Category: Science

Mensa Math

Apologies for links to political blogs. There’s some math here. The question is, what is the probability that one person could have survived two mass shootings (e.g., Gilroy and Las Vegas) ?

One fellow provides this calculation:

Las Vegas 2017 attendance: 20,000
Gilroy 2019 attendance: 80,000

I don’t know how many attendees were actually physically present at each event at the time of the shootings, but I’ll assume two thirds, so 14,520 and 52,800.

Proportion of US population present at LV shooting: 14,520 / 350,000,000 = .000041 or .0041%

Proportion of the population NOT at LV is the inverse or 99.9959%

Likelihood of one person being at both events is then: 1 – (.999959^52,800). Which is 88.8%. The number of times this apparently happened is 3, so it’s 0.888^3, or 70%.

In other words, through purely random chance it is more likely than not that 3 people who were at the LV 2017 shooting would also be present at the Gilroy shooting.

another fellow, who is a member of Mensa, provides this calculation:

The Gilroy Garlic Festival is a three-day event, so that 80,000 is reduced to 26,667 before being reduced another one-third as per Uncephalized’s assumption to account for the timing of the event. This brings us to an estimated 17,787 people present at the time of the shootings. Note that reducing the estimated 20,000 Las Vegas attendance by the same one-third gives us 13,340, not 14,520.
[…]
Gilroy probability: Dividing 17,787 by 350,000,000 results in a probability of 0.00005082, or one in 19,677.
Las Vegas probability: Dividing 13,340 by 350,000,000 results in a probability of 0.00003811428, or one in 26,237
Gilroy AND Las Vegas probability: Multiplying 0.00005082 by 0.00003811428 results in a probability of 0.0000000019369677096, or one in 516,270,868.

Someone posits in a comment to the second calculation, meekly, that perhaps the problem is analogous to the “birthday problem“. The Mensan responds:

No. That’s not relevant here because there is no equivalent to the finite number of birthdays in a year.

I’m personally not smart enough to be admitted to Mensa. However, it seems to me that the number of people in the United States is a finite number.

The Napkin Project by Evan Chen

This is what makes the Internet great:

I’ll be eating a quick lunch with some friends of mine who are still in high school. They’ll ask me what I’ve been up to the last few weeks, and I’ll tell them that I’ve been learning category theory. They’ll ask me what category theory is about. I tell them it’s about abstracting things by looking at just the structure-preserving morphisms between them, rather than the objects themselves. I’ll try to give them the standard example Gp, but then I’ll realize that they don’t know what a homomorphism is. So then I’ll start trying to explain what a homomorphism is, but then I’ll remember that they haven’t learned what a group is. So then I’ll start trying to explain what a group is, but by the time I finish writing the group axioms on my napkin, they’ve already forgotten why I was talking about groups in the first place. And then it’s 1PM, people need to go places, and I can’t help but think:

Man, if I had forty hours instead of forty minutes, I bet I could actually have explained this all.

This book is my attempt at those forty hours.

This project has evolved to more than just forty hours.

The most current draft is also available as a PDF.

my god, it’s full of stars

High-resolution original image here. Technical details about the EHT:

Creating the EHT was a formidable challenge which required upgrading and connecting a worldwide network of eight pre-existing telescopes deployed at a variety of challenging high-altitude sites. These locations included volcanoes in Hawai`i and Mexico, mountains in Arizona and the Spanish Sierra Nevada, the Chilean Atacama Desert, and Antarctica.

The EHT observations use a technique called very-long-baseline interferometry (VLBI) which synchronises telescope facilities around the world and exploits the rotation of our planet to form one huge, Earth-size telescope observing at a wavelength of 1.3 mm. VLBI allows the EHT to achieve an angular resolution of 20 micro-arcseconds — enough to read a newspaper in New York from a sidewalk café in Paris.

This image is fated to be as iconic as the Pale Blue Dot and Earthrise.

Of particular note is that the algorithm to combine the data from all the different sources was the product of research by Dr. Katie Bouman, who is the overnight face of women in STEM, deservedly so.

Here’s a wide angle shot of the area around the black hole, from NASA’s Chandra X-Ray telescsope:

Earthrise 50th anniversary

50 years ago on Christmas Eve (Dec 24, 1968), the astronauts aboard Apollo 8 took an amazing series of photos of the rising earth behind the limb of the moon, while in orbit. The first photo was black and white, and subsequent ones (with the earth having risen farther from the moon horizon) were color, and now with some digital magic, these are combined into one image. Glorious.

“Oh my God, look at that picture over there! There’s the Earth comin’ up. Wow, is that pretty!” — Astronaut Bill Anders, Apollo 8

Featured on APOD; Original image credit Apollo 8 / NASA; processing by Jim Weigang; CC license and google photo album.

Goodbye, Cassini

I met Cassini in 1996 at JPL before it departed for Saturn. For 20 years I have cheered its mission. That mission is over, and Cassini’s watch has ended.

I posted this six years ago here at haibane, but it’s worth reposting in salute: an incredible compilation of a flyby of the Saturnian system:

5.6k Saturn Cassini Photographic Animation from stephen v2 on Vimeo.

the hype about Hyperloop

Elon Musk comes to town
Elon Musk comes to town

This article makes an important point about the Hyperloop:

America has the means to reduce traffic and connect people to where they want to go in less time — but solving these problems entails politically difficult choices to shift travel away from cars and highways. Any high-tech solution that promises a shortcut around these thorny problems is probably too good to be true.

I can’t help but see an echo of the wishful thinking surrounding the EMDrive in the Hyperloop marketing campaign. Maybe I’ll be proven wrong.

Here’s the original white paper PDF from Elon Musk, and here’s a rather detailed critique by mathematician and transit analyst Alon Levy. Anyone who takes Hyperloop seriously should read both.

We Just Got Our ’30s Sci-Fi Plots Back

By now, you’ve heard that seven – count ’em, seven – terrestrial planets have been discovered orbiting the ultra-cool M8 star Trappist-1.  According to the paper that the research team released yesterday, all of them could potentially have liquid water on their surfaces, although only three are judged to be good candidates: the authors’ model considers it likely that the three innermost planets have succumbed to a runaway greenhouse effect and that the outermost is too cold.  But that still leaves three potentially habitable planets in a single system.

Those three – Trappist-1e, 1f and 1g – range from .62  to 1.34 estimated Earth masses, and as one would expect from a red-dwarf system, they’re  tidally locked and orbit close to their star with periods of 6 to 12 days.  Their orbits are also very close to each other.  The distance between the orbits of 1e and 1f is .009 AUs – about 830,000 miles – and 1f passes within 750,000 miles of 1g.  This is a system that, even according to its discoverers, shouldn’t exist – their model gives it only an 8.1 percent chance of surviving for a billion years – but as they point out, it obviously does.

There are many more fascinating details about the Trappist-1 system and still more that we have yet to learn.  The discoverers hope that further research, and the launch of the James Webb space telescope next year, will enable them to confirm the details of the planets’ atmospheres and possibly look for biological signatures.  But in the meantime, for those of us who write SF, the discovery of the Trappist-1 system means this: we just got our pulp-era plots back.

We’ve all read stories from the heady days of the 1930s in which the intrepid heroes travel to Mars or Venus in a few days, take off their space suits, breathe the air, encounter exotic life forms and interact with non-human societies.  As we learned more about our solar system, that all got taken away.  The jungles of Venus and the canals of Barsoom have long since been relegated to the realm of nostalgia, and if we want aliens in our stories, we have to cross impossible interstellar distances to find them.

But now, there’s a system where all that can happen!  Three habitable worlds with orbits less than a million miles apart, Hohmann transfers that can be done in a few weeks with inspired 1950s tech – we’ve got the ingredients for interplanetary travel that’s almost as easy as pulp writers imagined it.  And a citizen of Trappist-1f might actually find that Old Venus jungle world one planet in and an arid Old Mars one planet out, and generations of its people could watch their neighbors’ fields and cities grow and dream of one day visiting them.  All we need to do to make pulp stories into hard SF again is move them 40 light years.

All right, we’d need to do a little more than that.  The planets are tidally locked – and with zero eccentricity, they don’t have libration-generated twilight zones – so we’d need to model the day-side and night-side weather.  We’d need to account for the tidal and geological effects of so many worlds so close together, and the atmosphere had better have plenty of ozone to protect against UV and X-ray emissions.  But none of those constraints are deal-breakers, and within them, Weinbaum-punk is suddenly acceptable.

That may not last, of course.  By this time next year, the research team might have found that the Trappist-1 planets have reducing atmospheres or that there’s insufficient protection from stellar radiation or that some other factor makes pulp SF as impossible in that system as in our own.  But right now, it’s wide open to stories of the imagination.  We’ve found one spot in the universe where it’s the Golden Age all over again.