Tuesday, October 31, 2017

[prxhyjkv] Some goban variations

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

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

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

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

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

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

Two square boards overlapping at all corners and edges.  Again requires a spherical manifold.

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

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

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

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

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

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

[qgxjefyl] Keyboard for typing text

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


Uncommon punctuation should be relegated to shifted positions.


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

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

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

[iseswemp] Orbiting dust

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

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

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

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

[xwnzahyz] Some nice irrational numbers

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

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

Fractional powers of integers.

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

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

sin(r*pi) where r is a rational number.  By Niven's Theorem, one only needs to avoid r={0,1,1/6}.

gamma(r) where r is a rational number.  Staying between 0.0953252 and 4.39008 keeps values below 10.  Inspired by Watson's triple integrals and elliptic integral singular values.

zeta(r) within some nice range, avoiding negative integers.

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


Multiply any of the above by a rational number.

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

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

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

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


Tuesday, October 24, 2017

[mapuxbob] Ultimate deep cut

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

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

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

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

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

[olgybexs] Lap times of unrestricted race cars

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

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

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

[kawtunfn] Massively editing history

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

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

More complicated changes involve splitting or merging commits.

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

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


Sunday, October 22, 2017

[rfcvmehz] I lived in Somerville before it burned down

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

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

[riefkroc] Rational terrible behavior

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

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

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

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

[oruxepci] Simulating parliament

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

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

Saturday, October 21, 2017

[tiuahohk] Self-measuring self-qi

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

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

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

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

[rajxyghb] Asymmetric society producing capable women

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

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

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

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

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

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

[iiomamzg] Evolving artificial intelligence

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

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

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

[odwfsmzu] Murder upward only

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

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

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

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

[dughfscx] Rational logarithms

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

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

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

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

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

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

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

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

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

[yqkubvtj] Steroids in some sports

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

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

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

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

[jfimxvqx] Various astronomical planes

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

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

[rgwocfen] Where is the equator?

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

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

[tynurhyy] Two maps at the same scale

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

[hludclpz] Voluntary Stepford

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

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

[rulrzurd] Health levels in a game

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

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

Analogously, the positive feedback loop is also possible.

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

Wednesday, October 18, 2017

[pcdcujqh] Rat Park and all entertainment

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

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

Copyright probably affects production of entertainment.

[scnfyfkb] A nice range of reals

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

Similarly 0.5 to 2.

These seem numbers on a human-comprehensible scale.

[vqbjrmbd] GCD diagram

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

Shape as an equilateral triangle, not isosceles right.

[ytjxyyzh] Most interesting defense

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

[pxlrjngg] Mitigating the risks of offshore assets

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

Inspired by the Panama Papers.

[vttngych] Sampling fractions uniformly

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

[zzfydkni] Normally distributed integers

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

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

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

[gacogjwe] Catering to Chinese consumers

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

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

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

[xcsyydtv] Force battles

Alternate Star Wars:

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

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

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

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

Monday, October 16, 2017

[duimuqdd] Compressing prime numbers

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

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

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

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

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

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

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

Wednesday, October 11, 2017

[oicxhazu] Sherlock Taken

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

[gqksmejv] Smoothly transforming polyhedra

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

[rkzmrdnt] Central Limit Theorem and Hypersphere picking

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

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

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

Project the endpoint of a random walk to unit distance.

Sunday, October 08, 2017

[wbmowbjw] Print your own log tables

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

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

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

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

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

[bhfrgtxp] Screaming crossword

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

[zvetsujf] Contra dance panopticon

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

[kxdvmnew] Language for climate change

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

[zruxmgev] User-guided optimization and parallelization

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

Profiling could also guide automated parallelization.

[bvbbxjiv] insert-date

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

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