| Tuesday, May 13, 2008 | |
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Pat Corvini 2007 Course on Math Now Available
By Paul @ 12:01 AM   
In my 4/26/2008 blog post, "Are Mathematical Truths Discovered or Invented?", I referred to Dr. Pat Corvini's superb course at the 2007 OCON as an excellent example of applying the Objectivist epistemology to the concept of number. At the time, the course was not yet available for sale.As an update - the course is now available for purchase from the Ayn Rand Bookstore. Here's a slightly modified description of the course, per Dr. Corvini: Two, Three, Four and All ThatAccording to the Ayn Rand Bookstore, the course is a 6-CD set, selling for $61.95. Total run time is 4 hrs., 29 min., including Q & A.  E-mail Paul
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| Saturday, April 26, 2008 | |
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Are Mathematical Truths Discovered or Invented?
By Paul @ 11:23 AM
This question is one of the topics in the upcoming June 2008 issue of the European Mathematical Society Newsletter. As Science News reports, this subject "has provided fodder for arguments among mathematicians and philosophers" for thousands of years, with no seeming resolution.On one hand, there are Platonists who believe this: ...[A] mathematician discovers timeless truths independent of human observation and free of the transient nature of physical reality. "The abstract realm in which a mathematician works is by dint of prolonged intimacy more concrete to him than the chair he happens to sit on," says Ulf Persson of Chalmers University of Technology in Sweden, a self-described Platonist.But the Platonists are forced to deal with some tricky implications of their views: Those who espouse discovery note that mathematical statements are true or false regardless of personal beliefs, suggesting that they have some external reality. But this leads to some odd notions. Where, exactly, do these mathematical truths exist? Can a mathematical truth really exist before anyone has ever imagined it?In contrast, there are those who believe that such talk of an abstract realm is just mystical hogwash: Brian Davies, a mathematician at King's College London, writes that Platonism "has more in common with mystical religions than with modern science." And modern science, he believes, provides evidence to show that the Platonic view is just plain wrong. He titled his article "Let Platonism Die."But the latter school is faced with a different set of intractable questions: On the other hand, if math is invented, then why can't a mathematician legitimately invent that 2 + 2 = 5?The solution to this millenia-old argument is to abandon both the intrisicist approach of the Platonists and the subjectivist approach of their opponents. Instead, mathematical concepts (like all concepts) are neither intrinsic nor subjective but objective. It is in debates like this where the Objectivist approach to epistemology and concept formation prove their value -- in being able to cut through the errors made over the centuries by struggling philosophers and mathematicians. Of course, properly applying Rand's theory of concept formation to the philosophy of mathematics is a non-trivial task. Concepts of number are both seemingly self-evident, but also represent feats of tremendous abstraction. But scholars such as Dr. Pat Corvini have made a good start. Her course at the 2007 OCON, "Two, Three, Four and All That", was on precisely that topic -- namely how to apply the Objectivist theory of concept formation to concepts of number: The concept of number as used in science today is one of man's greatest achievements: a grand-scale integration capping centuries of effort and enabling a vastly expanded efficacy in all areas of life. But the growth in complexity of the number system has rendered the meaning of number ever more mysterious; number is seen both as a touchstone of certainty and as an arbitrary human construct whose applicability to the real world is a deep mystery. This is because the nature of number has not been properly identified; and as Ayn Rand pointed out, that imprecision is dangerous.She is also offering a follow-up course at this year's 2008 OCON, "Two, Three, Four and All That: The Sequel": Science shelves of bookstores are today awash in accounts of modern extensions of the idea of number, including infinity and the continuum, set theory, transfinite numbers, and the like. Many of these ideas, and the "mysteries" that proceed from them, figure prominently in modern philosophy and in popular discussion of the nature and limits of reason.I have long had an interest in those topics such as foundations of set theory, the nature of the concept "infinity", etc. Hence, if her 2008 course is as good as her 2007 course, then it promises to be a real treat. Diana and I have already signed up for it. Although I have a degree in mathematics (B.S., MIT, 1984), her courses do not require any advanced math background. Dr. Corvini is a very clear and engaging lecturer, and she is excellent at explaining the relevant mathematical concepts to a general audience. If you can count to 10 and you are a normal intelligent adult, then you can follow her lectures. So if you want to see how the power of the Objectivist theory of concepts can resolve questions that have stumped some of history's greatest minds for thousands of years, check out her courses! (I don't believe that her 2007 course is available yet through the Ayn Rand Bookstore, but I expect that it will be eventually. It was available for purchase by 2007 conference attendees as part of the usual post-conference package, and hence I think it will eventually make it to the main bookstore listing.) Labels: Objectivism, Philosophy, Science E-mail Paul
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| Sunday, April 20, 2008 | |
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Animal Minds
By Paul @ 7:44 AM
The March 2008 issue of National Geographic recently published an interesting article on research into animal minds. If the reported facts are reliable, then animals may have some ability to isolate similarities and differences between percepts. Here is an excerpt from the article on scientist Irene Pepperberg and her parrot Alex:...[B]ecause Alex was able to produce a close approximation of the sounds of some English words, Pepperberg could ask him questions about a bird's basic understanding of the world. She couldn't ask him what he was thinking about, but she could ask him about his knowledge of numbers, shapes, and colors. To demonstrate, Pepperberg carried Alex on her arm to a tall wooden perch in the middle of the room. She then retrieved a green key and a small green cup from a basket on a shelf. She held up the two items to Alex's eye.Of course, researchers have to be extremely careful not to anthropomorphize when interpreting such results. And even if animals are able to perform this sort of mental integration and differentiation of their percepts, this is not the same as being able to reason in the human sense. Hence, this post should not be construed as endorsing any form of "animal rights". But it is plausible from an evolutionary perspective that the human mental abilities that allow us engage in concept formation and reasoning would have primitive precursors in some of the higher animals, and that human cognition has a foundation based on those pre-existing building blocks. Hence, the exact abilities of various animal minds is a fascinating scientific subject worthy of study, even if it may not have any primary philosophical import. (I've been told that some Objectivists believe that animals are essentially automatons without any feeling or consciousness, like rocks or plants. In my opinion, this is untrue, and data such as this is further evidence against that erroneous position.) Labels: Science E-mail Paul
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| Tuesday, April 15, 2008 | |
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Death Spiral
By Paul @ 7:22 AM
Here is an interesting way of displaying mortality statistics.As the Wall Street Journal notes: It's tough to resist a graphic that begins, "Total odds of dying, any cause: 1 in 1."  Labels: Science E-mail Paul
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| Tuesday, February 19, 2008 | |
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Those Blue-Eyed Mutants
By Diana Hsieh @ 5:10 PM
Cool: "New research shows that people with blue eyes have a single, common ancestor. A team at the University of Copenhagen have tracked down a genetic mutation which took place 6-10,000 years ago and is the cause of the eye colour of all blue-eyed humans alive on the planet today."The full article has more details. Update: Thanks to Freddy, I fixed the link so that it doesn't ask you to print the page. Labels: Science E-mail Diana Hsieh
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| Wednesday, February 06, 2008 | |
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Biotechnology Marches On
By Paul @ 1:57 PM
In headline that would have sounded like science fiction just a few years ago, scientists have announced, "Embryos created with DNA from 3 people".To borrow a quote from this Onion story, "This has limitless scientific possibilities, which means one thing: We must keep Christians from finding out about it..." Labels: Science E-mail Paul
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| Tuesday, January 22, 2008 | |
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Dolphins Create Rings of Air Bubbles
By Paul @ 6:00 PM
Cool video: "Dolphins have been observed to create bubble rings by exhaling air carefully in the middle of the vortices caused by the motion of their fins through the water, among other techniques. Besides being nice to look at (and a neat demonstration of fluid mechanics), this phenomenon also might throw some light on dolphin cognition, since the skill to create the rings is a bit subtle and tends to be taught from one dolphin to the next via careful observation and practice."Labels: Science E-mail Paul
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| Thursday, January 10, 2008 | |
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Cold Weather? I Blame Global Warming
By Paul @ 7:10 AM
There's been a fair amount of extreme cold weather recently around the world. Of course, many environmentalists are attributing this to global warming. Geophysicist David Deming notes:Extreme cold weather is occurring worldwide. On Dec. 4, in Seoul, Korea, the temperature was a record minus 5 degrees Celsius. Nov. 24, in Meacham, Ore., the minimum temperature was 12 degrees Fahrenheit colder than the previous record low set in 1952. The Canadian government warns that this winter is likely to be the coldest in 15 years. Labels: Environmentalism, Science E-mail Paul
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| Tuesday, November 20, 2007 | |
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Theory of Everything?
By Paul @ 7:51 AM
Physicist/surfer Garrett Lisi may have come up with a physics theory that unites all the fundamental particles and forces of nature, including gravity, without relying on dubious multidimensional string theory. According to this related article:...[H]is proposal is remarkable because, by the arcane standards of particle physics, it does not require highly complex mathematics.In other words, it doesn't require invoking arbitrary new dimensions for which we have no evidence. Plus it makes testable predictions that are at variance with the so-called Standard Model. The New Scientist article states that his theory predicts: ...[M]ore than 20 new particles not envisaged by the standard model. Lisi is now calculating the masses that these particles should have, in the hope that they may be spotted when the Large Hadron Collider - being built at CERN, near Geneva in Switzerland - starts up next year.David Harriman mentioned in his lecture to our Front Range Objectivism group last year that any physicist who wants to challenge the dominance of string theory will have a very hard time, since nearly all the grant funding in academia for such foundational issues is controlled by people who believe in string theory. It seems that this is borne out by Lisi's experience, as reported by New Scientist: Most attempts to bring gravity into the picture have been based on string theory, which proposes that particles are ultimately composed of minuscule strings. Lisi has never been a fan of string theory and says that it's because of pressure to step into line that he abandoned academia after his PhD. "I've never been much of a follower, so I walked off to search for my own theory," he says. Last year, he won a research grant from the charitably funded Foundational Questions Institute to pursue his ideas.For those who are interested in the details of his theory, here's the link to his paper (click on "PDF" on the upper right). The abstract reads as follows: An Exceptionally Simple Theory of EverythingThose who want a semi-technical explanation (with video) can find one here. My own mathematics background is not strong enough to make an assessment of the merits of his theory. Nor do I know any more about the Foundational Questions Institute besides what's on their webpage. But for what it's worth, I did meet Garrett Lisi at a dinner party several years ago as a friend-of-a-friend, back when Diana and I lived in San Diego and he was still a graduate student in physics at UCSD. At the time, he struck me as an extremely intelligent man, so he would be a plausible candidate for someone who could have come up with a revolutionary new theory in physics. Labels: Science E-mail Paul
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| Thursday, July 05, 2007 | |
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Twinning
By Paul @ 2:37 PM
 These time lapse photographs show the exact moment when one embryo divides into two identical twins. If you're a Christian conservative, presumably this is also the exact moment that God infuses a second soul. I don't know how he decides which twin keeps the original and which twin gets the new one. (Via KevinMD.) Labels: Science E-mail Paul
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