Municipal regulations imposing a maximum height limit of buildings are silly. The cost of buildings increase more than linearly with height, diseconomies of scale, so economics will naturally induce a stringent height limit.
Similarly, operating hours for a business: decreased labor supply late at night and decreased consumer demand will naturally induce economic limits on when a business chooses to be open.
The real danger of vaccines is that they cause climate change.
Graphs of correlation. Plausible testable mechanism of causation.
Also, stem cells cause cancer.
Musical instruments, no matter how limited, have been made to sound good by composers and musicians thoughout the ages. Apply this idea to the electronic synthesizer (inspired by tone generators of 1980s computers). A synthesizer can play any arbitrary waveform, but that is too many degrees of freedom. Simplify and limit it.
We propose limiting it to sums of piecewise sine waves amplitude modulated by exponential decay (or growth). Macros can provide timbres of stacking fundamental frequencies and overtones.
Perhaps add the ability for the frequency to change exponentially, allowing smooth glissandi.
Drum hits, cymbals are not possible, or at least not easy.
Initially, it might seem one needs to think hard for examples of computer hacking leading to someone's death: one imagines a bad guy hacking into a life support system in a hospital or overriding the computer of a plane or self-driving car. The Blaster worm may have aggravated the severity of the 2003 Northeast blackout, which resulted in at least 6 deaths.
However, numerous examples abound in plain sight if one removes one's perception filter. Military intelligence regularly uses network intrusion to discover targets to kill. Law enforcement hacks in via wiretapping and subpoena (rubber-hose cryptanalysis) to acquire evidence leading to death penalty convictions. These deaths could have been avoided if the victims used, or could use, better network security. Do these entities perpetrating these killings deserve to be classed separately from the typical terrorist bogeymen we imagine hacking into systems and killing?
Another category is suicides induced by actions like doxxing, revenge porn, and other internet shaming.
(Inspired by a conversation elsewhere.)
Johann Sebastian Bach, Partida #2 in D minor for solo violin, BWV 1004, movement 5 "Ciaccona". Album "Hilary Hahn plays Bach".
Time point, measure number, description of major musical variations:
00:00 m1 theme "stretchy"
00:33 m9 dotted rhythm theme
01:07 m17 dotted rhythm higher register
01:39 m25 descending melody in 8ths and 16ths
02:10 m33 quieter, back to 8ths
02:27 m37 16ths
03:16 m49 quieter descending scales in 16ths
03:49 m57 triumphant theme in separated 8ths
04:01 m61 triumphant in 16ths
04:15 m65 triumphant elaborated in descending 32nds
04:29 m69 ascending 32nds
04:54 m77 slower lyrical slurred ascending arpeggios in 16ths
05:13 m81 descending arpeggios, diminished
05:47 m89 (arpeggio) 16ths, octaves
06:36 m101 top note repeated on arpeggios
08:04 m121 descending sextuplets (illusion)
08:20 m125 stately, m126 original theme
09:00 (D major) m133 reflective, sotto voce
09:35 m141 separated 8ths
10:05 m149 16ths
10:19 m153 descending arpeggios and scales
10:49 m161 three high accented notes and descending
11:05 m165 three mid accented notes
11:19 m169 low four accented notes
11:51 m177 slow legato
12:06 m181 stately walking theme
12:25 m185 original theme, loud
12:42 m189 again, higher
12:58 m193 again, ascending
13:14 m197 again, descending
13:29 m201 (arpeggio) rich doubled notes
14:02 m209 (D minor) quiet slower
14:42 m217 16th notes wandering, ascending arpeggios
15:00 m221 more sure wandering, descending arpeggio
15:18 m225 ascending call with low response
15:38 m229 descending and bouncing back to a constant high note
16:29 m241 triplet ascending arpeggios
16:42 m245 descending
16:59 m249 original theme
17:16 m253 final cadence in quarter notes
17:38 m257 final note dotted half
The length of the space diagonal of a 4 dimensional unit hypercube is an integer, namely 2. What interesting applications does this provide?
update, answer: 24-cell honeycomb and D4 lattice.
Most model rockets don't leave the atmosphere, so, in order to save weight, it seems it would make sense to carry only fuel, not oxidizer.
Prove that the general number field sieve is asymptotically the fastest non-quantum algorithm for factoring a general integer, or create a faster algorithm.
Prove that GNFS is the fastest algorithm for solving the discrete logarithm problem on the group of integers modulo a prime, or create a faster algorithm.
Prove that factoring the modulus is the fastest way to solve the RSA problem, or create a faster algorithm.
Prove that the quadratic gap in computational effort between the attacker and defender as seen in Merkle puzzles is the largest gap possible, or create a cryptosystem with a larger gap. (Appears to be solved in Barak, et al. "Merkle Puzzles are Optimal")
Each of these questions is critical for modern asymmetric key cryptography. There ought to be giant prizes similar to the Clay Millennium prizes.
Similar questions could be asked about elliptic curve cryptography, but I am not versed enough to be asking them.
A collection of chess piece symbols suitable for printing, cutting, pasting, and creating a chess set of counters (similar in style to shogi, rather than traditional carved figurine pieces usually used for OTB chess). The circle is approximately the size of a nickel (5-cent) coin. Three pennies and a nickel hot glued together.
They seem to print out the correct size from Linux but too large from Mac OS X.
Piece design based on SVG files from Xboard 4.7.3, so carries its GNU GPL 3.0 license.
Photograph below also demonstrates pawns can be promoted to queens by flipping them over. Underpromotion handled the traditional way (some captured piece).
Write a fictional story in which a government has done all it can to try to eliminate racism (etc.) from employment, public and private services, and now has moved on to try to eliminate racism in courtship, on the political assumption that this is the true root of the problem. Perhaps draconian measures to punish those who commit what are now crimes:
A sting operation in which someone suspected of being racist in choosing partners gets presented in a surreptitiously controlled manner with potential partners of different races.
Discovering and punishing those who inculcate racist romantic preferences into children.
This social goal is considered more important than the right to privacy.
Start with a graph. Select some subset of the subgraphs of the graph that have a large Hamming distance (adding or deleting edges from the original graph) between them, like bits in coding theory. Let these be letters in an invented alphabet whose letters are less likely to be confused for each other even if letters get damaged.
Restrict to Hamiltonian subgraphs, drawable in one stroke.
The starting graph could be a 7-segment display.
We present a fanciful alternative to the musical pitch standard A440 by having some piano key note, not necessarily A4, have a frequency that is an integer perfect power multiple of the Planck time interval.
Let Pf = Planck frequency = 1/plancktime = 1/(5.3910604e-44 s) = 1.8549226e+43 Hz.
We first consider some possibilities of modifying A = 440 Hz as little as possible. Sharpness or flatness is given in cents, where 100 cents = 1 semitone.
F3 = Pf / 725926^7 = 174.6141 Hz, or A = 440.0000 Hz, offset = -0.00003 cents
G3 = Pf / 714044^7 = 195.9977 Hz, or A = 440.0000 Hz, offset = -0.00013 cents
E3 = Pf / 135337^8 = 164.8137 Hz, or A = 439.9999 Hz, offset = -0.00030 cents
G3 = Pf / 132437^8 = 195.9978 Hz, or A = 440.0001 Hz, offset = 0.00045 cents
D#5 = Pf / 31416^9 = 622.2542 Hz, or A = 440.0001 Hz, offset = 0.00053 cents
A#3 = Pf / 12305^10 = 233.0825 Hz, or A = 440.0011 Hz, offset = 0.00442 cents
C#5 = Pf / 1310^13 = 554.3690 Hz, or A = 440.0030 Hz, offset = 0.01176 cents
A#3 = Pf / 360^16 = 233.0697 Hz, or A = 439.9770 Hz, offset = -0.09058 cents
A#1 = Pf / 77^22 = 58.2814 Hz, or A = 440.0824 Hz, offset = 0.32419 cents
D#4 = Pf / 50^24 = 311.2044 Hz, or A = 440.1095 Hz, offset = 0.43060 cents
E1 = Pf / 40^26 = 41.1876 Hz, or A = 439.8303 Hz, offset = -0.66769 cents
B5 = Pf / 22^30 = 990.0232 Hz, or A = 441.0052 Hz, offset = 3.95060 cents
F#3 = Pf / 10^41 = 185.4923 Hz, or A = 441.1774 Hz, offset = 4.62660 cents
A7 = Pf / 7^47 = 3537.6749 Hz, or A = 442.2094 Hz, offset = 8.67126 cents
G6 = Pf / 3^84 = 1549.3174 Hz, or A = 434.7625 Hz, offset = -20.73121 cents
G#7 = Pf / 2^132 = 3406.9548 Hz, or A = 451.1929 Hz, offset = 43.48887 cents
Next some modifications of other pitch standards, used by continental European orchestras.
Modifications of A = 441 Hz:
C#6 = Pf / 106614^8 = 1111.2503 Hz, or A = 441.0000 Hz, offset = -0.00007 cents
F2 = Pf / 39067^9 = 87.5055 Hz, or A = 441.0000 Hz, offset = -0.00011 cents
G#2 = Pf / 38322^9 = 104.0620 Hz, or A = 440.9995 Hz, offset = -0.00184 cents
G1 = Pf / 6022^11 = 49.1109 Hz, or A = 441.0006 Hz, offset = 0.00240 cents
B5 = Pf / 22^30 = 990.0232 Hz, or A = 441.0052 Hz, offset = 0.02044 cents
F#3 = Pf / 10^41 = 185.4923 Hz, or A = 441.1774 Hz, offset = 0.69644 cents
A7 = Pf / 7^47 = 3537.6749 Hz, or A = 442.2094 Hz, offset = 4.74110 cents
E7 = Pf / 5^57 = 2673.2253 Hz, or A = 446.0410 Hz, offset = 19.67702 cents
G6 = Pf / 3^84 = 1549.3174 Hz, or A = 434.7625 Hz, offset = -24.66137 cents
G#7 = Pf / 2^132 = 3406.9548 Hz, or A = 451.1929 Hz, offset = 39.55871 cents
Modifications of A = 442 Hz:
D#6 = Pf / 547981^7 = 1250.1649 Hz, or A = 442.0000 Hz, offset = 0.00014 cents
G6 = Pf / 530189^7 = 1575.1097 Hz, or A = 442.0002 Hz, offset = 0.00086 cents
G#6 = Pf / 525832^7 = 1668.7709 Hz, or A = 442.0003 Hz, offset = 0.00116 cents
F#4 = Pf / 122256^8 = 371.6759 Hz, or A = 441.9996 Hz, offset = -0.00170 cents
A5 = Pf / 30214^9 = 883.9990 Hz, or A = 441.9995 Hz, offset = -0.00194 cents
F#4 = Pf / 11744^10 = 371.6767 Hz, or A = 442.0006 Hz, offset = 0.00242 cents
A7 = Pf / 217^17 = 3535.9843 Hz, or A = 441.9980 Hz, offset = -0.00769 cents
D2 = Pf / 151^19 = 73.7503 Hz, or A = 442.0024 Hz, offset = 0.00939 cents
A2 = Pf / 62^23 = 110.4885 Hz, or A = 441.9539 Hz, offset = -0.18072 cents
D#3 = Pf / 38^26 = 156.2976 Hz, or A = 442.0764 Hz, offset = 0.29903 cents
D#4 = Pf / 37^26 = 312.6662 Hz, or A = 442.1768 Hz, offset = 0.69244 cents
A7 = Pf / 7^47 = 3537.6749 Hz, or A = 442.2094 Hz, offset = 0.81985 cents
E7 = Pf / 5^57 = 2673.2253 Hz, or A = 446.0410 Hz, offset = 15.75576 cents
G6 = Pf / 3^84 = 1549.3174 Hz, or A = 434.7625 Hz, offset = -28.58262 cents
G#7 = Pf / 2^132 = 3406.9548 Hz, or A = 451.1929 Hz, offset = 35.63745 cents
Modifications of A = 443 Hz:
F#5 = Pf / 590036^7 = 745.0342 Hz, or A = 443.0000 Hz, offset = 0.00003 cents
C7 = Pf / 508595^7 = 2107.2749 Hz, or A = 443.0000 Hz, offset = -0.00007 cents
F7 = Pf / 488038^7 = 2812.8743 Hz, or A = 442.9999 Hz, offset = -0.00020 cents
B2 = Pf / 140193^8 = 124.3126 Hz, or A = 442.9998 Hz, offset = -0.00093 cents
A5 = Pf / 109676^8 = 885.9985 Hz, or A = 442.9992 Hz, offset = -0.00296 cents
B7 = Pf / 25564^9 = 3978.0160 Hz, or A = 443.0012 Hz, offset = 0.00456 cents
G#1 = Pf / 5988^11 = 52.2668 Hz, or A = 442.9982 Hz, offset = -0.00722 cents
B1 = Pf / 391^16 = 62.1581 Hz, or A = 443.0125 Hz, offset = 0.04895 cents
A6 = Pf / 226^17 = 1772.0760 Hz, or A = 443.0190 Hz, offset = 0.07422 cents
F7 = Pf / 163^18 = 2811.5701 Hz, or A = 442.7946 Hz, offset = -0.80308 cents
A#3 = Pf / 60^23 = 234.8805 Hz, or A = 443.3954 Hz, offset = 1.54462 cents
E6 = Pf / 35^26 = 1326.0401 Hz, or A = 442.5128 Hz, offset = -1.90507 cents
E2 = Pf / 34^27 = 82.8696 Hz, or A = 442.4704 Hz, offset = -2.07100 cents
C#2 = Pf / 18^33 = 69.8768 Hz, or A = 443.6902 Hz, offset = 2.69500 cents
A7 = Pf / 7^47 = 3537.6749 Hz, or A = 442.2094 Hz, offset = -3.09255 cents
E7 = Pf / 5^57 = 2673.2253 Hz, or A = 446.0410 Hz, offset = 11.84337 cents
G#7 = Pf / 2^132 = 3406.9548 Hz, or A = 451.1929 Hz, offset = 31.72506 cents
Planck time is not known to high precision due to uncertainty of the gravitational constant G. Fortunately coincidentally, musical instruments are not tuned to greater than 7 significant digits of precision, either.
Source code in Haskell. The algorithm is not clever; it simply brute forces every perfect integer power multiple of Planck time, with base less than 1 million, and within the range of an 88-key piano. The code also can base the fundamental frequency off the hydrogen 21 cm line or off the frequency of cesium used for atomic clocks.
Inspired by Scientific pitch, which set C4 = 2^8 Hz = 256 Hz, or A = 430.538964609902 Hz, offset = -37.631656229590796 cents.
Create a device that can fire coins as projectiles. Have the coins spin like a frisbee for stability.
Yes, you can definitely put someone's eye out, or perhaps rip a hole through their body. This is not a toy.
Chess requires 6 different piece types, or 2*3. We consider representing each piece type by a 2 dimensional abstract symbol.
The outer shape can be a square or a circle. An inner symbol inscribed within the outer shape can be a circle, cross, or absent.
There remains the issue of depicting the 6 types both in black and in white.
Assume, non-controversially, that no one is born a good singer (a baby only knows how to cry). Also assume, perhaps controversially, that everyone can become a pretty good singer: this follows from the Polgar Experiment.
Then, roughly, the people who become good singers are those with the best opportunities to do so, and in particular, a pretty performer gets hired more frequently.
This is different from the conventional criticism of someone succeeding as a pop star just by being pretty and not actually being skilled at their art. In this model, the prettier person is objectively better at their art than someone who is not pretty, and has become so through more opportunities to perform or show, reinvesting income generated to practice and develop.
If a cellular automaton is allowed to run forever from a start state that can generate unlimited novelty, e.g. double breeder or decaying agar, will intelligent structures eventually evolve? More generally, will evolution occur?
The general idea is that our corner of the universe, say, our solar system at quantum resolution, is a finite computable system, and certain cellular automata are universal computers, so given enough time and unlimited novelty, a pattern simulating our corner of the universe, accurate enough to simulate our intelligent life, will form by chance. Yes, this will probably take longer than the lifetime of the universe and a computer larger than the universe. Perhaps less if evolution, survival and propagation of the fittest, occurs.
The key is probably whether stable structures can form that are mostly defended or isolated from interference from other nearby (or distant) structures. Intuitively, consider trying this experiment on 4-dimensional or higher grids. There's more space up there for things to miss each other. In two dimensions, even crossing glider streams is difficult.
If intelligent life were to evolve in this simulation, would they ever be able to deduce that the underlying fabric of their existence is a simulated cellular automaton? Probably not.
The hemiola (triplets) in the finale section of "The Great Gate of Kiev" in Mussorgsky's "Pictures at an Exhibition" is unexpected, distinctive, and very powerful. Has the idea been further improved by later composers?
Update: Used in the piano and orchestra section of the very famous 18th variation of Rhapsody on a Theme of Paganini, though the triplet rhythm is heard earlier.
One side believes someone deserves something, so frames their argument in terms of "respect"; being deprived of the something constitutes a deprivation of a basic human right, of dignity.
The other side believes someone does not deserve that something, so frames their argument in terms of those people feeling and acting "entitled" with the strong implication that no one is entitled to such a thing from birth (like a title of nobility); it must be earned.
These are duals: each time one argument is used, it can easily be converted to the other arguing the opposite direction.
Abstractly, how to frame the argument is pure politics: where to draw a property line.
Hyperinflation is a curious economic phenomenon because it seems not completely understood, despite being very dramatic and having happened many times around the world.
Fundamentally, the curious aspect is that a lot of people are acting irrationally regarding the currency, so one would expect rational actors in the market to be able to take advantage of their irrationality, stabilizing the value of the currency.
Even if a government is unable to effectively collect taxes, the government still holds monopolies (e.g., licenses, fines) and monopsonies (e.g., government procurement, government labor) on various goods and services, so assuming transactions for these things must be done with the fiat currency, they seem to be a stabilizing force that would define value of the currency.
We hypothesize that hyperinflation occurs when there is market failure in these stabilizing mechanisms. There must be something else going on: for example, overt or covert international forces deliberately wanting to reduce the target country's economy to chaos via hyperinflation, perhaps part of a political power struggle. What is the nature of these forces, and how do they cause market failure?
The inspiration is, of course, Greece, which according to one report, has a weak government unable to effectively collect taxes. If so, it would be practical to instead "raise" revenue through the inflation tax. (Perhaps correct its inherent regressiveness through other redistribution mechanisms, though I don't know what.) If Greece exits the European Monetary Union (euro), could it transition to a stable economy with high inflation, or is it doomed to hyperinflation? Greece certainly has made, or will make, a lot of enemies if it defaults on its debt. Can those enemies deliberately induce hyperinflation? Is that threat affecting policy?
Replace the standard shogi tiles with larger beautifully illustrated playing cards, inspired by Magic The Gathering, to make the game more accessible. The cards could also be annotated with piece movement diagrams and kanji. 40 card deck, a respectable deck size.
Also needed are 81 short platforms, each the same size of a card, part of a large 9x9 board, onto which the cards may be placed, because placing cards directly on a flat surface leaves them too difficult to pick up.
Inspired by the "dragon king" piece, which offers imaginative possibilities for illustration.
Could be done for chess, though promotion is less interesting.
If one wants to use a thrown spherical projectile as a weapon, what would be its optimal size, weight, and density? Not throwing knife, nor sling shot.
Similarly, exploring previous generations of weapons as alternatives to guns.
Preparing for World War IV.
Assuming tungsten lies on the price/density frontier, and we need to verify the claim that an object is (almost) pure tungsten, we need to measure its density. Mass is easy, volume is trickier. Although the volume of an arbitrary shape can (probably) be easily measured by displacement of liquid, we would prefer a less messy way, a geometric way. What shapes can have their volume easily determined geometrically?
The volume of a tetrahedron can be determined by measuring its edge lengths. Comparing with a straightedge can determine that the edges are straight. Is there a simple way to determine that the faces are flat? Especially need to detect concave.
Cube is more difficult because we need to determine that faces are at right angles.
How easy is to to determine the diameter of a sphere? How easy is it to verify that a shape is a sphere? Rolling won't work: Meissner tetrahedra.
In this modern age, probably laser scanning or structured light.
Tungsten is hard so maybe the vertices of the tetrahedron won't break off. But tungsten is brittle, so maybe they will.
Let "octave-tuning" be the very common 12 tone equal temperament tuning with a frequency multiplier of o=2^(1/12) between semitones. An octave will exactly double the frequency. Let "fifth-tuning" be an equal temperament tuning with a frequency multiplier of f=1.5^(1/7) between semitones. The fifth will be "perfect", with frequency exactly 1.5 times the base note.
(Octave-tuning is often called 12-TET. Fifth-tuning is often called 7-TET.)
Fifth-tuning causes intervals to be sharp by 0.27928583791248815 cents per semitone, 3.3514300549498590 cents per octave, in octave-tuned cents, compared to octave-tuning. 12 fifths equals 7 octaves, or 84 semitones, an interval which will be 23.460010384649013 cents sharp. (A piano covers a range of 87 semitones, though the highest and lowest notes are tuned differently because of psychoacoustic effects.)
Inversely, octave-tuning has its fifth 1.9495560314892994 cents flatter than a perfect fifth, in fifth-tuned cents.
If we split the difference per semitone, then the frequency multiplier between successive semitones is exp(2/(1/log(o)+1/log(f))). (Appropriately, harmonic mean in logarithmic space.) This yields a semitone that is d cents sharp in octave-tuning and d cents flat in fifth-tuning, where d=0.13944818943408673.
Alternatively, we can split the difference unequally in the following way: a frequency multiplier of exp(19/(12/log(o) + 7/log(f))) yields an octave that is d cents sharp in octave-tuning and a fifth that is d cents flat in fifth-tuning, where d=1.2325632573261429.
Let "twelfth-tuning" be an equal temperament tuning dividing the just interval of an octave plus a fifth (a twelfth) into 19, so a frequency multiplier of 3^(1/19) per semitone. Relative to octave-tuning, a semitone is 0.10289478238881145 cents sharp and the octave is 1.2347373886657375 cents sharp. Relative to fifth-tuning, the fifth is 1.2312985462037681 cents flat.
Incidentally, a twelfth in the "split the difference unequally" tuning is extremely close to, just 0.0034388362379609146 cents flat of, a perfect twelfth in twelfth tuning.
Take an already released movie, think up a new title for it, and create fake promotional materials for it: trailers, posters. (Similar exercises by others: fake trailers making the movie seem totally different, e.g., The Shining as a romantic comedy; Honest Trailers.)
Original motivation is for someone to distinguish themselves as a movie-naming specialist, creating a portfolio, for studios to hire.
Model the earth with and without the moon to gravitationally simulate the trajectory of meteoroids. Is there a significant difference in impact rate? Without the moon, add to the earth the mass of the moon, but possibly subtracting the mass of the impactor that created the moon.
Theory is, the freak giant impact that created our (almost) double planet is another of the reasons there is life, or intelligent life, on earth. If it weren't for the moon, we might be seeing Chicxulub-like impacts, and consequent mass extinctions, more often.
Year 2006 = "Twenty aught six"
Especially appropriate because in the .30-06 bullet, the "aught 6" refers to the year 1906.
Invert the premise of Terminator: a human pursues a robot trying to avoid being caught. This seems the "natural" version of the story: Humans are evolutionarily persistent, and robots struggle to be reliable over long periods.
Of course, Blade Runner.
Slice off 1 11/16 inches off the 8.5 inch width of US Letter paper to yield a golden rectangle.
More precisely, 1.7016261237511566697 inches.
Is the first immortal human alive already?
We liberalize the definition of immortality to mean capturing one's consciousness into a digital medium, which can then, in principle, be copied and perfectly preserved forever. Possibly also add as a requirement that the digital consciousness be able to be run on a computer. We ignore the difficulty of preserving information forever, or the thermodynamic difficulty of executing computer programs in the extreme future.
It won't be easy to say when immortality is invented, because technologies to digitize consciousness will progress toward higher and higher fidelity over time.
One could argue along these lines that the first immortal human has (paradoxically) already died. Perhaps an artist. Their consciousness, their "spirit", has been preserved well enough in their works that they might as well still be alive. One can interact with their works directly, or one can interact with people who have studied their works enough to accurately channel their consciousness. Jesus.
Another way immortality could happen, perhaps has already happened, is in people who have been recording their lives (or perhaps having had their lives been recorded against their will) in various ways, often to share with social media. Their entire digital footprint may capture enough of their lives to essentially be able to simulate them accurately, or correctly answer any question about them.
You may already be the first immortal human, your consciousness running in the NSA's servers.
Ghost in the shell.
Oppenheimer's quote from the Trinity atom bomb test is an agglomeration of two somewhat separated sections of the Bhagavad Gita, though both are about the same (very important) character, the deity Krishna.
The first part, about the radiance of a thousand suns, is from chapter 11, verse 12.
The second part, about the destroyer of worlds, is from chapter 11, verse 32. However, the quote is ironically somewhat of a misquote. The atomic bomb has very high power: a lot of energy is released in a very short time. The Bhagavad Gita quote is about the inexorability of time (not strictly death) and its ability to literally shatter worlds if you wait long enough (though the Bhagavad Gita was probably not anticipating proton decay). This requires energy far greater than all the atomic bombs the world has ever produced. However, the power output of "Time" is extremely low, exactly the opposite of an atomic bomb.
Create a car with low acceleration but very high top speed. It takes a long time to reach that top speed.
High acceleration is fun but practically not too useful. Also it might be more expensive to design and build an engine capable of doing it.
Might end up being more like a truck than a car.
One thing a social network could do well is discover sock puppets and multiple identities, which unsolved cause problems of spam and astroturfing. It's a little bit tricky because the social network has to induce people to maintain only one identity and make social network connections only with real people. There will be intense attempts to game the system.
Doing this is troubling from a privacy and broad social perspective. Multiple identities seems something that should be available for people to have.
Perhaps we can take solace in that the large social network corporations, and the three-letter agencies that tap and subpoena them, can and do already do this, and we are proposing such power, and the benefits of such power, be made available to everyone.
If we're going to put an additional person on the $10 bill (current plans are not to drop Alexander Hamilton), let it be Aaron Burr. I think I read somewhere (but can no longer find the citation) that one issue of contention in their fatal duel was states' rights versus the power of the federal government. This debate still rages today, representing an important issue in America, suitable for commemorating on currency.
Easy (sort of) is to write a fact: Q. Much harder is to define the context P within which the fact is true: P => Q.
P could be done by crowd sourcing.
Input is raw video, classified by which segments ended up being used in the final cut. Possibly also annotated with the processing done between raw and final.
Goal is a tool to make video editing easier by having the computer suggest which segments of raw video to use, what processing to do.
Assume laws permit some legislative districts to have multiple legislators representing them, all serving at large within the district. Create an algorithm that will partition a state into non-gerrymandered districts, some with multiple legislators, some with only one.
We anticipate that a dense area will be a single district with multiple legislators, but sparse areas will be partitioned into single-legislator districts.
Not sure how to define the metric to optimize. General idea is that geography defines ideology in rural areas, but in urban areas there is more mixing. Try to avoid legislators having to represent multiple ideologies.
Inspired by the districts of Colorado, which if done by the splitline redistricting algorithm results awkward pie slices around Denver, with each legislator forced to represent a mix of urban and rural.
What is the longest sequence of consecutively parallel streets in a city in alphabetical order?
Inspired by Back Bay Boston.
Fill an infinitely long rectangular prism with a uniform distribution of points. Compute the Voronoi partition of the points. Create an animation of the cross section traveling along the long axis of the prism: polygons constantly shift in size, appearing and disappearing.
What other interesting things can we add to the animation?
Dots move along line segments representing the Delaunay graph connecting the points. Connect the dots within a cell to form a polygon whose size shrinks to zero when a internal point intersects the cross sectioning plane.
Spheres centered at internal points intersecting cell vertices.
Inscribed a sphere into each cell. Maybe Apollonian spheres.
Dissection of each cell into pyramids with apex at the internal point, and each cell face a pyramid base.
How should colors of each cell be chosen to avoid adjacent cells of the same color? I suspect no finite number of colors is guaranteed to suffice.
How can we avoid having to place all the infinite number of points before calculating the Voronoi partition?
Inspired by cross sections of foams.
The dissenting Supreme Court justices in Obergefell v. Hodges claim the decision is judicial activism running amok, decreasing states' rights in its balance against federal power. However, I feel that marriage is such a singular institution, sui generis, among all human activity, that federal seizure of it from being a state's right to regulate represents at most a very small, limited, seizure. In particular, the case seems unlikely to have wide-ranging judicial implications to issues beyond marriage.
As an analogy, Loving v. Virginia, striking down bans on interracial marriage, seems not to be be cited in cases beyond marriage.
If you care about states' rights, this is not the case to get worked up about. There are other cases that gave the federal government wide-ranging ability to override the states in all kinds of different activities, often through the commerce clause.
In contrast, if Roe v. Wade were hypothetically overturned, it could also overturn or weaken Griswold v. Connecticut and the right to privacy, and then also overturn or weaken the entire framework of penumbras of rights enumerated in the Constitution. These would have very wide-ranging judicial implications.
To validate a given password, consider a program which tests every possibility of number of rounds of the password key derivation function, from 1 to infinity, until the validation succeeds, or the user signals "give up". This is in contrast to the common technique in which the number of rounds is encoded in the hashed password database (e.g., /etc/shadow), along with salt. The user selects the number of rounds probably by waiting an amount of time deemed within the limits of his or her patience when initially setting the password. This number of rounds is not recorded anywhere. Whenever the user enters the correct password in the future, he will she will have to wait that chosen amount of time for the password hashing to complete. It is an easy UI therefore for the user to wait longer when setting important passwords, automatically getting more rounds. If the user accidentally enters an incorrect password, he or she knows how long to wait (his or her internal measure of patience) before telling the UI to "give up" and let him or her try typing the password again. An attacker doing a dictionary attack, not knowing how long to wait, i.e., not knowing how many rounds, will have to wait a long time just to be safe, for each guess. This punishes incorrect password attempts.
There is a potential failure if the user had set the password on a much more powerful machine than later used to validate the password, e.g., mobile.
It also has the potential failure of an attacker being easily able to cause a denial-of-service attack if the server is validating the password.
This scheme could easily be implemented while maintaining the old password database schema. Just have the new software ignore the specified number of rounds. Could be useful for the GnuPG s2k-count parameter capped at 65 million rounds by the OpenPGP specification RFC 4880.
All this works fine if the password hashing algorithm has exactly one parameter, e.g., number of rounds, as is the case for the most commonly currently deployed password hashing schemes. However, if the algorithm has more than one parameter, e.g., both memory and CPU, it is less clear what to do.
One possibility is for the hashed password database to record a function or path, selected by the user, through the parameter space. When validating a password, it tries parameters along that path through parameter space until the password hash validates or the user signals to give up. One likely common path will be just to use a specified constant amount of memory, just increasing the number of rounds, similar to before: a horizontal path through the parameter space.
When only the number of rounds is being increased, the previous computation for a lesser number of rounds can easily be reused. The additional computation is just the additional rounds beyond the previous computation. However, if the memory parameter is increased for a memory-hard password hashing functions like scrypt, I suspect the computation must be started from scratch each time. This seems highly undesirable because it decreases the rate at which different parameters can be tried, lowering the number of possibilities for the attacker.
Can a multi parameter password hashing function be designed so that increasing any parameter can reuse the work of the smaller parameter? Yescrypt has a lot of parameters.
Inspired by a comment on the PasswordSafe mailing list. It is surprising that the Schneier-written software has a hardcoded unalterable number of hashing rounds.
Pointing the window fan in or out will (I think) be equally effective at moving air through the window. We assume other windows are also open: it is equally tricky either way to figure out through which other windows the air will flow. I suspect that both ways are equally effective at making the indoor temperature the same as outdoors.
However, pointing the fan inwards creates a small area immediately in front of the fan with high speed air. A person standing there can cool quicker because high speed air helps perspiration evaporate.
Memorize what countries border what other countries. Possibly more useful than memorizing where each country is.
Could be weird with borders between distant overseas territories.
In general, fail open rather than fail closed.
In an open system, market forces (broadly defined) can achieve an efficient outcome. If you zoom out far enough, failing open often results in at worst a "mere transfer", so macroeconomically neutral.
The canonical example is an door lock failing open, unlocked. Stuff gets stolen, "transferred". In contrast, the door failing closed, so that no one can unlock it, leads to a Pareto-dominated waste in which no one can access what's beyond the door.
But tragedy of the commons can occur in failing open.
A few evolutions of trying to modify bughouse chess into a two-player turn based game, removing the element of time. (Which arguably ruins the game.)
Evolution 1: A player has just completed a move on one of the boards. The other player can now reply on that board, reply on the other board if he or she is to play on that board, or pass, which counts as a move. If both players pass consecutively, then 1 "second" is removed from both game clocks. A "second" has no relation to actual time passage; it is just a decrementing counter.
The underlying idea is that it simulates both players playing infinitely fast, instantaneously, unless they are explicitly stalling.
Evolution 2: Whoever is losing on the diagonal clock difference is not allowed to pass.
Unfortunately, neither of these work, because the two game clocks always remain in sync, so the diagonal time difference never varies from zero.
Evolution 3: a pass permitted arrow which alternates between players each time a pass is invoked, inspired by the possession arrow in basketball. (Also similar to the "button" in poker.) Unfortunately, this does not work, because the players can can pass consecutively, causing the passing arrow to simply alternate 180 degrees out of sync with the passing.
Evolution 4: Some system to trade the privilege of forcing your opponent to make a move now, in return for giving your opponent that privilege some time in the future. Perhaps not an even trade. Perhaps an auction system. Perhaps an arrow or button signifying who has the initiative in the auction.
Apollonian network graphs drawn on the plane tend to be ugly, with many sharp angles. Draw them on a sphere, maximizing some measure of elegance.
Derive some shape, topologically a sphere, onto which a given graph can be drawn even more elegantly. Probably more bulbous where the network is dense.
The PGP biometric word list is pretty cool, probably doing better than my similar attempts, though with only 256 words instead of 1024.
Create a speech recognizer which recognizes precisely those words. Signal an error if it detects a parity error due to the even/odd word lists.
How well can a human memorize the word lists and be able to translate and speak words corresponding to a given series of numbers, or transcribe speech back to numbers?
Because it is byte-oriented, it might work well with Reed-Solomon error correcting codes.
The ChaCha cipher seems not to get as much love as Salsa20. Here is a step-by-step example of the ChaCha round function operating on a matrix. The format of the example is loosely based on the analogous example in section 4.1 of this Salsa20 paper: D. J. Bernstein. The Salsa20 family of stream ciphers. Document ID: 31364286077dcdff8e4509f9ff3139ad. URL: http://cr.yp.to/papers.html#salsafamily. Date: 2007.12.25.
original column [a;b;c;d] 61707865 04030201 14131211 00000007 after first line of round function 65737a66 04030201 14131211 7a616573 after second line of round function 65737a66 775858a7 8e747784 7a616573 after third line of round function dccbd30d 775858a7 8e747784 aab67ea6 after all 4 lines of round function, i.e., quarter round dccbd30d 395746a7 392af62a aab67ea6 original matrix, with the same original column above 61707865 3320646e 79622d32 6b206574 04030201 08070605 0c0b0a09 100f0e0d 14131211 18171615 1c1b1a19 201f1e1d 00000007 00000000 01040103 06020905 one round (4 quarter rounds on columns) dccbd30d 109b031b 0eb5ed20 4483ec2b 395746a7 d88a8f5f 7a292fab b06c9135 392af62a 6ac28db6 dfbce7ba a234a188 aab67ea6 e8383c7a 8d694938 0791063e after shift rows dccbd30d 109b031b 0eb5ed20 4483ec2b d88a8f5f 7a292fab b06c9135 395746a7 dfbce7ba a234a188 392af62a 6ac28db6 0791063e aab67ea6 e8383c7a 8d694938 after another 4 quarter rounds on columns 06b44c34 69a94c11 2ce99b08 216830d1 29b215bd 721e2a33 f0a18097 708e1ee5 2b0e8de3 b801251f 42265fb2 696de1c2 e6fef362 c96c6325 c6cc126e 82c0635a unshifting rows (concludes 1 double round) 06b44c34 69a94c11 2ce99b08 216830d1 708e1ee5 29b215bd 721e2a33 f0a18097 42265fb2 696de1c2 2b0e8de3 b801251f c96c6325 c6cc126e 82c0635a e6fef362 after 8 rounds (4 double rounds) f6093fbb efaf11c6 8bd2c9a4 bf1ff3da bf543ce8 c46c6b5e c717fe59 863195b1 2775d1a0 babe2495 1b5c653e df7dc23c 5f3e08d7 041df75f f6e58623 abc0ab7e Adding the original input to the output of 8 rounds 5779b820 22cf7634 0534f6d6 2a40594e c3573ee9 cc737163 d3230862 9640a3be 3b88e3b1 d2d53aaa 37777f57 ff9ce059 5f3e08de 041df75f f7e98726 b1c2b483 reading the above as bytes, little endian 20 b8 79 57 34 76 cf 22 d6 f6 34 05 4e 59 40 2a e9 3e 57 c3 63 71 73 cc 62 08 23 d3 be a3 40 96 b1 e3 88 3b aa 3a d5 d2 57 7f 77 37 59 e0 9c ff de 08 3e 5f 5f f7 1d 04 26 87 e9 f7 83 b4 c2 b1 same as above but with 20000 rounds (10000 double rounds) 11 a3 0a d7 30 d2 a3 dc d8 ad c8 d4 b6 e6 63 32 72 c0 44 51 e2 4c ed 68 9d 8d ff 27 99 93 70 d4 30 2e 83 09 d8 41 70 49 2c 32 fd d9 38 cc c9 ae 27 97 53 88 ec 09 65 e4 88 ff 66 7e be 7e 5d 65
The example was calculated using an implementation of ChaCha in Haskell, whose end results agree with Bernstein's C reference implementation. The Haskell implementation is polymorphic, allowing as matrix elements any data type (of any word width) implementing Bits, and parametrizable to matrices of any size 4xN. (Security is probably bad for N not equal to 4. For word width different from 32, you probably want different rotation amounts.) The flexibility comes at a cost: the implemention is 3000 times slower than Bernstein's reference C implementation (which is in turn is slower than SIMD optimized assembly-language implementations).
Also included in the same project is a similar Haskell implementation of Salsa20, parametrized to matrices of any size MxN because of the more regular structure of the Salsa20 quarter round function compared to ChaCha. We demonstrate taking advantage of polymorphism to use the same code both to evaluate Salsa20 on Word32 and to generate C code for the round function.
There has (by definition) yet to be a chess variant which offers a new mechanism so cool, so amazing, that the world takes it up by storm as an improvement to chess, that playing the new game is so much more fun.
Or is the path dependence effect too strong?
Compose a chess position in which both sides consecutively have exactly one legal move, for a long series of moves. The end position does not need to be anything special, just maximize the length of the sequence. For artistic effect, also try to maximize the number of different pieces which move, not just (say) a pawn that moves forward in an otherwise locked position.
Inspired by a joke chess problem that anyone should be able to solve.
Slightly loosen the restriction: more than one legal move may be possible in each position of the sequence, but all but one move is losing, where losing is defined as providing the opponent with a mate in 1.
Loosen the restriction further to mate in N. This begins to resemble many traditional chess problems.
In the absence of regulation, children will probably be forced by parents to enter the labor market too early. While a dependent, the parent can extract the entirety of a child's income. However, a child seeking to maximize lifetime income should probably invest the time in education. But all this gets very hairy, as labor is often a form of education: apprenticeship.
Possibly the regulation should be that parents lose government assistance given to families if a child is working.
We might need a very weird financial instrument in which a parent can take out a loan ostensibly to benefit the family that the child is obligated to pay back.
Commentary about a chess game in progress delivered not in the form of speech, but as music describing the state of the position, e.g., near loss or win, chaotic, quiet. Rather than technical lines, the ambiance.
Perhaps automatically composed, or perhaps a human team of commentators working with a DJ.
The Arkansas River is pronounced "Ar Can Zus" or "Ar C'n Saw".
The Kansas River is pronounced "Can Zus" or "Kaw", though the latter is also spelled that way.
Lisp is a prefix language (the operator goes first), but one could easily imagine a special form that introduces a "little language" which is parsed with infix:
(infix parameters-describing-the-little-language 1 + 2 * 3 + (4 + 5 * 6))
The parameters enumerate the infix operators, and specify their precedence and associativity. We probably also want some way of escaping infix parsing within the special form.
Is there any organization with power which exercises its power completely transparently?
Difficulty is there is a human element of any decision of how to exercise power, and humans are never transparent.
