. The Golomb sequence
grows asymptotically at a rate of 
where 
is the golden ratio.I’ve collected into one place the more interesting links I’ve previously posted, so that you have no reason to go hunting through the older posts. For slightly longer posts, see here.
Division of three for cardinals without the axiom of choice.
In 2017 a neutron star merger was observed by both gravitational and electromagnetic waves! Aside from the usual confirmations, in particular this confirmed that such mergers are the origin of short gamma ray bursts and are the origin of most heavy elements (heavier than iron). It is estimated that the gold and platinum produced was “vastly” more than the mass of the Earth.
“The worst result in a simultaneous [chess] exhibition given by a master occurred in 1951, when International Master Robert Wade gave a simultaneous exhibition against 30 Russian schoolboys, aged 14 and under. After 7 hours of play, Wade had lost 20 games and drawn the remaining 10”
Two interesting sequences: Gijswijt’s
sequence contains every positive integer, but grows so slowly that
the first 5 appears around term . The Golomb sequence
grows asymptotically at a rate of where is the golden ratio.
Near Xenon’s critical point at 58 atm and 17 C, Xenon gas has a
density of 1100 kg / m
, greater than liquid water at those conditions.
So what happens if you try to float liquid water on Xenon gas at those
conditions? You get a
solid.
There is a layer of sodium at an altitude of ~100 km in the Earth’s atmosphere caused by meteors.
“They lifted half a city block […] and an estimated all in weight including hanging sidewalks of thirty five thousand tons. Businesses operating out of these premises were not closed down for the lifting; […] One patron was puzzled to note that the front steps leading from the street into the hotel were becoming steeper every day and that when he checked out, the windows were several feet above his head, whereas before they had been at eye level. […] the practice of putting the old multi-story, intact and furnished wooden buildings – sometimes entire rows of them en bloc – on rollers and moving them to the outskirts of town or to the suburbs was so common as to be considered nothing more than routine traffic.”
An economics paper: “Japan’s Phillips Curve Looks Like Japan”.
A data structure that takes advantage of uninitialized memory to use less time than space!
I wrote a Newton fractal generator. See animation.
Special phenomena in 4 dimensions
Tarski’s theorem about choice. Fréchet wrote that an implication between two well known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest.
Measurements of the gravitational constant vary sinusoidally.
https://www.sciencenews.org/article/darwin-reluctant-mathematician “Fisher’s analysis was only possible because Darwin had designed his experiment so well. In fact, Fisher was often frustrated with the quality of other people’s experiments. ‘To call in the statistician after the experiment is done,’ he said, ‘may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of.’”
If a CPU cycle is one second, then accessing L1 cache is 3 seconds and accessing the disk takes 1 to 12 months.
“Viktor Klee, in a parody of the usual optimistic prophecies people like to make, wrote that: ‘…progress on this question, which has been painfully slow in the past, may be even more painfully slow in the future.’”
The third-closest known star system to the Sun was discovered only in 2013.
Let’s play… identify the city from its satellite picture! (To get the highest zoom, click on the icon in the upper right of each picture.) Total population between all the pictures is roughly 333 million people.
“Paper and Pencil: a Lightweight WYSIWYG Typesetting System” (page 88)
A review of What We Know About Climate Change by Kerry Emanuel.
Apparently x-rays are visible to the naked eye.
A remarkable collection of unique chess problems (with solutions). Problems 3, 4, 6, and 10 are easier.
A bug in “file” that made it unable to print on Tuesdays.
“An honest examination of the sky forced him to displace the center of the spiral pattern away from us by more than half the galactic radius in the direction of Cygnus, and his drawing gives the impression of a man struggling with the truth and losing.” An article about the 1920 debate on the existence of other galaxies
“Although the new calendar was much simpler than the pre-Julian calendar, the pontifices apparently misunderstood the algorithm for leap years. They added a leap day every three years, instead of every four years. According to Macrobius, the error was the result of counting inclusively, so that the four-year cycle was considered as including both the first and fourth years; perhaps the earliest recorded example of a fence post error.”
Natural nuclear reactors have occurred on Earth before, with a cycle time of about 3 hours, and lasting for hundreds of thousands of years before exhausting their fuel.
Vlad the astrophycisist performed by Peter Mulvey.
Parable of the broken window: war does not help the economy.
Death of an ant colony (fiction)
3 of 6 found this book review useful: “If you are looking for practical advice on the avoidance of large sea-faring vessels, this is not the book for you. I neglected to read the subtitle, as it was set in very small type and seemed utterly unimportant beneath the huge title. And so it was that I came to a bad pass, colliding with the tanker Condoleezza Rice some 150 miles east of the Bay of Fundy.”
“Prof. Loof Lirpa and colleagues were able to shorten Whitehead and Russell’s 360-page proof that 1+1=2 in Principia Mathematica to this remarkable proof only two steps long, thus establishing a new world’s record for this famous theorem.”
“This phenomenon shows how, after the more complex visual system is damaged, people can use the latter visual system of their brains to guide hand movements towards an object even though they cannot see what they are reaching for.”
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