Mathematics

Recently, Philippines president Rodrigo Dutarte threatened to resign if anyone could prove that God exists. It turns out that the great mathematician Leonhard Euler (1707–1783) offered a proof of the existence of God. Today, Euler is considered one of the greatest mathematicians of all time. His interests covered almost all aspects of mathematics, from geometry to calculus to trigonometry to algebra to number theory, as well as optics, astronomy, cartography, mechanics, weights and measures and even the theory of music. Much of the notation used by mathematicians today – including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns – was either created, popularized or standardized by Euler. Read More ›

From Brian Resnick at Vox: Zero is in the mind, but not in the sensory world,” Robert Kaplan, a Harvard math professor and an author of a book on zero, says. Even in the empty reaches of space, if you can see stars, it means you’re being bathed in their electromagnetic radiation. In the darkest emptiness, there’s always something. Perhaps a true zero — meaning absolute nothingness — may have existed in the time before the Big Bang. But we can never know. Nevertheless, zero doesn’t have to exist to be useful. In fact, we can use the concept of zero to derive all the other numbers in the universe. Kaplan walked me through a thought exercise first described by Read More ›

As we continue to explore the mathematical domain of abstract reality and objective truth, we come to first the Godel point (as summarised by Nesher): where, recall, the domain of facts starts with something like the surreal world of numbers: and then also, we come to the world of Mathematical Platonism/ Realism. So, let me continue by promoting a comment I just added to the objectivity of Mathematics thread: KF, 29 : >>Let’s see how IEP describes Mathematical Platonism (where, no, this is not equal to Plato’s theory of forms): Traditionally, mathematical platonism has referred to a collection of metaphysical accounts of mathematics, where a metaphysical account of mathematics is one that entails theses concerning the existence and fundamental nature Read More ›

In recent days, I have taken time to show that while subjects study the logic of structure and quantity (= Mathematics, in a nutshell), the body of knowledge — including axiomatised systems — is objective. Where, “objective” effectively means, tied to such a body of accountable warrant and to foundational self-evident facts that the substance of that body of knowledge is credibly an accurate description of facets of reality, as opposed to being dubious (though not necessarily false) figments of a subject’s imagination. Of course, while objectivity implies credible truth (truth being the accurate description of relevant reality) it cannot guarantee utter freedom from error or gaps; especially after Godel’s key incompleteness results. Why is that? For one, it has Read More ›

From Ann Gauger at ENST, from her essay, “Beauty leads us home,” Evolutionary biologists attribute our perception of beauty in nature to our evolutionary history. In 2004 two Russian artists, Vitaly Komar and Alex Melamid, commissioned a poll to determine which kinds of art people from various countries found beautiful, and which kinds they found ugly. The poll revealed that people in almost every culture liked landscapes with a heavy dose of blue. Why? Denis Dutton explains: The lush blue landscape type that the Russian artists discovered is found across the world because it is an innate preference. This preference is not explained just by cultural traditions…. This fundamental attraction to certain types of landscapes is not socially constructed but Read More ›

Over recent days, there has been an exchange at UD on the objectivity vs subjectivity of mathematical knowledge. This is relevant to our understanding of knowledge, and to our recognition of the credibility of Mathematical findings on debated matters. This instantly means that the specific concern and the penumbra of generalised perceptions of Mathematics, Science and objectivity of knowledge are relevant to the ID debate. So, it is appropriate to clip from the discussion in the axioms of math thread. First, BO’H and his suggestion that he and I actually in the end agree: BO’H, 34: >>[to:] EricMH – I believe that mathematics, in different respects, is both subjective and objective. [to:] kf – yes, some parts of mathematics are Read More ›

This is yet another significant issue that emerges from the ongoing exchanges on subjectivity, objectivity, possibility of objective moral truth, etc. And, the deep interconnectedness of what we are discussing is proving quite fruitful. So, I think it is useful to now headline Bob’s remark in the rebooting ethics education thread, which ties in Mathematics. And those who find it hard to follow use of indented text blocks to quote, please pardon that praxis: BO’H, 25 :>>but aren’t the axioms that mathematicians assume subjective? (they may be rational, but they’re not the only possible axioms that could be used) What follows after that is (or at least should be!) objective, of course.>> My response is: KF, 26: >>No. Instantly, an Read More ›

Coming soon to tax-funded schools near you: 😉 A well meaning math teacher finds herself trumped by a post-fact America. Brought to us by the folk behind Algebra Is Racist and Objectivity is Sexist. A gift to incompetent teachers, timeserving bureaucrats, and sleazy politicians everywhere. See also: Algebra is racist. Objectivity is sexist. and The war on freedom is rotting our intellectual life: Intersectionality

A philosophical question to wake you up. A reader directs our attention to a 2015 piece by cosmologist Alexander Vilenkin at Inference Review (2015): THE ANSWER to the question, “Did the universe have a beginning?” is, “It probably did.” We have no viable models of an eternal universe. The BGV theorem gives us reason to believe that such models simply cannot be constructed. More. He offers the Borde-Guth-Vilenkin (BGV) theorem by way of evidence: Loosely speaking, our theorem states that if the universe is, on average, expanding, then its history cannot be indefinitely continued into the past. More precisely, if the average expansion rate is positive along a given world line, or geodesic, then this geodesic must terminate after a Read More ›

In the isolated islands of function thread, Origenes cited the exact value of one of a big number. GP asked, how did you do it, as Excel and R are overwhelmed at that sort of level. Origenes answered: Origenes, 104: >> . . . I found this website: https://defuse.ca/big-number-calculator.htm >> Now, I have routinely used logs and high-capacity hardware calculators [e.g. HP 50] or software ones [X-Calc and Emu-48], but obviously these give rounded answers. I popped over to the linked page (now on speed dial, of course), and so — for reference: KF, 106: >>2^500 = 3 273 390 607 896 141 870 013 189 696 827 599 152 216 642 046 043 064 789 483 291 368 096 Read More ›

From David Nguyen at Think Tank Learning: See also: Science news fact check: Was a new organ really discovered? and Science blunder: Hormone therapy and cancer

From Emily Conover at ScienceNews, describing the work of physicist Nicholas Gisin: Gisin — known for his work on the foundations and applications of quantum mechanics — takes issue with real numbers that consist of a never-ending string of digits with no discernable pattern and that can’t be calculated by a computer. Such numbers (for example, 1.9801545341073… and so on) contain an infinite amount of information: You could imagine encoding in those digits the answers to every fathomable question in the English language — and more. But to represent the world, real numbers shouldn’t contain unlimited information, Gisin says, because, “in a finite volume of space you will never have an infinite amount of information.” Instead, Gisin argues March 19 Read More ›

It seems we cannot escape epistemological questions when we address ID issues. AK opens the squeaky-hinged door yet again in the US National Association of Scholars thread. My comment: KF, 9: >>[AK,] I see your: If they are published in reputable peer reviewed journals, they are scientific findings. We need to distinguish key terms and address underlying issues on logic and warrant. Truth (following Ari who got it right) says of what is that it is and of what is not that it is not — accurate description of reality. As potentially knowing, rational and responsible subjects, we face the challenge that we are finite, fallible, morally struggling (is is not ought) and too often ill-willed. To credibly know objective Read More ›

From Josephine Livingstone at New Republic, reviewing Michael E. Hobart’s The Great Rift: Literacy, Numeracy, and the Religion-Science Divide, In a new book called The Great Rift: Literacy, Numeracy, and the Religion-Science Divide, Michael E. Hobart offers a new twist on a huge old metanarrative: the death of God. Something or other happened in Renaissance Europe, the story goes, and it eventually distanced scientists from religion. Hobart locates this great shift in the field of mathematics. Other historians have given credit to experimenters who pioneered the scientific method, or astronomers like Galileo or Kepler, but Hobart claims that Renaissance mathematics is distinct from its medieval predecessor because it reconceived numeracy as a tool for describing the quantities of things into Read More ›

From M. Anthony Mills: In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities. This stubborn fact has led some philosophers, such as W.V.O. Quine, Read More ›