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Jeff Johnson
Lives in Milwaukee, WI, United States
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Jeff Johnson

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When I first started my “Seek the Good” project, it began with a dream to find voices that needed to be heard, to put a megaphone where there had been none, in order to pierce the darkness in our world with light–with hope. Something was stirring in my heart to tell meaningful stories locally ...

Jeff Johnson

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In Russia, there is a park all ready for woolly mammoths and scientists there say it's just a matter of time before they can bring back actual mammoths to enjoy it. But why bring back a species that went extinct thousands of years ago?

Evolutionary biologist Beth Shapiro takes a look at that question in her new book, How to Clone a Mammoth: The Science of De-Extinction.
De-extinction technology could soon bring back lost species -- or preserve endangered ones. In her new book, evolutionary biologist Beth Shapiro explores the scientific and ethical challenges.

Jeff Johnson

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Remove this rusted metal cap and the world’s deepest hole tunnels miles into the Earth. However, we know more about certain distant galaxies than we do about what lies miles beneath our very own feet. For that reason, Soviet scientists in the 1970s decided to probe deeper than humanity has ever done before. For the next 24 years, they drilled on and off into the Earth’s crust. 

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The New Horizons space probe is shaking off a deep sleep and getting ready to become the first spacecraft to visit Pluto.

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A massive asteroid, roughly twice the size of the Rose Bowl, will fly safely by the Earth. At its closest point, the space rock will be about 745,000 miles from Earth.

Jeff Johnson

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Lol yeah. Dumb users are our worst nightmare. 
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Small, exciting victories!
For the first time in more than a century, giant tortoises have bred successfully on the Galapagos island of Pinzón. The announcement raises hope for preserving some of the diversity that inspired Darwin's theory of evolution.

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Think your handwriting is pretty neat? Well here's your chance to share it with the world by turning it into a font, and it gets better, it's free to do thanks to the good people at

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Water often damages metals, causing rust, wear and decay. A new technique might make metal slicker than Teflon, though.

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The tautological clock

This humorous clock reminds me of the concept of a vector bundle in mathematics. To form a vector bundle over a space X, we associate a vector space (such as k-dimensional Euclidean space) to each point of X in such a way that the spaces fit together to form another space of the same type as X. What this clock is doing is associating a clock to each time of day, and then fitting those together to form another clock.

More specifically, I think this clock is reminiscent of the concept of a tautological bundle, which appears in the following context. The set of k-dimensional subspaces of an n-dimensional vector space forms a space called a Grassmannian, whose points are the k-dimensional subspaces. If we work over the real or complex numbers, the Grassmannian has the structure of a smooth manifold, which means that, within an n-dimensional space, it is possible to morph k-dimensional subspaces into each other in a smooth way. One can then form the tautological bundle over the Grassmannian by using the vector spaces given by the points of the Grassmannian itself! This sounds almost like a mathematical joke, and it is more or less the same joke that the clock in the picture is making.

The clock face shown is a discrete object in the sense that it only displays its configurations at intervals of one hour. However, vector bundles are continuous objects, and the analogy above suggests the following construction of a continuous version of the clock. For this, we need a three-dimensional clock in which the small clock faces are inserted into the rim of the large clock face at right angles, instead of being placed flat on it. This could be used to show the continuous motion of the clock hands over a 12-hour period. 

To make it easier to see what is going on, we could just keep track of the tips of each hand using fluorescent lighting. The continuous tautological clock would then have two coiled, illuminated rings running around its circumference: a larger, more tightly coiled ring showing the positions of the minute hand during a 12-hour period, and a smaller, more loosely coiled ring showing the positions of the hour hand during the same 12-hour period. It might not be a very useful timepiece, but I think it would look interesting as a work of art.

Is that the time? I should stop: it's almost 12-o'clock-o'clock.

Relevant links

Grassmannians have applications to video-based computer recognition of faces and shapes, as well as to particle physics. More information on Grassmannians can be found here:

Wikipedia on vector bundles:

Wikipedia on tautological bundles:

I don't know where this picture came from originally, and doing a reverse image search produces a large number of hits. I found it via +Maximilian Montserrat.

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Amateur photographer, baseball fan, movie junkie, always searching for great cheeseburgers and real wood-smoked bbq (outside chopped is my fav)

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Lovely outdoor setting - perfect on a sunny day - service was slow - food was good, although nothing to get excited about. The atmosphere is the draw here - if you have plenty of time and don't mind waiting for attention, it's quite nice.
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