Jul 5, 2023 04:15 PM
(This post was last modified: Jul 5, 2023 04:21 PM by C C.)
The forces of physics are the new magic
https://iai.tv/articles/the-forces-of-ph..._auid=2020
‘Spooky action at a distance’ is now used to describe quantum entanglement. But forces, like gravity, appear in the form of action at a distance too. Are forces spooky too? Physics professor, Sverre Holm, journeys the occult origins of forces, and the mysteries still looming over modern science.
INTRO: Isaac Newton is well known for having added, "I frame no hypotheses" to the second edition of Philosophiæ Naturalis Principia Mathematica in 1713, meaning that he could not explain the cause of gravitation.
Gottfried Leibniz’ view was that if such attraction at a distance is not explainable then it is a perpetual miracle, and added that it is “a chimerical thing, a scholastic occult quality.”
Leibniz’ dismissal is all the more strange in light of Newton’s seeming agreement with Leibniz. Newton himself had after all dismissed the medieval scholastics for their belief in substantial forms, like “sympathies” between similar objects. He had written that “to tell us that every Species of Things is endow'd with an occult specifick Quality by which it acts and produces manifest Effects, is to tell us nothing.”
How could Newton be so sure that his theory of gravitation did not fall under the category of such a scholastic form, and thus that Leibniz arguments were not valid?
In retrospect, we know that Newton was right and Leibniz wrong. The field concept, which plays such an important role in today’s physics, was well established by the end of the 19th century. Michael Faraday and James Clerk Maxwell played major roles through their work with electric and magnetic fields. Mary Hesses’s classical book from 1961 is the definite guide to this history... (MORE - details)
Should machines replace mathematicians?
https://johnhorgan.org/cross-check/shoul...ematicians
EXCERPT (John Horgan): . . . Perhaps because I romanticize mathematicians, I’m troubled by the thought that machines might replace them. I broached this possibility in “The Death of Proof,” published three decades ago in Scientific American. In response to the growing complexity of mathematics, I reported, mathematicians were becoming increasingly reliant on computers. I asked, “Will the great mathematicians of the next century be made of silicon?”
Mathematicians are still giving me grief about that article, even as the trends I described have grown stronger. Anthony Bordg, for example, worries that his field could face a “replication crisis” like that plaguing scientific research. Mathematicians, Bordg notes in The Mathematical Intelligencer, sometimes accept a proof not because they have checked it, step by step, but because they trust the proof’s methods and author.
Given the “increasing difficulty in checking the correctness of mathematical arguments,” Bordg says, old-fashioned peer review may no longer be sufficient. Prominent mathematicians have published “proofs” so novel and elaborate that even specialists in the relevant mathematics can’t verify them. Take a 2012 proof in which Shinichi Mochizuki claims to have proved the ABC conjecture, a problem in number theory. Over the past decade, mathematicians have organized conferences to determine whether Mochizuki’s proof is true—in vain. Some accept it, others don’t.
Bordg suggests that computerized “proof assistants” will help validate proofs. Researchers at Microsoft have already invented an “interactive theorem prover” called Lean that can check proofs and even propose improvements—much as word-processing programs check our prose for errors and finish sentences for us. Lean is linked to a database of established results. New mathematical work must be laboriously translated into a language that Lean recognizes. But souped up with artificial intelligence, programs such as Lean could eventually “discover new mathematics and find new solutions to old problems,” according to a report in Quanta Magazine.
Some mathematicians welcome the “digitization” of mathematics, which would facilitate computer verification and make mathematics more trustworthy. Others, such as Michael Harris, are ambivalent. Advances in computer-aided mathematics, Harris says, raise a profound question: What is the purpose of mathematics? Harris sees mathematics as “a free, creative activity” that, like art, is pursued for its own sake, for the sheer joy of discovery and insight.
Harris isn’t opposed to the mechanization of mathematics per se. In a recent article, Harris points out that mathematicians have used mechanical devices, such as the abacus, for millennia. And mathematicians, after all, invented the computer.
But Harris worries that tools such as Lean will encourage a “stunted vision” of mathematics as an economic commodity or product rather than “a way of being human...” (MORE - missing details)
https://iai.tv/articles/the-forces-of-ph..._auid=2020
‘Spooky action at a distance’ is now used to describe quantum entanglement. But forces, like gravity, appear in the form of action at a distance too. Are forces spooky too? Physics professor, Sverre Holm, journeys the occult origins of forces, and the mysteries still looming over modern science.
INTRO: Isaac Newton is well known for having added, "I frame no hypotheses" to the second edition of Philosophiæ Naturalis Principia Mathematica in 1713, meaning that he could not explain the cause of gravitation.
Gottfried Leibniz’ view was that if such attraction at a distance is not explainable then it is a perpetual miracle, and added that it is “a chimerical thing, a scholastic occult quality.”
Leibniz’ dismissal is all the more strange in light of Newton’s seeming agreement with Leibniz. Newton himself had after all dismissed the medieval scholastics for their belief in substantial forms, like “sympathies” between similar objects. He had written that “to tell us that every Species of Things is endow'd with an occult specifick Quality by which it acts and produces manifest Effects, is to tell us nothing.”
How could Newton be so sure that his theory of gravitation did not fall under the category of such a scholastic form, and thus that Leibniz arguments were not valid?
In retrospect, we know that Newton was right and Leibniz wrong. The field concept, which plays such an important role in today’s physics, was well established by the end of the 19th century. Michael Faraday and James Clerk Maxwell played major roles through their work with electric and magnetic fields. Mary Hesses’s classical book from 1961 is the definite guide to this history... (MORE - details)
Should machines replace mathematicians?
https://johnhorgan.org/cross-check/shoul...ematicians
EXCERPT (John Horgan): . . . Perhaps because I romanticize mathematicians, I’m troubled by the thought that machines might replace them. I broached this possibility in “The Death of Proof,” published three decades ago in Scientific American. In response to the growing complexity of mathematics, I reported, mathematicians were becoming increasingly reliant on computers. I asked, “Will the great mathematicians of the next century be made of silicon?”
Mathematicians are still giving me grief about that article, even as the trends I described have grown stronger. Anthony Bordg, for example, worries that his field could face a “replication crisis” like that plaguing scientific research. Mathematicians, Bordg notes in The Mathematical Intelligencer, sometimes accept a proof not because they have checked it, step by step, but because they trust the proof’s methods and author.
Given the “increasing difficulty in checking the correctness of mathematical arguments,” Bordg says, old-fashioned peer review may no longer be sufficient. Prominent mathematicians have published “proofs” so novel and elaborate that even specialists in the relevant mathematics can’t verify them. Take a 2012 proof in which Shinichi Mochizuki claims to have proved the ABC conjecture, a problem in number theory. Over the past decade, mathematicians have organized conferences to determine whether Mochizuki’s proof is true—in vain. Some accept it, others don’t.
Bordg suggests that computerized “proof assistants” will help validate proofs. Researchers at Microsoft have already invented an “interactive theorem prover” called Lean that can check proofs and even propose improvements—much as word-processing programs check our prose for errors and finish sentences for us. Lean is linked to a database of established results. New mathematical work must be laboriously translated into a language that Lean recognizes. But souped up with artificial intelligence, programs such as Lean could eventually “discover new mathematics and find new solutions to old problems,” according to a report in Quanta Magazine.
Some mathematicians welcome the “digitization” of mathematics, which would facilitate computer verification and make mathematics more trustworthy. Others, such as Michael Harris, are ambivalent. Advances in computer-aided mathematics, Harris says, raise a profound question: What is the purpose of mathematics? Harris sees mathematics as “a free, creative activity” that, like art, is pursued for its own sake, for the sheer joy of discovery and insight.
Harris isn’t opposed to the mechanization of mathematics per se. In a recent article, Harris points out that mathematicians have used mechanical devices, such as the abacus, for millennia. And mathematicians, after all, invented the computer.
But Harris worries that tools such as Lean will encourage a “stunted vision” of mathematics as an economic commodity or product rather than “a way of being human...” (MORE - missing details)