Friday, October 19, 2018

[ceuicnvo] Subtleties of log tables, part 1

Suppose we are making a base-10 logarithm table, calculating the entry that should go at log 1.41.  Seems easy: just calculate log10(1.41) = 0.149219, right?

However, the log table only knows the user wants the log of an input that is somewhere between 1.405 and 1.415, the range of inputs that round to 1.41.  To minimize the worst case error (minimax), it should actually give the mean of the logs of those endpoints, so the entry for 1.41 should be 0.149216.

This is a tiny bit smaller than the "easy" value calculated above because the logarithm function is concave down.  This only matters if one has a 6-place log table, which is absurdly high precision, exceeding the 3 significant digits of input.

It's a bit surprising we only need to calculate the mean of the endpoints and not have to calculate an integral and expected value.

[sshwlcuj] History is a political field

History is a survivor game.  Whoever's narrative about a historical topic is most accepted when the last primary source dies or disappears or loses its provenance wins.  Any later challengers won't be supported by primary sources so are inherently weaker.

Note well that there is no incentive for the winning narrative to be true: selectively pick from primary sources to tell the story you want to see become accepted.  Truth is occasionally useful only to the extent that it helps you win, perhaps to defeat an opposing narrative that has an attackable portion that isn't true.

Of course, politics is the reason people are creating and supporting the narratives that they want to see win.  Procedurally, how does one win?  Of course there's the labor of researching and writing history, but there are also political skills needed to emerge as the last fighter standing.  What are those skills?  How can you learn those skills?

Inspired by anecdotes that the academic faculty hiring and promotion process in humanities and liberal arts is a highly political process.

Also inspired by the date of Christmas.  It is curious that the date of Jesus's death and resurrection (Easter) are marked essentially as a fixed date on the Jewish calendar (then converted to a moving date on Gregorian via computus), but his birth is a fixed date on Gregorian.  At some point there were primary sources for the date of his birth, but they are all long gone.  Whoever declared the December 25 date, perhaps supported by some historical evidence still available at the time, has won, with no way of historically challenging it.  One modern theory states that the date is completely bogus, a purely political choice by Romans needing a midwinter holiday to replace Saturnalia in their process of converting people away from worshipping Roman gods to Christianity.

Also, history is written by the victors.

[ulpibfgq] Fun with projectiles

How many dimensions?  2 or 3.

Is there gravity?  If not, projectiles travel in straight lines like billiard balls or lasers.  If so, parabolas.

Is there energy loss when the projectile bounces (reflects) off an obstacle?  If not, then it's like a mirror: angle of reflectance equals angle of incidence.  If so, it's an inelastic collision; energy loss is (probably) proportional to normal component of velocity.

Simplest is for the projectile to always travel forever: the goal might be short distance or short time or robust trajectories.

We could have more realistic projectile motion but just the above conditions are probably enough to make things hard enough for a game.

Have nice graphics of the projectile traveling to and hitting the target.

Moving targets, moving obstacles, multiple projectiles hitting each other.

Point particle as projectile is easiest, then sphere.  Rigid uniform density ellipsoids, polyhedra.  Self-rotation becomes an adventure, e.g., T-shaped object spinning in space.

[ejhsazxj] Four moods in the bedroom

  1. Tired and happy
  2. Tired and irritable
  3. Happy and full of energy
  4. Irritated and full of energy

#1 is good for cuddling; #3 is good for sex.  Partners need to accurately communicate about which of the 4 states each person is in.

#2 and #4 might be associated with sexual assault, maybe #2 the survivor and #4 the perpetrator.

Wednesday, October 17, 2018

[gfromzkm] Physical Klotski

The traditional Klotski sliding block puzzle (Red Donkey) uses the same pieces and same goal (big square to bottom middle) as the Century Puzzle, Supercompo, and Supercentury, although the orientations of the 2x1 blocks differ.  This conveniently allows multiple ways to enjoy the same set of pieces (so long as they can be arbitrarily rearranged).

Inspired by a physical Klotski puzzle in which one can easily rearrange the pieces, and with a thin big square block and thin slot at the bottom of the frame indicating the goal.  The rest of the blocks are thick so will not fit through the slot.

What is the most difficult puzzle with this set of blocks and final goal?

Slightly simpler: Among all the goal positions for (say) the Donkey, what starting position has the greatest minimum distance?  That is, what is the most difficult starting position for the Donkey if you are not allowed to take pieces out?  This is a minimax graph distance problem.

Some collections of 4x5 sliding block puzzles:

http://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzRedDonkey.html

http://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzDadsFamilySet.html

http://www.johnrausch.com/SlidingBlockPuzzles/4x5.htm

http://www.pro.or.jp/~fuji/java/puzzle/slide/V1.0/fuji.index-eng.html

Maps of Dad's Puzzler, Donkey, and Century

Tuesday, October 16, 2018

[pszsinsd] Generalized Riemann zeroes everywhere

Associate different Dirichlet L-functions with locations on earth.  In an augmented reality game (inspired by Pokemon Go), prizes appear at a location at times corresponding to zeroes along the critical line for the L-function of that location.  The time at which a zero appears corresponds to its height, the imaginary component of the zero.  We will need to do some scaling so that prizes don't come increasingly frequently as density of zeroes increases with height.

I don't think we can't associate every point on a sphere with a different L-function because there are only countably infinite L-functions but uncountably infinite points on a sphere.  Also, there would be an infinite number of prizes popping up every moment within any region.

Best would be to subdivide the earth into regions then associate one L-function to each region.

Of course, anyone knowing the mapping can predict in advance when and where prizes will appear, but doing so requires learning about Dirichlet L-functions and the generalized Riemann hypothesis.  Can we instead design it so that predicting prizes actually requires assuming GRH, so that it will be very interesting if a prediction is ever wrong?

[opccpflr] Kazakh anthem

Recreate the scene in Borat and his fake Kazakhstan national anthem, but do it with the real Kazakh anthem.  It's a pretty good song, possibly capable of eliciting reverence even if you understand none of the words.

[jrkeayxw] Four moods, one terrorist

  1. Tired and happy
  2. Tired and irritable
  3. Happy and full of energy
  4. Irritated and full of energy

#4 is dangerous, a powder-keg for socially destructive actions.  What does society do to prevent them?

Seems to be "keep people tired" so only #1 and #2 are possible.

Idle hands are the devil's playings.

[andomzls] Fun with the three-body problem

Create a game of launching massless particles in a circular restricted three body problem, depicted in the rotating reference frame.  Investigate Lagrange points, halo orbits, and Lissajous orbits.  Orbits aren't simple ellipses anymore.

Maybe mod Kerbal Space Program.  This probably already exists.  Tasks: fly through to a given stationary point (fixed in which frame?); get to this orbit (from some other orbit); rendezvous with this orbiting craft.

[zuddgsiw] Getting BOTW hearts

Several good ways of increasing one's health in Legend of Zelda: Breath of the Wild:

  1. Cooked hearty durians, especially harvested from just northeast of Faron tower.
  2. Sleep for free at the Great Deku Tree inn.
  3. Hot springs, though I haven't tried this much.  Are there any conveniently near fast travel points?
  4. Apples widely available, especially the orchard on Satori Mountain.
  5. Baked apples, not cooked in a pot but instead thrown directly into fire or onto fiery ground in Eldin.  Maybe also Joloo Nah?  Regardless, rather time-consuming to make.

#4 and #5 conveniently stack up to 999 in a material or meal slot, in contrast to #1 which takes up a limited meal slot.

The Master Sword Beam only works when one is at full red hearts, suggesting one should normally operate with few red hearts and lots of yellow hearts from meals like #1.

In contrast, #2 and #3 are most effective when one has many red hearts.

It feels awkward that there are many mutually exclusive good choices, though I guess that makes it a game.

[skyrwayl] Some BOTW notes

Legend of Zelda: Breath of the Wild

Lots of energetic rhino beetles in Torin Wetland (at night, not raining, etc.), though one has to deal with 2 Guardians (which are part of the Hobbies Of The Rich side quest).

There are a pair of very fast respawning blue lizalfos in Cora Lake, easily accessible from Lake Tower. They respawn much faster than every blood moon: teleporting back to Lake Tower is enough.  They are useful for farming lizalfos tails for armor upgrades.

Neither of the above two show up on online published BOTW object maps.

One can safely farm arrows from the pair of bokoblin archers near the Great Plateau Tower.  Stand just out of range, collect arrows til they stop sticking (typically about 10), save, reload, and repeat.  It's neat that one could leave the Great Plateau for the first time armed already to the teeth with a huge number of arrows.

One can grind the lynel in the Coliseum Ruins with bombs because you have the high ground.  We may have also used some arrows.  When the lynel starts aiming arrows, run in a circle because the lynel extrapolates your position (leads its shot) only linearly.

One can safely and easily grind Molduga with just bombs thrown from high ground.  Quickest is to alternate throwing both types of bombs.

Hateno Village is pot lid city.  There's also a rusty shield on a roof.  Having a large stockpile of disposable shields is good for taking out decayed Guardians with shield parry, especially early in the game when you don't have powerful weapons.  A successful shield parry of a Guardian laser is a 600 HP attack.  Other easy shields can be found on item maps, e.g., https://f.leolam.fr/botw-map/.  Convenient ones are near teleport locations.

The 2 lizalfos swimming in the river between the Dueling Peaks can be safely killed with bombs thrown from Ree Dahee shrine.  This area is often one of the first areas visited after leaving the Great Plateau, so doing things safely without using weapons is highly preferable.  One can also safely destroy the bokoblin camp nearby with bombs from the ledge above.  This makes the river safe to farm for the Staminoka bass plentiful there, which are extremely useful early in the game.

Proposed project for YouTube etc: demonstrate killing various enemies from afar using only bombs.

There's a long road (with lots of monsters), Lanayru Road, extending from Kakariko Village to Naydra Snowfield.  It is not marked on the map.  Are there others?  Define "road" as "a path that a horse will naturally follow".

The first shrine I tried after leaving the Great Plateau was one visible from the Tower: Kaam Ya'tak the Trial of Power.  Ironically, this shrine is arguably the most difficult shrine, so it was kind of trollish of Nintendo to have put it invitingly right next to the Great Plateau.  With so many sections requiring so many different skills, and being so new to the game, it took me over 6 hours to complete.  I guess it thematically pairs with the nearby Central Tower which is arguably the most difficult tower.

Bokoblins of any color can easily be blown around with a Korok leaf, and also any color dies instantly in water.  This makes the Korok leaf a very powerful weapon late in the game when bokoblins have scaled up so are otherwise time-consuming or expensive to kill.  Unfortunately, the very mechanism (water) that kills them so easily also (probably) makes inaccessible the ores that silver bokoblins drop.

[huzzisbb] Thwarting interdiction

A state intelligence agency intercepts a computer or phone during shipping from the manufacturer/dealer to the customer, implants a surveillance device or backdoor, packs it back up and ships it the rest of the way to the customer.  This is standard practice by intelligence agencies (Snowden).

It's surprising we don't see more efforts to prevent this kind of attack.  There are a whole bunch of technologies, some ancient (e.g., wax seal), that would make things at least a little bit more difficult.  Nobody likes to be spied upon.

On one hand, interdiction is already difficult and expensive, so small efforts to prevent it will be defeated without much relative extra effort by the attacker.  On the other hand, it seems the defender has a tremendous advantage if all we want is tamper-evident.

Of course, if you buy your electronics at a high-volume big box store, it's unlikely the attacker has compromised every item on the shelves.  Or else it's no longer called interdiction but seeding.

Inspired as a response to "How China used a Tiny Chip to Infiltrate U.S. Companies".  It wants us to be concerned that a formerly theoretical attack, seeding, has happened for real, but that seems like something you should be concerned about only after you've already fully defended yourself from interdiction.  Have sensitive organizations already done the latter?

Interdiction of a computer part between a part manufacturer and the computer assembler feels somewhat in between interdiction and seeding.  Will the assembled computer with the compromised part reach the target customer?

[qqcrkfga] Scrolling around a floating figure

We imagine an electronic document consisting of text and figures which you scroll through.

Text, text, text, a diagram appears.  Once the diagram fully appears and scrolls to the desired position on the screen, it stays put.  Then text referring to the diagram scrolls around the diagram, reflowing to squeeze in between the margins made narrower because of the diagram (especially useful in landscape displays).  As long as the text keeps referring to the diagram -- as long as the diagram remains useful -- it stays on the page with text scrolling by like water flowing around a rock in a stream.  Once the diagram is no longer being useful, the rock rejoins the flow and scrolls away.  The author of the document has marked bounds in text during which the diagram should remain visible.

Other features:

Multiple diagrams entering and exiting at different times.

Two scrolling columns with a diagram positioned between columns, biting halfway into each column.

A computational challenge: text reflowing for every scroll event.  Not difficult if the diagram spans entire horizontal width.  Not too difficult for monospace font.

[bhsusukc] We are we are we are we are the engineers

"We can we can we can we can demolish forty beers.  Drink rum drink rum drink rum all day and come along with us, for we don't give a damn for anyone who don't give a damn for us."

In this song we see the following social class markers: cursing, heavy drinking, drinking of the following types of alcohols: beer, rum.  Each of these are markers of lower social class, and so the song is a historical artifact that has recorded that, at the time the lyrics were composed, engineering was a profession of lower social classes: get your hands dirty.  Previously.

Inspired be someone finds the lyrics offensive.

Things have changed / are in the process of changing, and through this lens we can easily see that many of today's social conflicts happening around engineering as a profession are class warfare:

Women in STEM: women not of lower social class and men of lower social classes do not get along.  (It may seem on the surface that this was a conflict about gender, but it's actually about class.)  There's probably something deep going on about how and why lower social classes had organized their courtship structures differently.

For the lower social classes, engineering, a profession formerly reserved only for them, was their window for upward social mobility.  We expect (and see) defensiveness, acts of protecting their territory, when outsiders encroach: behaviors and environments enjoyed or tolerable by their class but unpleasant or intolerable to the higher social classes.

Ultimately, the lower social classes will again be left holding shit end of the new stick, but with understandable struggles along the way.

Monday, October 15, 2018

[jhomitso] Haskell pack int to bytes

The following Haskell code demonstrates packing a 32-bit unsigned integer (Word32) into a (lazy) ByteString with big-endian byte ordering, using the Put monad of Data.Binary in the binary package.  Essentially, runPut . putWord32be is the Word32 -> ByteString conversion function.

module Main(main) where {
import qualified Data.Binary.Put;
import Data.Word(Word32);
import qualified Data.ByteString.Lazy;

value :: Word32;
value = 65539; -- 3 + 2^16

main :: IO();
main = out_bytestring $ Data.Binary.Put.runPut $ Data.Binary.Put.putWord32be value;

{- expected output:
0 1 0 3
-}

out_bytestring :: Data.ByteString.Lazy.ByteString -> IO();
out_bytestring = putStrLn . unwords . map show . Data.ByteString.Lazy.unpack;
}

This code is analogous to Perl's pack function.  Here is the mapping from Perl's pack template characters to Haskell functions:

L = putWord32host
N = putWord32be (network, big-endian)
V = putWord32le (x86, vax, little-endian)

To convert from lazy to strict ByteString, do Strict.concat . Lazy.toChunks

[cfbgkchf] 2 digit code

A=1, B=2, ... Z=26 is a fine code. Codes 27-99 (and 0) could be used for space, punctuation, escape codes to special characters, and common letter sequences.

Alternatively, straddling checkerboard (ESTONIA-R).

[ieeepkew] Old and new atomic mass units

Old "oxygen-16" chemistry atomic mass unit = 0.9999394 to 0.9999856 (new) carbon-12 daltons.  We put oxygen-16 in scare quotes because it was actually isotope-weighted.  The range is because the atomic weight (equivalently isotopic concentration) varies a lot depending on what mineral or gas the oxygen is part of.  The differing isotope concentrations is called the Dole effect.

oxygen-16 physics atomic mass unit = 0.9996821637225 carbon-12 daltons

We used modern measurements of oxygen.

Interestingly, the isotopically weighted old standard is closer to the new pure carbon-12 isotope standard than the old pure isotope standard.  Maybe it was more important to preserve the results from chemistry?  Or the chemists had more political power in defining the carbon-12 standard?

[nlzlxsyv] Avoiding the Pari/GP "wasteful" warning on repeated modular squarings

? c=precprime(2^50)
1125899906842597

? Mod(2,c)^2^10^7
*** _^_: Warning: Mod(a,b)^n with n >> b : wasteful.
Mod(599926376112046, 1125899906842597)

? Mod(2,c)^lift(Mod(2,c-1)^10^7)
Mod(599926376112046, 1125899906842597)

This works because of Fermat's Little Theorem, though I haven't seen a proof.\  It could go recursively, but c-1 is not prime, so we would need something more powerful than Little Theorem.

Saturday, October 13, 2018

[rwyqbffi] Ellipsoidal weighted Voronoi

In a regular Voronoi diagram, the distance function from seed points grows as circles or spheres of identical sizes from seed points.  In weighted Voronoi, the growing spheres have different sizes because they grow at different rates.

Consider another variation where instead of spheres, the distance functions grow as ellipses or ellipsoids.  In other words, the distance function is sqrt(xTMix) for positive definite Mi.  Each seed point i can have a different M matrix, so the elliposoids can have different orientations and growth rates.

Inspired how crystals prefer to grow in certain directions faster than others, probably corresponding to crystal structure.  Eventually space will be filled by a bunch of crystal domains, with boundaries between them.  We could add the further constraint of crystal weighted Voronoi, requiring connectedness of regions to the seed point.

Inspired by Widmanstatten patterns.  One can take a 2D cross-section of any higher dimensional Voronoi diagram.  Do the cross sections look different depending on what dimension they came from?

[vbasnscg] Summoning Eulerian spirits

The pentagram inscribed in a circle, classically drawn on the floor to summon spirits from alternate planes of existence, is an Eulerian graph: it can be drawn without lifting a pencil off the paper.  This suggests interesting ways to draw the figure, for example, with a single strand of EL wire or inflammable rope.

The pentagram requires 60.2% of the rope; the circumference of the circle uses up the remaining 39.8%.

Friday, October 12, 2018

[fjvphlki] Counterexamples to GRH

People have searched really hard for counterexamples to the Riemann Hypothesis, zeroes off the critical line of the Riemann zeta function.  They have searched less hard for counterexamples to the Generalized Riemann Hypothesis, zeroes off the critical line in any one of the infinite number of Dirichlet L-functions.  A huge number of conditional proofs rely on GRH being true (probably a greater number than those that rely on the regular RH being true), so finding a counterexample to GRH would be very important (though would not necessarily invalidate any particular conditional proof).

Can we construct L-functions that are heuristically more likely to have counterexamples, functions which should be searched first?  Perhaps those which are least similar to the Riemann zeta function by some metric.

[kucqpbml] Grammy waltzes?

Have any waltzes won Grammy awards?  Nominated?  It is a time signature for which composers still compose popular music.

[nnpmviub] One-ball 3-point basketball contest

How many three-point shots can you make in a given amount of time, using only one ball, and you have to go fetch your rebounds?  This is in contrast to contests which use racks of balls in set locations.

From where you get your rebound, do you run to the nearest point outside the arc, or to a possibly farther point along the arc from which it might be easier to make baskets, often top of the key because from there the backboard is most likely to be helpful?

How fast do you run?  Becoming anaerobically exhausted might affect shooting precision, similar to biathlon.

Or a team of shooters and rebounders.

[gtazzqyp] Fun with moment of inertia

Create a collection of spheres all with the same size and mass, but very different rotational moments of inertia.  Internal mass distribution is always spherically symmetric, but some have the mass concentrated at the center, some in a shell near the surface.

People can hold, roll, maybe throw them, noticing which are easier or harder to impart spin.

[czuxouev] Giant multiplayer maze

Create a multiplayer dungeon which is so large that it is exceedingly unlikely for players to encounter each other, but still creates the illusion of being near other players.  It feels social but avoids the typical problems of social conflict that occur in multiplayer games.  It's kind of a joke.

Players wander around a graph of 2^128 nodes.  Every user starts at a different node.  Each node is labeled with a 128-bit bitstring.  We have a function F(p) which bijectively maps an input bitstring p to an output bitstring.  F is implemented as a 128-bit block cipher, with the key concealed from all players.   Two nodes with labels x and y are connected if F(x) and F(y) have Hamming distance 1.  The game can enumerate the neighbors of a node because F is invertible with the key.  Each room connects directly to 128 other rooms, and every room is reachable from any other room by passing through at most 126 other rooms.  By the birthday paradox, two players could meet if they both explore 2^64 rooms.

The bitstring also is convertible to coordinates, but this mapping is not secret.  Easiest is 128-dimensional space.  Between connected rooms are corridors, the continuous space inside them also needing coordinates.  They need to be threaded between rooms in a way that they don't intersect.  The game designer can also put linear adventures inside these linear corridors.

Because players inhabit some Euclidean space, distances between them can be calculated.  Maybe you hear sounds of nearby players adventuring, or get notifications of the presence of players nearby.  However, it is a maze, so even if they are physically nearby through a wall, it is very difficult to find a path to reach them.

Even if the coordinate system is high dimensional, the UI can be 2D or 3D, because we are just traversing edges of a graph.  The fact that your coordinates change in a way that is different than what your movement indicates might be annoying.

Each room being a nexus with 128 corridors leading out might be a bit overwhelming.  But it's easy to break a large node into a connected subgraph of nodes with lesser degrees.  They could be mini-mazes.

You can draw graffiti on a wall (perhaps as a navigation aid), even upload pictures to hang.  It is unlikely anyone else will disturb it, or even ever see it.  People might start abusing this as a data storage medium.

[ushnscol] 7 segment movable type

Print a page of numbers (maybe sqrt 10) with up to seven presses of a single page, using the same principle as the seven-segment digital display.  One only needs 4 types of sorts (plus blank space), allowing rotating them 180 degrees.

This would be labor intensive and annoying (because the typesetter only sees one segment of a number at a time).  I don't know what it would be useful for.

One could also do it with only one sort, a segment that can be laid horizontally or vertically, and spacers of various dimensions.  This could be done in 1 pressing, or 3 if the inked part of a type can't go all the way to the edge: horizontals, one diagonal pair of verticals, the other diagonal pair.

Wednesday, October 10, 2018

[owlgqjmq] Primes up to 1000

This blog post, https://blog.plover.com/math/prime-mnemonics.html posed the intriguing task of memorizing the primes up to 1000.  The most straightforward method is just to memorize the 168 of them in order.

However, it might be slightly easier to break the task into 4 smaller roughly equal sized tasks. The numbers in each list below have the same last digit (residue classes modulo 10):

11 31 41 61 71 101 131 151 181 191 211 241 251 271 281 311 331 401 421 431 461 491 521 541 571 601 631 641 661 691 701 751 761 811 821 881 911 941 971 991

3 13 23 43 53 73 83 103 113 163 173 193 223 233 263 283 293 313 353 373 383 433 443 463 503 523 563 593 613 643 653 673 683 733 743 773 823 853 863 883 953 983

7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307 317 337 347 367 397 457 467 487 547 557 577 587 607 617 647 677 727 757 787 797 827 857 877 887 907 937 947 967 977 997

19 29 59 79 89 109 139 149 179 199 229 239 269 349 359 379 389 409 419 439 449 479 499 509 569 599 619 659 709 719 739 769 809 829 839 859 919 929

One also needs to add primes 2 and 5 to the above lists.

Incidentally, "Prime number races" by Andrew Granville and Greg Martin discusses the comparative lengths of these lists.

When memorizing the lists, it might be helpful to keep in mind that multiples of 3 occur periodically within each reside class.  For example, numbers in this arithmetic sequence will never occur in the first list because they are all divisible by 3:

(x mod 10)==1: 21, 51, 81, 111, 141,...

Similarly for the other residue classes:
(x mod 10)==3: 3, 33, 63, 93, 123,...
(x mod 10)==7: 27, 57, 87, 117, 147,...
(x mod 10)==9: 9, 39, 69, 99, 129,...

However, rather than remembering these, it might be easier just to do the digital-root divisibility test of 3.

Here are the lists for multiples of 7:

(x mod 10)==1: 21, 91, 161, 231, 301,...
(x mod 10)==3: 63, 133, 203, 273, 343,...
(x mod 10)==7: 7, 77, 147, 217, 287,...
(x mod 10)==9: 49, 119, 189, 259, 329,...

Multiples of larger primes yield diminishing returns; you end up just memorizing the composites.

We now turn our attention back to the idea explored in the motivating post mentioned above, that there can be at most 4 primes in each decade.  It's kind of the transpose of the four lists above.

We first thought we might be able to do better by considering blocks of 30=2*3*5 instead of 10.  There can be at most 8 primes in a block of 30, and 8/30 (eliminating 73%) is more efficient than 4/10 (eliminating 60%).  However the extra factor of 3 in 30 versus 10 doesn't buy us much because of the easy sum-the-digits divisibility test for 3.

The motivating post mapped the pattern of up to 4 primes within a decade to 4-bit binary numbers 0..15, then assigned the binary numbers to letters.  We don't go so far, and simply give below each decade with its corresponding little-endian binary number converted to decimal.  We can imagine learning these associations with flash cards.  For example, in the tuple (90,4), the 4 is 0010 in little-endian binary (NB: this is the reverse of the traditional big-endian, how binary numbers are typically written).  The bits correspond to offsets 1379, so the bit for 7 is set, so 90+7 is prime.

(0,6), (10,15), (20,10), (30,5), (40,7), (50,10), (60,5), (70,11), (80,10), (90,4), (100,15), (110,2), (120,4), (130,13), (140,8), (150,5), (160,6), (170,10), (180,1), (190,15), (200,0), (210,1), (220,14), (230,10), (240,1), (250,5), (260,10), (270,5), (280,3), (290,2), (300,4), (310,7), (320,0), (330,5), (340,12), (350,10), (360,4), (370,10), (380,10), (390,4), (400,9), (410,8), (420,1), (430,11), (440,10), (450,4), (460,7), (470,8), (480,4), (490,9), (500,10), (510,0), (520,3), (530,0), (540,5), (550,4), (560,10), (570,5), (580,4), (590,10), (600,5), (610,14), (620,0), (630,1), (640,7), (650,10), (660,1), (670,6), (680,2), (690,1), (700,9), (710,8), (720,4), (730,10), (740,2), (750,5), (760,9), (770,2), (780,4), (790,4), (800,8), (810,1), (820,15), (830,8), (840,0), (850,14), (860,2), (870,4), (880,7), (890,0), (900,4), (910,9), (920,8), (930,4), (940,5), (950,2), (960,4), (970,5), (980,2), (990,5)

Incidentally, the decades whose number is 15, e.g., 10 100 190, corresponding to 4 primes in a decade, are maximally dense groupings of 4 primes known as prime decades or prime quadruplets, cf., twin primes.

We improve upon the above list by noting that multiples of 3 are easily to eliminate by digital root.  In some decades (in fact, in 2/3 of them), two of the four possibilities are eliminated by divisibility by 3.  In those decades we only need to remember a 2-bit number, not 4.  It's trickier to figure out which bits correspond to which number, though.  In the list below, the number of bits is given after the slash, though it's not necessary to memorize that number.  For example, consider (90,2/2).  In the decade 91 93 97 99, two of the numbers (93, 99) are eliminated by divisibility by 3.  The number 2 before the slash is 01 in little-endian binary and corresponds to the remaining two {91,97}. Therefore 97 is prime and 91 is not.

(0,6/3), (10,15/4), (20,3/2), (30,3/2), (40,7/4), (50,3/2), (60,3/2), (70,11/4), (80,3/2), (90,2/2), (100,15/4), (110,1/2), (120,2/2), (130,13/4), (140,2/2), (150,3/2), (160,6/4), (170,3/2), (180,1/2), (190,15/4), (200,0/2), (210,1/2), (220,14/4), (230,3/2), (240,1/2), (250,5/4), (260,3/2), (270,3/2), (280,3/4), (290,1/2), (300,2/2), (310,7/4), (320,0/2), (330,3/2), (340,12/4), (350,3/2), (360,2/2), (370,10/4), (380,3/2), (390,2/2), (400,9/4), (410,2/2), (420,1/2), (430,11/4), (440,3/2), (450,2/2), (460,7/4), (470,2/2), (480,2/2), (490,9/4), (500,3/2), (510,0/2), (520,3/4), (530,0/2), (540,3/2), (550,4/4), (560,3/2), (570,3/2), (580,4/4), (590,3/2), (600,3/2), (610,14/4), (620,0/2), (630,1/2), (640,7/4), (650,3/2), (660,1/2), (670,6/4), (680,1/2), (690,1/2), (700,9/4), (710,2/2), (720,2/2), (730,10/4), (740,1/2), (750,3/2), (760,9/4), (770,1/2), (780,2/2), (790,4/4), (800,2/2), (810,1/2), (820,15/4), (830,2/2), (840,0/2), (850,14/4), (860,1/2), (870,2/2), (880,7/4), (890,0/2), (900,2/2), (910,9/4), (920,2/2), (930,2/2), (940,5/4), (950,1/2), (960,2/2), (970,5/4), (980,1/2), (990,3/2)

The pattern of bits needed is periodic: 422 422...

Is this list better?  It's of course subjective.  There are the same number of numbers to memorize, but the magnitudes are smaller.  Previously, hypothesizing that smaller numbers are easier to memorize.

[rjxhofvs] Real Infinity Gems

We propose magnetic monopoles as the real-world equivalent of the Marvel Universe's Infinity Stones.  (But this still mostly sci-fi.)

They arise from a topological point defect in spacetime left over from the creation of universe, so there are only a finite number of them in the universe, with no way of making more, short of making another universe.  (This seems actually false, with the LHC trying to produce and detect them.)

Because they are about spacetime, getting ahold of one gives you the ability to do things like make wormholes and do time travel, so they are worth the effort to acquire.

The topological point defect is similar to how in a geodesic dome, there are a few (precisely 12) vertices with 5 neighbors instead of 6.  This explains why there are only a finite number of them.  What polyhedron is our universe?  Maybe Poincare dodecahedral space.

This is in contrast to someone else who proposed gravitational singularities as real-life infinity stones.  Black holes are a dime a dozen and more are being made all the time.

Hint: there's an easy-to-get monopole buried in a neutron star, because magnetic monopoles are attracted to magnets.  Which one?  Just measure the total magnetic flux of each neutron star and pick the one which is nonzero by one Planck unit.  Then disassemble the neutron star: mining.

That was the easy one.  The others have run into supermassive black holes.  Not sure if the monopole is smeared over the event horizon or has become incorporated into the gravitational singularity at the center, but either way, let's say you have to disassemble the black hole: more mining.

By the way, when we said there are only a finite number of them in the universe, we didn't mean observable universe.  We meant universe.

Needless to say, collecting monopoles is not a hobby for low-technology races intimidated by the above tasks.

[fxyoyhxh] TV talking to peripherals

Attach your TV to peripherals with connecting cables.  You have one remote control which you aim at your TV that controls the TV and any peripherals.  The TV relays any communications from the remote to peripherals through its connecting cables.  You no longer need to place peripherals in line of sight to the remote.

This technology didn't happen, probably due to lack of standards and protocols.

[npagxtez] 3D Tetris

6 buttons for rotation around 3 axes.  4 buttons for translation along the horizontal plane.  Drop, etc.

2 buttons for movement of camera / rotate the scene.  2 (maybe 4) for movement of light source, as shadows are often helpful.  Also point the camera higher or lower?

Show both a 3D view and a stack of 2D cross sections.  The latter is needed to see hidden holes.  The views rotate in sync as the camera moves.

[umaeypvw] May December

What goes wrong more frequently or more harmfully during or at the end of a romantic relationship of disparate ages, versus one of similar ages?  We assume an older man and younger woman for ease of presentation and to explore the common stereotype.

Here are some possibilities, albeit not relying on real-world research but instead mostly enumerating common cultural assumptions.

  1. The obvious thing that could go wrong even in the best case scenario is, they stay together, have kids, but the older man dies or gets infirm because of old age, so becomes unable to support the family in child care.
  2. Similar is, even without considering child care, after death you are left with a middle-aged woman who will have to support herself by herself for a long time because middle-aged widows stereotypically rarely find new husbands.
  3. In light of #1 and #2, time spent by a young women in a relationship with an older man is very precious time wasted, because that time and effort should have been spent on finding a partner of similar age with whom the problems of #1 and #2 are less likely to occur.
  4. The problem of #3 is exacerbated because a relationship of disparate ages will go on longer than it "should", because the older man will likely have more skill (acquired through previous practice) than a younger man in maintaining a relationship, and more resources (acquired through life) to spend on maintaining the relationship.
  5. The skills mentioned in #4 could be skills that are genuinely good, most notably relationship communication skills which take a lot time, effort, and practice (often from past failures) to develop, or they could be skills of deception and manipulation, skills also honed through practice.  The latter encapsulates the common stereotype of older men preying on younger women through deception and manipulation, then keeping them trapped in a relationship with those skills.
  6. There is a power difference that results in abuse by the Power Corrupts mechanism.  Sometimes the power difference is explicit: the couple met while within some external power structure (e.g., employment, education) and still occupy unequal levels within it.
  7. Another source of power difference is the unequal resources mentioned in #4; this turns into power because the man has more resources he can threaten to withhold from the relationship.
  8. Over life, the older man may have accumulated power in the form of social standing and connections which stymies reporting or preventing his abusive behavior.  We will elaborate on this in a future post.
  9. The peers and support structures around the woman may disapprove of the relationship, so abandon her.  This exacerbates the problems of #5 (becoming trapped in a relationship) and magnifies the harm she suffers when the relationship ends.
  10. A variation of #9 is that the support structure is already gone for unrelated reasons before the relationship begins.  With no support structure, any relationship, disparate ages or not, may go or end poorly, so initially seems irrelevant to this list, which seeks only to enumerate things special to disparate-age relationships.  However, lacking a support structure, a woman may purposely seek an older man with more resources to replace the missing support.  This results in older men being disproportionately represented when this kind of situation (a relationship absent a support structure) goes or ends poorly.

#9 and #10 are interesting because a third party is involved in the harm.  They doesn't get mentioned much, perhaps because the third party (the former support structure) doesn't want to accept blame for being a party to the harm.  However, support structures are critically important in any discussion of psychological harm because people often survive extremely painful and difficult experiences without traumatic consequences when they have the right support structure around them.  We hypothesize it is the determining factor for whether a negative experience results in long-term psychological trauma.

We have not elaborated on what the support structure is nor how and when it decreases harm.  Leave it unknown for now.

In #9, exactly what is the mechanism that starts with a person disapproving this kind of relationship and ends with them abandoning being part of someone's support structure?  Equivalently, why do people at other times remain loyal, remaining part of someone's support structure?

We hypothesize one mechanism involving tribal behavior.  Tribe boundaries are invisible in modern society, but people definitely discriminate between One Of Us versus Not One Of Us.  People had joined and remained in the young woman's support structure for a somewhat selfish reason: for power, in particular, for the power of influencing the woman's romantic relationships toward the direction that most benefits the tribe.  Against a young man as suitor, the support structure can successfully use standard anti-personnel tactics to drive him away if they should disapprove of him, because the young man lacks the resources to defend against the attack.  However, an older man with resources can defend, but in so doing demonstrates that the support structure no longer has power over the young woman's romantic relationships.  This being demonstrated, they no longer have incentive to remain in her support structure, so abandon her.

Another mechanism by which a support structure may abandon the woman is the man manipulates (#5) the woman to behave in such a way that the support structure abandons her, e.g., poisoning her to her friends, or convincing her to abandon them, to isolate her and thereby gain more power over her.  This kind of behavior can happen in any relationship, disparate ages or not, but older men may be more skilled at it because of experience.  Also the promise of greater resources he could expend on the relationship might be effective in convincing her to abandon her support structure.

#3 and #4 require cost-benefit analysis, especially if the woman is consciously not planning for this to be a long-term relationship.  The cost is time and maybe trauma at the end of the relationship; the benefits may include practice at romantic relationships and using the resources of the older man to further herself during the relationship ("sugar daddy").  Are young women systematically doing this analysis wrong?  Perhaps yes, due to deception and manipulation (#5).

The young woman could practice romantic relationships with men of any age, but she may deliberately select an older man as a better practice partner, because the older partner may be more prepared and resilient, from experience, for the mistakes the less experienced younger partner will make in the practice relationship.  This is part of the cost-benefit calculation.

Previous musing on power differences of #6 and #7, speculating that the power difference might not be as great as it seems at first glance.  The young woman can withhold sex, which has a very powerful effect on the man especially in this kind of relationship, because that was the only reason he was interested in her.  Of course, he could rape her (a stereotypical form of abuse in disparate-age relationships), but that is a very different experience, usually much less pleasant for the rapist (and of course less pleasant for the survivor), than having sex with someone who really wants to have sex with you.

Every one of the items listed above has potential for harm, but harm doesn't occur every time.  Why is it only sometimes?  Which cases go which way?

Self-qi generically affects relationships in many ways:

  1. Those with low self-qi are more likely to engage in deceptive and manipulative behavior.
  2. A member of a support structure with high self-qi is more likely to be or remain supportive, not abandoning.
  3. The presence of a support structure around you increases your self-qi.

However, none of these issues seem correlated with age or are more relevant in disparate-age relationships.

Tuesday, October 09, 2018

[ccootnhf] Light days

The day is the natural unit of time, encoded into all life on the surface of the earth.  Therefore the light day ought to be the natural unit of length.

1 light day = 25902068371200 meter (exactly)

1 light day = 173.14463 AU (astronomical unit)

1 meter = 38.606955 femto light day

1 femtolightday = 1.0197665 inch

1 light nanosecond = 11.574074 femto light day

1 attoparsec = 1.1912862 femto light day

1 parsec = 1.1912862 kilo light day

1 light year = 365.25 light day (exactly) (NB: the "units" program gives an incorrect value for "light year" with a space but the correct value for "lightyear" or "ly" without a space.)

Unfortunately the length of the day, the day-night cycle encoded into life, changes as the Earth's rotation slows down (causing leap seconds).

[veztwone] Hot sauces labeled in Scoville units

Surprised this hasn't happened yet: it would be useful to consumers.  Why not?  Is there market failure?

[rhdcchyo] Why Einstein added the cosmological constant

Einstein added the cosmological constant lambda to general relativity to keep the universe from expanding.  We guess at his intuition.

Inspired by this video: Einstein's Famous Blunder, which makes no attempt to explain why Einstein was uneasy with a non-static universe.  I don't think it should be considered a blunder.

In a nutshell, we guess that Einstein's intuition was the mediocrity principle / Copernican principle.  According to the principle, the time point that we live in is not special within the lifespan of the universe.

If the universe is expanding, then things will become more and more spread out.  However, when we look at the skies, especially distant galaxies, we can imagine things being much, much more spread out.  We do seem to be living at a special time point in the universe when we can still see distant galaxies, their light not yet having been redshifted to invisibility.  This violates the Copernican principle.  By the principle, we should only be able to see our gravitationally bound Local Group.

Even slightly applying the anthropic principle doesn't help: that principle only requires that some intelligent life observe the universe, not necessarily intelligent life like us.  The black hole era of the future universe is a much larger block of time than the current stelliferous era.  It would have been much more likely for us to be intelligent life feeding off Hawking radiation, observing the (boring) universe and applying the mediocrity principle.

We could reason further, that intelligent life must cease, become impossible, in another 14 billion years or so.

The problem Einstein was trying to solve with the cosmological constant remains a problem, so his solution, while incorrect for setting up a static universe, shouldn't be considered a blunder:  Why is it that we seem to be living in a very special time point in the universe?  Why is the universe we observe not representative of the most likely states of the universe?

[tebiwyxz] Trial division before Miller-Rabin

How much trial division should be tried before doing a Miller-Rabin primality test?  It depends on the size of your number, the speed of your trial division, and the speed of your Miller-Rabin (modular exponentiation) implementation.

Doing one additional trial division by the next untried prime number typically requires constant time if you are reading the list of primes from a precalculated list, so you can estimate the time it takes to do one more by doing a bunch and computing the average.  (It's more complicated if you are generating the list of primes on the fly with a sieve or even a recursive call to Miller-Rabin.  We won't tackle this case.  Seriously, just use a precalculated list.)

Doing one additional trial division by prime p eliminates 1/p of the remaining composites.  Primes are independent (isn't that cool?), so this is true regardless of what composites have already been eliminated by prior trial division.

Measure the amount of time T for 1 Miller-Rabin failure ("definitely composite").  This is the time for one modular exponentiation.  (We ignore the situation of a composite passing the first Miller-Rabin trial and failing later, because it is rare.  We also ignore the possibility of Miller-Rabin exiting early because it found a nontrivial square root of unity.)  (Also note that the BPSW primality test also starts with a Miller-Rabin trial with base 2, so all this applies to BPSW.)  Doing one additional trial division eliminates 1/p composites, so avoids 1/p of these Miller-Rabin time costs, so the expected time savings of the Miller-Rabin phase is (1/p)*T.  But trial division takes longer because of the one additional trial division. Do trial division until net gain is zero.

In order to calculate the cutoff, you will need the size of the nth prime p as a function of n.  This can be estimated using the Prime Number Theorem as p(n)=n*log(n), or it can be precisely looked up online.  (Aren't both of these also cool?)

There will eventually be an n large enough: more trial division directly costs O(1/n) additional time but saves only O(1/(n*log n)) expected time in Miller-Rabin.

ispseudoprime() in Pari/GP does essentially trial division by primes up to (only!) 103, though very quickly using a clever application of GCD.  The fact that it does so little trial division is inadvertently useful: we can easily bolt on our own trial division filtering step beforehand.

GNU MP mpz_probab_prime_p does a variable amount of trial division, but the code has the comment: /* FIXME: tune this limit */

Sunday, October 07, 2018

[yaatsxzd] Rotating a Tetris piece

Tetris piece rotation could be much more sophisticated than typically done.

Choose the center of any square or any corner to be the center of rotation by 90 degrees, or the midpoint of any edge for rotation by 180.  With this much freedom, you can walk a piece upwards by successively choosing different centers of rotation, so maybe don't fight it and simply provide up as a valid direction.  The game will have to change, maybe playing only against a clock or limited total number of pieces.  Or, we could constrain only to rotations that do not raise the center of mass, keeping with the theme of Tetris that blocks only fall.

Does only the final orientation need to be clear of blocks or does the entire swath of space consumed during the rotation?  If the former, what about 180 rotations which have to pass through a blocked 90 rotation?

If the latter, it feels like threading a piece through holes.  More rotations could probably be made by making squares slightly smaller within the grid and rounding off corners.  The ultimate would be a skeleton of line segments connecting square centers.  Some rotations might only be possible when the piece starts not aligned with the grid.

Allowing simultaneous rotation and translation reminds us of the moving sofa problem.  Are there interesting shapes made of blocks for which simultaneous rotation and translation allow movements not possible with rotation and translation separately?

[gufrvhcs] Maze with graffiti

A large maze from first person perspective is hard to navigate because all the twisty passages look alike.  Mitigate this by allowing players to draw on the walls.  This could also be done in real life.  Pretty soon, especially if multiplayer, there will be landmarks everywhere.

Monetize in game: paint costs money.  Or you can buy a protective coating for a section you want to preserve (it doesn't have to have been drawn by you).  Painting over a protected portion costs in proportion to the thickness of the protective coating it has.  Good landmarks are likely to stay, which is useful for navigation.

We would like mechanisms to prevent similar landmarks from being drawn in different places, though maybe the normal process of graffiti will take care of that.  Even if something starts looking similar to something else, it probably won't stay that way.

Previously (1) and (2).

[czcezsqp] Curved manifold cross section

Embed a 2D manifold within a Euclidean 3D volumetric data set.  Mark the values of the 3D data onto the 2D manifold where it intersects.  If the 2D manifold is a plane, this would be cross section.

Let the 3D volumetric data be a 3D bar code with lots of error correction.  The marked 2D manifold samples only sections of the whole barcode, depending on the given shape of the manifold.  Recover the whole data using the forward error correction.

The intriguing 2D manifold is the skin surface of a human body, and tattoo marks the skin.  The exact shape of the manifold is a particular pose that the person has to remember and hit.  This provides a way of encrypting data in a way that can only be recovered if the person does that pose (and then is 3D scanned).  The password is not a word but a pose.  We need to be careful that the tattoo pattern does not give away too much information about the pose.  Randomly sample a point in the region in which the manifold intersects a voxel.

[ixyipdpa] Binary digits as turns through a maze

In first person perspective, it may seem like you are navigating a maze with lots of T intersections (the T could be oriented in 3 ways) but you are actually entering a binary number bit by bit, with each T representing a binary decision.  Four rights do not traverse a square, which might be confusing.  If you ever backtrack, you might lose track of which direction represents entering more bits versus backspace.

Random lengths of corridors, random choice of T orientation, throw in some random corridor turns.  Decorations, scenery, enemies and treasure.

An overhead view is completely useless with lots of intersecting corridors which don't actually intersect, but it could be drawn just for fun.  Maybe the maze could occupy real space if we permit many levels in 3D; however, ultimately a binary tree grows exponentially while space grows only by the cube.  The corridors between T junctions would have to grow exponentially longer the deeper you go into the maze.

Four-way intersections could do balanced ternary: straight naturally means a zero digit.  But having only 1 intersection type instead of 3 is boring.

Friday, October 05, 2018

[kujswynr] Revisiting Fermat 20

We repeat testing the primality of the twentieth Fermat number on a slightly faster computer.

? f=2^2^20+1;
? ispseudoprime(f)
time = 9h, 20min, 50,056 ms.
0

This computation can be sped up considerably by adding a flag:

? ispseudoprime(f,1)
time = 4h, 46min, 24,280 ms.
0

Without the flag, Pari/GP does the BPSW primality test, which begins with a Miller-Rabin test with base 2.  But Fermat numbers are special: they always pass Miller-Rabin base 2, regardless of whether they are prime or composite.  Interestingly, base-2 Miller-Rabin passes (false positive) extremely quickly.

? lift(Mod(2,f)^(f-1))
time = 9,917 ms.
1

This is because modular squarings number #22 through #1048576 are all just computing 1*1=1.

Without the flag, after base-2 Miller-Rabin passes, BPSW moves on to the Lucas probable prime test (so named because it uses Lucas sequences, not be confused with the totally different Lucas primality test which relies on the factorization of p-1), which is more complicated than Miller-Rabin so takes 9 hours.

With the flag 1, ispseudoprime instead does 1 Miller-Rabin trial with a random base (not 2, probably).  Unless we are unlucky, it will report that F20 is definitely composite.

Performing the Pepin test, which isn't probabilistic, is pretty easy to do in Pari/GP.  It does take some effort to look up the formula and interpret the result.

? r=Mod(3,f)^((f-1)/2);
time = 3h, 48min, 14,148 ms.
? r+1==0
0

We're not sure why the Pepin test was faster than Miller-Rabin to a random base, as they both seem to be the same amount of work.

Incidentally, the Pepin test is identical to the (second) Lucas primality test mentioned above which relies on the factorization of p-1.  p-1 is easy to factor for Fermat numbers.

We can verify the final residue with the remainders published in "The Twentieth Fermat Number is Composite" by Jeff Young and Duncan A. Buell.  The values published in their paper are in octal, a fact which they confusingly do not explicitly state.

? printf("%o",lift(r)%(2^36))
175517362761
? printf("%o",lift(r)%(2^36-1))
411337412531
? printf("%o",lift(r)%(2^35-1))
161572365764

The values are in octal probably following a tradition established by Selfridge and Hurwitz for F14.  However, Selfridge and Hurwitz do explicitly state in their paper that their values are in octal.

For reference, here is the final F20 residue modulo several bases in decimal:

? lift(r)%(2^36)
16865158641
? lift(r)%(2^36-1)
35626292569
? lift(r)%(2^35-1)
15265819636

Thursday, October 04, 2018

[kwzwbmia] Robots that make and repair robots need to manipulate small parts

Even if the robot being made is big, it will still have small parts, so concentrate on generic small manipulation as an important robot technology to be developed and improved.

Much of the work of colonizing space will be done by robots, perhaps robots built in space by other robots from material mined from asteroids to decrease launch costs.

[eskwontp] Mass shootings within sports

It's surprising that there aren't more mass shootings among sports players targeting each other.  Within sports are a disproportionately high number of people who are very competitive, "jacked up", "win at any cost".  Some of those people might have reasons (even valid reasons) to come to believe that "the system" of the sport is institutionally stacked against against them: compare this to similar motivations articulated by other mass shooters, e.g., upset that the courtship system is stacked against them.

The combination of factors leading to mass murder won't all occur all that frequently, but if they do occur, it seems they should occur more frequently among sports players than in society at large, because ultracompetitive.  But this seems not occuring.  Why not?

We hypothesize a mechanism:

Participation in sports is voluntary.  Therefore, mass shooters are preferentially volunteering not to play or stop playing a sport long before their mass shooting tendencies kick in.  What is the mechanism of exclusion?  Who else is it excluding?  Do we see the mechanism elsewhere?

Sports are physically and mentally taxing.  They are especially psychologically taxing at the beginning because you also spend a lot of time losing.  To survive these challenges and not choose to "voluntarily" leave, one needs mental fortitude, i.e., high self-qi.  We put "voluntarily" in scare quotes because, under this model, your fate was predetermined by your self-qi level at the start; there was only an illusion of free will in your voluntary decision to leave.

These barriers, this process, eliminates the mass shooters, who are characterized by low self-qi.  Only with low self-qi does frustration boil over into destructive action, though we haven't elaborated very much on this mechanism.

One more aspect of sports:  If you show up, you have to participate, so become subjected to its mental and physical demands.  You can't be a sports player without playing.  This idea is also seen and articulated in one of the Principles of Burning Man, and in Fight Club.

What other activities have this pattern?  Easy to voluntarily leave, or choose to not show up.  Participation required.  Mentally or psychologically taxing, especially toward the beginning, but it doesn't ever completely let up.  This culls away the mass shooters before they start shooting.

We notice the pattern in social partner dancing.  We may elaborate more on this in a future post.

Wednesday, October 03, 2018

[ehalcaab] Post-it Life animation

Depict an evolving pattern of Conway's Game of Life with square Post-It stickers on a window.  This should be easy.

Assuming one generation per day, what patterns would be good?

Period 7 oscillators
Period 30 oscillators, e.g., original glider gun

The above two allow easy look up of state based on the day of the week or month, if you miss a day or two, the latter fudging for months that don't have 30 days.  What are the least interesting two consecutive states of the Gosper glider gun, for skipping at the end of February?

Period 14 oscillators, e.g., Tumbler
Billiard table oscillators
Diehards

Still lifes would be good for the lazy, or for more permanent installations like tiles.  Arrange a collection of still lifes, or design a large one, into an aesthetically pleasing pattern.

Incidentally, 4 snarks reflecting 4 gliders in a loop is a billiard table oscillator.

Another static possibility is a pattern that will ultimately evolve into something interesting.  It's kind of a puzzle.  Diehards are one example.  Much research has been done into construction by glider collisions.

[sowovwwm] Square in circle in square

Start with a unit square. Add margins of (sqrt(2)-1)/2 = 0.207 to all sides, forming a larger square.  Crop off curved pieces from the corners to form a circle.  The entire original unit square remains intact.

Inspired by Facebook cropping profile images into discs.

A little tricker: start with a rectangle.

Even trickier: start with a general shape.  First find its circumcircle (I don't know of a general algorithm for this offhand), then put that circle in a square.

[nzappiux] Letter to Tabloid/Ledger

11x17 paper (tabloid) is narrower (less square) in aspect ratio than letter (8.5x11).  Therefore, to create documents easily magnifiable to 11x17, add an additional 0.69 inches to left and right margins of letter portrait.  It will look funny with such wide side margins.

Motivation is to have the option to create a large type version for low vision when needed.

When magnifying, one needs to magnify the visible (printed) area, not the page area, or else one will end up with very fat (but even!) margins on tabloid.

Or, format directly for 7.12x11 paper.

Or, format directly for tabloid, using fonts that are 17/11=1.55 times larger than normal.

This isn't necessary in A series papers (e.g., A4) which all have the same aspect ratio.

[xbbyusrf] Entropy of initial letters

Letter frequency of initial letters in English, extracted from Peter Norvig's analysis of Google N-grams:

t 118849337945
a 86893227065
o 56762601060
i 54256321754
s 49734339142
w 40889321958
c 38962746440
b 32978416403
p 32124438693
h 31238837884
f 29952197540
m 28460312383
d 23610994165
r 21020892617
e 20821104413
l 17967162608
n 16990703679
g 12211759680
u 8801470813
v 6129410533
y 5677068230
j 3801073430
k 3390029632
q 1647734497
z 336016172
x 335403585

sum 743842922321

Entropy (calculated as the sum of p log p): 4.1009 bits per letter.  Omitting Z and X lowers it to 4.0933.  Compare with uniform distribution: log2 26=4.7004, log2 24=4.5850.

The distribution above is from a corpus.  If the same word occurs multiple times, then it is counted multiple times.  T occurs so frequently because "the" occurs so frequently.  In contrast, the distribution is not from a word list with duplicates eliminated.  Such a word list approach would explain what section of a dictionary is thickest or what volumes of an encyclopedia are the thickest.

Create a memorable mnemonic sentence from randomly sampled letters.  Does having the letter distribution match real English make it easier to create mnemonic sentences?

Are some of the high frequency initial letters dominated by a few very frequent words?  Sampling will yield many Ts in a row, but the common word can't be repeated: "the the" (but we could continue adding extra words in between).  Maybe we want a first-order Markov chain.  Can't quite easily get it from Google N-grams because it treats comma as a word, but we freely allow adding commas to a sentence.

Calculating the entropy rate of a Markov chain is a bit more involved but well studied.

[elorqxjx] Cube interface

We imagine an interface for a virtual Rubik's cube of arbitrarily many layers.

Rotate a rigid cube containing accelerometers.  The orientation of the virtual cube changes on screen.

How large should this physical cube be for best manipulation?  Radically, not a cube but a small sphere held between two fingers.  Slightly flattened to keep your accelerometer-packed expensive marble from rolling away.  Manipulation resembles contact juggling.

Rotate the cube so that the desired face to turn faces a virtual arm of fixed orientation.

A keyboard with 4 buttons.  Two buttons move a virtual arm in and out, controlling the number of layers which will be turned.  Two more buttons control the direction of the twist.  A joystick or slider could also work.

Alternatively, for a small number of layers, a matrix of 2xN buttons for directly choosing the layer and direction.

Tuesday, October 02, 2018

[iuaesvbn] Calculate eclipses

Show how to calculate the times and locations of total solar eclipses (because they are awesome) from orbital elements of the earth and moon, sizes.  Also show how to measure those parameters.

Or more fundamentally, from Newton's Law of Universal Gravitation.

[blbahule] In praise of the physical No-Left-Turn maze

The experience of navigating a real-life "no left turn" maze seems difficult to replicate well in a first-person game or virtual reality.  Your sense of where you are space is affected by the physical effort it took to get there.  Often a sub-task of a no-left-turn maze is to return to where you are now, but facing the other direction.  Your sense of orientation is affected by how much your inner ear (and the rest of your body) has turned.  Orientation is of course important in No Left Turn mazes because of the prohibition of a certain change in orientation, namely the left turn.

Monday, October 01, 2018

[pnwqelcn] It's aluminium, tennessinium, and oganessium in Britain

In Britain, all new chemical elements must end in -ium, which is why they overrode the (British!) chemist's (second) proposed name for element 13, aluminum (which had followed the pattern of platinum).  (In contrast, Noah Webster was more respectful to Humphry Davy when Webster published his American dictionary.)  Therefore, we also expect the British to override the names for elements 117 and 118, tennessine (which follows the pattern of astatine) and oganesson (which follows the pattern of radon).  Or possibly they will concede that their insistence that element names end with -ium was stupid.

(Also Britain's minor outlying islands like Australia, and Australia's minor outlying islands like New Zealand.)

[ercjgetd] Pictures of molecules

Of increasing fidelity:

  1. molecular formula C3H8
  2. condensed formula CH3CH2CH3
  3. structural formula (2D diagram)
  4. structural formula with chirality indicated, e.g., Natta projection
  5. 3D diagram (e.g., ball and stick, or space filling), perhaps VR
  6. 3D animated diagram, showing the molecule rotating around all single bonds, cyclohexane changing confirmations
  7. animation accurately modeling stearic hindrance, wandering among conformations accurately according to expected probability.
  8. carboxylic acid (COOH) and similar (phosphoric acid) in aqueous solution: animation includes proton repeatedly popping off and reattaching to the other oxygen.

1 through 5 are common in print; the latter become possible with electronic presentation.

[homedpnk] SAT Life

Can satisfiability solvers find spaceships and oscillators in Conway's Game of Life?  Can they find them especially efficiently?

Expressing the number of neighbors as a Boolean expression is a little annoying.

[uyzkbotv] More classical elements

Now that we know a little more science, add a few more elements to the classical elements (earth, water, fire, air) without going full chemistry.  Goal is an artistic collection, not science.  One also needs to concoct stories of how these elements explain the world.

Some candidates: acid, base, electrical conductor, plasma, neutronium, Bose-Einstein condensate, gauge bosons, scalar bosons.

[rrjqetgk] Tetris without gravity

A piece moves down one unit only if you hit the down arrow.  On contacting a piece underneath, it remains horizontally slidable until you hit down again.  Separate button for drop.  Does a piece remain slideable after a drop?  Separate buttons for drop with or without commit.

How many rows can your clear in a limited amount of total time?  You can take as much time as you want with any individual piece; it just eats into your total time.  Or untimed but with a limited total number of pieces.  It's been proven you are guaranteed to overflow eventually even untimed and unlimited, but it could take a long time.

Allow Undo of a piece placement, or make the pieces deterministic so you can memorize the order and get better with practice.  Or show all the pieces upcoming.

Finer grained undo of last piece movement command; an illusion of "up" if you undo a down, but you still can't float a piece up into a cavity you enter from the bottom.

Or maybe you can.  A button to commit the location of a piece anywhere, including floating.  You'll still want to generally move pieces as far down as possible so as not to block new pieces which always enter from the top.

These have probably all been done.

Previously on evil Tetris, which don't have gravity because they are hard enough without it.

[uhpeqtdl] Small Fermat number factors

We list the smallest factors of Fermat numbers.  These factors constitute compact proofs to the compositeness of each Fermat number.  Additional larger factors are not useful for proving compositeness.

We choose a novel encoding to emphasize compactness.  For each entry (n,x,y): 2^2^n+1 is divisible by 1 + (3+2*y) * 2^(n+2+x)

Edouard Lucas showed that x>=0.  We conjecture that y>=0 (this seems easy to prove).  y=0 at n=38 (and others larger).

(0,Prime)
(1,Prime)
(2,Prime)
(3,Prime)
(4,Prime)
(5,0,1)
(6,0,534)
(7,0,58251551882320)
(8,1,302472256237)
(9,5,17)
(10,0,5564)
(11,0,18)
(12,0,2)
(13,1,20682941)
(14,0,892090498909563978798187208821078272555440547357)
(15,4,288)
(16,1,786)
(17,0,29625927)
(18,0,5)
(19,0,16813)
(20,Composite with no known factor)
(21,0,267343)
(22,0,1926979601222033828766816104)
(23,0,1)
(24,Composite with no known factor)
(25,2,24205)
(26,1,71581)
(27,1,70506)
(28,6,12854659685)
(29,0,560023)
(30,0,74519)
(31,0,2731780735650)
(32,0,738)
(33,Character unknown)
(34,Character unknown)
(35,Character unknown)
(36,1,1)
(37,0,637719231)
(38,1,0)
(39,0,9)

Some Pari/GP code for verifying factors:
val(n,x,y)=1+(2^(n+2+x))*(2*y+3)
test(n,x,y)=lift(Mod(2,val(n,x,y))^2^n+1)

For a much more comprehensive list, see http://www.prothsearch.com/fermat.html.

Sunday, September 30, 2018

[dptrkenh] Base-10 versus base-5 abacus

Most abacuses are base 5, or more precisely mixed radix (5,2,5,2,...).  However simple base-10 abacuses with 10 beads per pole, typically marketed toward children, are very intuitive and easy to learn how to use.

Base 10: adding 8 is equivalent to adding 10 and subtracting 2.  Just have a chart of complements base 10.

Base 5: adding 8 is equivalent to adding 5 and adding 3.  Adding 5 is equivalent to adding 10 and subtracting 5.  Adding 3 is equivalent to adding 5 and subtracting 2.

Color the beads on a base-10 abacus in a way that it's easy to count how many you are moving and how many are left.  I have used one that had just the 5th and 6th beads differently colored.

[jdxlngkq] Replacing h with an accent in digraphs

H participates in the following digraphs: ch gh ph rh sh th wh zh.

Consider replacing the h with a diacritical mark over the previous letter, maybe caron/hacek which is similar to what some other languages already do.  All the previous letters except t lack ascenders so there is conveniently room for a diacritic above.  The H comes back for text in all caps if there isn't room for the accent above a capital letter and the previous line.

th gets its own new letter, maybe thorn or theta.

gh is often silent, so I do like the idea of replacing ough with ô when silent: cookie dô not cookie douǧ, but sand is rouǧ.  though becomes þô.  þôt?

Then what about thigh, weighing, Hugh?  weîing wêiing wêîing wéìing wê wêing.  A spelling change that depends on pronunciation would be difficult to automate.  I don't know how shillelagh is pronounced, and it seems like something that could change or be pronounced differently in different communities.

kh sometimes occurs, but k has an ascender so isn't good for a diacritic above.  Just keep it kh.

Previously, replacing h with an apostrophe.

[sjciotcw] Six digits

When providing a number to the user, consider only using the digits 1 through 6 instead of the whole range 0-9.  Inspired by the verification codes of two factor authentication 2FA.  Obviously, one will need more digits to achieve the same amount of entropy: 7.7 base-6 digits equals the typical 6 digits of base 10.

Vaguely inspired by cubical dice (one can easily mentally picture the dot patterns) and Benford's Law.  The earlier digits seem less foreign than the higher ones so easier to memorize (e.g., in short-term memory for copying a 2FA code).  Also uses only two rows of a numeric keypad, so easier to type.  This might be especially useful if you have a fancy typing interface that scrambles the labels on the keys each time to thwart shoulder surfing.

99.03 base-6 digits for 256 bits.

Saturday, September 29, 2018

[klqgajgx] Factoring as a benchmark

When describing the speed of a processor or computer system, consider expressing it as the number of bits it could factor in a year.  That is, the size in bits of a RSA number (semiprime) for which the computer could complete by itself just the sieving portion of the general number field sieve.  Sieving is embarrassingly parallel so doesn't incur difficulties about how good your interconnect is for parallel computers.

It's a practical and easily explainable computationally intensive problem that one could imagine anybody doing.  Dedicating one year to a computation is something one could imagine an individual doing, or (because embarrassingly parallel) one could imagine an organization buying 365 such computers to complete within a day.

It gives a hint of what size RSA keys are in danger today.

[xezvztre] Humanity Star criticism as publicity stunt

Assuming the launch was successful (which it was), the Humanity Star was a publicity stunt in which any publicity is good publicity: it puts the name of the rocket launch company out there and establishes that they are competent.  Even negative publicity is effective toward this goal.  Negative publicity might be especially effective because controversy spreads virally.

And negative publicity they got: astronomers complaining of light pollution and the satellite potentially passing in front of Hubble's field of view, ruining science.  Class warfare between the rich putting self-aggrandizing baubles in space while the poor starve.

It seems the plan worked perfectly.  Too perfectly?  Was this negative publicity also engineered?  It seems like the kind of thing they could have hired a PR firm to astroturf.

The complaint that the satellite might pass in the field of view of a powerful telescope seems especially disingenuous.  They had chosen an low-earth orbit which quickly decays and burns up the satellite in the atmosphere, so the macro time frame for something bad to happen is very small.  The micro time frame is also small: it has to be daytime in orbit but night time on the ground (unless you are Hubble).  Finally, powerful telescopes have extremely narrow fields of view.  The chances of a particular satellite passing in front are literally astronomically low.

On the other hand, suspecting astroturfing is suspecting malice which could be explained by incompetence.

[cspdnymg] Cooking with distilled water

It's surprising there isn't already a social movement that dictates cooking only with distilled water, or a dietary movement saying one will only eat foods prepared that way, because tap water contains "chemicals".

Inspired by the perception that organic foods are healthier because of the homeopathic amount of "chemicals" present in conventionally grown.

Thursday, September 27, 2018

[shpsqrwe] Donating after terrorism

It's probably illegal to offer to pay someone before the fact for them to commit a political crime.  However, if you have no prior relationship with a perpetrator until after they've become famous for committing the political crime, donation afterwards seems very doable and legal, perhaps donating to the family of the perpetrator, because the perpetrator is likely on the run, imprisoned, or has been killed by the government, so unable to perform whatever prior role he or she had in the family.

For example, consider donating to James Hodgkinson's family.  The cover message, seemingly unassailable, is, "My condolences regarding the death of your husband/father/grandfather."  But the unspoken message is, "I support his politics and methods."  Interestingly, even if the recipients reject the donation, the unspoken message remains just as strong.  If you make a big public show in your act of donation, is that still protected speech?  The prosecution would argue something along the lines that your speech will induce future crimes through the implied promise of compensation afterwards.

Monday, September 24, 2018

[hfzcbieo] Decoding TSA locks

People made a big deal when the Washington Post published a photograph of the master keys for TSA luggage locks, and some people made working keys from the photographs using a 3D printer.  Was a photograph really necessary to make working keys?

It seems not too difficult to have created those master keys by disassembling locks and measuring the lengths of the key pins and distances between the pin stacks: no photograph necessary.  It's surprising that such reverse-engineered keys, or instructions or CAD drawings for making them, weren't widely available even before the picture was published.

Are TSA locks hardened against this kind of disassembly attack?  Maybe they make aggressive use of master wafers, so it's difficult to tell what is the master-key cut from examining just one lock.  However, this could be mitigated by examining multiple locks, perhaps a collaborative worldwide effort that the internet is good for coordinating within the already active lock sport special-interest community.

Were there laws forbidding this kind of activity, or disseminating information about this kind of activity?  If so, they would have also been invoked following the publishing of the photograph and subsequent discussion of making the keys, so we doubt it, unless the government were specifically trying to avoid the Streisand effect.

Skilled lockpickers laugh at 3D printing keys because they can quickly pick TSA locks with traditional lockpicking tools.  However, not everyone is a skilled lockpicker.

It would have been interesting if the TSA hadn't specified a master key backdoor to their locks but instead specified regulations forcing them to be able to be easily picked, for example: no weird keyways (or specifying a standard key blank), no more that 4 pins, no security pins, and all springs must be the same.  The pinning is random, different for every lock, just like normal locks, except a key is not distributed to the customer.  The TSA's "backdoor" would be traditional lockpicking, though with those regulations, very easy traditional lock picking, e.g., raking, lockpick gun, bump key, that could easily be taught to baggage inspectors.

[tizrsxko] Censorship by friends, or social networking through censorship

It seems straightforward to create a social network system like Facebook based on censorship carried out by friends.

A person makes a post, visible to friends.  One of the friends dislikes it so pushes the "Censor this" button which deletes the post.  Any friend can do this.  Then, the original poster is notified of who censored the post, and given an opportunity to un-friend, or create a friend group to make future posts not seen by that censor.  Typical friend groups in this context will be defined as exclusion, "all friends except some list", though inclusion groups are possible, too.

Censorship is transparent: you see who opposes your speech.  People will form communities of speech that they agree with, or at least tolerate.  (Tricky problem: what you can tolerate changes day-to-day; should people interact with you based on how you acted on your worst day?  We probably need something client-side -- something that understands your stress level that day -- that also limits what you see that day in your best interest.)

Should the metadata of who is and who is not able to see a post be visible with the post to those who can see it?  Maybe a rabbit hole of visibility of the metadata.

Public posts are trickier.  Several ideas: It's not possible to follow someone's feed of public posts without being their friend: public posts are indexed by cryptographic hash, so you definitely have to make an effort to go find a post (get a friend to snitch) to find the public URL of a public post.  Each public URL is unique to the friend who sees it, so knowing the leaked URL is enough for the original poster to identify who snitched and then un-friend or make limited.  (Public posts can still be limited about who is notified of its existence.)  Posts have watermarking that can similarly identify from screenshots.  Provide a utility with which anyone can easily forge a post from anybody with any content, for plausible deniability.

Comments on posts are also tricky.  A nice feature would be, if a post with comments is censored but the poster reposts to a more limited friend group, the old comments get migrated.

Previously on the theme of Anyone Can Censor.

Thursday, September 20, 2018

[uxmwuiea] VR to teach 3D

A killer app of virtual reality might be for education: illustrating concepts that are inherently 3D.  E.g., vector cross products, electromagnetism, much mechanical engineering, chemical molecules.

Create 3D diagrams (maybe 3D animations) of such inherently 3D concepts that other people can incorporate into their lectures.  Creative Commons would be good for this.

[tevtriwg] Density and Schwarzschild radius

For a sphere of given uniform density, what is the maximum size it can be before it collapses into a black hole?  This should be easy.

[mqlxmztd] Baseball diamond

The bases in baseball do not have to make a square: any rhombus will still have the bases the same distance apart.  Consider a narrower field: bring first and third closer to each other.

The original motivation was to bring spectators closer to the action, though they might need more protection from foul balls.

It will be harder to hit the ball in play because of the narrower angle between the base paths from home plate.  It will be harder to round second as a baserunner because of the sharp angle.  It will be harder for the catcher to throw someone out trying to steal second.

Previously, making the field of play much wider.

[xbmesnlg] Binary digital notebook

We imagine a digital notebook of cells: each cell can be 0, 1, or blank.  Select a 3xN rectangle and the computer can verify that the first two rows as binary numbers sum to the third.  Key idea: the computer does not do the addition for you; it only checks that you've done it right (of course; it has to do the addition internally to do the check).

Select two 1xN rectangles and the computer will verify that the contents are the same.  This helps you copy a number from one place in the notebook to another.

More fancy "copy": One rectangle can be horizontal and the other vertical.  The rectangles can have direction: this allows reversing the bits.  Strided copy: one rectangle can be (say) 3 times wider than the other. The digits in the wider copy should be separated by blanks.

This is probably enough gadgets to do binary long multiplication.  From there, to infinity and beyond.

Allow cells to have text annotations.  Resembles a spreadsheet.

More operations: AND, OR, NOT, XOR.  With these operations, one could remove addition.  The notebook becomes a trace of a binary digital computation.  It would be easy to set up SAT puzzles.

We might want more complicated templates than the addition rectangle, though that becomes less elegant.

Or, build this as a physical mechanical or electromechanical device.  Probably best to limit to simple Boolean operations (and 3-input 2-output adder).  We need some adjustable arm to work on a series of tuples of bits a fixed distance apart.

Sunday, September 16, 2018

[yvvhnbil] Cinderella XXX

The Cinderella story would become radically different if one detail were just slightly changed: the fairy godmother's transformation spell ends later, say at sunrise and not midnight.

They wake up together in bed the next morning.  The spell has dissipated, but that is irrelevant because they are naked.  (It's not a Disney story anymore.)  The prince assumes her clothing is misplaced somewhere in his expansive bedroom/private entertaining space (the kind of space that rich people tend to have, inspired by Michael Jackson's multi-story bedroom) where they had engaged in wide-ranging clothing-shedding late-night adventures after the Ball.  Eveningwear is not the right thing to rewear the next day anyway (Walk of Shame), so the Prince provides her with appropriate daytime clothing.  Cinderella has already broken the news, perhaps in conversation amidst post-coital bliss, that she is poor, but, consistent with the canon story, the Prince has no problems with this.  It's not surprising that her coach and attendants have already left (he assumes) instead of waiting around all night, so he provides her with transportation also.  (Though is there any reason she would want or need to go home?)

Saturday, September 15, 2018

[sxgaujlv] Density of planets

Create a collection of holdable objects with densities equivalent to the average densities of planets, smaller bodies, and star in our solar system.  The objects can be all the same size and shape to make them easy to compare.  This should be easy to create.

Previously, getting the sizes to scale also.

[rufudqzr] Verifying the compositeness of the 20th Fermat number

Pari/GP:

? ispseudoprime(2^2^20+1)
time = 12h, 17min, 47,643 ms.
%1 = 0

In 1987, this computation took 10 CPU days on a Cray 2 supercomputer, verified in 3.4 CPU days on a Cray X-MP, earning a journal publication for its authors ("The twentieth Fermat number is composite").  It's doable now on a personal computer without special-purpose software, but it's still not trivial to do.

This still remains the only way to demonstrate the compositeness of F20; still no small factors have been discovered in the years since.

The future looks bright for future speedups of this computation.  Multiplying million-bit numbers seems like something that GPU-accelerated FFT could do well on, but GPU-accelerated arbitrary precision arithmetic has not yet made its way into general-purpose software like GNU MP and Pari/GP.

Update: another attempt.

[umfurrgw] Weighted Voronoi

Multiplicatively weighted Voronoi diagrams have boundaries which are circular arcs.  Additively weighted Voronoi diagrams have hyperbolic arcs.  Is there anything that results in elliptical arcs?

Define a weighted Voronoi diagram which has star-shaped regions: every point in a region must have direct line of sight to the source point of the region.  Crystal weighted Voronoi doesn't quite do it.

Friday, September 14, 2018

[vwnkujwz] Basketball on a wider court

Consider playing basketball in a court with greater distance between sidelines.  How does the game change?  Plays can come from many directions.  Assuming the hoop and backboard suspended from the ceiling, consider also moving the baseline further back.  People probably won't shoot from back there -- the backboard is in the way -- but plays could travel through that space, kind of like hockey's considerable space behind the goal.

Spectators become further away from the action.  Perhaps floating cameras and VR can make this not important.

Thursday, September 13, 2018

[sfyehbzc] Pi for the universe

Consider a sphere of size on the order of the size of the observable universe.  Suppose we wish to compute its volume to the precision of a Planck volume (one cubic Planck length).  How many digits of pi are needed?

The question is complicated because we do not assume the universe is flat, a Euclidean manifold.  To what precision do we currently know the curvature of the universe?  That is, beyond how many digits of pi does the uncertainty of the curvature parameter drown out further precision in pi?  (There's also uncertainty in Planck length.)

What is the formula for volume of a sphere in a space with a given Gaussian curvature?

[zidodsvm] Earth is densest

Curiously, Earth (average density 5.5 * water) is the densest large body in the solar system, denser than the Sun (1.4 * water) or Jupiter (1.3 * water).  However, it does not have the highest surface gravity.  The Sun (274 m/s^2) has considerably higher surface gravity than the Earth's 9.8 and Jupiter's 24.8.  Earth has the highest surface gravity among planets with a solid surface that a human could reasonably access.

Gravity at the surface or above is "usable" gravity, e.g., for gravitational slingshots.

Supermassive black holes have average density less than water but a "surface" gravity (near event horizon) approaching infinity.  How quickly does the gravity fall off as a function of distance from the event horizon?  It probably isn't inverse square.

[xhmqrgrr] If you smash a proton, does it heal?

Smash a proton into something that is not an anti-proton.  Eventually, after all the high energy particles have decayed, are you guaranteed to be left with a proton again?  Seems yes, as that is the only stable particle that conserves the original charge and quark number.  Does quark number need to be conserved?

Wednesday, September 12, 2018

[gftkteax] Constructing large block ciphers with Feistel and SHA

It seems fairly straightforward to construct block ciphers with arbitrarily large block sizes using the Feistel cipher structure and a good cryptographic hash function as the mixing function F.  It won't be very efficient.  If the output of the hash function is limited to (say) 512 bits, then it becomes an unbalanced Feistel cipher for block sizes greater than 1024 bits.

The mixing function can be something like F=hash(key || round number || portion of block).  Keccak / SHA-3 based on the sponge construction seems for now to be able to handle concatenation just fine; one needs to be more careful with hashes of the Merkle-Damgard construction (e.g., SHA-1, SHA-2 family) which are vulnerable to length extension (but not sure if that kind of attack is relevant here).

There's a bunch of details that need to be hashed out (pun intended), ideally standardized.  There's one very large detail: number of rounds (probably a function of block size).  This requires cryptanalytic effort to determine the correct minimum number.  Easiest for now is if the standard were to be parametrized by number of rounds without specifying a number.  The user should choose as large as possible that doesn't cause the system to become unacceptably sluggish.

More ambitious: given a large block cipher, I recall it's possible to create a cryptographic hash function with large block size, so this can feed itself, allowing producing ciphers accepting large keys.

[emeqfxrq] QR code clock

5 QR codes and a blank space arranged in a 2x3 array.  Each code encodes Unix time as a decimal number.  Each second, a new code appears at the blank space, and the oldest code turns blank.  Critically, the codes do not move, keeping them easy to scan.  Previously.

We can also imagine a human-readable version, with date and times formatted as text.

Not sure what these would be useful for.

[asgmginy] Sunlight in the ocean and in space

Line up the amount of sunlight received at different planets in the solar system with the equivalent brightness of light reaching different depths of ocean.  This should be easy.

[qyichtym] Censorship of bulletproof

There is frequently censorship on how you can acquire, make, use, etc., weapons for hurting other people, e.g., guns and explosives.  However, is there equally censorship on ways to protect yourself from weapons being used against you?  For example, making materials and objects bullet-resistant.

Inspired by the Killdozer.  One can imagine law enforcement wanting to suppress information useful for someone else building something similar, especially information about how to make bullet-proof panels that would protect against the weapons the police would try to use to stop such a vehicle.

However, information for making things bulletproof does have legitimate uses, and suppressing information about how to stay safe seems sinister and possibly politically untenable.  Though it's unfortunate if freedom of speech is being granted politically only case by case.

Monday, September 10, 2018

[geefmech] Moby Dick / Khan

Is Star Trek 2: The Wrath of Khan a retelling of Moby Dick from the Whale's point of view?  Or, understanding it in that context, can we do a better retelling?  Someone trying to survive an attacker justifiably motivated by revenge is an intriguing plot, as the defender is in a no-win scenario.

* * *

From Hell's heart, I stab at thee; For hate's sake, I spit my last breath at thee!

This line seems more impressive printed than spoken.  Express the same sentiment more poetically.  It also seems like a line which could become impressive in another language.

[ivxobaqi] Decay of helium-4

Assuming proton decay, what are the probabilities of decay paths of helium-4 (alpha particle)?  Tritium and helium-3 are both possible, as proton decay also applies to neutrons stabilized in the nucleus.

[eccfjwqz] Chess with warp travel

Simplest: two boards.  In one move a chess piece jumps ("warps") off its current board into subspace (hyperspace), in between boards.  In a later move, a piece in subspace can be dropped onto the other board like shogi ("dropping out of warp").  Warp travel is expensive, costing at least two moves during which your other pieces do nothing.

Goal is to create a game with a feeling of a sum of weakly interacting smaller games, e.g., battles, like go 囲碁.  Previously on creating that feeling with a larger board.

More complexity: rules regarding when you can warp, where you can drop, subspace is its own board on which pieces can move and interact, more boards corresponding to different squares in subspace.

Maybe you can only drop on to a square you control.  Eliminating the opponent's last piece on a board makes that board permanently yours.