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How thick is the atmosphere? A derivation of the Boltzmann distribution
Let’s talk about a small question as a way of introducing a big question. How thick is the atmosphere? How far does Earth’s atmosphere extend into space? In other words, how high can y…
J.C. Bose: 60 GHz in the 1890s
(1) The National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under cooperative agreement by Associated Universities, Inc.
City street orientations around the world
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
Comparing City Street Orientations
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
Random Points on a Sphere
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy R…
Why FTL implies time travel
In science fiction, it is pretty standard fare to introduce some form of faster-than-light communication or travel. After all, space is big, and you can't write your swashbuckling Hornblower-in-space novel if you have to wait for a generation ship to crawl painfully slowly between the nearest stars,
How much is time wrong around the world? (2014)
Why Spaniards have dinner so late? A map of the difference between solar time and clock time around the world.
Lost in Math
Sabine Hossenfelder’s new book Lost in Math should be starting to appear in bookstores around now. It’s very good and you should get a copy. I hope that the book will receive a lot of a…
The Dipole Drive: A New Concept for Space Propulsion
It’s a fascinating concept but I’d like to see a comparison toDr. Young Bae’s laser thruster concept for solar system travel.
Why does a spray bottle work?
Exploring a simple machine I took apart a simple spray bottle to see how it kept fluid flowing only in one direction from the reservoir to the nozzle. It does so with simple check valves made of two pieces of plastic, a spring, and a small sphere. It’s a simple way to solve a tricky problem. A simple spray bottle One…
High-quality schools can increase academic achievement among the poor (2010)
Harlem Children’s Zone (HCZ), an ambitious social experiment, combines community programs with charter schools. We provide the first empirical test of the causal impact of HCZ charters on educational outcomes. Both lottery and instrumental variable identification strategies suggest that the effects of attending an HCZ…
Earth-Moon Fire Pole
My son (5y) asked me today: If there were a kind of a fireman's pole from the Moon down to the Earth, how long would it take to slide all the way from the Moon to the Earth?
Gödel and the unreality of time
In 1949, in a festschrift devoted to Einstein , Kurt Gödel published a very short but profound paper titled “A Remark About the Relati...
Genetics and Eugenics in Frank Herbert's DUNE
Observations on Frank Herbert’s 𝐷𝑢𝑛𝑒 series—the notes are probably overstated, the Butlerian Jihad was 𝑛𝑜𝑡 a robot uprising seeking to exterminate humanity, and precognition/prescience in the Dune universe appears to work backwards allowing for retro-causality and stable time-loops as exemplified by Leto II’s Golden…
The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
The Fable of the Dragon-Tyrant (2005)
An allegory against complacency about aging and death.
Mathematics I Use (2012)
An explanation of the forms of mathematics I use on a daily basis as a working software engineer.
Losing the Nobel Prize
There’s a fascinating new book just now appearing in book stores, Losing the Nobel Prize, by astronomer Brian Keating. An excerpt from the book is available at Nautilus, with the title How My…
Executing gradient descent on the earth
A common analogy for explaining gradient descent goes like the following: a person is stuck in the mountains during heavy fog, and must navigate their way down. The natural way they will approac......
Darwin: a genomics co-processor provides up to 15,000x acceleration
Darwin: a genomics co-processor provides up to 15,000x acceleration on long read assembly Turakhia et al., ASPLOS’18 With the slow demise of Moore’s law, hardware accelerators are needed to m…
Jupyter, Mathematica, and the Future of the Research Paper
Economist. Policy Entrepreneur. Geek. Co-recipient of the 2018 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. University Professor at NYU. Focused on urbanization; cooperation at scale of millions and billions; science; technology; economic development; long-term growth; code as language.
How people die vs. media coverage of death
Data collection and analysis by Hasan Al-Jamaly, Maximillian Siemers, Owen Shen, and Nicole Stone.
Notes on Resonance
Resonance occurs when two sources of excitation fall completely in sync, and reinforce one another endlessly. In this state, the sources convey an unbounded amount of energy over time.