The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve.
You don’t make a bagel by first baking a bialy and then punching out the center. No—you roll out a snake of dough and join the ends together to form the bagel. If you denied that a bagel has a hole, you’d be laughed out of New York City, Montreal, and any self-respecting deli worldwide. I consider this final.
The offering is naturally dependent on potential public health measures in September, which may also create a class limit on the number of attendees, so be sure to register as soon as it’s announced. For those who are interested in mathematics, but have never attended any of Dr. Miller’s lectures, I’ve previously written some details about his stye of presentation, prerequisites (usually very minimal despite the advanced level of the topics), and other details.
A few of us have already planned weekly Thursday night topology study sessions through the end of Spring and into Summer for those interested in attending. Just leave a comment with your contact information and I’ll be in touch with details.
I hope to see everyone in the fall.
“we hold these truths to be self-evident” wasn’t Jefferson’s line; his first draft of the Declaration has “we hold these truths to be sacred & undeniable.” It was Ben Franklin who scratched out those words and wrote “self-evident” instead, making the document a little less biblical, a little more Euclidean.
Me: We don’t Mississippi in this house! Maybe we should Tennessee since that’s where Grandma and Grandpa live?
Evie: I’ve Mississippi’ed since I was three.
Me: Maybe since we’re Welsh we should Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch? You know: 1-Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch, 2-Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch, …
Together: 3-Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch…
Evie (interrupting): Wait, what number are we on now???
The Chudnovsky brothers yearned to probe the mystery of pi, so they built their own supercomputer out of mail-order parts.
He was named professor emeritus after teaching in the Department of Philosophy for nearly four decades
How the pandemic has shaped our future: from the built environment, to the way we work, to the way we learn.
With vaccinations underway, we’re edging closer and closer to the end of the pandemic. This week, On The Media looks at how the pandemic has shaped what’s possible for the future — from the built environment to the way we work to the way we learn.
1. Sam Kling [@SamKling2], American Council of Learned Societies public fellow, on whether cities like New York were bound to become hubs for disease. Listen.
2. Vanessa Chang [@vxchang], lecturer at California College of the Arts, explains how pandemics of the past have been instrumental in shaping architecture; Mik Scarlet [@MikScarlet] delineates the social model of disability; and Sara Hendren [@ablerism], author of What Can A Body Do?: How We Meet the Built World, describes how the wisdom of people with disabilities can inform the redesign our post-pandemic world. Listen.
3. OTM reporter Micah Loewinger [@micahloewinger] tells the story of how distance learning saved his friend's life. Listen.
The Department of Mathematics at Johns Hopkins University solicits applications for one two-year postdoctoral fellowship beginning Summer 2021 (with some flexibility in the start and end dates). Th…
The ergodic hypothesis is a key analytical device of equilibrium statistical mechanics. It underlies the assumption that the time average and the expectation value of an observable are the same. Where it is valid, dynamical descriptions can often be replaced with much simpler probabilistic ones — time is essentially eliminated from the models. The conditions for validity are restrictive, even more so for non-equilibrium systems. Economics typically deals with systems far from equilibrium — specifically with models of growth. It may therefore come as a surprise to learn that the prevailing formulations of economic theory — expected utility theory and its descendants — make an indiscriminate assumption of ergodicity. This is largely because foundational concepts to do with risk and randomness originated in seventeenth-century economics, predating by some 200 years the concept of ergodicity, which arose in nineteenth-century physics. In this Perspective, I argue that by carefully addressing the question of ergodicity, many puzzles besetting the current economic formalism are resolved in a natural and empirically testable way.
Ergodic theory is a forbiddingly technical branch of mathematics. ❧
From the New York Times-bestselling author of How Not to Be Wrong, himself a world-class geometer, a far-ranging exploration of the power of geometry, which turns out to help us think better about practically...
From the New York Times-bestselling author of How Not to Be Wrong, himself a world-class geometer, a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything
How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess, and why is learning chess so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry.
For real. If you're like most people, geometry is a sterile and dimly-remembered exercise you gladly left behind in the dust of 9th grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps, only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. OK, it is geometry, but only a tiny part, a border section that has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.
Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word geometry, from the Greek, has the rather grand meaning of measuring the world. If anything, that's an undersell. Geometry doesn't just measure the world - it explains it. Shape shows us how.
