His idea takes us through Flatland, a two-dimensional world, and the tesseract, a four-dimensional cube.
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Legal scholar Jonathan Turley muses on the latest assault on math teaching in schools: We previously discussed the view of University of Rhode Island and Director of Graduate Studies of History Erik Loomis that “Science, statistics, and technology are all inherently racist.” Others have agreed with that view, including denouncing math as racist or a “tool of whiteness.” Now, as part of its “decolonization” efforts, Durham University is calling on professors in the math department to ask themselves if they’re citing work from “mostly white or male” mathematicians. According to the Telegraph and The College Fix a guide instructs faculty that “decolonising the mathematical curriculum means considering the cultural origins of the mathematical concepts, focusses, and notation we most commonly use.” It adds: “[T]he question of whether we have allowed Read More ›
A central problem in all computer security (branch of cryptography) is the one-way problem. Cryptography should function as a one-way street: You can go north but you can’t go south. So if a hacker doesn’t have the code to go north, he can’t go anywhere. Which is where the computer security expert would like to leave the hacker… Is there such a thing as a one-way function in mathematics? Mathematician Erica Klarreich says, probably yes, and explains what it looks like: To get a feel for how one-way functions work, imagine someone asked you to multiply two large prime numbers, say 6,547 and 7,079. Arriving at the answer of 46,346,213 might take some work, but it is eminently doable. However, Read More ›
It’s generally held that information does not have mass. However, physicist Melvin Vopson, reflecting on the work of Rolf Landauer (1927–1999), offers a somewhat alarming view: Not only does information have mass but that — at the rate we humans output it now — its energy will outweigh Earth. Yesterday, Eric Holloway offered a response to that claim: Let’s accept that creation of information can indeed increase the amount of energy and mass in a system. But, according to the conservation of energy, the energy in a closed system remains constant. So, if Vopson is correct we now have a mystery because his theory is in tension with the conservation of energy. The only solution is that the system is Read More ›
University of Bonn researchers think that they may have taught fish to count. They tested the fact that many life forms can note the difference in small quantities between “one more” and “one less,” at least up to five items. Not much work had been done on fish in this area so they decided to test eight freshwater stingrays and eight cichlids: All of the fish were taught to recognize blue as corresponding to “more” and yellow to “less.” The fish or stingrays entered an experimental arena where they saw a test stimulus: a card showing a set of geometric shapes (square, circle, triangle) in either yellow or blue. In a separate compartment of the tank, the fish were then Read More ›
With basketball fever at a high pitch… when LA Times sportswriter Jim Alexander talked to Pomona College business prof Gary Smith about what it takes to win, he got a different answer than some might have expected. If you are really good, it takes luck to win, Smith explained. What? Shouldn’t it be the other way around? No, because… “You can take the four best golfers in the world – any sport, but let’s do golf because it’s head-to-head,” Smith said in a phone conversation this week. “And they play a round of golf and see who gets the lowest score, and it’s pretty much random. Nobody’s going to win every single time. One guy might win more than 25 Read More ›
In Carl Sagan’s Contact, the extraterrestrials embedded a message in the irrational number pi (the circumference of a circle divided by its radius). But some other numbers are critical to the structure of our universe too — and why they are critical does not make obvious sense. ➤ Perhaps the most fundamental and mysterious one is the fine structure constant of the universe: A seemingly harmless, random number with no units or dimensions has cropped up in so many places in physics and seems to control one of the most fundamental interactions in the universe. Its name is the fine-structure constant, and it’s a measure of the strength of the interaction between charged particles and the electromagnetic force. The current Read More ›
Modern policy discussions in America almost always leave out the biggest question – why are we doing what we are doing in the first place? Leaving out first principles always leaves people trying to find the most practical way to accomplish nothing in particular. We have become accustomed to not asking questions about first principles because they always sound too doctrinaire, but then we wind up, at best, making the misplaced assumption that everyone is reaching for the same goal, or, far worse, viewing the activities themselves as the goals. One place where this problem repeatedly rears its ugly head is education, and especially mathematics education. Why are we teaching math? What do we want people to get out of Read More ›
Math teacher Ali Kayaspor has thought a lot about how mathematicians have come up with fundamental ideas about the nature of reality and he shares anecdotes that give us a glimpse. But first, the cold shower: Unfortunately, there is no clear way to answer the question of how a mathematician thinks. But we can approach this question as follows; if you watched any chess tournament, the game’s analysis is shared in detail at the end of the match. When you examine the analysis, you will see a breaking point in each game. Similarly, mathematicians also experience a breaking point while working on a problem before finding a solution. Ali Kayaspor, “How Does a Mathematician’s Brain Differ from Other Brains?” at Read More ›
In an excerpt from his new book, The Art of More: How Mathematics Created Civilization, science writer Michael Brooks offers the intriguing idea that the modern world arose from imaginary numbers: Imaginary numbers are not imaginary at all. The truth is, they have had far more impact on our lives than anything truly imaginary ever could. Without imaginary numbers, and the vital role they played in putting electricity into homes, factories, and internet server-farms, the modern world would not exist Michael Brooks, “Imaginary Numbers Are Reality” at Nautilus (February 9, 2022) Imaginary numbers, are we recall from school, are the square roots of minus numbers. Two plus numbers, multiplied, result in a plus number. But so do two minus numbers. Read More ›
Sam Baron, a philosophy prof at Australian Catholic University, whose specialty is the philosophy of mathematics, argues in a new paper that mathematics is not a human invention. It gives structure to the world we live in. We simply observe it. So do many life forms, it seems. He offers an example: There are two subspecies of North American periodical cicadas that live most of their lives in the ground. Then, every 13 or 17 years (depending on the subspecies), the cicadas emerge in great swarms for a period of around two weeks. Why is it 13 and 17 years? Why not 12 and 14? Or 16 and 18? One explanation appeals to the fact that 13 and 17 are Read More ›
New Scientist’s executive editor Richard Webb, a “recovering particle physicist,” offers a look at the current state of the idea that there might be an infinity of universes out there. Why believe it? Mainly, it turns out, to avoid believing something else: Gods and their intelligent designs are less in the mainstream of scientific thought now, yet similar ideas about an optimal universe still trickle through cosmology. That is principally down to some mysterious numbers that determine its workings. Tot them all up in the standard models of particle physics and cosmology, and you end up with about 30 constants of nature – numbers like the strengths of the fundamental forces and the masses of elementary particles that our theories Read More ›
In Define information before you talk about it, neurosurgeon Michael Egnor interviewed engineering prof Robert J. Marks on the way information, not matter, shapes our world (October 28, 2021). In the first portion, Egnor and Marks discussed questions like: Why do two identical snowflakes seem more meaningful than one snowflake. Then they turned to the relationship between information and creativity. Is creativity a function of more information? Or is there more to it? And human intervention make any difference? Many questions arose during the discussion. Does Mount Rushmore have no more information than Mount Fuji? Does human intervention make a measurable difference? That’s specified complexity. Putting the idea of specified complexity to work, how do we measure meaningful information? How Read More ›
Can anything happen if there are an infinite number of universes each with an infinite number of possibilities in each? Can you be bald in one universe and fully haired in another? Can you have two eyeballs in this universe and three in another? The answer is no. In a nutshell, the reason is that some infinities are bigger than other infinities. (And this is not a claim like infinity plus one is bigger than infinity. Infinity plus one is still infinity.) The number of points on a line segment from, say zero to one, is a bigger infinity than the number of counting numbers {1,2,3,…}. We can label the infinite number of universes in the multiverse as universe #1, Read More ›
In the “Does God exist?” debate at Theology Unleashed between theist neurosurgeon Michael Egnor and atheist broadcaster Matt Dillahunty (September 17, 2021), we now look at questions from the audience on whether singularities are really a part of science and whether atheism is really a belief system that can make predictions. Readers may recall that the debate opened with Egnor explaining why, as former atheist, he became a theist. Then Dillahunty explained why, as a former theist, he became an atheist. Michael Egnor then made his opening argument, offering ten proofs for the existence of God. Matt Dillahunty responded in his own opening argument that the propositions were all unfalsifiable. When, in Section 4, it was Egnor’s turn to rebut Read More ›
In early, easily-mocked sci fi, a little green man points his raygun at an unsuspecting passerby and barks “Take me to your leader.” Fast forward: If the little green man didn’t have the technology to figure out who the leader was before landing, he certainly wouldn’t have the technology to get here. In any real-world scenario, we must assume that extraterrestrial intelligences are doing common sense logical things that we would do: Check Earth’s inhabitants out first by monitoring our communications. Some analysts have pointed out that there are places they could even hide technology in our solar system (Lagrange points, for example) with much less chance of being noticed. But then the question is, what to say to them? Read More ›
Have you ever been in an online discussion where a vocal proponent confidently claimed that his opponent was the victim of the dreaded “Dunning–Kruger” effect? At Vox, Brian Resnick explains, “That’s where people of low ability — let’s say, those who fail to answer logic puzzles correctly — tend to unduly overestimate their abilities”: An obvious example people have been using lately to describe the Dunning-Kruger effect is President Donald Trump, whose confidence and bluster never wavers, despite his weak interest in and understanding of policy matters. But you don’t need to look to Trump to find an example of the Dunning-Kruger effect. You don’t even need to look at cable news. Brian Resnick, “An expert on human blind spots Read More ›
University College London cognitive neuroscientist Brian Butterworth, author of a forthcoming book, Can fish count? (Basic Books, 2022), reckons that, one way or another, in a modern urban society, we process about 16,000 numbers in an average day. Numbers create conceptual relationships between vastly different things. From the publisher’s introduction to his book, we learn, “The philosopher Bertrand Russell once observed that realizing that a pair of apples and the passage of two days could somehow both be represented by the concept we call “two” was one of the most astonishing discoveries anyone had ever made.” At The Scientist, Catherine Offord, discussing his work, offers a critical distinction between estimations of quantity and actual counting: “Our perception of quantity, separate Read More ›
Walter Bradley Center director Robert J. Marks has been doing a series of podcasts with Swedish mathematician Ola Hössjer, and Colombian biostatistician Daniel Díaz in connection with a recent co-authored paper on the fine-tuning of the universe for life in the Journal of Cosmology and Astroparticle Physics. In the first portion of this episode, podcast 153, “Why is there fine-tuning everywhere?” they look at whether life was seeded in our universe by advanced life forms (directed panspermia), as advocated by some prominent scientists. In the second portion, they discuss the view — again, held by prominent science figures — that our universe is an advanced computer sim. In the third segment, they tackle the idea that there is nothing to Read More ›
We are told that not only will AI take our jobs but it will take our bosses’ jobs and their bosses’ jobs and pretty soon., AI will be running the world… We can see those films on Netflix any night. Science writer and science fiction author Charles Q. Choi offers, in a longish piece at the Institute of Electrical and Electronic Engineers’ online magazine, Spectrum, talking about the real world where “Neural networks can be disastrously brittle, forgetful, and surprisingly bad at math.” AI frequently flubs and it is not clear how to make it flub less. Here are brief notes on three examples of the seven he offers: ➤“Brittle” 97% of AIs could not identify a school bus flipped Read More ›