according to "Schedules" on https://www.amtrak.com/ , 2026-05-07:
Thursday, May 28, 2026: Train 3 departs CHI 2:25p arrives LAX 7:57a (43h 32m). this is the last train on the old schedule.
Friday, May 29, 2026: Train 1003 (a special number) departs CHI 1:30p arrives LAX 8:12a (44h 42m)
Saturday, May 30, 2026: Train 3 departs CHI 1:30p arrives LAX 8:12a (44h 42m)
there is no information about this on "Service Alerts and Notices" https://www.amtrak.com/alert
when has a volcano's lava flow into water conveniently built a bridge over a gap that humans wanted to bridge?
there must be evidence of regular human crossings (over water) before the eruption. there must now be a road across the land bridge.
Sakurajima, Japan is one possible example. but the road is there (in part) to visit the volcano famous for the 1914 eruption that created the land bridge. is (was) there demand for travel to the peninsula (island) apart from that?
as a simple corollary to Euler's theorem, every road network in which all roads are two-way has an Euler cycle that travels on every road once in each direction. perhaps practically useful for road inspection or tours of the scenery.
which circuit is best? perhaps fewest sharp turns (including U turns), fewest left turns (assuming right-hand side driving).
on official diagrams, the MBTA Red Line is drawn to split into the Ashmont and Braintree lines south of JFK/UMass station. in reality, the lines have already split north of the station, and the station has separate platforms for each line. to catch the next northbound (inbound) train, you have to guess which platform to wait on. there is technology that announces which platform will have the next northbound train, but I don't know how reliable it is or how much advance warning it gives, in case stairs or elevator are slow for you.
but wait, it gets worse. even though the lines have split as of JFK/UMass, the tracks remain parallel and next to each other through the next station to the south, Savin Hill. only trains on the Ashmont line stop at Savin Hill. therefore, to get from North Quincy on the Braintree line to Savin Hill, you board the northbound train at North Quincy, watch from your train as it goes past but does not stop at Savin Hill, get off at JFK/UMass, walk up and over to the Ashmont platform, then take a southbound train back to Savin Hill.
who on earth thought all this was a good idea? I suspect it has something to do with communities on the Ashmont line being predominantly poor and African-American.
redraw the train diagram to reflect reality, as a way of drawing attention to the stupidity. JFK/UMass is effectively two stations with free transfer between them. both branches go through Savin Hill, but only the Ashmont line gets a white dot indicating the train stops there. only after Savin Hill do the lines go separate directions.
MBTA Red Line subway, Park Street station, southbound, 2022-12-17 (13 months ago), 15:46, vehicle 1861 according to Boston Bus Map app.
likely trying to speed up boarding by fooling people into not boarding a crowded train, the conductor lies over the PA speakers: "we do have a train right behind us."
the electronic displays indicate the next southbound subway train is 17 minutes away, definitely not "right behind us".
is it MBTA policy to always say this regardless of how far behind the next train is?
in the event of an emergency, passengers need to trust the conductor's instructions, need to trust that what the conductor says is the truth, need to trust that the conductor has the passengers' best interest in mind. previous lies break that trust.
the weekday commute of humans on earth is a large movement of mass. this movement, because it is not spherically symmetric, generates gravitational waves.
our movement is somewhat periodic but not quite: weekends, Daylight Saving Time, holidays, leap days, and leap seconds cause deviation. distant aliens with very sensitive gravitational wave detectors could observe these deviations from periodicity and determine that the source must be intelligent life: a civilization sophisticated enough to coordinate their actions with a calendar. many holidays, and the start and end of DST, are engineered to fall on a certain day of the week so are more complicated than yearly periodic. Easter (computus) is even more complicated, but it always occurs of a Sunday, so it probably does not affect people commuting to work. but maybe other holidays of major religions.
perhaps aliens will wonder what happened on Earth in March 2020 that caused our gravitational wave emissions to suddenly decrease. but those waves have yet to even reach Alpha Centauri.
our weekday commute being somewhat periodic and repeated many times helps boost signal to noise, though our signal will likely be dwarfed by (say) a pair of black holes, somewhere in the universe, orbiting each other with a period of 1 day (generating a gravitational wavefront every half day, mimicking to the round trip of a daily commute). a pair of supermassive black holes, each 1 million solar masses, circularly orbiting around each other at a distance of 2.47 au or 125 Schwarzschild radii would produce such waves:
You have: ((day / (2 pi))^2 G (1 mega sunmass)*2)^(1|3)
You want: au
* 2.4657235
You have: ((day / (2 pi))^2 gauss_k^2 au^3 day^-2 (1 mega)*2)^(1|3)
You want: au
* 2.4657235
You have: ((day / (2 pi))^2 gauss_k^2 au^3 day^-2 (1 mega)*2)^(1|3)
You want: 1 mega sunmass 2 gauss_k^2 au^3 day^-2 c^-2 / sunmass
* 124.90205
instead of the gravitational constant G, the second and third calculations use the standard gravitational parameter which is known to greater precision than G.
our weekday commute is much less than millions of solar masses.
is it appropriate to use the Newtonian formula of orbital period? how quickly do the orbits of such a pair of black holes decay? (do the black holes change faster than the commuting behavior of human civilization?) what is the expected number of binary systems with this period in the observable universe, i.e., how loud is the background noise at this frequency?
previously on using a single car as a gravitational wave generator.
create a grid of unit squares out of line segments of length 2. at each vertex meet the endpoints of two segments and the midpoint of an orthogonal segment.
randomly shift each segment. (many ways to do this.) lengthen or shorten segments to maintain adjacencies. most intersections will become T junctions. square grid becomes ugly.
inspired by a poorly planned road network with a lot of T junctions, sometimes two close T junctions controlled awkwardly by one set of traffic lights.
the U.S. Interstate Highway System is a direct copy of the Nazi Reichsautobahn. then-General Dwight Eisenhower ironically appreciated the usefulness of Hitler's roads for invading Germany, so he replicated them in America when he became President.
Hitler was quite a visionary for constructing the Reichsautobahn because there were not many cars at the time. (is the reason some parts of the modern Autobahn have no speed limit because the original Nazi design was so good?) or, even if Hitler took no part in the design, he did use his political power to cause good (but expensive) designs to be built. he appointed competent people to proper positions of power. in America, President Eisenhower gets all the credit for being the visionary: the U.S. would be a very different place if most of our Interstate highways were like "U.S." highways, one lane in each direction and narrow shoulders, which I think is the case in many modern countries which didn't copy the Nazis. such narrow roads were also the case in 1919 when then-Lt. Col. Eisenhower took an army expedition across the U.S. to determine whether U.S. roads were suitable for military transport (they were not).
(did Reichsautobahn have wide shoulders? some image searching seems to indicate not. a place to put disabled vehicles so they don't block traffic is a very good feature of U.S. Interstate highways.)
imagine U.S. Interstate highway signage in a hypothetical alternate universe which gives credit where it is due, even if politically unpopular. replace the blue "shield" design.
previously the other way: Hitler tries to copy what the United States did well.
(or, imagine an alternate universe in which both men are considered fools not visionaries: environmentalists correctly foresee the internal combustion engine causing climate change, so they (the true visionaries) steer transportation away from fossil fuels, perhaps toward electric trains.)
mark local extremal points of elevation on roads, because those are interesting (e.g., when bicycling).
2D contour maps are hard to make (though they exist); 1D along roads is easier.
in the diamond cubic crystal structure, each carbon atom connects to four others. this provides a way to navigate 3-space with only a 4-way decision at each point: 4 buttons suffice, less than the 6 of going orthogonally.
2D analogue: the vertices of a hexagonal honeycomb. each vertex has 3 neighbors, less than the 4 of the square honeycomb.
in both 2D and 3D, there are two different types of nodes (vertices) that alternate: one type with outgoing edges in one set of orientations, the other going the other way. the 4 buttons (for 3D) will correspond to different directions depending on which type of node you are at. perhaps repeatedly hitting the same button executes a 2-cycle, bouncing back and forth along an edge.
a dungeon whose rooms each have up to 4 exits (e.g., Zelda 1), but the topology is not a plane but 3-space.
the Voronoi cell is the triakis truncated tetrahedral honeycomb, corresponding to the equilateral triangular honeycomb in 2D, with every other triangle upside-down.
consider one tetrahedron in the tetrahedral-octahedral honeycomb. go to another tetrahedron by traveling orthogonally through a face, through an octahedron, to the next tetrahedron. this is possible because tetrahedra and octahedra alternate in the honeycomb, and an octahedron has opposite pairs of parallel faces. I strongly suspect this graph among tetrahedron centers is the diamond cubic lattice.
are there analogues in higher dimensions? first thought for 4D is the edges of the 24-cell honeycomb, 16 edges per vertex. but the edges of a tesseract honeycomb is better, 8 edges per vertex. it should be possible to do better.
any graph (starting from any lattice in any number of dimensions) can be made into a cubic graph (all node degrees 3 or less) by replacing nodes with too many edges by rings (traffic roundabouts). 3 buttons suffice. roundabouts allow U-turns by going all the way around, so one does not need to provide a "go back" button. 2 buttons suffice: exit roundabout or keep going around. we would still prefer roundabouts with fewer outgoing edges.
the electrification of the Northeast Corridor rail line was completed January 31, 2000. the MBTA Providence commuter rail line (Wickford Junction) runs on the Northeast Corridor. how long will it take for the Providence line to replace its loud, smelly, diesel locomitives with electric trains? (22 years and counting.)
this broadly demonstrates how America can't get its act together about rail. narrowly, what's the hold up?
electric trains are more energy efficient because they can easily do regenerative braking, pumping electricity back into the grid.
inspired by the electrified Philadelphia SEPTA regional rail.
xkcd "what if?" contemplates the grisly aftermath of the world's entire population brought (magically) to Rhode Island: "Within weeks, Rhode Island is a graveyard of billions."
but what if a lot of planning were done beforehand to prepare an exit strategy?
we explore cargo ships, because they are huge.
it is shamefully the U.S., in its slave trade, which has had extensive experience in shipping humans at ultra-high densities on cargo ships, so it makes sense to conduct the experiment in the U.S. (another country has experience in shipping humans at inhumanely high density by rail, not explored here. but how much of that knowledge is preserved?)
according to Wikipedia, the port of Ningbo-Zhoushan, China, handled 1 billion metric tons of cargo tonnage 2017. assuming a human weighs 100 kg, that port handles the mass equivalent 7 billion people every 250 days. satellite imagery of the port shows a great many unoccupied berths, suggesting a billion tons is the port still not operating at full capacity.
therefore, evacuating the world population from Rhode Island by ship in a reasonable time frame seems within the realm of possibility.
we imagine all of Narragansett Bay converted to a giant port to handle the exodus. perhaps shift the site of The Jump to the east by a bit to allow use of the whole coastline (e.g., Fall River, MA). probably have a fleet of special ships constructed and stocked in advance to densely transport humans, perhaps ideas from old slave ships scaled up to the size of modern cargo ships (or beyond, future post slzhkgde).
although humans (probably) don't pack as densely as ore, oil, or shipping containers (what is shipped to and from Ningbo-Zhoushan), we are self-propelled, so maybe loading can be done very quickly. how to load people quickly is the major unknown of this plan, the bottleneck.
the ships sail to many transshipment centers distributed anywhere but Rhode Island. they have been constructed in stocked in advance, so can process people more leisurely, eventually getting everyone home.
previously: strategic planning to make the exodus worse.
consider a Hilbert curve on a grid. navigate around the grid with 4 arrow keys. navigate along the curve in 2 directions, forward and backward. zoom in, zoom out (zooming has some tricky details). 8 buttons total.
I-5 exit 667A, Anderson, CA
US-101 exit 667A, Englewood, Redcrest, CA
the above two seem to be deliberately avoiding having an exit 666 by substituting 667A, perhaps to deter sign theft.
I-10 has exit 661 then exit 668, Flatonia, TX.
exit numbers as high as 666 are only possible on long highways in large states.
highway 401 in Ontario, Canada has exit 661 (Lansdowne) then 675 (Mallorytown).
globally direct cars on a graph of roads. which car gets priority at a merge? if there are multiple paths to destination, plan routes of all cars to maximally utilize all available roads. how difficult is this problem? need to specify an objective function, and how cars appear (enter), each with its desired destination.
graph of edges. each edge has capacity of 1 car.
inspired by Minecraft mine carts.
exit 880 I-10 eastern Texas
exit 796 I-5 northern California
exit 794 US-101 northern California
exit 635 I-20 eastern Texas
exit 549 I-90 southeastern Montana
exit 504 I-35 northern Texas
exit 454 I-80 eastern Nebraska
Alaska seems not to number highway exits.
exit 825 (in kilometers) highway 401 southeastern Ontario, Canada.
many games, e.g., go 囲碁 and hex, (sort of) do min-cut, but not many do max-flow.
vaguely inspired by Factorio.
first, consider roads drawn on 1x1 square tiles (monominoes). the midpoint of each edge is a connection point for a road going from one tile to an adjacent tile. examples: Truchet tiles, Carcassonne. label the sides of the square 0 1 2 3 in clockwise order. there are 7 possible types of tiles, not counting rotations:
p (0123)
p (01 23)
(02 13)
p (0 123)
p (0 1 23)
p (0 2 13)
p (0 1 2 3)
each cluster of digits represents a connected component of the graph drawn on the tile. a singleton connected component means there is no road along that side. (we'll consider another possibility later.)
the prefix "p" indicates the graph is planar. the only non-planar tile is the one with two roads going straight across at right angles, one flying over the other.
next, consider domino tiles. 6 possible connection points for roads along the sides of the domino. label them 0 through 5 around the perimeter. 0 and 3 are the short sides.
omit duplicates from 180 degree rotation.
omit from enumeration domino tiles whose road network can be represented by two monomino tiles. determine this as follows. consider the line segment dividing a domino into two squares. keep a domino if the road graph crosses the middle line segment at least twice. a connected component contributes one crossing if and only if it has nodes on both squares. for two crossings, there needs to be two connected components, both which cross the middle edge.
p (012 345) & (045 123)
(013 245) & (035 124)
(014 235)
(02 1345) & (04 1235)
(024 135)
(03 1245)
p (12 0345)
(14 0235) & (25 0134)
(02 13 45)
(02 14 35) & (04 13 25)
p (03 12 45)
(03 14 25)
p (0 12 345) & (0 45 123)
(0 13 245) & (0 35 124)
(0 14 235) & (0 25 134)
p (1 02 345) & (5 04 123)
(1 03 245) & (5 03 124)
(1 04 235) & (5 02 134)
(1 25 034) & (5 14 023)
(1 35 024) & (5 13 024)
p (1 45 023) & (5 12 034)
p (0 2 13 45) & (0 4 12 35)
(0 2 14 35) & (0 4 13 25)
p (0 3 12 45)
(0 3 14 25)
p (1 2 03 45)
(1 2 04 35)
p (1 4 02 35) & (2 5 04 13)
(1 4 03 25) & (2 5 03 14)
there are 47 possible domino tiles, counting chiral pairs as separate. chiral pairs are given on the same line separated by ampersand. (there are 29 if reflections are omitted.) 16 out of 47 are planar, marked "p". (if a tile is planar, so is its mirror image.)
future work: enumerate 2x2 big squares, omitting those which can be broken down into combinations of 1x1 or 1x2. perhaps also omit 3 square L, enumerating them first.
previously, we had declared that a singleton connected component represents no road through that side. alternatively, it could be a short stub of a dead-end road. allowing both possibilities, there are the 18 possible 1x1 square tiles:
p (0123)
p (01 23)
(02 13)
p (0 123)
p (123)
p (0 1 23)
p (0 23) & (1 23)
p (23)
p (0 2 13)
p (0 13)
p (13)
p (0 1 2 3)
p (0 1 2)
p (0 1)
p (0 2)
p (0)
p ()
the presence of a singleton connected component indicates a stub road; the absence of a side being mentioned at all means no road goes through that side.
future work: enumerate the domino tiles permitting both stub roads and no road. do we permit a short purely internal stub road across the middle of the tile? (such a road could be constructed from two monominoes.) similarly, do we permit a purely internal circuit inside a 2x2 tile?
much simpler: the only 1x1 tile is the 4-way intersection (or roundabout). similarly, the domino tile is a 6-way elliptic rotary. the 2x2 tile is a big 8-way rotary, maybe with decoration in the center. also include 3-square L? everything connects to everything.
One cannot transfer directly from the Blue line to Red line. Workarounds are to take the Green line between Government Center and Park Street, or the Orange Line between Downtown Crossing and State, or Silver line from South Station to Logan Airport terminals then Airport shuttle bus from terminals to Airport station. Hypothetical simple fix would be extension of Blue line from Bowdoin to Charles MGH.
One cannot take commuter rail or Amtrak between North Station and South Station. Workarounds are Orange line from North Station to Downtown Crossing then Red line to South Station, or Green line from North Station to Park Street then Red line to South Station. Both workarounds require two trains with a transfer in the middle, likely especially annoying if you have lots of luggage, as would be expected for intercity travel.
On one hand, most people are so used to these links being missing that they don't notice them. On the other hand, it's pretty amazing these links have been left uncompleted (not even started) for decades.
Consider cellular automata in which a cell's next state depends on both its local neighborhood and a few possible distant interactions. Inspired by chess (future post). The distant interactions could be with the first nonempty cell for each of the directions a chess queen can move (or no interaction if there is nothing along a ray).
"Mostly local but with a few distant interactions" tells a story that people can relate to (to be elaborated on in a future post).
