Diophantine equations are a certain class of equations for which solutions that consist only of integers are sought. So, for example, we know that Pythagoras’s theorem x2+y2=z2 has many sets of solutions such as the numbers x=3, y=4, z=5 or the set x=6, y=8, z=10. A lot of these problems involve existence claims such as whether any solution exists at all and if none can be found, whether it can be proved that no solution exists.
[Read more…]
The Cambrian explosion is the name given to the discovery of a vast range of fossils of organisms that existed about 500 million years ago. The first discovery of them was made in the Burgess Shale region of Canada in 1909 and other troves were later found in China and Australia. But now comes a report of an extremely rich new trove that has been discovered, again in China.
[Read more…]
(My review of the above book just appeared in the March 2019 issue of the American Journal of Physics (vol. 87, issue 4, p.319). You can access it here but I give the review below.)
A major problem with quantum mechanics is that the dominant Copenhagen interpretation is not conducive to providing visual images of what is going on. With special and general relativity, the initially unsettling ideas that time and distance are not invariants but depend upon the state of motion of the observer and that space can be warped by the presence of mass and energy have gone mainstream. Not so with quantum mechanics. Although of the same vintage as relativity, quantum mechanics has continued to greatly perplex people because it undermines the realist position that other theories, including relativity, take for granted, of a world existing independent of the observer, whose features we can discover by making observations. The denial of this made even Einstein uneasy.
[Read more…]
We all have in our minds short histories of how knowledge grew and a popular one is that there was a period of scientific and philosophical growth that began more than a couple of millennia ago with the ancient Greek, Arabic, and Chinese civilizations that slowed down sometime during the early second millennium where there were no real advances and indeed a regression with a loss of knowledge. That was then followed by the period we now call the Age of Enlightenment with its associated scientific revolution that began in the 17th century around the time of Galileo. Scholars of the much-maligned middle period that has come to be down as the Middle Ages (or more pejoratively the Dark Ages) take umbrage with characterizations that compare that period unfavorably with what existed before and what came after.
[Read more…]
The revulsion over the mass murder of Muslims in New Zealand by white supremacists has overshadowed an important news event today and that is the call for a global strike by students to call attention to the need for governments to take action on climate change. They are rightly pointing out that it is their generation and those that follow who will have to live with the consequences of inaction by my generation.
[Read more…]
I got a message from an acquaintance in Sri Lanka forwarding a video that said that the BBC had reported yesterday that there had been fish raining from the sky in Mumbai, India. This is one of those things that are circulated widely and was accompanied by a message that claimed that this was proof of a miracle and of a god in action. The acquaintance who forwarded it to me (who is a Roman Catholic believer) asked me if this could be a miracle. My acquaintance likely asked me because he knows I am a scientist and since I have not had any contact with him for decades, he probably thinks I am still religious and thus likely to support his beliefs.
[Read more…]
National Geographic had a segment about the Flat Earth movement. The ten-minutes piece begins at about the 11:30 mark.
What surprised me is that it said that 2% of the American population believes in it. That works out to about 6 million people and is said to be growing. The other thing that disturbed me is that there seemed to be a lot of young people in the group. The video shows a small model of a flat Earth.
[Read more…]
After showing that Blackadder clip a couple of days ago, YouTube (as is its wont) promoted another funny scene from the same show, this time about a famous theater superstition involving the play Macbeth.
I had an interesting discussion recently with some friends from my days in college about the extent that one should go to monitor one’s health and take steps to prolong one’s life. The discussion was prompted by an article that discusses one aspect of Barbara Ehrenreich’s new book where she looks at this question.
[Read more…]
Good metaphors can be powerful things, bringing a dull and difficult concept to vivid life by comparing it to something else that is believed to be true and can be easily visualized. But if a once powerful metaphor is found to be based on a false premise, should we continue to use it? This has become the case with the ‘boiling frog’ metaphor frequently used to discuss how we can be oblivious to major and potentially disastrous changes if those changes occur slowly. The metaphor is based on the belief that “a frog immersed in gradually heating water will fail to notice the creeping change in its circumstances, even as it’s literally being boiled alive.”
[Read more…]