Well, look who has a new book on the way (it could even be a game-changer... so to speak):
https://mathwithbaddrawings.com/2022/01/19/math-games-with-bad-drawings-2/
Well, look who has a new book on the way (it could even be a game-changer... so to speak):
https://mathwithbaddrawings.com/2022/01/19/math-games-with-bad-drawings-2/
So you say you always wanted to write sonnets, well....
https://mathwithbaddrawings.com/2021/09/30/a-hundred-thousand-billion-poems/
Blasphemies about mathematical proof versus explanations, courtesy of Ben Orlin:
https://mathwithbaddrawings.com/2021/05/12/against-mathematical-proof/
I haven't even had time to listen to this yet (sometime this weekend though), but Ben Orlin recommends it (ohh, and he happens to be on it), and that's good enough for me:
https://infinitelyirrational.podbean.com/e/the-strange-case-of-sir-newton-and-mr-leibniz/
"If my mental processes are determined wholly by the motion of atoms in my brain, I have no reason to believe that my beliefs are true... and hence I have no reason for supposing my brain to be composed of atoms."--- J.B.S. Haldane, "Possible Worlds" (1927)
“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”— Eugene V. Wigner
"Like any other mathematician, Euclid took a good deal for granted that he never noticed. In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means. Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn. These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."-- D. Berlinski (from "The King of Infinite Space")
“The second strand in my life was and is a strenuous practice of Zen Buddhism. Zen helped me confront aspects of my life that went beyond the logical and the mathematical. Zen has the reputation for being antilogical, but that is not my experience. My experience is that Zen is not confined to logic; it does not see logic as having the final word. Zen demonstrates that there is a way to work with situations of conflict, situations that are problematic from a normal, rational point of view. The rational, for Zen, is just another point of view. Paradox, in Zen, is used constructively as a way to direct the mind to subverbal levels out of which acts of creativity arise.”
“…every human being lives in a bubble. This bubble contains all their perceptions and cognitions. What exists outside the bubble is not knowable. Radical constructivists 'do not make claims about what exists in itself, that is, without an observer or experiencer.' This is a point that I also made earlier when I claimed that there exists no mathematical knowledge that is completely objective. Mathematical knowledge and truth must be considered as a package with both objective and subjective aspects. The belief in ‘objective mathematical knowledge,’ that is, knowledge that is independent of the beings who know it, is itself a belief and therefore nonobjective. There is no knowledge that is independent of knowing. There is no absolute, objective truth.”
"It is certainly conceivable that the clarity we perceive in the world is something we bring to the world, not something that is there independent of us. The clarity of the natural world is a metaphysical belief that we unconsciously impose on the situation. We consider it to be obvious that the natural world is something exterior of us and independent of our thoughts and sense impressions; we believe in a mind-independent reality. Paradoxically, we do not recognize that the belief in a mind-independent reality is itself mind-dependent. Logically, we cannot work our way free of the bubble we live in, which consists of all of our sense impression and thoughts. The pristine world of clarity, the natural world independent of the observer, is merely a hypothesis that cannot, in principle, ever be verified. To say that the natural world is ambiguous is to highlight this assumption. It is to emphasize that the feeling that there is a natural world 'out there' that is the same for all people at all times, is an assumption that is not self-evident. This is not to embrace a kind of solipsism and to deny the reality of the world. It is to emphasize that the natural world is intimately intertwined with the world of the mind. In consequence, the natural world is a flow just like the inner world. By stabilizing the inner world through language, logic, mathematics, and science, we simultaneously stabilize the outer world. The result of all this is the recognition that the clarity we assume to be a basic feature of the natural world merely masks a deeper ambiguity. One of the functions of mathematics and science is precisely to deny this ambiguity. This is really the motivation behind the science of certainty."
"Orlin's ability to masterfully convey interesting and complex mathematical ideas through the whimsy of drawings (that, contrary to the suggestion of the title, are actually not that bad) is unparalleled. This is a great work showing the beauty of mathematics as it relates to our world. This is a must read for anyone who ever thought math isn't fun, or doesn't apply to the world we live in!" ―John Urschel (blurbing for Ben Orlin's new book)