = True, baz = "hello" }

If an argument is omitted, there are several things that could happen, depending on how the language is defined.

  1. Compile time error.
  2. It becomes a partial function application, a lambda function of the missing arguments.  Haskell does this with currying when trailing arguments are omitted.  (Tangentially, in Haskell, creating a lambda for a missing argument that is not the last one requires a little bit more work.)
  3. The missing arguments get silently assigned a lazy "undefined" value, which results in a run-time error if the "undefined" is ever evaluated.
  4. The language permits the function definition to provide default values to some omitted arguments.  If there is no default value, then compile-time error.  C++ does this.

It would be nice if a language could provide all of these options, even though strictly speaking they are mutually exclusive.

An imperfect solution is to have special keywords invoking #2, #3 and #4, perhaps something like f { foo = 3, REST UNDEFINED } or REST DEFAULT or REST LAMBDA, explicitly indicating indicating what do with the rest of arguments omitted at a call site.

I have seen default values implemented in Haskell using its typeclass mechanism, e.g., configuration values in xmonad.  Default values are overridden using record modification syntax.

A hybrid between #1 and #4 would have the compiler always produce an error if arguments are missing, but indicate in the compile error that a default value is available via an explicit keyword (as above) when one is.

A list of named parameters and their values looks kind of like a record or struct.  Make such a list a real type and allow variables of that type to be declared and assigned.  A special syntax allows invoking a function with a record instead of a named argument list.  If two functions have the same named parameters, are their parameter record types the same?  Duck typing.

This scheme also gets​ messy when arguments may be omitted; we need to be able to define record types with only a subset of the parameters of a function, as well as possibly allowing REST UNDEFINED or REST DEFAULT as dynamic values in the record.  If using REST LAMBDA, and whether a record field is defined is only known dynamically, then type checking and kind checking has to be postponed until run-time.

One of the things that makes me uneasy about Haskell record syntax is the following: REST UNDEFINED (#3) occurs implicitly when records are constructed whereas REST LAMBDA (#2) occurs when omitting trailing arguments when using positional constructors.  The latter will usually cause a type checking error if the argument was omitted accidentally whereas the former waits for a run-time error.

Previously: Same idea.

Having to specify a function name as well as all its parameter names might become tedious for the programmer.  Perhaps have mechanisms for a programmer to define alternate parameter names or omit a name.  Vaguely related: by type.

Saturday, April 22, 2017

[tpfqrkkk] Earth surface area

Approximating the shape of the earth as an oblate ellipsoid, we use the following values from wikipedia (which cites IERS):
a=6378136.6 meter
c=6356751.9 meter
f=298.25642^-1

Note that the values are not consistent.  If we compute flattening from a and c, we get f=298.25701^-1.

We can compute eccentricity from c and a:
e = sqrt(1-c^2/a^2) = 0.081819221

Or we can compute it from flattening:
e = sqrt(2*f-f^2) = 0.081819301

We use the following formula from Wikipedia for the surface area of an oblate ellipsoid to compute the area of the Earth in square meters:
2*Pi*a^2*(1+(1-e^2)/e*atanh(e))
= 5.1006556e14 m^2
= 5.1006555e14 m^2
using the two different values of eccentricity computed above.

We have tried to use significant digits correctly.  The above two values of the earth surface area are considerably higher precision than typically reported values of earth surface area, which usually give only 2 significant digits.

We have not made any corrections for general relativity.

[cogfpzpk] Trump apology for Holocaust denial

Of the many, many groups that the Trump adminstration has offended thus far, is "Hitler did not use chemical weapons" the only offensive thing said by the administration (through its mouthpiece Sean Spicer) that it has apologized for?

Does this speak to the political strength of Jews compared to that of other groups the administration has offended?

Using toxic chemicals for execution of prisoners is qualitatively very different from using toxic chemicals for killing on the battlefield.  It seems bad faith to equate them, though taking a political opponent's words and interpreting them in bad faith is (cynically) synonymous with politics.

The type of chemical differs considerably between gas chambers for execution (carbon monoxide, hydrogen cyanide) and battlefield (mustard gas, sarin, VX).  The delivery method differs considerably between execution (pump the gas into a room) and battlefield (bombs and munitions, outdoors).  On the battlefield, there is much more danger of the gas hurting your own soldiers, for example, due to a change in wind direction.

Even the U.S. has used gas chambers for execution, and continues to use toxic chemicals for the execution of criminals.  Does that mean the U.S. is doing the same evil as Hitler and whoever it was in Syria (presumed to be Assad)?  There are of course considerable differences in the justice system preceding each use of chemicals for killing, but the prohibition of the use of chemical weapons does not specify a standard of justice that makes using the weapons OK.

Incidentally, Imperial Germany did use mustard gas on the battlefield in World War I, and presumably the technical knowhow survived into the Nazi regime, so Hitler may have consciously chosen not to use chemical weapons on the battlefield in World War II, even though he easily could have.  Use of weapons of mass destruction in WWII would have to wait for another country.

Friday, April 21, 2017

[frhoywsb] Money can't buy happiness

Why not?

Like Soylent Green, the answer is, it's people of course, perhaps the presence of people you do trust, and can trust because they see you as One Of Us.  People are social animals with happiness deeply ingrained into tribe membership.  The tribe boundaries are equally deeply ingrained into identity.

Interesting extreme examples are celebrity marriages failing.  If money could buy happiness, those people could afford it.

[qwfubouw] Symmetric Hamiltonian cycle of the faces of a cube

Top, side, side, bottom, then the two remaining side faces in the order which preserves bilateral symmetry.

[gvkjyyui] Base 6

Consider base 6.  Testing divisibility by 2 and 3 can be done by examining the last digit.  Similarly, decimal (hexal hexary) expansions of fractions with those denominators​ terminate.  Testing divisibility for 5 and 7 can be done by methods​ analogous to 9 and 11 in decimal.

6 = 3! might be useful.  Number of faces of a cube.

Previously, base 30.

Inspired by, the fingers on one hand can specify one digit in base 6.  Though finger counting is unary.

[tdenfgzv] Dumbbell escape horizon

As two black holes merge, is there a moment when the escape horizon is shaped like two tangent or slightly overlapping spheres or spheroids?  Space and spacetime are shaped very weird -- not convex -- in the vicinity.

[fgmfgmql] Checking base 10 arithmetic

One can check arithmetic in base 10 by casting out nines, and similarly computing remainders by alternating sums for 11 and the beautiful 1001=7*11*13.  (So 11 is repeated effort.)  We can also get 999=37*27 and prime 101.  Is base 10 especially nice in its ease of checking arithmetic?  We are probably looking for large least common multiple of b^n plus/minus 1, over small n.

Monday, April 17, 2017

[ughuslfb] Brain-damaged cockroaches

Mythbusters demonstrated that cockroaches seemingly recover after being submerged underwater for 30 minutes.  However, were they permanently damaged by the experience?  Humans suffer permanent brain damage after oxygen deprivation in cases of near drowning.

Initially, it seems comical to try to measure whether a cockroach suffered brain damage, as they didn't have much of a brain to start with.

[czyaeert] Continuously extruded baguette

Create a very long baking system in which dough is continuously extruded onto a conveyor belt, allowed to rise, then baked, all while on the same long straight constantly moving belt.  Out the other end comes an infinitely long baked baguette.  Probably not practically useful.

Inspired by the baking machinery at Krispy Kreme, including the zig-zagging proofing section.

Same idea for constructing starships.

[jkbtasqi] Proofs of specific NP or P

Collect interesting or clever proofs of specific instances of NP-complete problems being proved to have no solution.  Inspired by proofs that certain graphs have no Hamiltonian path, where the general Hamiltonian path or cycle problem is NP-complete.  Also easily applicable to satisfiability.

We're probably wandering into co-NP.

A proof that a problem has no solution done by enumerating all possibilities is mundane (and exponentially long (actually just super-polynomial), by the nature of NP).  Interesting proofs avoid the exponentiality.  Such proofs, perhaps many taken together, might provide insights into the nature of class NP, of course aiming for resolving the P versus NP problem.  Ultimately we are looking for indications that there exist problems for which one cannot avoid exponential computation to prove there is no solution.

Conversely, a solution to a specific NP (not NP-complete) problem (for which no polynomial time algorithm is originally known) found by brute force is mundane.  Solutions found in a way that generalizes to polynomial-time are interesting, essentially proving that the problem is in P.  Collecting many such proofs may be useful.  Again, we are looking for commonalities in ways problems get interestingly proven to be in P.

[jyketcyj] Humans improving a chess engine

Given a game in which a chess engine loses (probably against another engine), ask unassisted human players to identify the losing move (perhaps allowing probabilities to express degree of certainty).  (The answers can be verified with longer computation.)  Moves which human players can quickly and accurately identify as bad are candidates for areas of improvement for the losing engine, perhaps even automated improvement using machine learning.  (This assumes anything a human can compute quickly, a computer should be able to, too.)

Previously, on ways a human can help improve a chess program.

[slnpxpzm] Graphs with surprisingly large chromatic number

Create a gallery of graphs with surprisingly large chromatic number, where "surprising" is subjective.  Perhaps graphs which are almost planar, having very few edge crossings, but require far more than 4 colors.

[ymjknqvs] First perfect game of chess

When was the first game-theoretically optimal game of chess played, where neither player made moves which altered the theoretical game value of the opening position?  We do not require players to put up the strongest resistance (for example, if a position is lost).  Has the first perfect game already been played or has it yet to be played?

Of course, barring tremendous improvements in computing, we can never prove whether any given game is a perfect game, though we can disprove some games.

Consider a contest (of hubris), nominating games (the older the better) believed to be perfect games, that stand up to all current human and computer analysis, and that are predicted to stand up to all future analysis.  Neither player makes a half-point (or full-point) mistake.

I suspect the game value of the opening position is a draw, so unfortunately we are looking for old insipid draws where both players play very safe moves: "grandmaster draws".

Comically, if we allow game results by mutual agreement, then one of these zero-move games must be the perfect game:

1. Draw agreed 1/2-1/2

1. Black resigns 1-0

1. White resigns 0-1

In a similar vein, if the game value of the opening position is decisive (say, white can force a win), then a game in which black immediately plays very bad moves and quickly gets checkmated may be a perfect game: we do not require black put up the best resistance from the losing opening position.

Sunday, April 16, 2017

[vsbfzrka] Preventing DoS against stretched passwords

Apply key stretching to your login passwords, e.g., /etc/shadow.  Unfortunately, this makes easier denial-of-service attacks with remote ssh logins by spamming a server with password attempts, each which consume considerable CPU to test and reject.  How can this be avoided?

Easiest is proof-of-work (e.g., Hashcash) submitted by each client for each password validation attempt.  Client requests with more Hashcash can preempt currently running validations.  Clients also need a way to query the current queue to know how much Hashcash to submit to aim for the front of the queue to be able to log in when a DoS attack is in progress but not waste time computing Hashcash when there is no attack happening.  Even this scheme may be insufficient against a distributed denial of service attack (DDoS).

Harder is for the password validation computation be done by the client.  I do not know how this could work.  The delegation capability of Makwa might be useful.

Asymmetric key (e.g. RSA public and private keypair) logins do not have to do an expensive hash a password, at least not on the server side.

[rynazulu] Grim reaper pendulum

Create a kinetic sculpture of a grim reaper swinging his scythe at a frequency that matches the actual average rate of death in the world.

Thursday, April 13, 2017

[jtzxkpvw] First against the wall when the revolution comes

Who should be assassinated / executed / otherwise incapacitated when consolidating power, to eliminate and prevent formation of opposition?

Seemingly obvious are leaders of the opposition, but after that things become less obvious:  People who could potentially become leaders of the opposition.  Any competent people who could potentially be useful to the potential opposition, not necessarily as a leader (but they could be potentially useful to your side as well).  Who else?  And how can one find these people?  Answering these questions​ requires understanding how society operates and adapts in response to changes.

Inspired by real mass political executions, e.g., Katyn, in which the Soviets executed a great many competent Polish people, seemingly with considerable success: it took many generations for effective opposition to form.

Vaguely similar is brain drain, which also weakens a region by depriving it of competent people.

Tuesday, April 11, 2017

[nznriibb] Two useful functions

For a calculator: Modular exponentiation, extended GCD.  Latter needs two outputs.

Other number theoretic functions: Floor, mod, factorial (gamma), nCr.

Previously: factoring

[rgettuwe] Swimming to the center of the sun

Indestructible Superman visits the Sun and tries to swim to the core.  How difficult would this be?  How strong is the radiation pressure?  Assume Superman can't just change his density and sink the whole way.

Same questions, except for a white dwarf, maybe Sirius B.  Assume he remains indestructible despite being away from the yellow sun.

[nzvscjxd] Rational roots of a polynomial

Given a polynomial with integer coefficients, determine all of its rational roots.  What is the computational complexity of this problem?  At first glance, it seems one must factor the leading coefficient and constant term, but maybe there are tricks of solving the polynomial in floating point using for example Newton's Method, then testing whether each found solution is a rational number.

Given a monic polynomial, determine all of its integer roots.  Determine all of its Gaussian integer roots.  Monic polynomial with Gaussian integer coefficients.

[edptgsmd] African-American immigration

To what extent is the conflict between blacks and whites in American society similar or identical to conflict between immigrants and natives (less recent immigrants)?  The model is that the apartheid culture that existed for African-Americans before the civil rights movement (and probably still partially exists now) could just as well have been another country, and the civil rights movement represented an relaxation of restrictions on travel across the border.

Understanding one in terms of the other may help propose or eliminate potential solutions.

[kjpopgqp] Murdering your spouse to marry another

A classic noir plot involves one partner murdering their spouse for the purpose of marrying another, perhaps someone they love more.  (Interestingly, the plot is done in both gender directions without either seeming like an inversion of a trope.)

Assuming this happens in real life, what is going on in society that sets up the incentives for murder?  Obviously, living is so much better than dying that it is surprising that some sort of Pareto-improvement deal could not be worked out that avoids killing.  It might be that the surrounding society prohibits or otherwise punishes divorce, though that still begs the question why, especially since such a practice incentivizes murder.

One possible such incentive, good for noir, is that the jilted first partner will kill the new second partner to eliminate the new competition, so the first partner must be killed to save the second: game theory.

[ocilzptj] Arithmetic in any quadratic field

If providing arithmetic with complex numbers (in an application, library, or calculator), it is only slightly more complicated to provide arithmetic in any quadratic field.  For a + b*sqrt(D), I think a, b, and D can be any real number, though mathematicians have identified rational a and b and integer D to be especially "interesting".  D=-1 is complex arithmetic.

[orgxasdy] Inverting a regex

Given a regular expression, list all possible strings that match it, perhaps in order of length.  This seems relatively easy, perhaps breadth-first on the nodes of a finite automaton.  Easiest is if the regular expression is anchored with ^ .

Sunday, April 09, 2017

[qzdahqpt] Turing machine walking a tree

Instead of walking along an infinite tape, modify a Turing​ Machine to walk along an infinite binary tree.  In each state transition, the head can move to the parent or to one of the two children (or possibly stay in place).  Data can be written at each node, analogous to tape cells.

Perhaps make available in the state whether a node is a left or right child.

The tree could have a root node, analogous to a Turing machine tape that is only infinite in one direction, or the parents could continue upwards forever, analogous to a tape that is infinite in both directions.  A regular Turing machine can be simulated by just traversing the leftmost nodes.

This machine model seems attractive to write real programs for because it can address exponential amounts of memory in linear time, unlike the traditional Turing machine which takes linear time to get to an address.

Previously on tree-structured Turing machines.

[ezfobhcr] Non equal temperament

When using a tuning system that is not equal temperament, transposing a piece to a different key can make it sound significantly different​, with some intervals sounding more in tune and others sounding less.  This could be used artistically.

With a synthesizer, one could invoke different tuning systems with a touch of a button.