Wednesday, November 15, 2017

[wvaejjpf] A collection of divergent sums

Riemann zeta function:
zeta(0) = 1+1+1+1+... = -1/2
zeta(-1) = 1+2+3+4+... = -1/12
zeta(-2) = 1+4+9+16+... = 0
zeta(-1/2) = sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+... ~= -0.2078862
zeta(1/2) = 1/sqrt(1)+1/sqrt(2)+1/sqrt(3)+1/sqrt(4)+... ~= -1.4603545
zeta(1) = 1/1+1/2+1/3+1/4+... diverges (harmonic series)
zeta(2) = 1/1+1/4+1/9+1/16+... = pi^2/6 (not a divergent series, but still cool)

Dirichlet eta function:
eta(0) = 1-1+1-1+... = 1/2 (Grandi's series)
eta(-1) = 1-2+3-4+... = 1/4
eta(-2) = 1-4+9-16+... = 0
eta(-1/2) = sqrt(1)-sqrt(2)+sqrt(3)-sqrt(4)+... ~= 0.3801048
eta(1) = 1/1-1/2+1/3-1/4+... = ln 2 (not a divergent series, but still cool)

Geometric series:
1+2+4+8+... = -1
1-2+4-8+... = 1/3
1+10+100+1000+... = -1/9
1-10+100-1000+... = 1/11

Series involving factorials:
0!-1!+2!-3!+4!-5!+... ~= 0.5963474 (Wikipedia)
0!+1!+2!+3!+4!+... = ExpIntegralEi[1]/E ~= 0.6971749 (infinite sum of factorials) (unsure about this one, derived the analytic continuation myself, have not seen published elsewhere)

Although using analytic continuation to obtain values is a legitimate real thing (well, it's actually complex, ha!), saying a divergent series "equals" a certain value is kind of a mathematical in-joke, understandable only if you understand analytic continuation.

Friday, November 10, 2017

[pfsvuyvq] 10x10 chess

A straightforward way to extend chess to a 10-wide board is simply to leave 2 empty spaces on the first rank.  Or, add 1 more queen, leaving 1 empty space.  No new piece types are introduced, in contrast to Capablanca Chess.

If using Chess960-style randomization, then there are 42000 start positions for either possibilty (because of the duality of where to put the 1 queen and 2 empty spaces, or where to put the 1 empty space and 2 queens).

10 pawns on the second rank.  Castling travels longer, leaving the king the same distance (1 or 2 squares) from the corners as orthodox chess.

With 2 queens per side, it might be better to limit to initial positions in which every pawn is initially guarded by a non-king piece.  I have not enumerated these.

Maybe add one more piece, leaving no empty spaces: a Man, a nonroyal piece that moves like a King, a very conservative (compared to Capablanca Chess) new piece type.  RNBQMKQBNR is an initial position that mimics orthodox chess.  Again, 42000 shuffled positions.

Initial pawn move remains 2 spaces.  Assuming a 10-rank board, this will likely induce a lot of maneuvering before contact with the enemy.  This could be interpreted as richer possibilities in the opening, lessening the need for initial randomization.  What is the optimal initial position?

10x8 is also possible, but eliminates opposite flank pawns racing to promotion in the endgame, but whoever queens first attacking the opponent's promotion square in the opposite corner.

[xwlbtoiw] Creating jets

How much physics is necessary to recreate astronomical relativistic jets in simulation?  Is Newtonian gravity enough, or do we need general relativity?  Do we need electromagnetism?  High energy particle physics?

The answer right now, as I understand it, is nothing can quite fully explain jets.

[vaoysdrs] What are neutron stars made of?

Even if the particle physics desert is true, we still might be able to observe phenomena at the grand unified theory energy scale, astronomically of course.

Understanding the inner layers of neutron stars might require a GUT.  Normally these inner layers are inaccessible to observation, but neutron stars spill their guts (pun intended) during mergers with other neutron stars and black holes.  These mergers can be observed as gravitational waves and as short duration gamma ray bursts, kilonovae.

Neutron stars also undergo starquakes, which may also reveal details about their core much like seismology reveals details about the Earth's core.

What are electrons made of?  What are quarks made of?  What are neutron stars made of?  Answers to all these questions requires (at least) a GUT.

Cosmic rays are usually below 10^20 eV, but the GUT scale is 10^25, so just a little short, though one could continue to hope to observe a freakishly high energy one.  If we discover the sources of ultra high energy cosmic rays, we could observe them at their source.  One hypothesis of their source is collapsars.  A GUT might be necessary to explain all that is going on during stellar collapse.

The GUT scale is so energetic, a trillion times more than the LHC, that we will never build a particle accelerator on Earth to probe it.  But that doesn't preclude nature from building such an atom smasher in space.

Finally of course, explaining observations of the Big Bang, including the cosmic microwave background, requires a GUT.

[zvfsnjgi] Displays all around

Have a bunch of TVs on the walls of a room show the same object or scene but filmed from different angles.

Two possible ways the cameras and TVs could match up:

TVs go where the cameras were.  Best if the recorded video is mirror reversed.  The TVs are like mirrors showing the viewer the scene behind them.

TVs go on the opposite side of the cameras.  The image is a projection, as if the camera emitted light and one is viewing the shadow.

The orientation difference is 180 degrees, which is irrelevant because the cameras aren't there any more.  The actual only difference is the mirror reversal.

Small technical challenge of getting the multiple displays to play videos in sync.  All displays connected to one computer is straightforward but requires a fancy computer.  Multiple computers synchronized in time (e.g. NTP) requires video playback not lag due to system processes.  Previously, same problem for music playback.

Inspired by a sports bar, with lots of TVs.

[lelockyv] Cthulhu sun

"I believe in Cthulhu as I believe that the sun has risen: not only because I see it but because I see everything else."  ("By it" has been elided from the original CS Lewis quote.)

Accompany "everything else" with images of the horrors and evils of the world.

[bdwsnlmn] Sex while manic

If a bipolar person is having sex while in a manic state, are they able to notice that their partner is not consenting?  Are they able to notice that their partner is not enjoying the experience?  Does it occur to them to ask for consent beforehand?

Hypersexuality is common while manic.

There is a lot of undiagnosed or untreated bipolar out there.  Assuming "no" as answers to the above questions, how much rape and sexual assault can be explained by it?  What should society do about it?

[vzgekoag] A few notes on the Riemann zeta function

  1. Show that the infinite series Sum(n=1, infinity, 1/n^(1+t*i)) diverges for all t, not just for t=0 which is the harmonic series.  It seems that the curvature induced by the imaginary part might be able to nudge the slow growth to infinity of the harmonic series back down to finiteness; however, this is almost certainly incorrect.  Despite the series presumably diverging, zeta(1+t*i) can be computed by analytic continuation.
  2. Riemann's reflection functional equation for zeta allows calculating zeta(1-s) given the value of zeta(s).  The defining series converges for Re(s)>1, so from that, we can also calculate zeta for Re(s)<0.  The only region we can't calculate is 0<=Re(s)<=1.  But that is the critical strip!  That's where all the interesting stuff happens!  That's where the million dollars lies!  (Obviously there are other formulae to calculate zeta within the critical strip.)
  3. Although the series converges for all Re(s)>1, it converges quite slowly near 1.  This is not too surprising, since it diverges quite slowly at 1.

    ? s=1.01
    ? zeta(s)
    ? sum(n=1,1000000,n^(-s))
    time = 7,485 ms.

  4. Something I would like to see (this probably exists in a textbook or maybe Riemann's original paper): Here is a expression for zeta which can be used to compute its value for the entire complex plane, and a proofs of analyticity of the expression and that it coincides with the p-series for Re(s)>1.  If the expression is defined piecewise, then we need to show the function remains analytic across the piece boundaries.
  5. The transformation (1-2^(1-s))*zeta(s)=DirichletEta(s) (from Mathworld) (also this YouTube video) does provide an expression which converges for Re(s)>0, thanks to the alternating series.  The rest of the complex plane can be gotten by using the reflection functional equation.  The critical strip can be evaluated both directly through eta and through applying the reflection equation.  This probably explains why zeroes in the critical strip are symmetric around Re(s)=1/2.
  6. Getting zeta(0) using the method above does not straightforwardly work.  Although eta(1)=log 2, one runs into madness like zeta(1) being undefined, log 2=0*zeta(1), and the gamma function being undefined at zero.
  7. The gamma function is also undefined at negative even integers, but I don't think that matters for any other place we would like to use the reflection equation.

[pggkliin] Solvable polynomials

Given a polynomial with integer coefficients, give an algorithm to determine whether it is solvable (in radicals), if only partially (some of the roots).  All polynomials of degree 4 or less are solvable.  Work by Cayley provides the answer to the quintic case.  But beyond that?

Motivation is to avoid collisions between irrational numbers formed with RootOf and irrational numbers formed with radicals.

[agskecwb] Sexy clothing in public

A person, stereotypically a woman, wears sexy clothing in public and garners attention, some from desirable people and some undesirable people.  Dealing with the unwanted attention requires mental fortitude.  Therefore, wearing the sexy clothing in public serves as a game-theoretic signaling mechanism of having that mental fortitude: those without it are less likely to wear such clothing.

This is analogous to a person, stereotypically a man, wearing clothing that showcases large muscles.  Such a display signals physical fortitude.

Mental fortitude (like physical fortitude) is of course a highly desirable quality in a mate, so it makes sense that people will signal it during courtship.  Mental fortitude is identical to self-qi.

How correct is this model?  How much does it explain why people wear sexy clothing?

Other reasons why someone might wear sexy clothing are identity and peer pressure.

Another reason why someone might judge sexy clothing as attractive is, some sexy clothing is delicate, so expensive to purchase and expensive to maintain.  Possessing such clothing signals wealth, another very important aspect of courtship.

What other mechanisms signaling mental fortitude, high self-qi, are occurring in courtship?  Assuming social movements and measures to decrease catcalling and other unwanted attention become effective, this will decrease the effectiveness of sexy clothing as a signaling mechanism, so other methods will have to take its place.

The "public" in "sexy clothing in public" might be complicated: the audience may have already been pre-selected against the undesirable people, those who would give unwanted attention.  Or, there may be social mechanisms in place so that those who give unwanted attention do not have access to the person wearing the sexy clothing, even if they see it.

Inspired by, the psychological effect of seeing sexy clothing in public is different from seeing it in private.

[ustsrdnq] Extended Goldbach conjecture

The shape of Goldbach's comet strongly suggests that the Strong Goldbach Conjecture is true: there are usually many, many ways (not just at least 1) to write a large even number as a sum of two primes.

This suggests a stronger conjecture: finder a tighter lower bound on the number of ways to express an even number as the sum of two primes.  Maybe O(n/(log n)^2).

Tangentially, generating quickly the image of Goldbach's comet is a computational challenge.  Probably AND and POPCOUNT of two long bitvectors, one the reversal of the other.

[stkxunqx] Radiating heat from an ecumenopolis

Pack a quadrillion or quintillion people onto Earth, and we will face the challenge of dissipating all the waste heat, not only from just our bodies but also our machinery and agriculture.

One way is to pump the heat to giant radiators in space.  The coolant can be pumped using a space elevator or space fountain.  The latter seems especially attractive because space fountains require constantly circulating some mass anyway.

However, the argument goes, if we have robust space elevator or space fountain technology, it would be better just to have the people live in many orbiting space stations.  Dissipating waste heat will be less of a problem.  Food could be grown in space as well.  It would be a lot less crowded and seemingly more pleasant.

Is this argument true?  How much more difficult is it to transport people via space elevator or fountain versus transporting coolant?  How much more difficult is constructing a habitat versus a radiator?

[vznoeiwf] Governments and economies failing

In a bad economy, all forms of government are unstable, vulnerable to public uprising.  In a good economy, pretty much any form of government remains stable.

Which forms of government are stable when the economy is medium, somewhere between good and bad?  Do some forms of government collapse faster as the economy goes downhill?  Is this the right question to be asking?

Or, is the better question to be asking, which forms of government promote a better, stronger, more robust economy?

[fnhgrewi] Aliens observing rare events

Aliens observe a rare astronomical event, realize it is rare, and broadcast their observations of it for the benefit of intelligent life in the rest of the universe.

Perhaps they are in close proximity to something rare and interesting.  Perhaps more dramatically, perhaps they are in close proximity to an astronomically violent event that will destroy their civilization, so they choose to broadcast it as a fitting monument to their existence.  (Rather more useful than launching Superbaby into space.)

If we see an interesting distant astronomical event (e.g., supernova, gamma ray burst), perhaps continue observing it for alien signals from nearby it providing on-the-scene data about it.

If the astronomical event is a beam (e.g., relativistic jet), then the aliens only need to broadcast in the same direction as the beam.  That is the only portion of their sky, the portion of the rest of the universe, that will notice the astronomical event occurred.  This decreases the power requirement of the alien transmitter.

Invert the situation: What rare events are we able to observe?  What should we be broadcasting?  How can we (or anyone) broadcast scientific information loud enough to be heard throughout the universe?

It might be that we are one of the earliest intelligent life in the universe (which explains why we don't see evidence of anyone else out there).  If so, we should record and broadcast what our universe, the "early" universe from the point of view of much later intelligent life yet to come, is like.  Maybe broadcast the cosmic microwave background pattern before it redshifts to invisibility.  What else is interesting about our universe now as we observe it?  Maybe stars will become even more metal-rich, so the behavior of our Population I sun will be interesting to future astronomers (much like how we wish we had information about Population III stars of the distant past).

[dytiyjdb] Primes on a music box

Start with an integer A with lots of factors, typically a primorial.  Consider the families primes of the form A*t+B, where B is relatively prime to A and 0<B<A.

Assign each family a musical note, and sound the note for each value of t that there is a prime.  The value of t represents time.  If there are many Bs for a given t that are prime, then a chord will sound.

Previously on the music of the primes.

[hatiatak] Sun at the middle of the day

Under Standard Time, the sun reaches its highest point in the sky at noon.

Under Daylight Saving Time, the sun reaches its highest point at 1pm, which is the midpoint of the workday, assuming a 9-5 workday.

[bjbfubbm] Real factorial

If a scientific calculator already has a factorial function, then it would be easy to extend it to all real values, providing the value of gamma(n+1), the capital Pi function of Riemann.

Similarly, the binomial coefficient function, nCr, can be extended to all real numbers via the Beta function, offset and scaled.

These can be further extended to complex inputs and outputs, if the calculator does complex numbers.

[xpcrzhxn] Complex calculator

Among scientific calculators which handle imaginary and complex numbers, not choking on sqrt(-1), which ones handle complex inputs and outputs for other functions, for example ArcSin(2)?

[lprwbbia] zeta(1/2)

Interesting things happen with the Riemann zeta function on the critical line Re(s)=0.5.  This suggests that the point 1/2+0i might be special, as it is the only real point on the line.  The value of zeta at that point is approximately -1.46.

Because zeta is analytic, everything about the function (including its behavior in the critical strip) is contained in the evaluation of it and all its derivatives, at any point except the pole s=1.

[ttadzrfs] Three little words

Set up a story in which some initially unstated three-word phrase is very important, and it is strongly suggested that those three words will be "I love you".  But the surprise ending is "Carthago delenda est".

Inspired by jokes that Cato the Elder included the phrase at the end of sexy talk with his wife, wished his little kids good night with that phrase, and orders a cheeseburger with fries and Carthage must be destroyed.

Variants, ending in "-go": Chicago delenda est.  Fargo delenda est.  Wells Fargo delenda est.  Others?  Probably need to modify to have gender agreement (in the original, delenda and Carthago are feminine).

Incidentally, Carthago was probably pronounced closer to Cart-hago, not the "th" sound in English.  Theta in ancient Greek similarly (but not modern Greek).  Neither Latin nor ancient Greek had English's "th" sound; don't know about Phoenician.

[dgxxljll] Does socialism erase class divisions?

Many socialist and communist countries worked very hard to create a classless society, erasing class divisions and class structures from the previous (overthrown) society.  Did it work?  Socialism and communism cause a lot of problems, especially economic stagnation and political corruption, but does it at least solve (or make significant headway) against this one social evil of classism?

On one hand, class divisions seem extremely insidious, so difficult to erase.  People discriminate at a very personal level toward those they feel are Not One Of Us.  Such behaviors are deeply connected to identity.  It seems impossible for a government to regulate people's behavior at such a personal, intimate level.  The breakup of communist countries after the Cold War suggests that much identity survived efforts to erase or homogenize it.

On the other hand, this question was inspired by a Georgian, Joseph Stalin, becoming leader of the Soviet Union.  I don't know how Russians and Georgians regarded one another, but clearly they (now) see each other as the Other enough to be separate countries and fight wars against each other.  It is therefore very surprising that that otherness did not prevent Georgian Stalin from gaining power, in fact, gaining ultimate power, within the likely highly Russian Marxist/Communist/Leninist movement.  (With how much of an accent did Stalin speak Russian?  Presumably it was a second language.)

If the Communists had won the U.S. in the 1950s and successfully imposed communist rule for a few generations, what would be the state of race relations in America now?  I can see it going either way: race relations in that alternate universe U.S. might be just as bad as here, or it could be much better.  (The communist U.S. economy would of course be crap.)

[nvcwxhyc] Black hole refrigerator

Enclose a large black hole with a spherical shell radiator with the radiator fins pointed toward the hole.  Pull heat from a refrigerated compartment outside the shell and dump the heat via the radiator into the black hole.  This system of the refrigerated compartment and black hole seems weird, seemingly violating some law of thermodynamics: The refrigerated compartment can keep getting colder and colder but no where else seems to be correspondingly getting hotter.  (I suppose the resolution is the Hawking radiation that the black hole ultimately emits.)

Practically, this won't work so well: an occasional atom falling off the radiator will radiate a significant portion of its mass energy in an accretion disc around the black hole.

Is there any situation which dumping waste heat into a black hole is better than radiating it out into space?

Maybe there are huge extraterrestrial civilizations out there, completely tapping the energy output of stars (Dyson spheres) or galaxies (Kardashev type 3), but they are hiding their heat output from us by dumping their waste heat into black holes.

[zgjhfiqh] Text for package recommendations

For a software package system which allows packages to softly recommend installing other packages (in addition to hard dependencies), e.g., Debian dpkg apt, let it also include free-form text for each recommendation, explaining why the package is recommended.

[vnxqazhy] Casanova

Tell a story of a Casanova-type character who seduces a great many women (though this story can easily be told gender-swapped or other sexual orientations).  However, the different women want greatly different things in a man (hinting at realism).  So the Casanova has great skill -- probably superhuman skills only possible in fiction -- to be appealing to the great many women.  What "works" on one woman might be utterly abhorrent to another.  The Casanova must be a chameleon, able to convincingly don vastly different roles and personalities.

In contrast, a typical Casanova story builds on the premise that all the women want the same kind of man, the type of man embodied by Casanova.  This ends up being a highly unrealistic portrayal of women.

Inspired by James Bond.  His profession requires seducing women.  What if the different women he encountered differed greatly between them instead of all being the same Bond-girl type?  Particularly striking might be, some women want a meek man, so Bond must act very differently from his established all-powerful character.  Bond must act.  The portraying actor must doubly act.

[ytvxxvxc] VR waves

You are on a fixed platform at sea.  Waves of various heights pass by and over you.  They break over you, so you experience the oncoming wall of water at its maximum steepness.

Waves in nature can be very big; virtual reality might be the best for depicting the sense of scale.  It is of course also much safer to experience such large waves virtually.  You don't get the feeling of being carried by the wave, or a sense of its power.  Maybe with VR plus a powered chair, like an amusement park ride.

What would it have been like to surf the Chicxulub impact?

[tsvpafoh] Long time no see

Are there any actual languages which "long time no see" translated word by word results in a grammatical, preferably natural, sentence expressing the meaning "It has been a long time since we have last seen each other."?  Ideally we want a language which does not conjugate verbs and which can omit implied words.  Alternatively, a synthetic language which the 4 words each have enough modifiers to make it a grammatical sentence.

Mandarin Chinese apparently gets very close to the first case: 好久不見.  The four characters translate respectively to "it is good" "long" "no" "see".  The first two characters fuse to form a word or idiom meaning "long time".  I don't know whether it is a grammatical sentence and a natural way to express the meaning.

Also, "No can do."

[nqxhnabz] Many ways to git

Given multiple projects with similar code, there are several different ways to use git:

Separate repositories for each project.

Separate subdirectories within the same repo.

Different git branches of the same directory.

For given circumstances, which is best?  If circumstances change, how can you change which way?

[aarorpxt] Space groups

Space groups (wallpaper groups in 2D) offer a convenient way to populate a whole space with stuff while only needing to design a finite part.

Characterizing and enumerating all the space groups for arbitrary Euclidean dimensions seems unsolved.  We may also be interested in hyperbolic spaces.

Wednesday, November 01, 2017

[vsfjnsxg] Not quite full virtual display

Create a virtual reality headset which has a gap for seeing down in actual reality.  This should be easy because covering up the nose area was difficult anyway.

Being able to see down allows using traditional keyboards and mice.

[azsesvxc] Barriers to education

1. By placing barriers to education, society ensures itself a large pool of unskilled labor which can be paid low wages because high supply.

2. By placing barriers to education, it artificially decreases supply of high-skilled labor, resulting in higher wages for the educated.

Are barriers actually happening for these reasons?  Cynicism would predict yes, but several difficulties:

There would both be demand and supply for education without the barriers.  Free market must be thwarted.

Several other models of education must be at least partially wrong: Education does not teach anything.  There are barriers after education.

Tuesday, October 31, 2017

[prxhyjkv] Some goban variations

Here are some variations on go 囲碁 boards.  Go can be played on arbitrary graphs, but we mostly stick with geometries in which each point (node) has 4 neighbors.

Traditional 19x19 square go board but with 1 corner point removed.  May need to significantly adjust komi because the first player can grab the 2 "easy" corners.

Start with a square but remove a small square or rectangle of points from a corner, so L shaped board.  This introduces 2 more corners and 1 concave corner (270 degree vertex).

Two square boards sharing (overlapping at) a corner point.

Two square boards overlapping in a square or rectangle of points around a corner.

Two square boards overlapping at all 4 corner points.   This requires drawing on a spherical manifold.

We next consider several square boards joined as in the faces of a cube:

3 squares around a vertex of a cube.  This introduces one point (at the vertex) with 3 neighbors.

4 squares: 2 adjacent to an edge and another 2 whose corner is an endpoint of the edge.

5 and 6 squares (previously discussed).  Some creativity possible in drawing these manifolds on a flat surface or display.

We can also consider a diamond-shaped board.  The diamond is equivalent to considering only the squares of one color on a checkerboard.  Edge play will be very different; there are corners along every edge.

Repeat all the above modifications to square boards with diamond boards (turned 45 degrees so that it is square again).

[qgxjefyl] Keyboard for typing text

Consider remapping keys on a keyboard to increase the efficiency of typing English text.  Common punctuation should be made available unshifted:


Uncommon punctuation should be relegated to shifted positions.


Perhaps exclamation point remains uncommon, allowing things to be moved around without doing anything radical.

If we are OK with doing something radical, the numbers can be moved to shifted positions.

For typing text, digraphs and other common letter sequences could be placed on single keys.

[iseswemp] Orbiting dust

Consider a collection of particles scattered with approximate uniform density in a sphere.  Each particle travels in a circular orbit around a central point mass.  The particles do not influence each other gravitationally.  This is easy to set up in simulation.  For each particle, pick an orbital inclination uniformly randomly.

Next, consider a collection of particles all with the same speed but traveling in uniformly random directions.  Easiest first is probably to consider a spherical shell of such particles.  Place a point mass at the center and let gravity do its work.  Again, none of the particles interact with each other so this is a simple 2-body problem repeated for each particle.  Some particles may escape.  For a given initial velocity and shell radius, what is the spatial distribution of (non-escaped) particles averaged over time, as a function of distance from the central point?  Add some more shells to get a somewhat uniform density collection of particles (within a certain radius) buzzing around the central mass in elliptical orbits.

The point of all of this is then to add another massive body to make it a 3-body problem.  Dust will get ejected from certain regions, collect in other regions (Lagrange points).

Useful are synplectic integrators, e.g., Verlet.

[xwnzahyz] Some nice irrational numbers

Some ways of getting some nice irrational numbers from integers or rational numbers, where "nice" is subjective.

sqrt(d) where d is a positive squarefree integer.

atan2(y,x).  If x and y are both normally distributed, then this yields a number uniformly distributed between -pi and pi.  Avoid the temptation to scale the result to between -1 and 1 because that will result in rational numbers sometimes.

log(x) where x is an integer greater than 1.  log(x)/log(y) where gcd(x,y)=1.  x and y could also be positive rational numbers, equivalently quotients of the form (log(a) - log(b)) / (log(c) - log(d)).  Previously.

exp(r) where r is a rational number between -1 and 1.  This one seems less aesthetically satisfying because terms like that don't seem to naturally occur in math and science.  exp(z*pi) does occur, with z often complex, but the famous examples, z=i and z=sqrt(163) result in an integer and an almost-integer, which is precisely what we are trying to avoid: we want irrational.

Multiply any of the above by a rational number.

Sums of any of the above.  We enter realms in which we're not sure whether values are irrational, but they probably are.  d=1 in sqrt(d) and r=0 in exp(r) above are obviously not irrational, but keeping them around allows us to form (a+b*sqrt(d))/c, the quadratic surd.  We limited d to squarefree above to avoid situations like sqrt(2)-sqrt(8)/2=0.

Need to be careful with logarithms, e.g., 4/3*log(8)-log(16)=0.

If positive, square root of any of the above.  Probably any non-integral rational power.  Maybe other functions.  Need to be careful to avoid things inverting and becoming rational.

Some care needed to avoid numbers from becoming too big or too small in absolute value.  Central limit theorem might be useful.


Tuesday, October 24, 2017

[mapuxbob] Ultimate deep cut

Consider a twisty puzzle that has the motions of all the order-2 deep-cut puzzles on a cube: the 2x2 Rubik's cube, the Skewb, and the 24-cube.  The cuts on each face are an orthogonal cross and each quarter square is divided into 4 diagonally, so 16 isosceles right triangles per face.  Additionally there are cuts along the edges.

Also add all the additional turns that are possible using these cuts which preserve the shape of the cube after the turn.  I think these are: Dino cube vertex turn, very small vertex turn in the style of Pyraminx, Helicopter cube edge turn.

These extra cuts make it a 2 layer puzzle between opposite faces, a 4 layer puzzle between opposite edges, and a 6 layer puzzle between opposite corners.

This seems very difficult to build mechanically so is best done virtually.  Virtual can also prohibit jumbling moves which alter the cube shape.

Inspired by 2 xscreensaver hacks, one demonstrating various twisty puzzles and the other the Lament cube.

[olgybexs] Lap times of unrestricted race cars

For a given race track, what are the fastest lap times ever done on it, with little or no restrictions on the type of equipment?  Cars run alone to decrease the danger of collisions.  Of course this takes the fun out of it being a spectator sport with lots of complicated strategy.

Inspired by restrictions on race cars.  What if those restrictions were removed?

We probably care about records for 2 or more laps also.

[kawtunfn] Massively editing history

git blame (or similar in other version control tools) is code documentation: why is the code like this?

Then, much like other documentation, we probably want processes to make this documentation nice, and iteratively making revisions to improve it.  git commit --amend can make a new version of a commit message, but we cannot undo, cannot view the history of the history.

More complicated changes involve splitting or merging commits.

There's a temptation to clean up history, but recording the thing that didn't work is again useful as code documentation: why is the code like this?

Perhaps one path which documents how the code was actually made over time, and separate paths (arriving at the same destination) written by the documentation writers which provide the clearest story.  Paths can be continually revised by creating new paths, keeping old ones. Documentation writers can promote their path as the main line, even though it chronologically wasn't what happened.


Sunday, October 22, 2017

[rfcvmehz] I lived in Somerville before it burned down

Under what conditions can there be significant urban fires, a whole neighborhood or more burning to the ground?  (Inspired by the Santa Rosa fire.)  Hypothesize that all that is required is high density of wood-frame buildings (frequently residential), some vegetation, and severe drought.

Climate change can bring about severe drought in areas which may have never previously experienced it.

[riefkroc] Rational terrible behavior

There seems to be growing evidence that people behave rationally more often than commonly believed, or more often than we commonly want to believe.

People also behave terribly, for various subjective measures of terrible.

Put the two together and conclude that terrible behavior is often rational, a depressing conclusion.  Efforts to directly decrease the behavior through morality ("that's bad; don't do it") are doomed to fail, because, in rationality, it's worse not to do it.

Efforts to further understand how the terrible behavior is rational are more likely to be fruitful.  Change the incentives.

[oruxepci] Simulating parliament

A president could simulate one aspect of a parliamentary system of government by appointing Cabinet members from the legislature.  While previously serving on legislative committees, they have presumably acquired expertise in an area suitable for a cabinet post.  Appointment only from the legislature has the feature (maybe benefit) that the legislators have all undergone election, so have been vetted by the public.

In a true parliamentary system, the ministers also remain members of parliament.  What happens if they face a conflict of interest between their duty as a minister of their the country versus their duty to represent their district in parliament?

Saturday, October 21, 2017

[tiuahohk] Self-measuring self-qi

Huge amounts of courtship and employment screening are probably to measure someone's average self-qi.  Employment screening includes the education system and promotion decisions.

Consequently we expect, by game theory, much effort devoted to concealing and being deceptive about low self-qi.

However, one situation where deception shouldn't occur is if you want to measure your own self-qi, perhaps to avoid situations in which low self-qi will have bad consequences for you.  How can you measure your own self-qi or stress level?

A few starting points: are you tired?  Are you hangry?  Are you sick?

[rajxyghb] Asymmetric society producing capable women

Consider the stereotypical historical society which assigned asymmetric roles to men and women: women remained at home, men went out and won bread.  Exactly what was expected of women and how did society produce women who did those tasks well?  (For the men, the labor market and wages induced incentives to work well.)

The obvious first possibility is that society expected child-rearing of women.  However, we discount that possibility in two ways in preparation for a radical second possibility below: child-rearing in historical societies was not just done by the mother but also by the extended family.  Because many people were involved, no one needed to be particularly good at it, yet things would still turn out all right.  The other is that children seem to be evolutionarily designed to grow up and to be able to turn out all right despite pretty bad parenting, so long as their basic needs are met.

The provocative second possibility is that the main thing such asymmetric societies expected of women was to provide emotional and psychological support for their husbands, ultimately to improve the work productivity of their husbands.  (Inspired by the complaint that society still expects this of women, who are now also working jobs and still being the primary in child-rearing, nowadays without the help of extended family.)  If true, this second possibility raises several questions: exactly what kind of emotional and psychological support did women provide to their husbands?  How, psychologically, did that support work to improve productivity of their husbands?  How did they train girls to provide such support?  What mechanisms rewarded learning how to do it well?

One cannot provide emotional support to someone else if one is oneself emotionally overwhelmed or drained, a common complaint of the stresses of modern society.  In order for a society of asymmetric gender roles to work according to the second possibility, there would have needed to have been some mechanism to shield women from outside stresses.  What was that shielding mechanism?

One cannot do a good job at anything is one is unhappy about doing it, especially for tasks so personal and intimate as providing psychological and emotional support: body language will betray one's unhappiness.  Therefore, in order for a society of asymmetric gender roles to actually work, there needed to have been some mechanism for women to be content in their roles, not resentful about the opportunities they were denied solely because of their gender.  What was that mechanism?

Understanding the mechanism of contentment versus resentment is also useful for politics: those who wish to maintain power in status quo seek to induce contentment in the populace; those who wish to gain power by changing the status quo seek to induce resentment in the populace, most famously through victim identity.

[iiomamzg] Evolving artificial intelligence

Create a simulation with artificial creatures evolving in a virtual environment that rewards evolving more and higher intelligence (though need to define "intelligence" which may be tricky).  Can we create a general AI by simply running that evolution simulation at high speed?

What is the difference between non-intelligently adapting to an environment and intelligently understanding an environment and acting according to understanding?  Both succeed in exploiting the environment to maximize benefit.  Intelligence probably adapts quicker to change, not taking generations to discover the best adaptation.

Exactly how should the simulation work?  How can it reward intelligence?

[odwfsmzu] Murder upward only

In a highly stratified society, hypothesize that all crimes are committed upward in social class: the lower committing crimes against someone above them.  This is because when the upper class wants something from a lower class, whether property, mating prospects, or the death of someone in the lower class, they will just do it or take it legally: it will not be considered a crime (legally).  (It perhaps remains morally a crime.)

Inspired by, if someone wants to commit mass murder, they could unleash powerful weapons on a crowd, or they could legally work in the cigarette industry, or they could work to restrict access to health care.  Who chooses to do what?

How true is this model?  Obviously there are also many crimes committed within each class as members struggle for promotion and demotion, so the model is not complete.  If one class is just slightly higher than another class, we don't see the upper one completely brutalizing the lower one as the model seems to predict.

Assuming true this model of crime, the institutions of crime prevention and criminal justice become quite sinister: maintain the status quo of the class hierarchy.

[dughfscx] Rational logarithms

Consider log(a)/log(b), the logarithm base b of a.  Is the answer rational?

Compute g=gcd(a,b).  If g=1 then the answer is irrational.

Compute x=log(a)/log(g).  If x is not an integer then irrational.  Because we only care if it is an integer, x can be found by binary search, looking at powers of g.

Similarly y=log(b)/log(g).

If x and y are both integers, then the answer is x/y.

Next, consider log(a1/a2)/log(b1/b2).  Assume the fractions have both been reduced and a2 > 1 and b2 > 1.

Run the procedure above with (a1, b1), then (a2, b2).  If the answers are both rational and equal to each other, then that is the final rational result.  Otherwise, irrational.

These methods have the nice feature that we never have to factor any integer.

Not sure if they are correct, or whether there are more efficient ways.

[yqkubvtj] Steroids in some sports

Why are steroids prohibited in some sports but permitted in others (e.g., bodybuilding, pro wrestling, strongman)?  What is it about how society perceives those sports that has caused different amounts of public outcry about steroids than in other sports?  Or, what determined the order in which sports banned steroids?

I would not be surprised to find steroid use in other professions that involve a lot of physicality: e.g., dance, circus.  Inspired by, the heaviest users of steroids in baseball seem (surprisingly) to be the catchers (crouching and standing a zillion times per game) and pitchers.

Best guess: the people who pursue careers in steroid-banned sports, football, basketball, baseball, bicycling, swimming, etc., are often One Of Us, whereas the people who pursue careers in bodybuilding, pro wrestling, strongman, circus, and men who pursue dance as a career are Not One Of Us.  (There are a great many women who are One Of Us who pursue careers in dance, but the body shape changes induced by steroids preclude women from using them.)  The argument of "good role model" carries the day.

One Of Us here is a shorthand for a group that has enough political power to enact steroid bans in sports they care about, probably white middle-class and above.

[jfimxvqx] Various astronomical planes

Create a sculpture which is just a plane that is parallel to the plane of the equator.  This should be easy.  Add a stick that points out orthogonally toward the north or south celestial pole.

Create similar sculptures that illustrate the plane of the orbit of the moon, plane of the ecliptic, plane of our solar system's orbit through the Milky Way galaxy, plane of the disc of the galaxy.  The planes can have markers pointing to a relevant object: the moon or the center of the orbit.  These need to be kinetic sculptures, because the planes need to continually reorient because of the earth's motion.  The plane of the equator also slowly moves.

[rgwocfen] Where is the equator?

The north and south poles very slowly drift.  There are ceremonies at South Pole "Station" (therefore not actually stationary with respect to the pole) to mark the new location of the pole each year.  Consequently, we expect the equator to move over time also, but there aren't ceremonies that I've heard of.

The equator probably remains fixed according to some coordinate system for geolocation and navigation, so is not actually exactly halfway between the poles.

[tynurhyy] Two maps at the same scale

Instead of (or in addition to) a scale on a map to signify zoom level, provide an additional map to the side, a map of an area you are already familiar with distances, perhaps the area around your home.  Then, it is easy to visually gauge the distance between two points on the main map as similar to a distance you already know on your home map.

[hludclpz] Voluntary Stepford

The horror of the Stepford Wives could be increased by changing it so that the wives are aware of the what the process entails yet are voluntarily submitting to it, perhaps even competing for the "privilege" of being Stepforded.  (Change the process so that it is brain reprogramming and not murder and replacement by a robot.)

Obvious metaphor for real life in which people try to adapt to their partner.

[rulrzurd] Health levels in a game

Create a game in which the character has 2 health meters: physical health and self-qi.  Various ways the two meters and the main environment of the game interact:

Low self-qi makes succeeding at some tasks in the game more difficult, possibly then making it difficult to improve or maintain physical health.  Low physical health may directly lower self-qi.  This is the disastrous negative feedback loop.

Analogously, the positive feedback loop is also possible.

In real life, you don't have reliable access to your own health meters.

Wednesday, October 18, 2017

[pcdcujqh] Rat Park and all entertainment

Hypothesize that Rat Park is true for humans, and further radically hypothesize that it applies not just to drugs but broadly all entertainment: things that stimulate the same part of the brain that heroin does.

Look at how much entertainment a person consumes to be able to accurately guess the state of the social structures around a person.  Look at how much entertainment a society consumes and get a measurement of how the society is structured.

Copyright probably affects production of entertainment.

[scnfyfkb] A nice range of reals

1/e to e, or numbers whose natural logarithm ranges between -1 and 1.

Similarly 0.5 to 2.

These seem numbers on a human-comprehensible scale.

[vqbjrmbd] GCD diagram

In the style of the Sierpinski gasket (or Pascal's triangle), depict the greatest common divisor of two integers.  Easiest is black if relatively prime, white otherwise.  More complicated is some way of depicting what the GCD is if it is not 1, maybe color or 3D.

Shape as an equilateral triangle, not isosceles right.

[ytjxyyzh] Most interesting defense

A computer can easily win a won chess position, or find the most stubborn defense of a lost position.  However, finding the most interesting defense of a lost position requires human aesthetics.

[pxlrjngg] Mitigating the risks of offshore assets

Moving your financial assets to another country with more favorable tax policies requires trusting that the other country will remain stable and won't arbitrarily seize your assets.  How are those other countries kept stable?  How are their governments being controlled by the foreign account holders so that the government doesn't, say, start taxing savings? It is probably through corruption.

Inspired by the Panama Papers.

[vttngych] Sampling fractions uniformly

Uniformly sample among reduced fractions between 0 and 1 whose denominator is less than N.  For example, for N=5, we want to uniformly sample among 5 items 1/2, 1/3, 2/3, 1/4, 3/4 (excluding 2/4).  At first I thought this might be difficult to do for large N, but upon further consideration, it looks easy: choose a numerator and denominator, then reject and try again if GCD not equal to 1.  What is the expected number of repetitions?  This is a well studied problem in number theory whose answer is related to zeta(2)=6/pi^2.  To first order, failures are dominated by choosing 2 even numbers.  Rarely does one need to try more than a few times.

[zzfydkni] Normally distributed integers

Consider a random walk among the integers, starting at 0.  Transition in the direction +1, +0, -1 each with probability 1/3.  After a large number of steps, the endpoint is normally distributed around 0.

If you would like 95.45% (2 standard deviations) of the endpoints to be between -x and x, then take 3x^2/8 steps.  (The variance of the original distribution is 2/3, from whence the factor of 3.)

150 steps yields normally distributed numbers usually between -20 and 20.  15000 yields -200 to 200.  (We artificially induce Benford's Law: an initial digit of 1 seems more natural.)

[gacogjwe] Catering to Chinese consumers

Our big-budget movies are determined by what is acceptable in China, hence superhero action movies.

Our smartphones are determined by what will sell well in China, hence phones with huge screens (a status symbol in China) that don't fit in small pockets.

When did the American market become an afterthought, even for American producers?

[xcsyydtv] Force battles

Alternate Star Wars:

Anakin and Obi-wan fight, and their collateral damage turns a nice world into a volcanic wasteland.

The Emperor and Yoda meet, perhaps very briefly spar but both realize that their collateral damage would literally destroy the galaxy.  Not sure who would win, but surely everyone else would lose.  They instead trade words.

Illustrates how the power of the Death Star really is insignificant compared to the Force, but not everyone knows this.

Primary weapon in fights between masters is not the lightsaber but telekinesis scaled up (or down) to manipulation of the fundamental fabric of space.  (Yoda does not use a lightsaber!)  Parried attacks generate vast amounts of heat, causing collateral damage.

Monday, October 16, 2017

[duimuqdd] Compressing prime numbers

Given a large prime number p not of any special form, can one data-compress it to specify it in less than log_2(p) bits?

Straightforward is to say it is the m-th prime.  Expressing m will take about log_2(p/log(p)) bits by the prime number theorem.  This is the theoretical optimum by some measure, because the m's map 1-to-1 with the primes.  The number of bits saved is log_2(p)- log_2(p/log(p)) = log_2(p) - [log_2(p) - log_2(log(p))] = log_2(log(p)) which, because of the twice-iterated logarithm, is a very small savings.  For 370-bit primes around exp(256), the savings is 8 bits, or a reduction of 1 part in 46.  For larger primes, the relative savings is even less.  Around exp(2^16), the reduction is 1 part in 5909.

Despite the mostly uselessness of this endeavor, we charge forward.

Computing m is not practical for large primes.  For a practical method, we form a new number x = 2^k * floor(p / 2^k), equivalent to setting k lower bits of p to zero.  Then we can encode p as the n-th prime larger than x.  For small k, n is easy to compute, and it is easy to recover p from n and x (e.g., with a prime sieve starting from x).  Storing n instead of the lower bits of p results in some data savings because primes are less dense.  Curiously, the number of bits saved on average is log_2(log(p)), which is the theoretical maximum, and not dependent on k.  However, we also need to store k, which eats up some of those savings.  Because the number of bits saved is constant, this method paradoxically works less and less well for larger k.  However, with small k, n might vary significantly from the average, which could be good or bad.  Here is some Haskell code to compute n.  Here is some example output on the prime 3^233 + 176, which is around exp(2^8).  We can see there is generally around 8 bits of savings, except for 2^21 where we got lucky.

input 1476564251485392778927857721313837180933869708288569663932077079002031653266328641356763872492873429131586567699
prime # 1 after 2^ 9 * 2883914553682407771343472111941088244011464274001112624867338044925843072785798127649929438462643416272630015
prime # 3 after 2^ 10 * 1441957276841203885671736055970544122005732137000556312433669022462921536392899063824964719231321708136315007
prime # 8 after 2^ 11 * 720978638420601942835868027985272061002866068500278156216834511231460768196449531912482359615660854068157503
prime # 12 after 2^ 12 * 360489319210300971417934013992636030501433034250139078108417255615730384098224765956241179807830427034078751
prime # 24 after 2^ 13 * 180244659605150485708967006996318015250716517125069539054208627807865192049112382978120589903915213517039375
prime # 59 after 2^ 14 * 90122329802575242854483503498159007625358258562534769527104313903932596024556191489060294951957606758519687
prime # 129 after 2^ 15 * 45061164901287621427241751749079503812679129281267384763552156951966298012278095744530147475978803379259843
prime # 252 after 2^ 16 * 22530582450643810713620875874539751906339564640633692381776078475983149006139047872265073737989401689629921
prime # 526 after 2^ 21 * 704080701582619084800652371079367247073111395019802886930502452374473406441845246008283554312168802800935
prime # 8789 after 2^ 22 * 352040350791309542400326185539683623536555697509901443465251226187236703220922623004141777156084401400467

Future exploration:  "Luck" above is easily explained by long internal strings of zeroes in the binary representation of p: the least significant 21 bits of p are 000011111111000010011.  We could also try to take advantage of long internal strings of ones.  More generally, sieving for primes works well for regions defined by arithmetic progressions.  We might search generally for representations of p as the "a-th prime number of the form b*x + c larger/smaller than d*e^k".  Above we explored b=1, c=0, "larger", e=2, d unrestricted.  We could also explore anchor expressions more complicated than d*e^k.

Previously a completely different way to encode large prime numbers in a small amount of space.

Wednesday, October 11, 2017

[oicxhazu] Sherlock Taken

Get Benedict Cumberbatch (as Sherlock), or an impressionist, to read Liam Neeson's famous speech from Taken: "I have a very particular set of skills... I will find you..."

[gqksmejv] Smoothly transforming polyhedra

What pairs of nice polyhedra can be smoothly morphed to each other avoiding ugly shapes in between?  Ugly is of course subjective.  They form a graph.

[rkzmrdnt] Central Limit Theorem and Hypersphere picking

One can pick a point on the surface of a unit hypersphere of any dimension by first picking a point in that dimension whose coordinates are all sampled from the normal distribution, then scaling by the distance to the origin, i.e., projecting to the (hyper-)sphere.

One can approximately sample from a normal distribution by sampling a bunch of times from any distribution satisfying the central limit theorem, then computing the mean (or just sum) of the samples.

Together, these seem potentially useful, though not sure what.

Project the endpoint of a random walk to unit distance.

Sunday, October 08, 2017

[wbmowbjw] Print your own log tables

Ceate a device to print out log tables, inspired by Babbage's Difference Engine.  Obviously, a modern computer and printer.  There exist many fine details.

How much precision in input?  Printed tables of logarithms are already unwieldy (compared to calculators and computers) so go for the max and make it many volumes, maybe 90.  This will be very expensive.  How much precision in output?  The logarithm function changes rapidly near 1.0 but slowly near 9.9 so perhaps more gradations in input around 1.0 and more precision in output around 9.9.  We need that precision to invert (exponentiate).  Sampling along arc length seems like the right thing to do, but not so convenient for actual use of the table, typically doing interpolation.  Around 9.9 perhaps express output as 1-output.

All this assumes base 10.  Maybe binary, octal, or hexadecimal is better.  Perhaps invent new robust compact notation for those bases.   Previously, base 100.

Many many fine printing and bookmaking details of exactly how to format the tables to make it quick to find a desired entry.  A fancy dictionary has a thumb index.

What functions other than log?  Sine and cosine seem appropriate as the continuation of exponentiation into the complex plane.  Tangent and arc tangent?

[bhfrgtxp] Screaming crossword

Create a joke crossword puzzles whose clues indicate every answer is a scream: "Aaaaaa..."  Every box is A.  Maybe also battery sizes and minor league baseball.

[zvetsujf] Contra dance panopticon

The contra dance style which has inactives standing along the sides and actives dancing between them resembles the panopticon prison.  Do they serve similar purposes, preventing bad behavior by making people feel watched?  What were the social circumstances surrounding the creation and popularity of that style?  What are the circumstances surrounding its decline?  Will it come back?

[kxdvmnew] Language for climate change

Climate change will induce changes in language.  What new words, terms, or constructs will get invented?  Perhaps invent them now, as art, or to get ahead of the curve.

[zruxmgev] User-guided optimization and parallelization

Provide tools to improve the user experience of profile-guided optimization.  Perhaps something like, within a running program, trigger starting gathering profiling data, trigger recompilation with the gathered profiling data.  The user knows, "This is the use case of the program I want to optimize for."

Profiling could also guide automated parallelization.

[bvbbxjiv] insert-date

Some Emacs Lisp to insert the current date into the buffer:

(defun insert-date ()
  (call-process "date" nil t nil)

Wednesday, September 27, 2017

[bcqozgyq] Addressing the Apollonian gasket

The circles in the Apollonian gasket fractal form a hierarchy with every circle having 3 parents.  Devise an addressing system which gives directions to a given circle, directions on how to construct it.  Do it efficiently: avoid constructing or consuming namespace on circles which are irrelevant to the given circle.

[jzwsfuye] Random binomial generator

Generate random or pseudorandom events from two possibilities at given probabilities.  This is easy.  Allow correlation with the immediate previous event.  This is also pretty easy given the Markov transition probabilities.  We could also have probabilities given as constraints, for example, one event occurs 3 times more frequently than some other event..  This requires linear algebra to solve for the transition probabilities.  Easily expand to more than 2 outcomes.

[mxlmdzml] Comfortable work chairs

The two types of chairs people often sit for many hours in are recliners and car seats.  Why aren't office chairs shaped like them?

[vswediqc] Rationally not learning

Mastering a skill requires both instruction then opportunities to practice what you learned.  Hypothesize that people rationally choose not to attend instruction because they correctly estimate that they will not have adequate opportunities to practice afterward.

Of course, this is broadly applicable to dropping out of school, or choosing not to continue education.

Inspiration was partner dancing lessons.  The opportunity to practice, social dancing outside of lessons, may be quietly sinister: effective practice involves making mistakes, so you can only learn in practice if you dance with someone whom you are comfortable making mistakes with, someone who is comfortable with you making mistakes.  That feeling of comfort, the decisions and behavior that make people comfortable or not, are very personal, and so we hypothesize harshly reflect social boundaries such as class or race, and ultimately induces the class and racial makeup of a dance scene.

Tuesday, September 26, 2017

[snmhvicc] Donating to government hurricane relief

In searching for a good charity to donate to, consider donating to the U.S. government:

"No," you say: "I want to donate it to a specific effort or incident, for example hurricane relief.  It's my money and I want to control where it goes.  I don't want the government deciding where my money goes; they'll do it wrong."

"No," you say: "Private entities are more efficient and effective at distributing relief."

"No," you say: "I can't put my finger on exactly why, but the idea is inherently distasteful."

Of course, these arguments exactly mirror arguments that small-government conservatives make against welfare programs of the government in general.  When are such arguments valid?  When not?  Is it simply mundanely political: "I support big government when government supports me and Us, small government when the government supports Not One Of Us"?

Inspired by people looking for charities to support hurricane relief that are not the American Red Cross, because that charity is reportedly inefficient.

[dlfeonqj] Generic permutation puzzles

A Rubik's cube can obviously be generalized to an ordered set and a set of permutation operations on that ordered set.  The goal is to restore a permuted ordered set to its original order.

(This does not cover puzzles in which certain moves become not possible in certain states, e.g., bandaging.)

How difficult is solving these problems in general?  I would not be surprised if it is something like PSPACE-hard.  There are several questions: Is a given puzzle configuration solvable?  What is a solution?  That is, give an algorithm which will find a solution from any initial scramble.  What is the shortest solution, or some relatively short solution?  Analyzing the Rubik's Cube with group theory offers heuristics leading to short solutions (Kociemba): how does one do this for general permutation puzzles?

[ekqeulsi] Self-qi must be wrong

Meta criticism: The theory (not yet fully described) is simple, perhaps too simple.  Being so simple, someone else must have thought of it already, and therefore it must have already been subjected to tests of correctness.  If it has survived those tests, then we would expect the theory to already be widely known.

Yet, I am currently not noticing major problems with it.  There's a giant hole regarding what causes stress level to go up or down, but this is not yet a flaw.

[wwqjgwga] Highlighted pieces and squares

From a given chess position, consider the best line (principal variation) or the best few lines if there are multiple that are equally good.  For every square that is a destination of a piece in the lines, shade that square a certain color.  Squares that get involved only deeper in the line get less shading.  Square that get hit multiple times get darker shading.  We could also allow sophistication in which the shading color differs depending of the color of the piece or pieces that land on it.

Similarly, in the board diagram of the current position, highlight pieces that will move, perhaps darker if they move sooner or a lot, perhaps a different shade if they will be captured.

In general, these highlights annotate the "hot" squares and pieces in the line about to happen (assuming best play) from the current position.  This may be useful for spectating chess.  Previously.

[nyzwinpq] Very slow Death Star

The aliens arrive and unleash their planet-busting weapon on the protagonists' populated home planet.  However, the weapon works very slowly, taking millions of years to completely disassemble the planet and take it rock by rock into space.  This kind of time scale is normal for anyone engaged in interstellar space travel.

The inhabitants are not too concerned.

Inspired by futurists' plans or predictions to slowly disassemble planets to create many, many space stations providing more habitable area.

[kgharqcv] N queens of 2 colors

Place N white queens and N black queens on a chess board so that no queens of opposite colors attack each other.  Queens of the same color may attack each other.

The standard N queens problem is N queens of N different colors.

More sophistication possible with rooks and bishops.

[akmdjseh] What if no SUV?

CAFE and the Gas Guzzler Tax are (probably) examples of regulation gone terribly wrong: attempting to increase fuel economy instead brought about popularity of the SUV, not classified as a passenger car, and fuel economy did not increase.  The market did what the market does.

What would the streets of America be like today if those laws had not been passed?  We would probably have gas guzzling cars instead of gas guzzling SUVs, which seems better in several respects.  A gas guzzling car tends to be smaller and lighter than a gas guzzling SUV, increasing average safety: there is less total kinetic energy on the streets.  The large SUVs on the streets induced a zero-sum game where everyone else felt they needed a large SUV to feel safe.  A gas guzzling car, being smaller, likely has better fuel economy than a gas guzzling SUV.

The correct way to increase fuel economy would have been a gasoline tax, inducing market mechanisms toward better fuel economy (or possibly black markets or other ways to avoid the tax).  Even more problematically, even after the SUV made it clear the regulations weren't working, there were no attempts to repeal them or improve them.

[sjtyqosh] Free and not free speech

Post on Facebook, "Freedom of speech does not mean freedom from consequences," and see who likes it.  This will give you a convenient list of people whom you need to self-censor your speech around.  Even if someone else posts it, the mutual friends who like provides a partial list.

One problem with this approach is a person's tolerance or intolerance of offensive speech changes day to day, likely due to stress levels.

[xesqugtd] Flying in a suit of armor

Consider air travel wearing a medieval suit of metal armor, to protect against the increased radiation levels at the altitude planes fly.  How much does the armor help?  It might be worth it for people who fly a lot.  Can you get armor through TSA security (it will of course block body scanning X-ray machines)?  Are some parts of the body more important to protect against radiation than other parts?  Make less unwieldy garments concentrating on those areas.  Soft lead is probably better than steel when protecting against radiation and not swords.

What are the main sources of the harmful radiation that make it into the passenger compartment of an airplane?  I suspect it is cosmic rays and cosmic ray decay products.

It's kind of interesting that more research into astronomy, to understand cosmic rays, and high energy particle physics, to understand their decays may be directly applicable to health.  Radiation penetrating into the spacecraft will also be very relevant to astronauts on long missions beyond the Van Allen belts.

[bqetbyhd] Fine-tuned advertising

Suppose you wish to create an advertisement targeted to one specific person, perhaps because technology has made such targeted advertising on a mass scale possible, or perhaps because the specific person is a high value target worth spending very large amounts of effort to try to influence.  How should the advertisement be?

Motivating example was fashion models: in the not-too-distant future, an advertiser will be able to virtually make a model look any way they want, e.g., size, shape, race.  What settings should be chosen to maximize the effectiveness of a fashion advertisement tailored (pun intended) to a given person, assuming the advertiser knows everything (thanks Google) about the targeted person?  I don't think the answer is to make the model look exactly like the target.  It might be to make the model look like who the target aspires to be or look like.  Who does the target aspire to be or look like?  Why?  The answers to these questions may reveal a totem pole of society.

[kdjykabg] Go on a sphere

Playing go 囲碁 on the surface of a cube is the easiest way to transport the game to a topologically spherical manifold while preserving the square-lattice feel of the original game.  Other ways are possible: subdivide the rhombic faces of a rhombic dodecahedron, or similarly any polyhedron whose faces are all quadrilaterals (preferably parallelograms).

Inspired by HEALpix, which subdivides a sphere into 12 squarish regions, then subdivides those "squares".

Given a polyhedron with all triangular faces, join pairs of adjacent faces forming non-planar quadrilaterals, which can then be subdivided into topological square lattices.  Slightly tricky in preferring pairs forming convex quadrilaterals, though nonconvex can be subdivided with curved lines.  There might be a few triangles left over representing topological defects where the game might be more interesting (similar to fights for a corner or edge in the original game).  Of course, if a face has more than three sides, it can be triangulated.

[ahhgjncw] Sphere eversion sculpture series

Create a sequence of sculptures, probably 3D printed, that illustrate sphere eversion.  Maybe convince yourself that there are no pinch points.

[zdsztbdt] Splicing dramatic pauses

Take 2 (or more) songs which hit a dramatic pause of silence and splice them at that point.  Also possible is starting a new song at the pause.  This should be easy.

[ridqqyie] Sniper crater

A sniper looks through the scope, puts the target's head in the crosshairs, then pulls the trigger.  The entire city block is destroyed, leaving a crater centered on the (former) target.  There's no kill like overkill.

Previously, a surprisingly less powerful weapon, and weapon power selectable by zoom level.

Tuesday, September 19, 2017

[uhifqhlj] Hazing decreasing sexual assault

Hypothesize that members of organizations which haze, sterotypically college fraternities, commit less sexual assault than similar organizations which do not haze.  More specifically, all other things being equal (which is difficult assumption to control for), we hypothesize that hazing decreases membership of people who are more likely to commit sexual assault.  The hypothesized mechanism is that hazing often consists of humiliation, and sexual assault is often retaliation for humiliation.  Hazing often includes sexual humiliation.  Those who survive hazing have proven they can handle humiliation well enough to satisfy the organization, so are therefore less likely to react badly to humiliation in a sexual encounter.

More fundamentally, we hypothesize that hazing selects people with high self-qi, and sexual assault, reacting badly to humiliation, is committed by people with low self-qi.

Several problems with this hypothesis:

Self-qi (stress level) changes rapidly, day by day.  A high self-qi level during the hazing initiation ritual (allowing surviving the hazing) might have very little correlation with levels later.

Hazing requires the members to haze the initiates.  Such behavior requires members to override their instincts for compassion and instincts against cruelty.  People who can easily override those instincts, perhaps because of having had many occasions to do so, seem more likely to commit sexual assault.

[zwlevyom] VR desktop environment

Can virtual reality replace the monitor as a computer desktop environment for work, for example an IDE for computer programming?  Expand VR beyond entertainment and play.

Pros: potentially large display area.  Depth can be used to organize things.

Difficulties: heavy headset worn for many hours.  Typing blind (perhaps need a completely new kind of keyboard, maybe also add speech recognition).  Monitors offer higher pixel density.

[uytyhhho] Random color

Sample uniformly in Cielab color space and reject if it not in the RGB/sRGB gamut.  This (probably) decreases samples in the near-white and near-black regions.  Using a quasi random sequence would avoid colors close to each other.

Random colors of a given lightness also easy.  Previously, random saturated color, avoiding grays.

Saturday, September 16, 2017

[xxzqtrku] Vertical life-sized chess

Demonstrate a chess game on a board with people depicting pieces, but orient the board vertically.  Perhaps the performers use some circus-like athleticism as the pieces they represent move around this vertical board.

[tmsokqhu] Random polyhedron

Start with a "nice" 4D polytope, perhaps regular or convex uniform.  Take random a 3D slice through the center and depict the resulting 3D polyhedron.  It'll probably be oddly shaped but hints at underlying symmetry.  Perhaps the slicing hyperplane rotates and the shape changes.

Same thing could be done with 2D slices through the center of nice 3D polyhedra.

[hyygzocu] Keeping language the same

The invention of the printing press has caused some aspects of language, e.g., orthography, to change much more slowly than before.  Can (or will) further technology further slow language evolution?

Language kept constant over time allows knowledge to reliably be transmitted through time.  But could this also be bad for society?

Language is always embedded within a culture.  Constant language means constant culture, so this might be impossible.

Wednesday, September 13, 2017

[alfojqcb] Password entropy

If a password consists of all characters of the same class except possibly for the first or last characters, then: if they are all digits, then log(10) bits of entropy per character.  If they are all uppercase or all lowercase, then log(26).

If there is a capital letter in a place other than at the beginning, or a number or punctuation other than at the end, then log(95) per character.

Some corner cases remain to be specified.

Then, simply require a certain amount of entropy (thus defined) in users' passwords.  Users can choose whether to use a long password with little entropy per character or a short one with lots of entropy per character.

Perhaps forbid characters which cause the underlying data storage or UI to become confused (e.g., space).

Consecutive repeated characters count as 1+log of the repeat count.

[kxewbfgr] YB punctuation

The B and Y keys are far from the home position of fingers on a typical qwerty keyboard.  Put punctuation there, and move B and Y somewhere more convenient, probably where semicolon and slash are.

[llcqoetm] Torrenting web server

It seems conceptually simple for web server software (e.g., Apache) to provide a feature or plugin such that every static file also is made available as a torrent, perhaps trackerless, or a tracker also plugged into the server.

Friday, September 08, 2017

[ornqoevi] Genetically rebellious teenagers

Parents and greater society indoctrinate their kids, but during the rebellious teenager phase, they reject much of that indoctrination.  Hypothesize that that phase exists because of evolution: the indoctrination, despite well meaning, is actually so often harmful to the species that evolution preferred those who had strong genetic predisposition to cast it off when entering adulthood.

What terrible things were parents attempting to indoctrinate their children over the course of human evolution that induced such a strong natural selection for rebellious teenagers?  Is it still happening now?

The most obvious thing you are taught to do as a child, but should not do as an adult, is blindly and mindlessly obey.

[nflofxpg] Liquid NaK

Was the liquidness of sodium-potassium alloy discovered or predicted first?  Either way it must have been quite surprising and perhaps mysterious to combine two solids to make a liquid.

[tczxzgeg] 4-chord piano pedagogy

Create piano pedagogy based around the I-V-vi-IV chord progression.  Learn it in many keys and arpeggiations.  Lots of sophistication and variations eventually possible.  Guitar also possible.

[tgrwodlv] T/V from God

When you speak to God, perhaps in prayer or curse, you use tu and not Usted (in Spanish, similarly in other languages which distinguish between informal and formal you) because your relationship with God is supposed to be intimate, like close family.

Which form should be used when God speaks to you, for example in fiction?

[dwxxqhdw] Logan Shane

If the movie Logan had ended like Shane, as a good western should, with a mortally wounded Logan riding off into the sunset to an unknown fate, then subsequent movies could elegantly confirm his death by showing an adamantium skeleton by the roadside.  Or, if profit desires a subsequent movie, he simply rides back: nope I didn't die.

(X-Men Origins Wolverine apparently already did a reference to Shane.)

Instead, with him getting buried in the movie, it sets up a super corny return when profit desires it: zombie Logan claws out of the ground.

[chahihkh] On earth orbit

Construct an evacuated tube over a great circle around the Earth.  Have a vehicle traveling so fast within it that it experiences zero gravity: it is orbiting the earth at the surface.

This represents an engineering challenge so massive it will probably never be built.  Probably a political challenge too as the tube goes through many countries.  Motivation was to provide an easy way to provide long experiences of zero g for amusement (or perhaps science).

Does it have to be at the equator?  How strong are Coriolis forces if not at the equator?  If not at the equator, what about the oblateness of the earth?

Doing it around smaller astronomical bodies might be more feasible, though we have to get to them first, in which case, why not just experience zero g in space getting to them?

Previously, black holes in low orbit.

[vrgvwska] Usefulness of unattractiveness

If you are unattractive and someone behaves positively toward you, then you know they are in a good mental state (have high levels of self-qi).

If you are attractive, you gain no such useful information about the other person by their positive behavior toward you.  (You might gain information in negative behavior.)

Accurately gauging (even defining) what is genuine "positive behavior" is challenging.  Attractiveness is also in the eye of the beholder.

[kxybxqub] Macbeth on steroids

Game of Thrones / Song of Ice and Fire feels like a greatly expanded and updated version of Shakespeare's Macbeth.  Perhaps not too surprising since both authors used the history of Scotland as source material.

It is an interesting way to create a derivative work.  Does it inspire others?

If copyright lasted as long as Disney wants it to -- forever -- and as wide as as wide as the Marvin Gaye estate wants it to, Game of Thrones would have never been made because the threat of copyright infringement lawsuits.

[dmwmdsgh] 4D Klein bottle

In four dimensions a Klein bottle can exist without the ugly puncture that is required in 3D.  Describe (give a explicit mathematical description) of an elegant, probably symmetric, embedding of a Klein bottle in 4D.

Does this help understand 4D better?

[bexormhc] Rocks fall from the sky

The adventuring party is aware of the prophecy that at the end, rocks will fall and everyone will die.  Accordingly, they take care to avoid cave-ins while exploring underground and rock slides while near mountains.

Little did they know the prophesied rocks would fall directly from the sky: asteroid impact.

[dkrhtugg] Punishment and trauma recovery

A victim suffers trauma as a result of criminal wrongdoing by a perpetrator, who is apprehended and punished.  Does the severity of the punishment that the justice system metes to the perpetrator affect the victim's long-term recovery rate from the trauma?

Of course, severe punishment induces the temporary elation of Schadenfreude.

Friday, September 01, 2017

[aivneynr] Turning to the Dark Side in a week

Palpatine: We're going to turn Anakin Skywalker evil.  It'll take a decade and machinations spanning an entire galaxy.

Philip Zimbardo: I can do it in a week.

Write new prequels of Anakin's fall grounded in real psychology.

[qhlkaarn] High density around transit stations

In some small neighborhoods around transit hubs, consider modifying zoning to permit extremely high density, inspired by Kowloon Walled City.

This maximizes the usage of transit.  Surely this has been tried, though not to KWC levels of density.

Politically, NIMBY of course.

[mhkqqzwt] Upside-down pyramid numbers

A very fast growing integer sequence: 10, 10^100, 10^100^1000, 10^100^1000^10000,...

It is faster growing, and fatter at the top, than a plain tower 10^10^10^...

NB: exponentiation is evaluated right to left.

[itduickj] Fairy chess problem contest

Is orthodox chess the chess variant which permits the widest range of interesting chess problems?  (Subjective are "range" and "interesting".)  Run some contests in fairy chess to find out.


[fzayrazu] Self play contest

Compose a beautiful chess game from a given starting position.


[ajcstplo] Chess problem exhibit

Create a museum exhibit of chess problems.  This should be fairly easy as there already exist many collections of beautiful chess problems.  Some curation challenges still exist of choosing which ones, and organizing them into a physical space: perhaps by theme, perhaps in order of difficulty?

Large board diagrams so the problems can be seen from anywhere in the room, many physical boards available so people can try solving them, FEN available encoded as a QR code so people can examine them on their mobile devices.

More ambitiously, art can accompany a board diagram which illustrates the theme of a problem.

Thursday, August 31, 2017

[pxbmjtaa] Stress or self-qi

We will consider, over many posts, a model with only a single variable which we hypothesize can explain a great deal of human behavior.

We currently lack a good name for the variable, so we borrow terms from several from other fields, knowing that it does not quite match each term's definition in other fields (so sadly likely inducing confusion at some point).

One term is stress or stress level, borrowing the idea of psychological stress.

Another term, with the scale oriented in the opposite direction, is self-qi, borrowing the term qi from Eastern medicine.  More stress is equivalent to less self-qi.

Tuesday, August 29, 2017

[kumjhbfa] Large type keyboard

Draw letters on keyboard keys as large as possible.  Is there any good reason not to do so?  Maybe to save paint.

Obviously, large type is useful for people with poor vision, or in poor lighting conditions.  It is also more robust to paint becoming scratched off and letters becoming difficult to read.

Unrelatedly, possibly useful for learners of a language is to have both the upper and lower case versions of a letter on the keycap (and also alternate letterforms e.g., two- and one-storey a and ɑ).

[cauwyegu] Who vets third-party Javascript?

A website relies on Javascript provided by a third party.  Who evaluates that code to check that it is secure and functions properly?

Ideally the website operator does, but they actually cannot see what code the third party provides to the user's browser at the moment the client visits the site.

In principle, the user can and should examine the code before running it, though this seems difficult and annoying.

The website could refer to the third-party code not by URL but by content hash, thereby suggesting to the user that they have examined at least that version of the third-party code.  This encourages the development of robust content distribution networks based on content hash.

Considerably more sophisticatedly, the website could refer to the third-party code by a formal specification of what the third-party code is supposed to do.  The third party provides some code and the user's computer automatically verifies that the code obeys the specification.

[wppxzqmr] Musical key dice

Create a d12 die marked with the 12 notes of the chromatic scale.  The application is to randomly pick what key to play in.  For major keys, F-sharp and G-flat are both common names for the uncommon key.

This could easily also be done with a standard d12 die: just count up the scale the given number of half steps from some standardized start note, probably C.

[ucdemxih] Solving then solving elegantly

Create a puzzle which first invites the player to solve it, then invites the player to tweak their solution to make it more pretty or elegant.

Helpful is a way of recording and replaying a solution.

[frtsjule] Long lived patches

Create a source-based software distribution ecosystem in which optional patches are also distributed like the software.  Patches have maintainers like the software, and versions and dependencies.

Conflicting patches present a challenge.

[rfncsbuj] Astronomy and Mathematics in the wizarding war

It would have been interesting if the Astronomy and Arithmancy professors at Hogwarts remained neutral during the wizarding war.  The powers and forces of the heavens, and those of the abstract realm in which mathematics operates care not about the trivial concerns of humans.

Monday, August 28, 2017

[lsvbcsga] Portrait movie

With so many people viewing entertainment on phones and tablets, directors may soon starting filming movies and shows in portrait format.  (Many mobile games are already in portrait.)  Filming in portrait will require new thinking in cinematography.

[qllbwysh] Truncating or extending to a sphere

Given a regular polyhedron and inscribed sphere (insphere), truncate its vertices creating new faces that are tangent to the original inscribed sphere.  This process can be done on any polyhedron, and the successively truncated polyhedron approaches a sphere.  The new faces do not need to be constructed where old vertices were: the grinding stone could be applied anywhere, grinding to tangency to the insphere.

Dually, consider a starting polyhedron and sphere it is inscribed within (exsphere).  Above a face construct a vertex on the exphere then add edges joining the new vertex to the vertices of the face it is above.  These new faces will typically be triangular.  The successively truncated polyhedron also again approaches the sphere.  There is freedom of where above each face to construct the new vertices (perhaps one of the many triangle centers).  Sometimes edges of the starting polyhedron disappear as adjacent faces are coincident.  I suspect this happens when a cube is grown into a rhombic dodecahedron.

[xoylkfsz] All of society as a crowded theater

A person speaks inflammatory speech.  How society responds -- perhaps incited to commit acts of violence -- depends on the state of society.  Define a model which can predict, based on measurements of a society, how society will respond to inflammatory speech.

It is illegal to falsely shout "Fire!" in a crowded theater because a nervous audience might stampede for the doors, causing death and dismemberment.  If society is sufficiently on edge like that, we could consider it similar to a crowded theater and restrictions on the freedom of speech could be justified consistently.

However, if society is really on edge like that to be justified in punishing speech so aggressively, then society has significantly bigger problems than just the speaker.  The speaker, and the subsequent actions incited, reveal something terribly wrong with society: perhaps systematic oppression.

[nwkomoys] Fighting the enemy with apathy

Hate directed at the enemy -- acts of aggression or defiance -- strengthens them by inducing and reinforcing their identities of victimhood.  Conversely, love would weaken them.  However, if you are not capable of loving the enemy, perhaps because your hate toward them is too entrenched in your psyche, then consider instead aiming for apathy toward them as the next best weapon to weaken, or at least not strengthen, them.

[iwntlvjv] War of attrition

The stakes getting larger is a common trope to increase dramatic tension.  Tell a story of the stakes becoming smaller, while still keeping the audience interested.  This might be difficult.

Previously, Game of Thrones as a parable of climate change.  Perhaps the characters fight over less and less habitable land.

[dzoyuqpm] Dumb phone with tethering

A device which does not exist, but perhaps should: a basic phone, capable of phone calls and texts, also with the capability of tethering -- providing internet capability to another (more powerful) device.  The phone can become a wi-fi hotspot, or provide Bluetooth or USB tethering to a computer or tablet.  Thus, you use only the phone when you only need basic communication services, and augment it when you need something more sophisticated an powerful.

We are currently somewhat stymied by the many text-based communication protocols that users might want a basic phone to support; unfortunately, supporting all of them, including those which don't exist yet, seems to require the capabilities of a general-purpose computer.

[xlaxvsrh] Very cold planets

In the far future universe, the ambient temperature of the universe (cosmic background radiation) will have dropped enough that any normal matter left, e.g., planets, may exhibit weird quantum properties: perhaps planets with oceans of superfluid helium.

[snvpjcpd] Defeated civil war leaders

Many nations around the world fight civil wars.  Enumerate monuments honoring the losing side, perhaps leaders of the losing side.  These might be rare; the winning side likely wishes to eliminate positive sentiment toward the enemy.  Are there statues of Chiang Kai-shek in mainland China, statues of Tsars in Russia, statues of Kings or Emperors in France?

Inspired by statues of Confederate leaders coming down.  How unusual was it for the statues to have stood for so long?

Sunday, August 27, 2017

[gzagyvxt] Pinhole and inverse pinhole

Common is projecting the partial phases of solar eclipse through a pinhole camera.  In the moments before and after totality, shadows cast by objects in the tiny sliver of the sun are extremely sharp.  These are two manifestations of the same phenomenon, curiously both occurring during an eclipse, though the pinhole works all the time.

Friday, August 25, 2017

[gkymwnwl] Goblet of Fire mashup

Barty Crouch, Jr. does too good a job mimicking Mad-Eye Moody, too good a job at being a good Defence Against the Dark Arts professor.

This can easily be explained in real life by hypothesizing that in an early draft, it was the real Mad-Eye Moody the whole time, then in later drafts the plot required someone to have infiltrated Hogwarts, so the Polyjuice mimicry was added much later, but the original character was not modified much (because it was so good), even though it should have been: the plot would have been much stronger if there were more persistent and consistent hints that Moody was not who he said he was, and he was not fully committed to teaching students Defence Against Dark Arts.

Tell a better story of the DADA instructor being a double agent.

[svnuzzrd] Standard dice quiz

Given an isometric view of 3 faces of a cubical die, determine if the view could be the view of a standard die.

Toggle whether the orientation of the markings of asymmetric numbers (2,3,6) matter.  Is there a standard orientation?

Motivation is to recognize cheating dice.

Monday, August 21, 2017

[liczukhs] L1 sun shield

It is very convenient that the L1 Lagrange point exists between the sun and earth.  Put a bunch of stuff there to partially shield the earth from sunlight, decreasing the earth's temperature, either to combat short-term global warming or long-term increasing power of the sun.

L1 is not stable, so stuff there will require station keeping: maybe lasers.

[tjlnlazp] Tori eating tori

When you eat a donut or bagel, you are sending a torus through torus (alimentary canal).

[ckcwathr] Out-biking a sprinter

How difficult is it to bike faster than a world-class sprinter, i.e., 400 meters in less than 45 seconds?  Probably not so easy for regular people.

[mkxmvdmc] Square pieces with large bounding box

Cut a square into 4 rectangles by 2 orthogonal cuts.  Rearrange the rectangles into a new shape with all 4 meeting at a vertex.  Consider the bounding box around the new shape.  Over all cuts and rearrangements, which has the largest bounding box?

Repeat with a cube.  Repeat with only the subset of arrangements possible for a 2x2 mirror cube.

[suzmcjzw] Storing data in library borrowing

Records about library book borrowing (and video rentals) seem to be enjoy an extra level of legal privacy protections.  Use this to encode and store private information.

[bbgqvfum] Sum of the reciprocals of the midpoints of twin primes

The even numbers between 2 odd twin primes are often rather smooth.  This suggests computing exact partial sums of their reciprocals because the denominators may have many factors in common.

The infinite sum is (almost certainly) a finite, probably irrational, number, similar to Brun's constant.

[flulmebe] Retirement to Chess960

There seem to be very few chess players declaring they are done with orthodox chess and retiring to only play Chess960 because they are tired of memorizing openings or losing straight out of the opening.  This seems contrary to what Fischer (implicitly) predicted, motivating him to invent FRC.

Perhaps among all the efforts needed to get or stay strong at chess (at any level), opening preparation remains a relatively minor proportion of the work.

[ndpdarla] Leech lattice

Generate the 196560 24-dimensional points in in the Leech lattice closest to the origin.

What are the dimensions of a rectangular parallelopiped Leech lattice unit cell which can be tiled to generate the whole lattice?

These should be easy.

Saturday, August 19, 2017

[rcmtzzqf] Yoda is your father

Luke: No, that's not true, that's impossible!

(Allusion to racism.)

[icqzdzoh] Science during the Big Rip

Assume the Big Rip scenario will occur as the ultimate fate of the universe.  Although the universe currently conceals its workings at its tiniest subatomic levels (what are quarks made of? Electrons?), all will be revealed (perhaps strings, but what are strings made of?) in the final moments of the Big Rip as expanding space itself functions like the ultimate atom smasher, tearing even the sturdiest of particles apart.

Unfortunately, it's hard to imagine life surviving until that point, and even if it does, after learning the secrets of the universe, they won't get to enjoy that knowledge for long.