Mathematics

From Erica Klarreich at Quanta: In January, Ziegler traveled to San Diego for the Joint Mathematics Meetings, where he received (on his and Aigner’s behalf) the 2018 Steele Prize for Mathematical Exposition. “The density of elegant ideas per page [in the book] is extraordinarily high,” the prize citation reads. The 2014 book is Proofs from the Book (that is, a book of God’s alleged proofs, the most beautiful ones). Here’s the interview with Günter Ziegler (his co-author of Martin Aigner) at Quanta, with a sort of assist from Paul Erdős (1913-1996) Quanta: You’ve said that you and Martin Aigner have a similar sense of which proofs are worthy of inclusion in THE BOOK. What goes into your aesthetic? Ziegler: We’ve Read More ›

Here at Uncommon Descent, we never really celebrated Pi Day (March 14) this year because other stuff intervened. But pi is a really important irrational number: Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits. More. Indeed, In Carl Sagan’s novel Contact, the main character (Ellie Arroway) is told by an alien that certain megastructures in the universe were created by an unknown advanced intelligence that left messages embedded inside transcendental numbers. To Read More ›

From Ethan Siegel at Forbes: why, and when, can we use mathematics to learn something about our physical Universe? We don’t know the answer to why, but we do know the answer to when: when it agrees with our experiments and observations. So long as the laws of physics remain the laws of physics, and do not whimsically turn on-and-off or vary in some ill-defined way, we know we can describe them mathematically, at least in principle. Mathematics, then, is the toolkit we use to describe the functioning of the Universe. It’s the raw materials: the nails, the boards, the hammers and saws. Physics is how you apply that mathematics. Physics is how you put it all together to make Read More ›

From Meghan Bartels at MSN: Hawking approaches the problem by offering a detailed analogy, comparing space-time to any other continuous, curved surface, like the surface of the Earth. “There is nothing south of the South Pole,” Hawking says. The same principle holds with the universe: “There was nothing around before the Big Bang.”More. “Nothing” is actually a big word. It can mean many different things while purporting to be one big Nothing. Fine print. Ken Francis replied to this line of thinking at New English Review: About seven years ago, during a talk on Hawking at a university, I raised my hand and criticised comments he made in his then latest book, The Grand Design, which he co-wrote with Star Read More ›

One of the more astonishing points of debate that has come out at UD is that at least some defenders of the evolutionary materialistic view are prepared to argue for or assume as default that we have had a beginningless past for the physical world.  This has come up several times in recent years and was again discussed last week. I will share my take-away conclusion so far. But first, why are such willing to put up such a spectacularly untestable, unobservable claim? Because, we first know that non-being has no causal powers so if there were ever utter nothing, such would forever obtain. That a world manifestly is implies that SOMETHING always was. The question is what, given that Read More ›

The hyperreals are an extension of the real number line that brings to bear a reciprocal relationship between the very large and the very small. By so introducing extensions to the real number continuum, it forms a base for an infinitesimals approach to the calculus and makes sense of a lot of the tricks used by early pioneers of Calculus from Leibniz and Newton to Euler and beyond. (Though, it is clear in retrospect that they missed a lot of the pathologies that are now part of the far more cautious approaches of today.) And yes, here is a case where Wikipedia does some good (likely, in a context where there are few basement trolls capable of making a mess): Read More ›

From William Basenerand John Sanford at The Skeptical Zone: Joe Felsenstein and Michael Lynch (JF and ML) wrote a blog post, “Does Basener and Sanford’s model of mutation vs selection show that deleterious mutations are unstoppable?” Their post is thoughtful and we are glad to continue the dialogue. This is the first part of a response to their post, focusing on the impact of R. A. Fisher’s work. Paper. R. A. Fisher was one of the three founders of population genetics, and is considered by many to be the first and primary founder. His Fundamental Theorem of Natural Selection contributed significantly to a “revival of Darwinism” (see Koonin quote above and Wikipedia). His theorem has been considered by many a Read More ›

He continues (HT, BA77): >>Mathematicians are capable of grasping a world of objects that lies beyond space and time …. … Come again … DB: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with Read More ›

From theoretical physicist Paul Davies at Cosmos: It turns out that the set of all points on a continuous line is a bigger infinity than the natural numbers; mathematicians say there is an uncountably infinite number of points on the line (and in three-dimensional space). You simply can’t match up each point on the line with the natural numbers in a one-to-one correspondence. … If it is continuous (and some physicists think it may not be) then it will contain an uncountably infinite number of points. But that doesn’t mean it has to go on forever. As Einstein discovered, it may be curved in on itself to form a finite volume. More. One would have thought that once we get Read More ›

For some time now, objector DiEb has been raising the question, what do we mean by speaking of “search” in the context of evolutionary search. At 311 in the parody thread, she [IIRC] remarks: >>Search is a central term in the work of Dr. Dr. William Dembski jr, Dr. Winston Ewert, and Dr. Robert Marks II (DEM): it appears in the title of a couple of papers written by at least two of the authors, and it is mentioned hundreds of times in their textbook “Introduction to Evolutionary Informatics“. Strangely – and in difference from the other central term information, it is not defined in this textbook, and neither is search problem or search algorithm. Luckily, dozens of examples of Read More ›

Proven. From SETI’s Seth Shostak at NBC News: Simple math shows how many space aliens may be out there: It’s a lot more than you might imagine! We start with recent research showing that one in six stars hosts a planet hospitable to life. No, not one in a million. One in six. So let’s take that number and run with it. Next we have to make a few assumptions. In particular, if you were given a million Earth-size worlds, what fraction do you think would ever beget technically sophisticated inhabitants? Wait a minute. The NASA bulletin referenced does not use the term hospitable to life. It says The quest to determine if planets like Earth are rare or common Read More ›

In the Tabby’s Star”extraordinary claims” follow-up thread, one of the usual objector personas tried to pounce on the corrective: To do so, he tried to counter-pose the concept of Bayesian analysis, then professes to find that a discussion of the difference between risk and radical uncertainty is little more than meaningless verbiage. This is, however, little more than a play to keep going on business as usual in science in the teeth of warning signs: Where, we must also reckon with the subtleties of signals and noise: I have responded onward and think it worth the while to headline: KF, 53 : >>Let me clip Barsch as a public service for those dipping a tentative toe in the frigid, shark-infested Read More ›

From Toni Airaksinen at Campus Reform: In the postmodern tradition, Gillborn and his team also argue that racism can be reinforced through numbers because they are social constructs. “Numbers are social constructs and likely to embody the dominant (racist) assumptions that shape contemporary society,” they write. As a consequence, they assert that “in many cases, numbers speak for White racial interests.” Despite the purported danger of statistics being used to reinforce white privilege, they predict that if used properly, statistics can “expose and delegitimize the racist (and sexist, classist, hetero-normative, and ableist) assumptions, policies, and practices that are currently supported by the uncritical use of quantitative data.”More. In short, statistics can useful if manipulated (“properly used”). Post-modernism, welcome to science! Read More ›

From Thomas P. Sheahen at American Thinker: We all learned in elementary school that “you can’t divide by zero.” But what happens when you divide by a number very close to zero, a small fraction? The quotient shoots way up to a very large value. … There are several indices being cited these days that get people’s attention because of the big numbers displayed. But the reality is that those particular big numbers come entirely from having very small denominators when calculating a ratio. Three prominent examples of this mathematical artifact are the feedback effect in global warming models, the “Global Warming Potential,” and the “Happy Planet Index.” Each of these is afflicted by the enormous distortion that results when Read More ›

From Sal Cordova at Creation-Evolution Headlines: Bill Basener and John Sanford recently provided a correction to Fisher’s equations in the FNSF-FTNS (12/22/17) that demonstrated real evolution proceeds toward destruction rather than construction of biological function. It basically flips Fisher’s theorem upside down. Concurrently, and equally comedic, something odd happened at the 37th memorial lecture on January 4, 2018 meant to honor the memory of the late R. A. Fisher. Joe Felsenstein (a National Academy of Science member) condemned Fisher’s work with faint praise. Basically, he criticized Fisher’s famous theorem but tried to do it in a nice way. (After all, this was a memorial lecture intended to honor Fisher’s accomplishments.) As with many eulogies, Felsenstein tried to put as much Read More ›