Thursday, November 30, 2017

[lxysjiii] Automatically rotating screen

Create a display which can play through a slideshow with some pictures in portrait orientation and others in landscape.  The motorized display automatically turns depending on the orientation of the picture.  Best is if each picture remains upright during the turn: more comes into view as the display turns to the correct orientation.  This requires the software to rotate the image in sync (in the opposite direction) with the physical rotation.

[yerocdsx] Three layers thick

A 2D display can depict something in 3D if the 3D object is at most 3 discrete layers thick.  Easiest is some voxel object 3 layers thick.  The three layers are assigned colors: red green blue.  The presence or absence of a voxel on in a color layer causes different colors to occur.

Similarly, 3D is enough to depict something in 4D at most 3 layers thick in the 4th dimension.

Possibly useful for the point growth fractal.  Just a little bit of 3D might be enough for points to slide past each other.

[kujuygyv] A snapshot of Starbucks prices

At the Seattle-Tacoma airport, where prices are inflated:

  • Frappuccino venti 5.95
  • Flavor shot 0.65
  • Substitute soymilk 0.75
  • Espresso shot 0.95

With sales tax, it is possible to have a 9 dollar coffee.  Inspired by the song "All about the Green" from "The Wedding Singer" musical.

[kylntajw] Summing partial wins for pitchers

Given a won baseball game, divide the win among all the pitchers on the winning side in proportion to the number of innings (or portion of an inning) pitched.  This allows relief pitchers to be compared with starting pitchers.  Who has the largest sum of partial wins?

Of course this is a little unfair because a pitcher might have done a terrible job but the team still won.

Denominator might not be 27 because of extra-inning games.

[zsfdmdyl] VR code history

Create a virtual reality interface to a revision control system. Browse history, including branches and merges, by traveling through branching and merging corridors. Code, or diffs, are plastered on the walls of the corridors.

[ipnxgezr] Coloring a dynamic map

Given a graph, let the nodes wander around the plane, maintaining connectivity with straight edges between the nodes.  Color the polygonal regions bounded by edges by standard map coloring: no two adjacent regions share the same color.  Maintain the map-coloring property as the nodes move and the regions change.  Regions will probably have to change color, maybe a gradual fade.  Minimize the amount of regions changing color: regions typically stay the same color as they change shape.

[igjeepkh] Good Samaritan Laws versus prosecutorial misconduct

Good Samaritan Laws prevent a prosecutor from prosecuting someone for some action protected by the Good Samaritan Law.  However, if a prosecutor wants to prosecute someone, a Good Samaritan Law isn't going to stop them: the prosecutor can easily find something else -- not covered by the Good Samaritan Law -- to charge them with: this is the thesis of "Three Felonies a Day".

Therefore, even if you think you will be protected by a Good Samaritan Law in aiding someone about to become harmed, you actually aren't, because prosecutors can and do abuse their power.  It is better to let the harm happen to the person and remain uninvolved rather than attract the attention of a prosecutor who will put effort into digging up dirt on you to circumvent the Good Samaritan Law.

The standard scenario, the scenario Good Samaritan Laws were intended for, is someone is overdosing on an illegal drug (possibly illegal because underage alcohol).  The person in a position to help, the potential Good Samaritan, who can connect the overdosing person to medical care, has had some involvement in providing the illegal drug in the first place.  (Perhaps this person is also black, recalling the racial bias in the justice system.)  Following the logic above, it is better not to call for medical help because of the legitimate fear of prosecutorial misconduct.  The Good Samaritan Law has failed its intended purpose.

Can this problem be solved?  The problem is deep, because a prosecutor is a political position, often elected.  If a (say) racist populace wants a prosecutor to abuse their power as described above, then the prosecutor is pretty much obligated to do so, or else they will be politically replaced by someone who will.

[oyfiqzue] Zipf Huffman

Define a standardized set of Huffman-coding trees for alphabets with a distribution following Zipf's law.  This should be easy.  The first character in the alphabet has the highest frequency, and so forth.  To use the tree, the user needs to specify a permutation to put the letters in order ranked by frequency.  Probably parameterize the Huffman tree by the size of the alphabet.

[mtyqxgmm] Renormalization and some string theory

According to one description, renormalization is necessary because we don't have a theory of quantum gravity yet.  Pick one string theory (we don't know if it's the correct one) and demonstrate how renormalization is no longer necessary assuming it is true.

[anqbyekg] To Pluto

In an alternate universe, the New Horizons probe flies by Pluto, sees something, and suddenly all of humanity's efforts to send humans to Mars become completely abandoned and shifted to Pluto.  What did New Horizons see?

Inspired by a Pluto Halloween costume.

[lbeqvjms] Many elements

The protagonists of The Fifth Element enter the ancient temple and are greeted with many pedestals, not just 4 or 5.  There is much cursing.  Leeloo Multipass dutifully provides boron, the 5th element, fulfilling her purpose.

[dpwdorza] What if the twin prime conjecture is false?

Maybe the reason the twin prime conjecture has eluded proof is because it is false.  It does not seem unreasonable that the primes eventually thin out so much that locally high density concentrations of primes stop occurring.  (This would contradict the Hardy-Littlewood conjecture in "Partitio Numerorum III".)

If it is false, how would we prove it to be false?  Could we find the last twin prime?

Some wider prime constellations are conjectured like twin primes to have infinite instances, but not a single example is known.

Some relevant OEIS entries: A083409, A008407, A020497.

[ohqromsj] Modern ship in a bottle

Use modern technology to create more amazing sculptures in the style of ship in a bottle. Probably laparoscopy. Maybe magnetic levitation.

Consider building large metal structures within the bottle by doing metalworking within the bottle.

[okzidagr] Mesh wifi home

Use mesh networking among a bunch of overlapping residential wireless networks to reach your home router, then use your uplink (your ISP) to reach the broader internet. You are not consuming your neighbors' external bandwidth, and we assume your neighbors' internal bandwidth has capacity to spare.

This creates the effect of greatly extending the range your home WiFi, to a neighborhood or even a city. Latency will probably be pretty bad.

[ocbdzgay] Weighted Lego pieces

Create LEGO-compatible bricks of a significantly higher density than normal bricks. Inspired by wanting to create a bottom-heavy stable pieces for a weighted chess set.

Monday, November 27, 2017

[iipefngs] Choice-maximizing maze

Start with a tessellation of rooms and make some doors between them, forming a maze.  Minimize the number of rooms that have only 2 doors (it is trivial what to do in those rooms: go out the door you didn't come in from) while keeping it an interesting maze (this is subjective): probably things like all rooms connected, no loops.  We could also maximize rooms with 3 or more doors.

Best is probably to start with the regular hexagon tessellation.

[fsxvlsyu] Making a man

An easy way to create a Man piece for a physical fairy chess set is to take a king and grind away the cross and crown.

[zxlrmbjs] Messy capital gains

Purchase a good X as part of a bundle including other goods and services.  Sell good X later, not bundled.  How much capital gains was realized on X (for the purposes of taxation)?

Vaguely similar problems to problems for income tax if wages are paid as a bundle of monetary compensation and exchanged (in both directions) non-monetary goods and services.

Are their clean solutions?  If not, either unfair taxation or loopholes will abound.

[wrobgsoz] Lego rebar

Tall stacks of Lego bricks are unstable.  This can be mitigated by adding compression: maybe a spring threaded through the center of the bricks pulling the top and bottom toward each other.

This is similar to reinforced concrete.

[dkvpopqm] Curving fruit

Throw a roughly baseball-sized fruit or vegetable with techniques used in baseball for breaking-ball pitches, e.g., curveball.  Fruits and vegetables, e.g., sky potatoes or potatoes, are more irregularly shaped than a baseball so might curve more dramatically.

[wimcnqzf] Imminent power loss signal over power lines

Create a data protocol over power lines for signaling that there will imminently be a planned power outage.  Computers tuned to that signal through their power supplies can automatically initiate orderly shutdown procedures.  Or they can deliberately ignore the signal if there is too great a chance for a Denial-of-Service attack through this protocol.  Because this protocol communicates over power, the computer does not need to have other network capabilities.  It does seem that anyone can induce signal variation in the power lines can credibly shutdown power as well.

Less radically, create an internet-based protocol that a computer can subscribe to for power shutdown updates.  It should be hierarchical, covering larger and larger regions which might have a planned power outage.

Inspired by the difficulty of manually shutting down many computers prior to a planned power outage.

[ndkzkyas] Game of bad moves

Consider a human versus computer chess game.  Human tries to win.  Computer tries to induce as many bad moves as possible.  Or maybe, the human tries to avoid as many bad moves as possible, to keep the game zero-sum.

Normally, when a strong computer program plays a human, after the human makes just one bad move, it's all over and the computer will curb-stomp its way to victory from there.  Now, even after the computer gains a winning advantage, the computer may try to deliberately give up the advantage in hopes of inducing more bad moves by the human.

This requires knowing the kinds of positions humans tend to make bad moves.

Objectively a "bad move" could be defined as giving up half a game point or more.  Should the definition be expanded to more subjective bad moves?  There is also the practical difficulty of determining whether half a point has been lost.

[twdujyec] Potato of the sky

Inspired by French, call apples "potatoes of the sky".

Other possibilities: sky potatoes, heaven potatoes, potatoes of heaven, sky apples, apples of the sky, heaven apples, apples of heaven.

Riffing further: hell potatoes, potatoes of hell, hell apples, apples of hell.  Potatoes of the earth, earth potatoes.

Create a meaning for the phrase "apple of the earth" that is not "potato", and is so opposite from "potato" that it dangerous to assume it means potato. This will cause havoc when the phrase is translated to or from French.

How do you say "fried apples" in French in a context where "pommes frites" will be assumed to mean "French fries"?  Probably something like "apples not apples of the earth which have been fried".  Though maybe "fried apples of the sky" is enough to disambiguate.

[dehgpihw] Sales tax included AR

Create an augmented reality app which rewrites prices adding sales tax.

Thursday, November 23, 2017

[ccyzhjzt] Words colliding on merged letters

What if two letters in English were written with the same symbol?  Which pairs of letters would result in little ambiguity -- only one of the letter possibilities forms a valid word?  Which result in a lot of ambiguity -- the ambiguous symbol being either letter both resulting in valid words?

We investigate this using the /usr/share/dict/american-english-huge word list from the wamerican-huge package version 7.1-1 in Ubuntu 14.04.  For each pair of letters we calculate a score based on the number and size of collisions that occur if both letters were replaced by the same symbol.

For a collision set of size N, we assess a quadratic penalty of N*(N-1)/2.  This choice of penalty formula was somewhat arbitrary. The largest set was of size 6, when D and S are merged to the same glyph: dodded dossed dosses sodded sossed sosses.  This contributed a penalty of 15.  The sum of penalties for all the collisions merging D and S was 9379.  We give the scores for all 325 pairs of letters below.

Merging D and S actually had the worst score.  Many verbs ending with E have a 3rd-person singular conjugation -ES and a past tense conjugation ending -ED.

We took some care with capital letters.  The assumption was, when merging two letters, the lowercase letters would be merged in to one glyph, and the corresponding uppercase letters would be merged into a different single glyph, different from the merged lowercase glyph.

Future work:

Incorporate word frequencies into the score.  Google Books n-grams (with n=1).

Design a keyboard layout in which pairs of letters which score poorly (so yielding errors not catchable by a spell checker) are far apart.  Having D and S next to each other is terrible on the QWERTY keyboard layout.  Having I and O adjacent is also very bad if word frequency is considered: if/of in/on.

Considering pairs of letters gives us the best way to reduce the alphabet from 26 to 25 letters.  This could be taken further.  What is the best way to reduce the alphabet to 24 letters while minimizing the ambiguity created?  Maybe merge 2 pairs, or maybe merge 3 letters into 1.

Source code in Perl, and output listing all the word collisions for all letter pairs.

Scores for every pair:

jq=3 qu=3 qz=3 qy=4 aq=6 iq=6 qx=6 ju=7 qv=7 eq=8 hq=8 oq=9 fq=10 qw=10 bq=13 lq=13 nq=14 pq=15 qr=16 jx=19 uz=19 mq=20 ux=20 qt=21 aj=29 dq=30 qs=30 cq=31 ej=33 jo=34 fx=37 ix=39 uv=42 hx=43 gq=44 iz=45 oz=48 ox=50 az=54 ex=54 ij=54 kq=60 ov=61 hu=64 iv=64 xz=65 av=67 fu=68 ku=73 ax=76 ez=77 jz=81 bu=87 fi=90 ev=94 xy=96 bx=99 vx=101 yz=103 kx=109 wx=110 bi=111 mu=119 cu=120 gu=126 du=127 jv=131 jk=134 vy=134 fo=137 gx=142 hi=142 mx=143 cx=147 im=150 hz=151 wz=151 ik=152 ip=155 pu=155 dx=157 fz=161 lx=165 vz=165 jy=166 px=169 ko=178 ci=179 gi=180 kz=184 iw=187 ef=190 bo=194 fy=195 af=202 cz=211 go=211 jw=214 aw=216 sx=223 rx=231 tx=234 bz=239 hv=239 am=244 uy=244 ab=245 di=246 tu=247 jn=257 uw=258 ky=260 ak=262 ag=263 mo=265 ow=267 fj=270 gz=271 cj=274 do=276 cy=279 lu=283 ew=288 co=297 nu=297 mz=298 nx=298 ho=299 ah=301 pz=304 hj=309 rz=309 op=315 su=319 nz=321 no=325 be=328 js=328 jm=337 dj=338 fk=339 ap=343 gj=353 lz=353 jp=362 ad=364 em=364 fv=366 it=367 jl=374 hy=376 vw=379 jr=381 jt=383 ce=392 by=395 gy=398 kv=399 wy=404 bj=405 gv=406 my=413 ly=414 in=417 ot=427 py=427 dz=428 cv=441 eh=456 bk=468 ny=469 ru=470 bv=474 ep=479 kw=480 ir=510 ek=512 at=524 tz=529 os=554 lo=563 is=567 an=568 nv=569 gh=574 il=576 dv=587 dy=593 fh=593 oy=603 eg=604 hk=622 rv=626 mv=627 ty=630 pv=633 ry=637 ay=639 sv=642 al=657 fw=658 lv=668 or=678 hn=690 gw=703 tv=709 sz=711 fn=730 nw=742 en=743 gk=745 dw=765 de=775 ar=782 ac=784 kr=785 dh=788 mw=800 km=816 cw=844 fg=858 bh=874 cf=882 sw=887 fr=895 kp=896 kn=902 hw=903 df=904 rw=904 ks=912 bw=921 lw=927 fm=928 bn=953 ch=955 dk=965 kl=994 gm=1041 gr=1055 hm=1067 pw=1074 as=1078 gl=1083 er=1087 el=1091 et=1099 fl=1101 fs=1112 cl=1128 hr=1132 hp=1146 iy=1155 ck=1161 cg=1167 cm=1197 fp=1197 cd=1200 gn=1219 hl=1230 cr=1231 tw=1244 bc=1292 bs=1313 gp=1316 gs=1316 bl=1321 ft=1324 hs=1332 bf=1342 kt=1378 mn=1387 pr=1402 ms=1428 cn=1478 dp=1505 bd=1516 ht=1523 cp=1542 mr=1550 bg=1576 br=1578 bm=1657 dg=1660 np=1660 lp=1679 ps=1726 dm=1732 lm=1795 bt=1809 cs=1838 bp=1860 eu=1870 ct=1874 gt=1926 dl=1944 es=2024 dn=2056 mp=2182 ns=2195 ls=2246 ey=2276 ou=2326 ln=2412 sy=2524 nt=2562 rt=2582 pt=2585 iu=2639 lt=2657 dt=2755 nr=2827 io=2875 au=3006 st=3566 lr=3713 mt=3765 eo=4036 ai=4498 ei=4616 rs=4661 ao=5230 ae=5982 dr=7439 ds=9379

[zwgxqhmi] Humans converting mass to energy

Assuming 2000 calories a day and a lifespan of 70 years, an average human converts 2.4 milligrams of matter total into energy by Einstein's famous equation E=mc^2.

The 7 billion people on Earth convert 650 grams per day, 240 kilograms per year.

Molecules get heavier and lighter as chemical bonds get formed and broken.

[ljboaidm] Quadrant Cartesian notation

Consider a chess notation which describes a location of a square on the chessboard first by (somehow) specifying a quadrant, then specifying a location within the quadrant with coordinates using the corner of the containing quadrant as the origin.

The quadrants could be named White's Kingside, White's Queenside, Black's Kingside, Black's Queenside.

Then, four corner squares are named wka1, wqa1, bka1, bqa1.  All corner squares have "a1" as a suffix.

There is a little bit of awkwardness where b stands both for Black and the B files.

One can then say things like, it is a bad idea to put a knight on a1; it can easily get trapped there.  Or, talk about endgame technique involving a passed pawn on the a file.

This notation captures the symmetry of the chess board, at the expenses of being less compact.  But more verbosity is useful for pedagogy.

One could introduce an abbreviation in which if a location is on the same side of the board as the player to move, then the color of the quadrant can be omitted.  A symmetric c pawn opening (1. c4 c5 algebraically) might then be notated 1. qc4 qc4.  This resembles the symmetry of descriptive notation 1. P-QB4 P-QB4.

Add an additional symbol o meaning "opponent's color" or "opponent's half of the board".  A classic back rank checkmate on the king file would be Rokd1# ("Rook to opponent's kingside d1, checkmate").

Saying "advance your pawn to the opponent's 1st rank" is just as straightforward as "to your 8th rank" (and certainly less wordy than "to the 8th rank for white or to the 1st rank for black" strictly following algebraic notation).  Avoiding rank numbers outside the quadrant allows easily extending the notation to larger boards.  The "opponent's 1st rank" always means the promotion zone, whereas it might be the 8th 9th or 10th rank depending on the board size in algebraic notation.

[ezcyektu] Daily routine

  1. Wake up.
  2. Check if the world is destroyed.
  3. Resolve to do better next time.

[kmqlpaia] May merry Mary marry May

Kind of a palindrome, assuming the middle 3 words are pronounced the same as they are in American English.  (The final "May" is a person's name.)

Can the sentence be infinitely extended like buffulo?  (Of course, the adjective merry can be repeated for emphasis.)

[sfqwfdqo] Socialism versus negative population growth

In countries suffering from low or negative birth rate, it would seem that more socialism -- more support of parents who choose to have children -- would easily fix that problem.

Does it not work?  If not, why not?  There is some counterintuitive evidence that providing free education to daughters decreases birth rates (of the next generation).

Or, are efforts to increase socialism running into political resistance?

Does decreasing socialism decrease population growth for countries (actually, the one country, China) that want to do that?

[twveubtl] Freedom of panorama

Some countries, e.g. France and Italy, do not have freedom of panorama.  Is architecture noticeably different -- better -- in those countries, as architects are incentivized to create better works by the financial promise of the additional copyright royalty revenue stream from all photographs of their works?

I strongly suspect architecture is no different in countries without freedom of panorama.  Architects (and those who commission them) will create the works they create regardless of whether they control who photographs their buildings afterward.  I strongly suspect there is ample evidence that restricting freedom of panorama makes no difference in incentivizing creativity (the point of copyright), consequently, such laws should obviously be repealed.

Nevertheless, some countries have not repealed such laws.  Freedom of panorama can therefore serve as a canary, indicating to what extent a government is broken, unable to pass or repeal laws that benefit their country.

Belgium very recently (June 2016) granted freedom of panorama.

[jdjkvcsh] Immorting the immortal hydra

The hydra, a tiny organism, is believed to be immortal, assuming good living conditions.  Challenge: keep one alive for at least 5000 years, surpassing the oldest trees (of today).

This requires maintaining its environment to be conditions suitable for living, not losing track of it amongst its descendants (babies from buds probably need to be removed from its tank), and some way of periodically or continuously recording (probably photograph or video) the organism as proof that the organism at the end is the same as the organism which started.  Create machines to make these tasks easier.

I think currently the oldest confirmed hydra is a decade or two old.

Because a hydra periodically replaces every cell, it is a biological ship of Theseus.

It's of course hard to imagine a human institution surviving 5000 years able to continuously care for a collection of hydras seeking the longevity record.

Will the 5000-year-old hydra be older than the oldest human alive at that date?

[lutfjpnb] Not (power and network)

Consider a rechargeable battery-powered computing device which obeys a policy of never being simultaneously connected to power (charging the battery) and network.  The goal is security.  When connected to network, it is vulnerable to remote attacks, but the window for remote attacks lasts at most until the battery runs out, at which point, the device shuts off.

A powered-off device protects data in encrypted filesystems.  When powered on, the key is in memory.

General idea is, keep the device in a state that is useful for the legitimate user (or a remote attacker) for only the least time that is necessary (minimizing the window for attacks).

Saturday, November 18, 2017

[ikuukgir] Sierpinski number music box

Consider a Sierpinski number and its (minimal) covering set.  Assign a musical note to each member of the covering set.  For each Proth number with the Sierpinski number as the multiplier, calculate which numbers of the covering set divide the Proth number.  Sound the corresponding music notes.

For the Sierpinski number 78557, there are 7 pitches and they cyclically repeat with a period 36.

Previously, primes on a music box.

[xxcdzzbc] 3D keyboard

When learning to touch type on a typical flat keyboard, one needs to learn the location of keys in a flat 2D area.  When learning to touch type on a Kinesis keyboard with its keys arranged in a bowl, one needs to learn the location of keys and directions to push in 3D space.

Hypothesize that the latter (despite more dimensions) is easier, because tactile things arranged in 3D space is more natural.

Kinesis is a concave bowl.  Consider the opposite, keys on a convex dome.

Or, from a given rest position, fingers may move in multiple directions in 3D to push different keys.  Inspired by woodwind instruments.

[jnlsisth] 69 is an illegal number

Illegal numbers are most commonly associated with copyright, trade secrets, and sometimes national security, but the concept can also occur in the context of regulations around sexual harassment (e.g., Title IX Dear Colleague).

Inspired by someone choosing/needing to say "about 70" items in a container, even though the exact number was known.

[girapvjq] Qu'un sang impur abreuve nos sillons

Create art depicting or inspired by the vivid and disturbingly violent lyrics of La Marseillaise, the French national anthem: fertilize our fields with the blood of our impure enemies.  Perhaps invoke existing racial tensions in France between whites ("purity") and Arabs.

One radical possibility: somehow, collect some blood spilled in a relevant act of violence.  Grow some plants, using the blood as fertilizer.  Collect seeds of the grown plants.  Distribute the seeds as art.

Or, art could expose "they are coming to kill our children and rape our women, so any amount of preemptive violence against them is justified" as a standard propaganda tactic.

The performance of La Marseillaise in the opening ceremony of the 1992 Winter Olympics in Albertville, France is the most "metal" musical performance (of any song) I have ever seen: it juxtaposes the symbolic innocence of the young girl and the symbolism of peace in releasing a dove with the monstruously gruesome lyrics of the anthem, and does it on the largest stage possible (a world-wide audience).

I do wonder how long the above-linked YouTube video will stay up.  Someone will find an excuse to censor that which makes them uncomfortable.  Currently, the top comment is, "Gotta love a little kid singing a song about plowing your field with the blood of your enemies."

Perhaps its irony, its cognitive dissonance, was lost on practically everybody.  For most French and Francophiles, the words of the song no longer have their literal meaning; it simply is abstractly a song that represents their country: it might as well be instrumental.  For most others, they don't understand the language and were unaware of the violent lyrics being contrasted with the staging.

Albertville did inspire a movement in France to modify the lyrics.  It almost worked.  Or cynically, it -- the artistic staging at Albertville -- did work: inasmuch as the subsequent movement failed, it revealed France's true identity, bloodthirsty, racist, and unwilling to change that.

(Though such an identity is probably common in many countries.)

[asuwohry] Emotionally drained

"Emotionally drained" is a synonym for low self-qi or high stress level.

[kmlfpspr] Sierpinski covering set bounds

Pretend there exists a theorem along the lines of, if S is a Sierpinski number, then it has a covering set whose maximum value is bounded by some function B(S).  Then, it would often be easy to disprove a certain number k from being a candidate Sierpinski number: find a composite k*2^n+1 whose smallest prime factor is larger than B(k).

No such theorem exists to my knowledge.

[twbhlwpx] Gasoline tax and illiquid labor

With a high gasoline (or carbon) tax, people prefer to commute a lesser distance to work.  This induces geographic monopoly (actually monopsony) effects in the labor market; an employee can't as easily quit and work somewhere else without incurring higher commuting costs or high moving costs.  Previously similar.

In practice, many employers within the same industry might set up shop near each other, perhaps in a dense urban city where there are many consumers, so this will not be much of a problem in those industries.  Where (both geographically and across industries) might we see labor problems induced by a gasoline tax?

[hihdgmdb] High precision science

What science has experiments whose results can be measured to high precision, agreeing with theory to high precision?  Consider concentrating on those areas early in science education, inspiring learning the mathematics to compute the theoretical result, because there is a tangible physical experiment to compare the computed answer with.

How early is too early to be teaching kids quantum field theory and quantum electrodynamics?

Unfortunately, experiments which produce replicable high-precision results are often expensive and difficult.

How early is too early to be giving kids particle accelerators to experiment with?

[sjqoeljl] Best shitposter of all time

Imma let you finish, but Martin Luther was the best shitposter of all time.  Of all time!

Inspired of course by the 95 Theses and the subsequent events over the next 500 years.

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.

Previously, higher dimensional chess.

[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 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.  Using a pentatonic scale avoids dissonance.

Speed up time logarithmically to compensate for the primes thinning out.

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.