## Posts Tagged ‘**set theory**’

## “Control of consciousness determines the quality of life”*…

Peter Carruthers, Distinguished University Professor of Philosophy at the University of Maryland, College Park, is an expert on the philosophy of mind who draws heavily on empirical psychology and cognitive neuroscience. He outlined many of his ideas on conscious thinking in his 2015 book

The Centered Mind: What the Science of Working Memory Shows Us about the Nature of Human Thought. More recently, in 2017, he published a paper with the astonishing title of “The Illusion of Conscious Thought.”…

Philosopher Peter Carruthers insists that conscious thought, judgment and volition are illusions. They arise from processes of which we are forever unaware. He explains to Steve Ayan the reasons for his provocative proposal: “There Is No Such Thing as Conscious Thought.”

See also: “An Anthropologist Investigates How We Think About How We Think.”

*Flow: The Psychology of Optimal Experience*

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**As we think about thought,** we might spare one for Georg Ferdinand Ludwig Philipp Cantor; he died on this date in 1918. Cantor was the mathematician who created set theory, now fundamental to math, His proof that the real numbers are more numerous than the natural numbers implies the existence of an “infinity of infinities”… a result that generated a great deal of resistance, both mathematical (from the likes of Henri Poincaré) and philosophical (most notably from Wittgenstein). Some Christian theologians (particularly neo-Scholastics) saw Cantor’s work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor, a devout Lutheran, vigorously rejected.

These harsh criticisms fueled Cantor’s bouts of depression (retrospectively judged by some to have been bipolar disorder); he died in a mental institution.

## From the Not-Sure-I-Really-Want-To-Know Department…

As readers know, some physicists believe that the universe as we know it is actually a giant hologram, giving us the illusion of three-dimensions, while in fact all the action is occurring on a two-dimensional boundary region (see **here**, **here**, and **here**)… shadows on the walls of a cave, indeed.

But lest one mistake that for the frontier of freakiness, others (c.f., e.g., **here** and **here**) believe that the existence we experience is nothing more (or less) than a *Matrix*-like simulation…

A common theme of science fiction movies and books is the idea that we’re all living in a simulated universe—that nothing is actually real. This is no trivial pursuit: some of the greatest minds in history, from Plato, to Descartes, have pondered the possibility. Though, none were able to offer proof that such an idea is even possible. Now, a team of physicists working at the University of Bonn have come up with a possible means for providing us with the evidence we are looking for; namely, a measurable way to show that our universe is indeed simulated. They have written a paper describing their idea and have uploaded it to the preprint server arXiv…

Phys.Org has the whole story at “**Is it real? Physicists propose method to determine if the universe is a simulation**“; the paper mentioned above can be downloaded **here**.

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**As we reach for the “reset” button,** we might send carefully-calculated birthday greetings to Paul Isaac Bernays; he was born on this date in 1888. A close associate of David Hilbert (of “**Hilbert’s Hotel**” fame), Bernays was one the foremost philosophers of mathematics of the Twentieth Century, who made important contributions to mathematical logic and axiomatic set theory. Bernays is perhaps best remembered for his revision and improvement of the (early, incomplete) set theory advanced by John von Neumann in the 1920s; Bernays’s work, with some subsequent modifications by Kurt Gödel, is now known as the Von Neumann–Bernays–Gödel set theory.

Lest, per the simulation speculation above suggest that cosmology has a hammerlock on weirdness: Set theory is used, among other purposes, to describe the symmetries inherent in families of elementary particles and in crystals. Materials such as a liquid or a gas in equilibrium, made of uniformly distributed particles, exhibit perfect spatial symmetry—they look the same everywhere and in every direction… a condition that “breaks” at very low temperature, when the particles form crystals (which have some symmetry, but less)… Now Nobel Laureate Frank Wilczek has suggested that there may exist “**Time Crystals**“– whose structure would repeat periodically, as with an ordinary crystal, but in time rather than in space… a kind of “perpetual motion ‘machine'” (weirder yet, one that doesn’t violate the laws of thermodynamics).

## It’s kind of like a Sofia Coppola film…

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Well, now there’s a cooler, more moderne choice: **Hipster Ipsum**: “Artisanal filler text for your site or project.” A sample…

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Head on over to **Hispster Ipsum** for the coolest of layouts…

**As we affect a posture of amused indifference,** we might wish a symbolically-logical Happy Birthday to mathematician Guiseppe Peano; he was born on this date in 1858. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much of the symbolic notation still in use.