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“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”*…

No scripture is as old as mathematics is. All the other sciences are younger, most by thousands of years. More than history, mathematics is the record that humanity is keeping of itself. History can be revised or manipulated or erased or lost. Mathematics is permanent. A² + B² = C² was true before Pythagoras had his name attached to it, and will be true when the sun goes out and no one is left to think of it. It is true for any alien life that might think of it, and true whether they think of it or not. It cannot be changed. So long as there is a world with a horizontal and a vertical axis, a sky and a horizon, it is inviolable and as true as anything that can be thought.

As precise as mathematics is, it is also the most explicit language we have for the description of mysteries. Being the language of physics, it describes actual mysteries—things we can’t see clearly in the natural world but suspect are true and later confirm—and imaginary mysteries, things that exist only in the minds of mathematicians. A question is where these abstract mysteries exist, what their home range is. Some people would say that they reside in the human mind, that only the human mind has the capacity to conceive of what are called mathematical objects, meaning numbers and equations and formulas and so on—the whole glossary and apparatus of mathematics—and to bring these into being, and that such things arrive as they do because of the way our minds are structured. We are led to examine the world in a way that agrees with the tools that we have for examining it. (We see colors as we do, for example, because of how our brains are structured to receive the reflection of light from surfaces.) This is a minority view, held mainly by neuroscientists and a certain number of mathematicians disinclined toward speculation. The more widely held view is that no one knows where math resides. There is no mathematician/naturalist who can point somewhere and say, “That is where math comes from” or “Mathematics lives over there,” say, while maybe gesturing toward magnetic north and the Arctic, which I think would suit such a contrary and coldly specifying discipline.

The belief that mathematics exists somewhere else than within us, that it is discovered more than created, is called Platonism, after Plato’s belief in a non-spatiotemporal realm that is the region of the perfect forms of which the objects on earth are imperfect reproductions. By definition, the non-spatiotemporal realm is outside time and space. It is not the creation of any deity; it simply is. To say that it is eternal or that it has always existed is to make a temporal remark, which does not apply. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is. The physical world is temporal and declines; the non-spatiotemporal one is ideal and doesn’t.

A third point of view, historically and presently, for a small but not inconsequential number of mathematicians, is that the home of mathematics is in the mind of a higher being and that mathematicians are somehow engaged with Their thoughts. Georg Cantor, the creator of set theory—which in my childhood was taught as a part of the “new math”—said, “The highest perfection of God lies in the ability to create an infinite set, and its immense goodness leads Him to create it.” And the wildly inventive and self-taught mathematician Srinivasa Ramanujan, about whom the movie “The Man Who Knew Infinity” was made, in 2015, said, “An equation for me has no meaning unless it expresses a thought of God.”

In Book 7 of the Republic, Plato has Socrates say that mathematicians are people who dream that they are awake. I partly understand this, and I partly don’t.

Mathematics has been variously described as an ideal reality, a formal game, and the poetry of logical ideas… an excerpt from “What is Mathematics?” from Alec Wilkinson— eminently worthy of reading in full.

* Albert Einstein


As we sum it up, we might send carefull-calcuated birthday greetings to Georgiy Antonovich Gamov; he was born on this date in 1904. Better known by the name he adopted on immigrating to the U.S., George Gamow, he was a physicist and cosmologist whose early work was instrumental in developing the Big Bang theory of the universe; he also developed the first mathematical model of the atomic nucleus.

But mid-career Gamow began to shift his energy to teaching and to writing popular books on science… one of which, One Two Three… Infinity, inspired legions of young scientists-to-be and kindled a life-long interest in science in an even larger number of other youngsters (like your correspondent).


“Be a good ancestor”*…

The planned underground repository near the Olkiluoto nuclear-power plant in Finland could teach us the merits of long-term thinking

The Greek philosopher Plato once imagined a city that provides full justice to its citizens. Setting out his ideas in the Republic almost 2500 years ago, Plato did not, however, think that such a city could ever be realized. Radical (and surely unachievable) transformations in education, culture and government would be required to establish and sustain it. “Ridiculous,” Plato concluded.

In a similar vein, the US cultural anthropologist Vincent Ialenti envisions a fictional city whose citizens have been trained to think so that humans don’t need to flee the planet to survive. So utopian is the picture that Ialenti – writing in his new book Deep Time Reckoning – calls it “absurd”. Yet that notion is no less absurd, he continues, than the way humans are now acting, “careening toward an Anthropocene cliff”.

Based at George Washington University, Ialenti developed this picture by drawing on three years of fieldwork in Finland, where he’d studied experts who were evaluating the risks of a permanent repository for nuclear waste…

The Finnish experts developed various strategies to envision “deep time”. For example, they implemented unusual computer modelling methods to integrate a variety of datasets, scenarios, maps and reports over an unprecedented range of issues, including climate change, geological events, shorelines, human demographics, vegetation growth and ecosystems. For clues on the long-term evolution of materials and planetary landscapes, they studied everything from ancient Roman nails and 2100-year-old Chinese cadavers to cannons from a sunken 17th-century Swedish warship and traces of a crater in Finland caused by a meteor 73 million years ago.

Ialenti is fully aware of the deficiencies and partialities of the Finnish project and of his own study…

Climate-change predictions, even for 2050, seem hopelessly far in the future, and tainted by politics, guesswork and subjectivity. Thinking about the present seems more do-able, while thinking about tens or hundreds of thousands of years in the future appears starry-eyed and abstract. But Ialenti believes the exact opposite is true. What’s abstract (in the sense of detached from reality) is what Ialenti calls “a manic fixation on the present”, and not being able to think about humanity thousands of years hence.

Ialenti is less interested in the conclusions reached by the Finnish experts than by their audacious aims, which are to develop methods to break free from what he calls our “shallow time discipline”. He then tries to devise ways to retrain our habits to encourage humans to think long-term; for him, Deep Time Reckoning is not a stale academic treatise but more of a “practical toolkit”.

 This toolkit includes high-school civics classes devoted to teaching long-term developments: of the universe since the Big Bang 13.8 billion years ago; of Earth since 4.5 billion years ago; of Earth’s life, dinosaurs and humans; and of the evolution of languages and technologies. It envisions school pupils reading about futuristic visions by Ray Kurzweil and Marxist descriptions of world utopias.

Ialenti even asks his university students to examine the tools that the insurance industry uses to protect companies against future calamities, and the methods that the Catholic Church uses to maintain institutional continuity. Practiced over generations, Ialenti thinks, such an education would eventually make deep time thinking “less wacky and aloof”, and more second-nature…

Plato meant the Republic to be a beacon for humans to think about justice in the present, not as the blueprint for an actual city to be realized in the future. After all, if you head straight towards a lighthouse, you usually end up on the rocks.

Somewhere in deep time looms a catastrophe that we don’t yet have the imagination to envision, nor the will to confront. Ialenti thinks he finds in the Finnish nuclear-risk experts glimmerings of what it might take to cultivate the human behaviour needed to do so. Humanity’s long-range hope, Ialenti suggests, hangs on what we might call the Finlandization of the planet.

Professor Robert P. Crease (@rcrease) explains how a nuclear-waste program in Finland can help us to envisage the world thousands of years from now: “Very Deep Thinking.”

See also Ingrid Burrington‘s interview with Yale architecture and design professor Keller Easterling, “How to Design Better Systems in a World Overwhelmed by Complexity, ” and Jeremy Lent‘s “What Does An Ecological Civilization Look Like?

* Marian Wright Edelman


As we play the long game, we might spare a thought for Alfred Habdank Skarbek Korzybski; he died on this date in 1950. Trained as an engineer, he developed a field called general semantics, which he viewed as both distinct from, and more encompassing than, the field of semantics. He argued that human knowledge of the world is limited both by the human nervous system and the languages humans have developed, and thus no one can have direct access to reality, given that the most we can know is that which is filtered through the brain’s responses to reality.

Korzybski was influential in fields across the sciences and humanities through the 1940s and 50s (perhaps most notably, gestalt therapists), and inspired science fiction writers (like Robery Heinlein and A.E. van Vogt) and philosophers like Alan Watts.

His best known dictum is “The map is not the territory.”


“PLATO was my Alexandria. It was my library, it was the place where I could attach myself to anything.”*…




One upon a time [in the 60s and 70s], there was a computer network with thousands of users across the world. It featured chat rooms, message boards, multiplayer games, a blog-like newspaper, and accredited distance learning, all piped to flat-panel plasma screens that were also touchscreens. And it wasn’t the internet.

It was PLATO (Programmed Logic for Automatic Teaching Operations), and its original purpose was to harness the power of the still-obscure world of computing as a teaching tool. Developing PLATO required simultaneous quantum leaps in technological sophistication, and it worked—college and high-school students quickly learned how to use it, and also pushed it to do new things.

Despite decades of use at major universities, it all but vanished in the 1980s and from popular memory in the years that followed, a victim of the microcomputer revolution. At its peak, PLATO was surprisingly similar to the modern internet, and it left its DNA in technology we still use today…

The story of the ur-internet: “PLATO.”

* novelist Richard Powers (who was a coder before he turned to literary fiction)


As we log on, we might send super birthday greetings to Seymour Roger Cray; he was born on this date in 1925.  An electrical engineer and computer architect, he designed a series of computers that were the fastest in the world for decades, and founded Cray Research which built many of these machines– effectively creating the “supercomputer” industry and earning the honorific “father of supercomputing.”


With a Cray-1



Written by LW

September 28, 2019 at 1:01 am

I forget…

 source: Flickr/Lord Rex

As we worry about the skills being lost in our growing dependence on new technologies, we might contemplate Plato’s recounting of Socrates’ dialogue with Phaedrus:

Socrates: Among the ancient gods of Naucratis in Egypt there was one to whom the bird called the ibis is sacred. The name of that divinity was Thoth, and it was he who first discovered number and calculation, geometry and astronomy, as well as the games of checkers and dice, and above all else, writing.

Now, the king of all Egypt at that time was Thamus, who lived in the great city in the upper region that the Greeks call Egyptian Thebes; Thamus they call Amun. Thoth came to exhibit his arts to him and urged him to disseminate them to all the Egyptians. Thamus asked him about the usefulness of each art, and while Thoth was explaining it, Thamus praised him for whatever he thought was right in his explanations and criticized him for whatever he thought was wrong.

The story goes that Thamus said much to Thoth, both for and against each art, which it would take too long to repeat. But when they came to writing, Thoth said, “O king, here is something that, once learned, will make the Egyptians wiser and will improve their memory; I have discovered a potion for memory and for wisdom.” Thamus, however, replied, “O most expert Thoth, one man can give birth to the elements of an art, but only another can judge how they can benefit or harm those who will use them. And now, since you are the father of writing, your affection for it has made you describe its effects as the opposite of what they really are. In fact, it will introduce forgetfulness into the soul of those who learn it: they will not practice using their memory because they will put their trust in writing, which is external and depends on signs that belong to others, instead of trying to remember from the inside, completely on their own. You have not discovered a potion for remembering, but for reminding; you provide your students with the appearance of wisdom, not with its reality. Your invention will enable them to hear many things without being properly taught, and they will imagine that they have come to know much while for the most part they will know nothing. And they will be difficult to get along with, since they will merely appear to be wise instead of really being so.”

Via Lapham’s Quarterly. (C.f. also Josh Mostel’s hysterical dramatization on Media Probes, if you can find it…)

As we chill, we might recall that it was on this date in 1982 that the final episode of The Lawrence Welk Show was taped (for syndicated release on April 17).  The series aired locally in Los Angeles for four years (1951–55), then nationally for another 28 years via the ABC network (1955–71) and– supported by anti-aging tonic Geritol,  sleep aid Sominex, and laxative Serutan–in first-run syndication (1971–82).  Then in 1986, lest a generation of Americans forget the polka, Oklahoma Public Television acquired the rights and began redistributing the programs to PBS stations…  on which they run to this day.

And a one, and a two…


Written by LW

February 24, 2012 at 1:01 am

What we have here is a failure to communicate…

Summer’s ending, and with it, the Summer Reading Season…  So, as readers shift back into gear, and think back over the books that occupied their breaks, Dan Wilbur offers Better Book Titles, where one will find such clarifying emendations as:

AKA, Guns, Germs, and Steel: Jared Diamond

AKA, The Symposium: Plato

AKA, The DaVinci Code: Dan Brown

AKA, The Girl with The Dragon Tattoo: Stieg Larsson

One can find many, many more– and submit one’s own– here.

As we vacuum the sand from our volumes, we might wish a happy birthday to author Jacqueline Susann; she was born on this date in 1921.  Having been disappointed by her luck as an actress and a model, Ms. Susann turned to the typewriter.  Her first novel, Every Night, Josephine (or as Better Book Titles might have it, My Poodle and Me), was a best-seller.  Her second, Valley of the Dolls (or, a la BBT, Booze, Babes, and Pills) was the best-seller:  it topped the chart for 22 weeks, and by the time of Susann’s death in 1974, had sold over 17 million copies, making it the best-selling novel of all time.  According to The Internet Public Library, it’s still Number One, with current cumulative sales of 30 million (two million copies ahead of runner-up Gone With the Wind).

Jacqueline Susann (source)

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