The Great Math Mystery

Last night we watched The Great Math Mystery, a NOVA episode on PBS television. It was excellent and I recommend it. It can be watched on-line here at least temporarily. There is a full transcript, too. The mystery is:  Is math invented by humans, or is it the language of the universe? Reasons are given for both -- some math is invented and some is discovered.  I believe the best answer came near the end. Math concepts such as numbers are abstracted by humans, but then they and their relationships are found to apply beyond their origin and lead to further discoveries.

The topics include the Fibonacci sequence, the number pi, Galileo's mathematics of falling bodies, Maxwell's equations, Marconi's discovery of radio telegraphy, the quantitative intelligence of lemurs, and the difference between pure math and applied math. Regarding the last, pure math is exact and imaginative but becomes much more useful via approximating with short-cuts such as done by engineers.

How a self-driving car works

Tragically, an Uber self-driving car struck and killed a woman in Tempe, Arizona three days ago. It appears she was walking her bicycle across the road, not at a crosswalk or near an intersection. Uber immediately stopped its test program in Arizona and elsewhere. Link.

I'm posting the link not because of the accident, but because it includes a good graphic about how a self-driving car works.

Addendum: The NYT article was updated -- the part about the safety driver -- after I posted the above.

Personal Knowledge #1

Personal Knowledge is a book by Michael Polanyi published in 1958. He was a chemist and philosopher. It is an inquiry into the nature and justification of scientific knowledge. He rejects the ideal of scientific detachment. There is personal participation of the knower in all acts of  understanding, without making it subjective. Knowing is objective in the sense of making contact with a hidden reality, such contact being the condition for anticipating an indeterminate range of yet unknown true implications.

Polanyi uses the the Copernican revolution and subsequent ones in physics to elaborate this with reference to skills and explicit versus tacit knowledge. I may try to summarize what he said later after finishing the book. I will cite some of his interesting points on the nature of science in this and later posts.

"Scientists -- that, creative scientists -- spending their lives in trying to guess right. They are sustained and guided therein by their heuristic passion. We call their work creative because it changes the world as we see it, by deepening our understanding of it. The change is irrevocable. A problem that I once solved can no longer puzzle me; I cannot guess what I already know. Having made a discovery, I shall never see the world again as before. My eyes have become different; I have made myself into a person seeing and thinking differently. I have crossed a gap, the heuristic gap which lies between problem and discovery.
     Many discoveries change our interpretive framework. Here it is logically impossible to arrive at these by the continued application of our previous interpretive framework. So we see once more that discovery is creative, in the sense that it is not to be achieved by the diligent performance of any previously known and specifiable procedure.  This strengthens our conception of originality. The application of existing rules can produce valuable surveys, but does not advance the principle sof science. We have to cross the logical gap between a problem and its solution by relying on the unspecifiable impulse of our heuristic passion. ... Originality must be passionate" (143).

Trucks with no driver?

This story shows that the term driverless truck or a truck with no driver should be used with caution. I have seen many stories about how "driverless" trucks will greatly reduce the number of drivers employed by trucking companies.  There are exceptions, such as this one.  The Uber truck shown in the video in the first link gives reason for the caution. The truck doesn't need the driver as much as a traditional truck does, but it still employs a human being. The trucker's job will be reshaped but not eliminated. There are several things that will still require human help, such as hitching, unhitching, and maneuvers near loading docks. The driverless technology will mainly change the nature of long-haul highway trips when there is little traffic.

Automated driving seems more fitting than driverless or no driver.

Tiger and sloth bear fight

Tiger and sloth bear fight.  This occurred in Tadoba National Park in central India.

For a while it appears the tiger will win. With the bear is on its back, the tiger has its mouth around the bear's neck. However, sloth bears have a lot of fur, preventing the tiger from getting a good bite. They both walk away to end it.