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Archive for November 19th, 2020

Scientists Uncover the Universal Geometry of Geology

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Interesting article in Quanta by joshua Sokol. I didn’t know about the Gömböc, but now I see you can buy copies (or 3-D  print your own). The article begins:

n a mild autumn day in 2016, the Hungarian mathematician Gábor Domokos arrived on the geophysicist Douglas Jerolmack’s doorstep in Philadelphia. Domokos carried with him his suitcases, a bad cold and a burning secret.

The two men walked across a gravel lot behind the house, where Jerolmack’s wife ran a taco cart. Their feet crunched over crushed limestone. Domokos pointed down.

“How many facets do each of these gravel pieces have?” he said. Then he grinned. “What if I told you that the number was always somewhere around six?” Then he asked a bigger question, one that he hoped would worm its way into his colleague’s brain. What if the world is made of cubes?

At first, Jerolmack objected. Houses can be built out of bricks, but Earth is made of rocks. Obviously, rocks vary. Mica flakes into sheets; crystals crack on sharply defined axes. But from mathematics alone, Domokos argued, any rocks that broke randomly would crack into shapes that have, on average, six faces and eight vertices. Considered together, they would all be shadowy approximations converging on a sort of ideal cube. Domokos had proved it mathematically, he said. Now he needed Jerolmack’s help to show that this is what nature does.

“It was geometry with an exact prediction that was borne out in the natural world, with essentially no physics involved,” said Jerolmack, a professor at the University of Pennsylvania. “How in the hell does nature let this happen?”

Over the next few years, the pair chased their geometric vision from microscopic fragments to rock outcrops to planetary surfaces and even to Plato’s Timaeus, suffusing the project with an additional air of mysticism. The foundational Greek philosopher, writing around 360 BCE, had matched his five Platonic solids with five supposed elements: earth, air, fire, water and star stuff. With either foresight or luck or a little of both, Plato paired cubes, the most stackable shape, with earth. “I was like, oh, OK, now we’re getting a little bit metaphysical,” Jerolmack said.

But they kept finding cuboid averages in nature, plus a few non-cubes that could be explained with the same theories. They ended up with a new mathematical framework: a descriptive language to express how all things fall apart. When their paper was published earlier this year, it came titled like a particularly esoteric Harry Potter novel: “Plato’s Cube and the Natural Geometry of Fragmentation.”

Several geophysicists contacted by Quanta say the same mathematical framework might also help with problems like understanding erosion from cracked cliff faces, or preventing hazardous rock slides. “That is really, really exciting,” said the University of Edinburgh geomorphologist Mikaël Attal, one of two scientists who reviewed the paper before publication. The other reviewer, the Vanderbilt geophysicist David Furbish, said, “A paper like this makes me think: Can I somehow make use of these ideas?”

All Possible Breaks

Long before he came to Philadelphia, Domokos had more innocuous mathematical questions.

Suppose you fracture something into many pieces. You now have a mosaic: a collection of shapes that could tile back together with no overlaps or gaps, like the floor of an ancient Roman bath. Further suppose those shapes are all convex, with no indentations.

First Domokos wanted to see if geometry alone could predict what shapes, on average, would make up that kind of mosaic. Then he wanted to be able to describe all other possible collections of shapes you could find.

In two dimensions, you can try this out without smashing anything. Take a sheet of paper. Make a random slice that divides the page into two pieces. Then make another random slice through each of those two polygons. Repeat this random process a few more times. Then count up and average the number of vertices on all the bits of paper.

For a geometry student, predicting the answer isn’t too hard. “I bet you a box of beer that I can make you derive that formula within two hours,” Domokos said. The pieces should average four vertices and four sides, averaging to a rectangle.

You could also consider the same problem in three dimensions. About 50 years ago, the Russian nuclear physicist, dissident and Nobel Peace Prize winner Andrei Dmitrievich Sakharov posed the same problem while chopping heads of cabbage with his wife. How many vertices should the cabbage pieces have, on average? Sakharov passed the problem on to the legendary Soviet mathematician Vladimir Igorevich Arnold and a student. But their efforts to solve it were incomplete and have largely been forgotten.

Unaware of this work, Domokos wrote a proof which pointed to cubes as the answer. He wanted to double-check, though, and he suspected that if an answer to the same problem already existed, it would be locked in an inscrutable volume by the German mathematicians Wolfgang Weil and Rolf Schneider, an 80-year-old titan in the field of geometry. Domokos is a professional mathematician, but even he found the text daunting.

“I found someone who was willing to read that part of the book for me and translate it back into human language,” Domokos said. He found the theorem for any number of dimensions. That confirmed that cubes were indeed the 3D answer.

Now Domokos had the average shapes produced by splitting a flat surface or a three-dimensional block. But then a larger quest emerged. Domokos realized that he could also develop a mathematical description not just of averages, but of potentiality: Which collections of shapes are even mathematically possible when something falls apart?

Remember, the shapes produced after something falls apart are a mosaic. They fit together with no overlap or gaps. Those cut-up rectangles, for example, can easily tile together to fill in a mosaic in two dimensions. So can hexagons, in an idealized case of what mathematicians would call a Voronoi pattern. But pentagons? Octagons? They don’t tile. . .

Continue reading.

Written by Leisureguy

19 November 2020 at 6:51 pm

Posted in Daily life, Math, Science

Tracks of vitamin D

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The Eldest pointed out an interesting pattern in the charts in this post: Southern states, whose populace gets more sunlight, do better than northern states given the same level of effort.

For example, look at the first chart at the link. Neither Montana nor Florida did much to counter the pandemic, but Montana is much worse off than Florida. It may be due to differences in average vitamin D levels due to differences in exposure to sunlight. And after the autumnal equinox, not only do northern latitudes get fewer hours of sunlight, the sunlight is also weaker.

Just a thought — but I am upping my intake of vitamin D.

Written by Leisureguy

19 November 2020 at 1:39 pm

Posted in Daily life, Health

Amber Elliott, county health director: ‘This is how we treat each other? This is who we are?’

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As told to Eli Saslow in the Washington Post:

I don’t really know if I should be talking about all of this. It makes me worried for my safety. I’ve had strange cars driving back and forth past my house. I get threatening messages from people saying they’re watching me. They followed my family to the park and took pictures of my kids. How insane is that? I know it’s my job to be out front talking about the importance of public health — educating people, keeping them safe. Now it kind of scares me.

But people need to know what’s going on. It’s happening all over the country, and it’s not acceptable. I know we can do better. We have to do better.

I don’t base our whole response to this pandemic on my own opinion. That’s what makes the backlash so confusing. This job is nonpartisan. I’m not political in any way. I go off of facts and evidence-based science, and right now, all the data in Missouri is scary bad. We only have about 70,000 people in St. Francois County, but we’ve had more than 900 new cases in the last few weeks. Our positivity rate is 25 percent and rising. The hospital is already at capacity. They’ve basically run out of staff. We can’t keep up. It’s an uncontrolled spread. I have these moments when it feels like I’m a nurse at the bedside, and my patient is dying, and I’m trying every possible intervention to save them. More social distancing. More masks. More contact tracing. Warnings and more warnings. What else can we try? But in the end, it doesn’t matter how much you do. Nothing will work, because it almost seems like the patient is resisting your help.

I get the same comments all the time over Facebook or email. “Oh, she’s blowing it out of proportion.” “She’s a communist.” “She’s a bitch.” “She’s pushing her agenda.”

Okay, fine. I do have an agenda. I want disease transmission to go down. I want to keep this community safe. I want fewer people to die. Why is that controversial?

We weren’t set up well to deal with this virus in Missouri. We have the worst funding in the country for public health, and a lot of the things we’ve needed to fight the spread of covid are things we should have had in place 10 years ago. We don’t have an emergency manager. We don’t have anyone to handle HR, public information, or IT, so that’s all been me. We didn’t get extra funding for covid until last month. I’m young and I’m motivated, and I took this job in January because public health is my absolute love. It doesn’t pay well, but would I rather be treating people who already have a disease or helping to prevent it? That’s what we do. We help take care of people. At one point this summer, I worked 90 days straight trying to hold this virus at bay, and my whole staff was basically like that.

We hired 10 contact tracers to track the spread, starting in August, but the real problem we keep running into is community cooperation. We call everyone that’s had a positive test and say: “Hey, this is your local health department. We’re trying to interrupt disease transmission, and we’d love your help.” It’s nothing new. We do the same thing for measles, mumps, and tick-borne diseases, and I’d say 99 percent of the time before covid, people were receptive. They wanted to stop an outbreak, but now it’s all politicized. Every time you get on the phone, you’re hoping you don’t get cussed at. Probably half of the people we call are skeptical or combative. They refuse to talk. They deny their own positive test results. They hang up. They say they’re going to hire a lawyer. They give you fake people they’ve spent time with and fake numbers. They lie and tell you they’re quarantining alone at home, but then in the background you can hear the beeping of a scanner at Walmart.

I’ve stayed up a lot of nights trying to understand where this whole disconnect comes from. I love living in this county. I know in my heart these are good people, but it’s like we’re living on different planets. I have people in my own family who believe covid is a conspiracy and our doctors are getting paid off. I’ve done press conferences and dozens of Facebook Live videos to talk about the real science. Even with all the other failures happening, that’s the one thing we should be celebrating: better treatments, nurses and doctors on the front lines, promising news about vaccines. But the more I talk about the facts, the more it seems to put a target on my back.

“We’re tracking your movements.” “Don’t do something you’ll regret.” “We’ll protest at your house.”

The police here have been really great. The elementary school says they’re watching over my kids and they’re on high alert. . . .

Continue reading.

More in this story from local paper.

Written by Leisureguy

19 November 2020 at 12:46 pm

Rebecca Newberger Goldstein interview: “Plato, Gödel, Spinoza, Ahab”

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Richard Marshall does the interview at the blog 3:16:

Philosophical advances in epistemology and in ethics profoundly shape our points of view. We don’t see them precisely because we see with them. It’s like the fish who responds to the question “How’s the water today?” with “Water? What’s water?”’

‘Gödel proved that, in any formal system that is rich enough to express arithmetic, there are truths that are expressible within it that can’t be proved. That’s the First Incompleteness Theorem. The second is that one of the things that can’t be proved within such a formal system is its own consistency.’

‘Since Gödel had interpreted his First Incompleteness Theorem in the light of his mathematical realism, then yes, postmodernists are barking up the wrong tree. The proof shows that there is a mathematical truth—the Gödel sentence—that is not provable within the system. He’s not in any way attacking the notion of objective truth in mathematics. Quite the contrary.’

‘Spinoza, the great monist, objected to dualities in just about every domain. He was everywhere interested in fusing, in unifying, what seemed to be polarities, collapsing dualities. The supernatural is fused with the natural, the ontological with the logical (which is entailed in his a priori methodology), the mental with the physical, the intellectual with the emotional, the normative with the descriptive.’

‘Maybe Reality really is inconsistent with the reality of the self, and maybe then, driven by our conatus, we ought to resist Reality. That’s the path that Ahab takes, and it doesn’t end well for him, nor for those under his leadership, who have relinquished their wills to his. After all, why is it even worthwhile to struggle to know Reality, to struggle after anything at all, if the self that’s motivating the struggle is ultimately nothing at all?

Rebecca Newberger Goldstein is an American philosopher, novelist and public intellectual. She has written ten books, both fiction and nonfiction. Here she discusses the relationship between science and philosophy, the nature of philosophical progress, Gödel’s theorems, Incompleteness, Einstein, Realism and postmodernism, Gödel and Wittgenstein, Spinoza, Spinoza and his appeal to imaginative writers, the Spinoza War, and Moby Dick.

3:16: What made you become a philosopher?

Rebecca Newberger Goldstein :  I started out mostly interested in math and physics. There were problems that obsessed me in both fields—How can math be a priori? How can quantum mechanics be connected to a reality that is recognizably our own? I discovered, while in college, that these were actually philosophical problems. My senior year in college I went to speak to one of my professors, Sidney Morgenbesser, an amazing guy. He was the Socrates of his day. Socrates never published anything, but instead engaged in deeply probing dialogues. That was Sidney’s m.o. as well. Over the course of several long conversations Sidney convinced me that I was a philosopher, rather than a scientist. His clinching argument was that scientists are like the bourgeoisie, never questioning the system, whereas philosophers were like socialists, always examining the system critically: even if it seemed to be working, ought it to be working? That argument struck home. I basically applied to graduate school in philosophy on the strength of Sidney’s metaphor.

3:16: In your book Plato at the Googleplex’ you have Plato brought into our century to discuss philosophy with our contemporaries. So first, can you say what you take philosophy to be and why you think it hasn’t gone away and isn’t going away soon?

RNG: I think that philosophy is the systematic and rigorous investigation of one of the deepest urges that we humans have, which is the urge to get our bearings in the most general sense possible. In particular, (1) We want to know where we are. What is the nature of this universe in which we find ourselves? What fundamentally different kinds of things, belonging to different ontological categories, are there, and how do they operate? 2. We want to know our own place in the universe, whether we’re made of the same stuff, are a special category of being, and whether the universe itself has any attitudes towards us. 3. We want to know what we are meant to do with our lives. We want to know what it is to live a life worthy for a human to live, a good life.

The first two questions are ontological, the third is normative. Science, as it eventually developed, has the lead role in answering the ontological questions, but science is often pushed on by philosophy, in its critical probing role. And the more subtle the science becomes, the bigger the role for philosophy, since it falls to philosophy’s special techniques to figure out what is and isn’t entailed by the science. For example, what changes are we required to make to our concept of time in light of Relativity Theory? And as far as the normative questions go, there the ball falls squarely in philosophy’s court, though it’s sometimes advancements in science and technology that generate the balls, that is, new normative questions.

Consider the normative questions generated by advances in AI, or the question of what obligations we have to future generations, given the threat of climate change. As long as science and technology advance, philosophers will have new questions to work on.

3:16:  You place Plato in rooms having philosophical debates with all sorts of people but you never have him decisively concluding a debate or argument. For those hostile to philosophy this might be a hostage to fortune – it suggests that philosophy can’t decide anything and actually we would be better off listening to scientists, historians and novelists. Why should we heed the philosopher in our time if not even Plato can answer its questions? What do you say to those physicists who say philosophy is just pointless and has been supplanted by – well, in their case – physics?  . . .

Continue reading.

Written by Leisureguy

19 November 2020 at 12:36 pm

Posted in Books, Philosophy

Not exactly a surprise: States That Imposed Few Restrictions Now Have the Worst Outbreaks

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Update: The Eldest raised an interesting point. Vitamin D has been found to help, and it shows in looking at the graph below. Look at the states that have not done much to contain Covid-19 and compare the southern states with the northern states — the southern states are doing much better, perhaps because of more exposure to sunlight and thus more vitamin D. I’m upping my intake of vitamin D. /update

Anyone who did not expect this should do some introspection on their decision-making process. Lauren Leatherby and Rich Harris report in the NY Times:

Coronavirus cases are rising in almost every U.S. state. But the surge is worst now in places where leaders neglected to keep up forceful virus containment efforts or failed to implement basic measures like mask mandates in the first place, according to a New York Times analysis of data from the University of Oxford.

Using an index that tracks policy responses to the pandemic, these charts show the number of new virus cases and hospitalizations in each state relative to the state’s recent containment measures.

Outbreaks are comparatively smaller in states where efforts to contain the virus were stronger over the summer and fall — potential good news for leaders taking action now. States and cities are reinstating restrictions and implementing new ones: In recent days, the governors of IowaNorth Dakota and Utah imposed mask mandates for the first time since the outbreak began.

The index comes from Oxford’s Blavatnik School of Government, where researchers track the policies — or lack thereof — governments use to contain the virus and protect residents, such as contact tracing, mask mandates and restrictions on businesses and gatherings. Researchers aggregate those indicators and assign a number from 0 to 100 to each government’s total response.

At its highest level of containment efforts, New York state scored an 80 on the index. At the beginning of November, most states were scoring in the 40s and 50s. Though many have taken fresh steps to contain the virus since then, the Times analysis compares cases and hospitalizations for a given date to a state’s index score from two weeks before, since researchers say it is reasonable to expect a lag between a policy’s implementation and its outcome.

Most states imposed tight restrictions in the spring even if they did not have bad outbreaks then. After reopening early, some Sun Belt states, including Arizona and Texas, imposed restrictions again after case counts climbed. Now, Midwestern states have among the worst outbreaks. Many have also done the least to contain the virus.

When cases first peaked in the United States in the spring, . . .

Continue reading.

Written by Leisureguy

19 November 2020 at 10:40 am

D.R. Harris Rose shaving cream with the Fine Marvel and D.R. Harris Pink After Shave

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Another shaving cream day — I got turned toward shaving creams for a while by an article in Sharpologist: “What Is The Most Popular Lathering Shave Cream?” My two favorites (J.M. Fraser shaving cream and Nancy Boy Signature shaving cream) are not mentioned, but I imagine their sales volume is low compared to the heavily marketed creams featured in the article.

I do also like TOBS Avocado (preferable in a tub, not a tube: the price per shave from a tub is about half of what it is from a tube), and I’ve had some good Truefitt & Hill and D.R. Harris shaving creams, but years back I decided to focus on shaving soaps rather than shaving creams. As a result, I stopped exploring shaving creams. I also like I Coloniali a lot, but alas, that has been discontinued. I’ll use it tomorrow.

I of course got an excellent lather, since shaving creams easily produce good lather. Indeed, my foray into soaps began when I found that, while I could easily get a good lather from a shaving cream, I had trouble making lather from shaving soaps. So I decided to set shaving creams aside and use only shaving soaps in order to master the skill, and when I did, I found I preferred soaps to creams.

Still, shaving creams are pleasant. I enjoyed using the Rose this morning, and again found pleasure in using the Copper Hat brush. Fine’s Marvel razor head (here on a bronze UFO handle) is excellent, and it offers good guidance to the best angle.

Three passes and my face was perfectly smooth, ready for a good splash of Pink After Shave.

As soon as I was dressed (and before writing this), I got the beef shank ready and in the oven. What I actually did differed from my plan, so I’m revising that post (the one just before this one) to reflect the changes.

Written by Leisureguy

19 November 2020 at 8:44 am

Posted in Shaving

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