To infinity and beyond

Mathematician Eugenia Cheng has written a popular, amusing, and fascinating book on the concept of infinity.

Beyond Infinity:  An Expedition to the Outer Limits of Mathematics takes up its paradoxes, mathematical conundrums, and important uses.

For example, one mathematical axiom is that:

infinity X infinity = infinity.

But if you work out this equation by dividing both sides by infinity, you get:

infinity = 1

Since that can’t be, infinity must not be a number, exactly.  But what is it?

Read an excerpt from her book, taken from Science Friday. [Read more…]

All mammals can swim, except for two

tiger-455804_640Contrary to what used to be thought, virtually all mammals can swim.  Cats?  Yes, though they hate it.  Camels?  Yes, despite seldom seeing water.  Pigs?  Yes. Elephants?  They are excellent swimmers.  Throw a bat into the water and it will use its little wings like oars.

From what we know now, apparently there are only two mammals–one species and one genus–that can’t instinctively swim.  Guess, and then see what they are–along with a fascinating article on the subject–after the jump.


Photo of tiger swimming by cuzitwasgood, Pixabay, Creative Commons, Public Domain

[Read more…]

The social implications of the Second Law of Thermodynamics

15559246066_b31a92f623_oIn discussing the debacle at the Oscars, government incompetence, political surprises, and unintended cultural consequences, Jonah Goldberg invokes the Second Law of Thermodynamics.  This is the principle in physics that closed systems will increase in entropy (become less ordered) unless energy is introduced to maintain the order.  (A lay definition by me, a layman.  Feel free to explain it better.)

Goldberg applies this to social systems as well.  I suspect this is more of a figure of speech than an actual application of physics.  (Again, those of you who know, weigh in.)

But his point seems to hold true:  Our political system needs our continual input of energy to keep it going, otherwise, it will degenerate.  Societies, cultures, and institutions need the continual effort of their members to keep them from descending into chaos.  By extension, we could observe that marriages need continual work to keep them strong.  So do churches.

What other applications do you see? [Read more…]

“We’re the ones that are going to start contaminating the water.”

Dakota_Access_Pipeline_-Elder_Addressing_Crowd-Thousands of protesters joined the Standing Rock Sioux to protest the Dakota Access Pipeline.  They were trying to stop an oil pipeline because it crossed sacred lands and for fear that it would pollute the Missouri River.  The protests led President Obama to stop the pipeline, but President Trump has approved it.

Now the protesters are gone.  But the environmentalists, so insistent on preserving a pristine natural environment, have left behind some 48 million tons of garbage.  They also abandoned some of their pets.

But the biggest urgency is that the amount of human waste and toxic material left behind threatens to pollute the Missouri River! [Read more…]

Pluto might get promoted back to “planet”

Nh-pluto-in-true-color_2x_JPEG-edit-frameThe recent space probe to Pluto revealed it to be no mere frozen rock but a complex world.  Now NASA scientists involved with that project are proposing a new definition of “planet” that would restore Pluto to its former planetary status.

Possible problems:  The new definition would also make the Earth’s moon a planet.  Also 110 other celestial bodies in our solar system.

But read the reasoning after the jump. [Read more…]

Bringing back the woolly mammoth