Toots for boarders@mathstodon.xyz account

Written by Boarders on 2025-01-27 at 17:21

“the utilitarian or servile arts enable one to be a servant—of another person, of the state, of a corporation, or of a business—and to earn a living. The liberal arts, in contrast, teach one how to live; they train the faculties and bring them to perfection; they enable a person to rise above his material environment to live an intellectual, a rational, and therefore a free life in gaining truth." - Sister Miriam Joseph

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Written by Boarders on 2025-01-27 at 05:28

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Written by Boarders on 2025-01-18 at 22:40

0 cannot be a counting number for it doesn’t make sense to count zero things. But then, why would one count only one thing? Counting one item seems like not counting at all, one just can’t be a counting number. In fact, if n is not a counting number, it doesn’t make any sense for n+1 to be a counting number, since how could one reach such a number count without having counted the previous number, which, you’ll recall, we have assumed is not a counting number? As such, it follows, by induction, that the most sensible definition of the counting numbers is the empty set considered as a subset of the natural numbers.

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Written by Boarders on 2025-01-17 at 15:19

The semicolon was invented in an act of creative expression by the Italian humanists. The use of any written mark represents an attempt to change our shared symbolic consciousness, not as a return to Babel, but as an opening towards new, yet undiscovered, meadows. Attempts to impose “rules of grammar” or “style”, attempts to punish such novel acts, are projects to sequester us in old, perhaps obsolete, modes of thinking; tales of halcyon days of yore, wherein such rules were respected, are similarly expressions of primitive impulses towards class hierarchy. The only true judge of good style is the profound creative judgment transmitted to us by the entirety of our shared lineage, not any book of purported transhistorical laws.

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Written by Boarders on 2025-01-17 at 02:40

Some of Einstein’s colleagues were probably 10x patent examiners

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Written by Boarders on 2025-01-13 at 03:45

It's common to unfairly summarize the medieval scholastic university as engaged in the debates of utterly pointless questions

• "how many angels fit on the head of a pin". Any time I find myself reading about the founding of the university in this period I wish that our age re-discovered such noble beliefs as in the sharing of knowledge, reverence of received texts (that so many ancient texts were re-produced on such expensive parchment shows quite the commitment to books that was possessed), the importance of scholars beyond the politics of the city/state, the rights and necessity of visiting students in the life of the university, the freedom to ask genuinely wide ranging, if frivolous, questions - via the practice of

'questiones quodlibetales' - and receive serious, considered answers, and so on.

This is not to say we do not possess these virtues in pockets of society, nor to too seriously paint these institutions as some lost golden age or even as worthy of modern adulation (in Europe this takes place concurrent to the many crusades). And yet the entrenchment of the logic of instrumentalism under capital moves us each day away from such lives of contemplation.

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Written by Boarders on 2025-01-10 at 22:23

The Catholic condemnation of Galileo came not out of an inherent anti-rationalism - the church was chiefly responsible for the development of universities throughout the Middle Ages and the dominant intellect edifice, scholasticism, was a fundamentally Hellenistic project to see god in the rational order of the world. The pope of the time even gave earlier praise to Gallieo’s findings. Instead, this was a political move to quell the literalist fundamentalism of the reformation which saw the Bible as sacrosanct. Such placation is seen everywhere throughout history and everywhere it is seen it has only led to disaster for those that believe they can quell man’s most destructive negative spirits.

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Written by Boarders on 2025-01-10 at 04:41

“At this historic moment—when the ascendancy of Europe is so rapidly coming to an end, when Asia is swelling with resurrected life, and the theme of the twentieth century seems destined to be an all-embracing conflict between the East and the West—the provincialism of our traditional histories, which began with Greece and summed up Asia in a line, has become no merely academic error, but a possibly fatal failure of perspective and intelligence. The future faces into the Pacific, and understanding must follow it there.”

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Written by Boarders on 2025-01-08 at 17:23

“The findings revealed a significant negative correlation between frequent AI tool usage and critical thinking abilities, mediated by increased cognitive offloading. Younger participants exhibited higher dependence on AI tools and lower critical thinking scores compared to older participants.”

https://www.mdpi.com/2075-4698/15/1/6

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Written by Boarders on 2025-01-07 at 20:49

There similarly used to be “lit bro” men who were supposedly the height of embarrassing because they liked reading Infinite Jest, but now men don’t read or exclusively read airport business trash like Atomic Habits

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Written by Boarders on 2025-01-07 at 20:48

There used to be a big contingent of drug culture into vaguely countercultural stuff like zen or Alan Watts or Noam Chomsky and not great replacement theory or rise and grind. As with most things, you’ll miss it when it is gone

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Written by Boarders on 2025-01-05 at 06:05

Just finishing “Time of the Magicians: Wittgenstein, Benjamin, Cassirer, Heidegger, and the Decade That Reinvented Philosophy” which has been a pleasing diversion to start the year. Main takeaways are:

• the life of Benjamin is that of a charmingly pitiful permanent grad student throughout much of the twenties making his ultimate tragic end really quite sad

• Heidegger comes across as a relentless social climber par excellence

• that we still study and revere Heidegger’s thought and hardly anyone knows or reads Cassirer is sort of shameful to me (his book on special relativity is marvelous if you are willing to endure a, now dead, tradition of neo-Kantian writing - which in any case seems to me far superior to pure tosh about daesin and authentic peoples…)

• Nothing new on Wittgenstein here, but it is amusing that he is included in a book about philosophy of the 1920s which he spent largely in a self-imposed man-of-the-people exile as primary school teacher and then as mad man architect

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Written by Boarders on 2025-01-05 at 05:00

In the New+ Math we will teach that solving simultaneous equations is an equalizer and so we can use the usual approach via pullbacks i.e. look at the intersection of their graphs

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Written by Boarders on 2024-12-31 at 21:59

“Undoubtedly, the capstone of every mathematical theory is a convincing proof of all of its assertions. Undoubtedly, mathematics inculpates itself when it foregoes convincing proofs. But the mystery of brilliant productivity will always be the posing of new questions, the anticipation of new theorems that make accessible valuable results and connections. Without the creation of new viewpoints, without the statement of new aims, mathematics would soon exhaust itself in the rigor of its logical proofs and begin to stagnate as its substance vanishes. Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.” - Felix Klein

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Written by Boarders on 2024-12-30 at 17:56

Books in the images are:

• Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Needham

• Sets For Mathematics by Lawvere and Rosebrugh

• Visual Complex Analysis by Needham

• Intuitionistic Set Theory by Bell

• Sheaf Theory Through Examples by Rosiak

• Data Analysis: A Bayesian Approach by Sivia

• Higher-Order Computability by Longley and Normann

• Axiomatic Method and Category Theory by Rodin

• A Book of Abstract Algebra by Pinter

• Mathematical Logic and Computation by Avigad

• Sheaves in Geometry and Logic : A First Introduction To Topos Theory by Moerdijk

• Structure and Interpretation of Classical Mechanics by Sussman and Wisdom

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Written by Boarders on 2024-12-30 at 17:50

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Written by Boarders on 2024-12-30 at 17:48

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Written by Boarders on 2024-12-30 at 17:47

Mathematics adjacent books I am aiming to finish next year (some re-reads, some new):

What are on some of your lists?

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Written by Boarders on 2024-12-18 at 02:56

What are the most interesting languages that model partial functions (interpreted loosely), but where the halting problem is decidable (by a Turing machine)?

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Written by Boarders on 2024-12-07 at 22:04

“If you can’t read books you’re illiterate, and if you don’t read books you’re functionally illiterate” - same principle also applies to people getting LLMs to do their thinking for them

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