Friday, November 27, 2015

[vbiesnqs] Experimenting with larger groups

As computers have become more powerful and, in particular, have gotten more memory, has it become possible to easily do interesting experiments on certain finite groups which previously had been infeasible?

A group of order N can easily require N^2 memory for the "multiplication" table, and then N^3 or N^4 memory or time to run a computation over all elements or all multiplications.

Pedagogical experiments are interesting: groups beyond the cyclic group, especially the sporadic groups, often are difficult to understand.  Working with them through computer-aided experiments might help provide an intuitive understanding of them.  They lower the "barrier to entry" into advanced group theory, equivalently steepness of the learning curve.

Details of group presentation and group representation will probably be very important.

Thursday, November 26, 2015

[xulyrnew] Large optimization puzzle

Create an interesting but very difficult puzzle, allowing computer scientists to solve it over a very long time, perhaps centuries.  An optimization problem allows a solution to be improved over time, which seems nicer than having it remain unsolved until it is solved then forgotten.

For example, a very high dimensional Rubik's cube (twisty puzzle), scrambled using a specified determinstic pseudorandom number generator.  The goal is to find the shortest solving sequence.  This puzzle has the feature that some solution is known from the start: just reverse the initial scramble.  The high dimensional puzzle is interesting because of group theory, perhaps more interesting than just a very high-order 3-dimensional cube.  Can we design a harder puzzle based on other finite simple groups?

On the other hand, the Cunningham project already exists, and number theory is very interesting.

A cryptographic puzzle seems aesthetically not very interesting if based on symmetric cryptography primitives, e.g., AES, because symmetric cryptographic primitives are ugly compared to other elegant problems out there.

Inspired by, the traveling salesman problems for very large numbers of cities on Earth have been effectively solved.  We need something harder.

[drutokoo] Postscript as a target language

Create a compiler which translates code written in some high level language to PostScript.

Motivation was a "safe" language which can do nothing beyond displaying things.  This is probably overkill.

Tuesday, November 24, 2015

[qplamlpi] Interpersonal conflict in the Manhattan Project

Scientists and engineers are famously bad at social skills, leading to destructive interpersonal conflict.

How was such conflict, or its consequences, avoided in the Manhattan Project, which probably had the most "scientisty" scientists needing to work with each other?  The space race?  (Questions are also applicable to countries beyond the United States who completed similar engineering projects.)

[uldlnodz] Flying through checkerboards

Fly around a virtual universe composed of many equally spaced parallel planes colored in a checkerboard patten.  The camera always looks in the same direction, rendering the checkerboards with perspective.

The checkerboards provide a visual cue of motion and velocity in the X and Y directions.  The rate at which one approaches and flies through planes provides a visual cue of motion and velocity in the Z direction.

Inspired by, what would it be like to be a particle floating through a Lorenz system?

[umhxikue] Poincare conjecture game

Create a game in which one flies around a closed 3-manifold, not necessarily a 3-sphere.  The player constructs loops within the manifold out of a material which gradually shrinks, tightening the loops.  Perhaps the goal is to construct a loop which does not shrink down to a point.

Even closer to Perelman's proof would be to have the manifold undergo Ricci flow, and then require the player to perform surgery around the singularities.

[mjqyawgs] Liquid planet

What would a planet with a much deeper ocean be like?  Perhaps entirely composed of water all the way to the core.  Simulate the ocean currents and waves.  For waves, we also need to specify an atmosphere.

Under high pressure, water might become exotic phases not seen on earth.  Are there other materials which a liquid planet could be composed of that are physically or chemically more interesting than water?

Perhaps add a core emitting heat via radioactive decay (in addition to solar radiation heating the surface.)

It would be also interesting to have landmasses to cause interactions between land, air, and sea.  However the shape of the solid portion of the planet with such a deep sea would be preposterous, maybe spiny or a lattice.  Or maybe the landmasses float.

[szsbrpzv] Perfect Pythagorean spiral

Modify the Spiral of Theodorus to start with a right triangle with legs of length x and 1, and then each successive triangle using another unit leg.  (Traditionally, x=1.)  Choose x so that the last triangle after one winding lines up with the first.

This should be easy.

Extend the sides meeting at the center into rays out to infinity.

Friday, November 20, 2015

[ugtvnilk] Artificial hypercane

With enough underwater nuclear reactors, could we induce the formation of hypercanes?

Perhaps a nuclear accident.

Or a doomsday weapon: a cargo ship loaded with reactors ready to be sunk off an enemy coast.

[fbjitzoz] Theory of gossip

When do people gossip about other people behind their backs?  When do they not?  When do they talk trash directly to their face?

[muckaiqv] Gradually deleting content in Freenet

An adversary wanting to delete some target content on Freenet constantly inserts an unending quantity of random junk data.  Eventually, junk data will hit the hash bucket of each accessible copy of the target content and overwrite them.  How effective is this attack?

I suspect it is effective: old content remains available, not displaced by new content, only if it is popular, i.e., only if people are accessing it.  This pits the efforts of people against a machine that works constantly, never tiring.  The machine will eventually win; the humans are doomed to lose.

In practice, an adversary does not need to constantly insert junk data.  Enough normal users are constantly inserting that any content will eventually disappear.

Can the censorship be accelerated by a powerful adversary unleashing a great many nodes constantly inserting junk data?  (Also probably helps to constantly fetch the junk data from different nodes.)

These problems could be mitigated if Freenet had a mechanism by which a user could permanently save and serve chosen data from his or her machine, perhaps data the user feels is important to keep accessible.  However, this seems difficult or impossible given Freenet's architecture.  Even if the user serves the data, preventing it from being overwritten, there's no way to guarantee that other nodes seeking the data will be routed to it.

Probably the best way is to augment Freenet with an additional storage system.  Previous thoughts on monetizing data storage.

In the absence of mechanisms for data permanence, Freenet is better thought of as a ephemeral broadcasting medium than a permanent publishing medium.  The interface presented to the initial user, hyperlinked web pages, is probably wrong.  Better would be a collection of recent messages, organized into forums and topics.  FMS is the most famous software offering this.  It could be further skinned with metadata, though it runs into the problem (though possibly feature) that metadata, for example a user's profile of actions, is also ephemeral.

Thursday, November 19, 2015

[cllaynyn] Four slashes in a square

Divide a square into four equal squares.  In each little square place a forward or backward diagonal slash, yielding 16 possible characters, an encoding of hexadecimal.

To be able to distinguish which slashes belong to which character in a series of characters next to each other, let the slashes that radiate from the center be drawn wedge shaped, like a windmill blade.  Inspired by cuneiform.  Draw the tangential slashes curved, quarter circles which can join to form half, three-quarter, or full circles.

Previously.  Using color seems a good way of avoiding needing to choose stroke thickness.  Is it always possible to color avoiding horizontal or vertical color boundaries?  Update: no, for example a 3/4 circle and 1 radial slash.  Though this could be colored with a gradient.

There are 6 distinct shapes not counting rotations (and no reduction omitting reflections also). One requires 3 colors, and the 3/4 circle is otherwise the only difficult case.

This can of course be generalized to 9 slashes and so forth.

[toyfpgzm] Paradoxical effectiveness of racial profiling of criminals

If the police can detect using racial profiling a certain class of criminals with accuracy higher than random, and the police do do racial profiling, then one would expect people of those races to preferentially not enter that class of crime, and people of races not targeted by racial profiling to preferentially enter, or survive, in that class of crime.  Negative feedback.

Is this happening?  It generally seems not to be, meaning there are more powerful forces at work.

The canonical example is African-Americans and drug dealing.

The standard narrative of those more powerful forces is that people of certain races face such tremendous barriers to entry to other professions due to race that, despite racial profiling, that class of crime still remains the choice with maximum expected utility.

Monday, November 16, 2015

[jxvceogq] Sunrise and moonlight

"Every" composer composes a song named "Moonlight" and a song named "Sunrise", even if they have to be retroactively named that way (Beethoven).

[lomthmbn] Neutrally buoyant particles

Create a tank with interesting currents, and place some neutrally buoyant particles in it to see the current.

Neutral buoyancy is tricky, so easier might be very small bubbles which, with light, can be very visible due to total internal reflection.  Perhaps a gas that is denser than air to make them rise even slower.

Another easier route would be simulation with computer graphics, but we need a way of viewing the particles in 3D: virtual reality.  Lorenz system.

[msmvglck] Equalize passing and rushing

In football, count the total passing and rushing yards league-wide and modify the rules between seasons to keep them roughly equal.

Also interesting would be to equalize the points scored on touchdowns versus field goals.

Not sure what rules to modify.

Friday, November 13, 2015

[envxsvol] Doublethink is mentally taxing

If you find that defending your side of an argument is mentally taxing, exhausting, perhaps exhibited by a feeling of animosity or infuriation toward the opposing side, it could be because your side requires doublethink: maintaining a paradoxical viewpoint in your mind.

Knowing this effect could be useful if you recognize these symptoms within yourself.  The cause, the actual paradox, might be very deep, beyond your conscious ability (at the moment) to express or comprehend, but these consequent symptoms are far more accessible and obvious.

Inspired by, I'm tired or avoiding arguing this point: go read this instead.

On the other hand, thinking about a non-paradoxical but complicated concept could also be mentally taxing.

[hzjexooq] Reputation mechanisms violate privacy

Any mechanism by which one can establish a reputation, especially of an online identity, will also decrease privacy: decrease the ability to stay anonymous and provide more rope for attack by enemies.  Is this unavoidable?

It is difficult for a person to know whether they are making a correct choice regarding an action which will establish reputation but also decrease privacy: it is difficult to estimate or bound the repercussions of the decrease in privacy.

Wednesday, November 11, 2015

[zxubpcuu] QR code on a T shirt

What would be an interesting QR code to print on a T-shirt?  How much data can be effectively and robustly printed, given that T-shirts undergo wear and tear?  T-shirts are mostly monochromatic, rarely having gradients, so a good match with QR codes.

Perhaps code that generates an image.  We want a programming language optimized for generating images, hopefully better than image formats that already exist.

Previously similar: code and applications.

Tuesday, November 10, 2015

[qphancgb] Octagonal mesh

Orient a regular octagon so two sides are horizontal and two are vertical.  (The other 4 are at 45 degrees.)  Mark nodes on each edge subdividing each edge into the same number of segments.

Straightforward would be to draw lines parallel to the edges through the nodes.  However, this results in a great many intersections in the interior.

Instead, first draw only the horizontal and vertical interior lines.  This divides the interior into a bunch of rectangles and some isosceles right triangles along the edges.  Connect the remaining nodes to the node "across" from them by a series of line segments that are diagonals of these interior rectangles.  This will create fewer internal intersections because we are reusing the orthogonal intersections.  There will be a few more intersections created at the centers of some of the rectangles.


The density of the internal intersections will be much greater near the edges of the octagon compared to the center.  Do some sort of energy minimization to move the intersections inward, dragging the lines with them.  The initial horizontal and vertical lines will no longer remain that way.  Maybe use curved edges.

Color the regions. I suspect only two colors are needed.  Inspired by, how can polyhedra with subdivided octagonal faces be colored?  Possibly an interesting board for a game.

The Petaminx twisty puzzle (and variations) demonstrate subdividing a pentagon with lines parallel to each edge.