Conversations

My Mystical Moment

Frank Wilczek
[5.18.21]

It came to me, viscerally, that the intricate calculations I’d done using pen and paper (and wastebasket) might somehow describe this entirely different realm of existence—namely, a physical world of particles, tracks, and electronic signals, created by the kind of machinery I was looking at. There was no need to choose, as philosophers often struggled to do, between mind or matter. It was mind and matter. How could that be? Why should it be? Yet I somehow, I suddenly knew that it could be so, and should be so.

FRANK WILCZEK is the Herman Feshbach Professor of Physics at MIT, recipient of the 2004 Nobel Prize in physics, and author of Fundamentals: Ten Keys to RealityFrank Wilczek's Edge Bio Page


MY MYSTICAL MOMENT

I’ve had many varied experiences in my scientific career, including some that took me into unusual states of consciousness. Indeed, when I’m doing interactive work with my computer, I not infrequently enter trance-like states in which the passage of time seems suspended. At the end of a session, I can rise from my chair honestly thinking that a few minutes have passed, when in fact it’s been a few hours. Three times, upon suddenly seeing right through important problems that I’d been struggling with, I’ve had quasi-orgasmic experiences of mental release.

But I’ve had only one experience that qualifies as mystical. It satisfied William James’ two main criteria for such experiences.

Hands On

Patricia S. Churchland
[4.28.21]

During my first neuroanatomy lecture, the patient presented to us was a former dean of the medical school who had suffered a small brainstem stroke. As he started to identify the stroke location, the former dean suddenly began to sob piteously. Deeply concerned, we waited in utter stillness a long minute until, abruptly, his sobbing stopped. Unbothered by the interlude, he calmly went on to explain that the episode was caused by the stroke—damage to a tiny region of the brainstem which released reflexive crying when triggered by high levels of adrenalin. Conscious control was futile. A not uncommon sequel of a brainstem stroke, the condition is known as pseudobulbar affect. Adding to our bewilderment, he commented, almost as an aside, that throughout the crying episode he had felt no sadness whatever, though he did admit to finding pseudobulbar affect a nuisance. This was the first result in my new neurophilosophical world: The disconnect between despondent behavior and despondent emotions was the sort of event that many philosophers, trusting entirely in their own imagination, said was inconceivable and could not happen. But it did happen, right before our wondering eyes. This was the first of a host of “philosophically impossible” revelations from brain-damaged patients.

PATRICIA S. CHURCHLAND is professor emeritus of philosophy at the University of California, San Diego, and adjunct professor at the Salk Institute. Her research has centered on the interface between neuroscience and philosophy, with a current focus on the association of morality and the social brain. She is the author of Conscience: The Origins of Moral IntuitionPatricia S. Churchland's Edge Bio Page


HANDS ON

Throwing my anatomy textbook at the wall, I was forced to admit that my goal was doomed. What goal? To teach myself the organization of the thalamus, a brain structure deep under the cortex. Why the thalamus? Because in mammals, all sensory input (except smells) go through the thalamus and from there to cortex. It is kind of the heart and soul of all mammalian brains. In my textbook, each page showed a slice of the thalamus, advancing from back to front, each two millimeters thick. The trouble was, from one page to the next the thalamus looked completely different. From slice to slice, I could not get any sense of continuity, of what this walnut-sized thing really looked like. Visualizing a 3-D thalamus from 2-D illustrations was a dead end. Maybe going whole-hog on real 3-D is a better way. The University of Manitoba has a medical school, and the medical school has a department of brain anatomy. Surely some neuroanatomist can show me what the thalamus looks like.

Cancelling my office hours with students (okay, my bad), I drove my rusty VW downtown and found the neuroanatomy department. The sign on the door read: John Baskerville Hyde, Head. Warmly welcoming the interruption, Hyde listened to my tale of woe with intense interest and encouragement. “Yes,” he agreed, “philosophers need to know about the brain if they want to understand the mind. Here is what we can do. Can you attend regular neuroscience lectures with the first-year medical students? For the lab component, the students will get a human brain to dissect. I will arrange for you to have your own human brain to dissect. Then you’ll begin to learn brain anatomy.”

Mary Catherine Bateson: Systems Thinker

Mary Catherine Bateson
[1.18.21]

Mary Catherine Bateson
1939–2021 

Introduction
by John Brockman

From the early days of Edge, Catherine Bateson was the gift that kept giving. Beginning in 1998, with her response to “What Questions Are You Asking Yourself?” through “The Last Question” in 2018, she exemplified the role of the Third Culture intellectual: “those scientists and other thinkers in the empirical world who, through their work and expository writing, are taking the place of the traditional intellectual in rendering visible the deeper meanings of our lives, redefining who and what we are.”

Her Edge essays over the years focused on subjects as varied as "ecology and culture," systems thinking, cybernetics, metaphor, gender, climate, schismogenesis (i.e., positive feedback), the nature of side-effects, among others, and are evidence of a keen and fearless intellect determined to advance science-based thinking as well as her own controversial ideas.

She once told me that "It turns out that the Greek religious system is a way of translating what you know about your sisters, and your cousins, and your aunts into knowledge about what’s happening to the weather, the climate, the crops, and international relations, all sorts of things. A metaphor is always a framework for thinking, using knowledge of this to think about that. Religion is an adaptive tool, among other things. It is a form of analogic thinking."

"We carry an analog machine around with us all the time called our body," she said. "It’s got all these different organs that interact; they’re interdependent. If one of them goes out of kilter, the others go out of kilter, eventually. This is true in society. This is how disease spreads through a community, because everything is connected."

She used methods from systems theory to explore "how people think about complex wholes like the ecology of the planet, or the climate, or large populations of human beings that have evolved for many years in separate locations and are now re-integrating.” 

"Until fairly recently," she noted, "artificial intelligence didn’t learn. To create a machine that learns to think more efficiently was a big challenge. One of the things that I wonder about is how we'll be able to teach a machine to know what it doesn’t know that it might need to know in order to address a particular issue productively and insightfully. This is a huge problem for human beings. It takes a while for us to learn to solve problems, and then it takes even longer for us to realize what we don’t know that we would need to know to solve a particular problem."

Mary Catherine Bateson was present at ground zero of the cybernetic revolution, the home of her parents, Margaret Mead and Gregory Bateson.

As a child, I had the early conversations of the cybernetic revolution going on around me. I can look at examples and realize that when one of my parents was trying to teach me something, it was directly connected with what they were doing and thinking about in the context of cybernetics.

One of my favorite memories of my childhood was my father helping me set up an aquarium. In retrospect, I understand that he was teaching me to think about a community of organisms and their interactions, interdependence, and the issue of keeping them in balance so that it would be a healthy community. That was just at the beginning of our looking at the natural world in terms of ecology and balance. Rather than itemizing what was there, I was learning to look at the relationships and not just separate things.

Bless his heart, he didn’t tell me he was teaching me about cybernetics. I think I would have walked out on him. Another way to say it is that he was teaching me to think about systems. Gregory coined the term "schismogenesis" in 1936, from observing the culture of a New Guinea tribe, the Iatmul, in which there was a lot of what he called schismogenesis. Schismogenesis is now called "positive feedback"; it’s what happens in an arms race. You have a point of friction, where you feel threatened by, say, another nation. So, you get a few more tanks. They look at that and say, "They’re arming against us," and they get a lot more tanks. Then you get more tanks. And they get more tanks or airplanes or bombs, or whatever it is. That’s positive feedback.

At the beginning of the war, my parents, Margaret Mead and Gregory Bateson, had very recently met and married. They met Lawrence K. Frank, who was an executive of the Macy Foundation. As a result of that, both of them were involved in the Macy Conferences on Cybernetics, which continued then for twenty years. They still quote my mother constantly in talking about second-order cybernetics: the cybernetics of cybernetics. They refer to Gregory as well, though he was more interested in cybernetics as abstract analytical techniques. My mother was more interested in how we could apply this to human relations.

My parents looked at the cybernetics conferences rather differently. My mother, who initially posed the concept of the cybernetics of cybernetics, second-order cybernetics, came out of the anthropological approach to participant observation: How can you do something and observe yourself doing it? She was saying, "Okay, you’re inventing a science of cybernetics, but are you looking at your process of inventing it, your process of publishing, and explaining, and interpreting?" One of the problems in the United States has been that pieces of cybernetics have exploded into tremendous economic activity in all of computer science, but much of the systems theory side of cybernetics has been sort of a stepchild. I firmly believe that it is the systems thinking that is critical.

At the point where she said, "You guys need to look at what you’re doing. What is the cybernetics of cybernetics?" what she was saying was, "Stop and look at your own process and understand it." Eventually, I suppose you do run into the infinite recursion problem, but I guess you get used to that.

How do you know that you know what you know? When I think about the excitement of those early years of the cybernetic conferences, there have been several losses. One is that the explosion of devices and manufacturing and the huge economic effect of computer technology has overshadowed the epistemological curiosity on which it was built, of how we know what we know, and how that affects decision making.

She expressed concern that one her favorite topics, "ecology and culture," was "most commonly taught in terms of the way a given environment determines the possible cultural patterns that human societies develop to adapt to that environment, sometimes also in terms of the impact of a given human community. What I was mainly focusing on, however, came out of work that I'd done with my father, namely the relationship between the ideas, the beliefs, the understandings, and so on, of a group of people, and the way they impact their environment."

Bateson was a prolific author who wrote seven books, co-authored two, and recently completed a new book, Love Across Difference, scheduled for publication in 2022. Her writing is notable for the way in which she purged abstractions from her books to make way for stories, almost always focused on women, and who were often not known to the public. This allowed her stories to carry the kernel of the ideas. "And in the process" she said, "the ideas become more nuanced, less cut and dried." 

"Famous people are interesting," she said, "but there's a kind of a distancing phenomenon there. I'm interested in the creativity that we all put into our lives. Picasso's life story is not empowering to the creativity of ordinary people. What is empowering is looking at someone that they can identify with. And becoming aware of what they're already doing."

Given her interest in storytelling, I once asked her "what's the purpose of asking people to make that jump, instead of directly addressing the more general questions?"

"People learn from stories in a different way than the way they learn from generalities," she replied. "When I'm writing, I often start out with abstractions and academic jargon and purge it. The red pencil goes through page after page while I try to make sure that the stories and examples remain to carry the kernel of the ideas, and in the process the ideas become more nuanced, less cut and dried. Sometimes reviewers seem to want the abstractions back, but I figure that if they were able to recognize what's being said, it didn't have to be spelled out or dressed up in pretentious technical language."

"I am concerned about the state of the world," she told me the last time we sat down together in 2018. 

One of the things that we’re all seeing is that a lot of work that has been done to enable international cooperation in dealing with various problems since World War II is being pulled apart. We’re seeing the progress we thought had been made in this country in race relations being reversed. We’re seeing the partial breakup—we don’t know how far that will go—of a united Europe. We’re moving ourselves back several centuries in terms of thinking about what it is to be human, what it is to share the same planet, how we’re going to interact and communicate with each other. We’re going to be starting from scratch pretty soon.

One of the most essential elements of human wisdom at its best is humility, knowing that you don’t know everything," she said. There’s a sense in which we haven’t learned how to build humility into our interactions with our devices. The computer doesn’t know what it doesn’t know, and it's willing to make projections when it hasn’t been provided with everything that would be relevant to those projections. How do we get there? I don’t know. It’s important to be aware of it, to realize that there are limits to what we can do with AI. It’s great for computation and arithmetic, and it saves huge amounts of labor. It seems to me that it lacks humility, lacks imagination, and lacks humor. It doesn’t mean you can’t bring those things into your interactions with your devices, particularly, in communicating with other human beings. But it does mean that elements of intelligence and wisdom—I like the word wisdom, because it's more multi-dimensional—are going to be lacking.  

In this special edition of Edge, we honor the memory of Mary Catherine Bateson by taking a deep dive into her ideas through her conversations, her essays, and her responses over a twenty year period to the Edge Annual Question. Read on at the link below. Mary Catherine Bateson's Edge Bio

—JB
    Editor, Edge

A Very Bumpy Ride: Life in the Time of COVID, Part 2

Topic: 

  • Conversations
https://vimeo.com/486868658

[EDITOR'S NOTE: At the beginning of the COVID-19 outbreak, I called on Dr. Larry Brilliant, a leading  epidemiologist and pandemic expert with unique experience and expertise, to ask him to talk about how we could begin to think about COVID-19 and what was in store for us. Now, eight months later, in this Thanksgiving Day talk, he provides an update from the field. —JB]

A Very Bumpy Ride, Part 1

Life in the Time of COVID
Larry Brilliant, MD
[11.26.20]

[EDITOR'S NOTE: At the beginning of the COVID-19 outbreak, I called on Larry Brilliant, a leading epidemiologist and pandemic expert with unique experience and expertise, to ask him to talk about how we could begin to think about COVID-19 and what was in store for us. Now, eight months later, in this Thanksgiving Day talk, he provides an update from the field. —JB]

We need to have a strong WHO, a strong United Nations, a strong global alliance for vaccines and immunizations (GAVI), a strong Global Fund, and all these different organelles that make it possible for us to deal with global threats. I would extend it a little bit out of my lane to say we need desperately to deal with climate change, nuclear proliferation, drought, and famine. But in the area that I know, we can't stop a pandemic without having global collaboration. We have failed to learn the lessons of Taiwan, Vietnam, Singapore, Korea, New Zealand, Iceland—the countries that have done really well—because we don't have a strong way to take the best lessons from the success stories in dealing with this pandemic and globalizing them. This is because we deal with disinformation, and because we hold up the Swedish example even though it wasn't a good example of how to deal with the pandemic, and because we don't have a love of science in the leadership of the world, and because we don't talk to each other in the way that we need to.

Epidemiologist and pandemic expert LARRY BRILLIANT, MD, is on the advisory board for Ending Pandemics. He is also on the board of the Skoll Foundation and was the founding executive director of Google's non-profit organization. Dr. Brilliant lived in India for more than a decade while working as a United Nations medical officer, where, in 1971, he helped run the successful World Health Organization (WHO) smallpox eradication program in South Asia. He also worked for the WHO polio eradication effort and chaired the National Bio-Surveillance Advisory Subcommittee, created by President George W. Bush. He has won the TED Prize, TIME 100, and many honorary doctorates and is the author of Sometimes Brilliant: The Impossible Adventures of a Spiritual Seeker and Visionary Physician Who Helped Conquer the Worst Disease in History. Larry Brilliant, MD, Edge Bio Page 

THE REALITY CLUB: Jennifer JacquetFrancesca Vidotto, Daniel Kahneman, Lee Smolin, Nick Bostrom, Jesse Dylan, John BrockmanCarlo Rovelli, Jacob Burda

Best-Case and Worst-Case Scenarios

Life In the Time of COVID
Jared Diamond
[5.7.20]

[ED. NOTE: This is the first in a series of reflections by Edgies on the new world in which we are all living.]

My best-case scenario for what's going on now is—assuming that within the next half year, we do deal successfully with the COVID crisis—that it will become a model for people all around the world recognizing common problems, rallying together to deal with a common problem. My best-case scenario is that, having defeated COVID, we will go on to attempt to defeat and succeed in defeating climate change. For that reason, I see a potential silver lining, and that's my best-case scenario for what's going on now.

Worst-case scenario is that countries try to deal one by one. There's already talk of a race to produce vaccines, where a country that has the vaccine will use the vaccine for itself in order to gain advantage rather than spreading it around the world.

JARED DIAMOND is a professor of geography at the University of California, Los Angeles. He is the author, most recently, of Upheaval: Turning Points for Nations in Crisis. Jared Diamond's Edge Bio Page

Remembering Freeman Dyson

Freeman Dyson
[3.19.20]

Photo credit: Ann Yow

"A unique intellect—and a great and kind man." —Martin Rees

NEW!! THE REALITY CLUB: John Brockman, Esther Dyson, Martin Rees, David Kaiser, George Dyson, Jennifer Jacquet, Max Tegmark, Rich Muller, Susan Schneider, Gino Segre, Frank Tipler, Danny Hillis, Brian Keating, Lee Smolin, John Brockman


DAWKINS & DYSON: AN EXCHANGE

In July 2007, Freeman wrote a provocative essay in the New York Review of Books entitled "Our Biotech Future" in which he wrote: 

Biology is now bigger than physics, as measured by the size of budgets, by the size of the workforce, or by the output of major discoveries; and biology is likely to remain the biggest part of science through the twenty-first century. Biology is also more important than physics, as measured by its economic consequences, by its ethical implications, or by its effects on human welfare.

These facts raise an interesting question. Will the domestication of high technology, which we have seen marching from triumph to triumph with the advent of personal computers and GPS receivers and digital cameras, soon be extended from physical technology to biotechnology? I believe that the answer to this question is yes. Here I am bold enough to make a definite prediction. I predict that the domestication of biotechnology will dominate our lives during the next fifty years at least as much as the domestication of computers has dominated our lives during the previous fifty years.

Citing the work of Carl Woese, an expert in the field of microbial taxonomy, and Nigel Goldenfeld, a physicist, Freeman called for "a new biology for a new century":

Woese’s main theme is the obsolescence of reductionist biology as it has been practiced for the last hundred years, with its assumption that biological processes can be understood by studying genes and molecules. What is needed instead is a new synthetic biology based on emergent patterns of organization. Aside from his main theme, he raises another important question. When did Darwinian evolution begin? By Darwinian evolution he means evolution as Darwin understood it, based on the competition for survival of noninterbreeding species. He presents evidence that Darwinian evolution does not go back to the beginning of life. When we compare genomes of ancient lineages of living creatures, we find evidence of numerous transfers of genetic information from one lineage to another. In early times, horizontal gene transfer, the sharing of genes between unrelated species, was prevalent. It becomes more prevalent the further back you go in time.

Whatever Carl Woese writes, even in a speculative vein, needs to be taken seriously. In his "New Biology" article, he is postulating a golden age of pre-Darwinian life, when horizontal gene transfer was universal and separate species did not yet exist. Life was then a community of cells of various kinds, sharing their genetic information so that clever chemical tricks and catalytic processes invented by one creature could be inherited by all of them. Evolution was a communal affair, the whole community advancing in metabolic and reproductive efficiency as the genes of the most efficient cells were shared. Evolution could be rapid, as new chemical devices could be evolved simultaneously by cells of different kinds working in parallel and then reassembled in a single cell by horizontal gene transfer.

Freeman's article appeared in July 2007. The following month, I hosted a seminar at Eastover Farm to explore new definitions of life required by the recent advances in genomics. I invited three of the participants—Freeman, and genomic pioneers George Church and J. Craig Venter—to come up a day early in order to spend time discussing and evaluating the import of Freeman's essay. It was interesting that Freeman, a mathematician and physicist, was now making pronouncements about evolution. Why would the mainstream evolutionary biologists care about what he has to say?

What better way to find out than to ask Richard Dawkins, the author of The Selfish Gene, and the standard bearer of Darwinism. I wrote to Richard and asked if he would comment on Freeman's ideas about horizontal evolution and "the end of the Darwinian interlude." Richard promptly responded (while noting that his hastily written piece was solely for the purpose of the meeting).  

Freeman Dyson: 1923 - 2020

Freeman Dyson
[2.28.20]

Photo: Freeman Dyson, August 1939, compliments of George Dyson

Freeman Dyson (1923 - 2020)

ED. NOTE: On February 3, 2019, Freeman Dyson wrote to me in response to my interest in commissioning him to write a new essay for Edge:

From: [email protected]
Dear John,

Thank you for your message of January 2 announcing your new agenda and including the piece from George.

I have written a piece with the title, "Biological and Cultural Evolution: Six Characters in Search of an Author'', which I am offering for you to publish. I have adopted the design of Pirandello's play to introduce my six characters. The purpose is to give a public hearing to some unorthodox ideas about evolution.

Evolution is a dominating force in human affairs and in the workings of nature. An improved understanding of evolution may help us to deal wisely with human problems and also with the preservation of natural diversity.

Please let me know whether you find this piece appropriate for your new agenda. I send you a first draft. It will need some editorial work and some references to the literature before it is published.

I am sending you the text by a separate E-mail. With thanks for your consideration, yours ever, Freeman.

Freeman at that time was in La Jolla, and we were unable to sit down together for a videotaped interview. Nor would there be an audio. I asked if he could read the essay, and he agreed. A few days after sending him a USB microphone, my associate Russell Weinberger received an audio file with this note:

Thank you for your help this morning with the audio transfer. I could never have done this without guidance from both you and Imme. We sent it to you as soon as it was finished without checking the quality. I suspect the quality may be poor, since I was struggling with the GarageGang, a computer program that I still do not understand. If you find the quality unacceptable, I will be happy to do the whole recording over again. This will not take so long, now that we have some experience with the technical problems. In any case, I apologize for my incompetence in dealing with computers. Yours, Freeman Dyson.

Freeman, at the age of 96, had gone back to school to spend three days mastering the intricacies of Apple's "GarageGang." 

So, we are pleased to reprise his piece, "Biological and Cultural Evolution: Six Characters in Search of an Author.” But, do yourself a favor. While the text of the essay is below, don't read it. Honor Freeman by listening to it: a wonderful way to spend an hour.

John Brockman
Editor, Edge

p.s. In the coming weeks, we are planning a tribute to Freeman, a founding member of both Edge, in 1996, and before that, The Reality Club, in 1980. Stay tuned.

 

Biological and Cultural Evolution
Six Characters in Search of an Author
An Edge Original Essay by Freeman Dyson [2.19.19] 

In the near future, we will be in possession of genetic engineering technology which allows us to move genes precisely and massively from one species to another. Careless or commercially driven use of this technology could make the concept of species meaningless, mixing up populations and mating systems so that much of the individuality of species would be lost. Cultural evolution gave us the power to do this. To preserve our wildlife as nature evolved it, the machinery of biological evolution must be protected from the homogenizing effects of cultural evolution.

Unfortunately, the first of our two tasks, the nurture of a brotherhood of man, has been made possible only by the dominant role of cultural evolution in recent centuries. The cultural evolution that damages and endangers natural diversity is the same force that drives human brotherhood through the mutual understanding of diverse societies. Wells's vision of human history as an accumulation of cultures, Dawkins's vision of memes bringing us together by sharing our arts and sciences, Pääbo's vision of our cousins in the cave sharing our language and our genes, show us how cultural evolution has made us what we are. Cultural evolution will be the main force driving our future.

FREEMAN DYSON was an emeritus professor of physics at the Institute for Advanced Study in Princeton. In addition to fundamental contributions ranging from number theory to quantum electrodynamics, he worked on nuclear reactors, solid-state physics, ferromagnetism, astrophysics, and biology, looking for problems where elegant mathematics could be usefully applied. His books include Disturbing the UniverseWeapons and HopeInfinite in All DirectionsMaker of Patterns, and Origins of LifeFreeman Dyson's Edge Bio Page 


BIOLOGICAL AND CULTURAL EVOLUTION: SIX CHARACTERS IN SEARCH OF AN AUTHOR

In the Pirandello play, "Six Characters in Search of an Author", the six characters come on stage, one after another, each of them pushing the story in a different unexpected direction. I use Pirandello's title as a metaphor for the pioneers in our understanding of the concept of evolution over the last two centuries. Here are my six characters with their six themes.

1. Charles Darwin (1809-1882): The Diversity Paradox.
2. Motoo Kimura (1924-1994): Smaller Populations Evolve Faster.
3. Ursula Goodenough (1943- ): Nature Plays a High-Risk Game.
4. Herbert Wells (1866-1946): Varieties of Human Experience.
5. Richard Dawkins (1941- ): Genes and Memes.
6. Svante Pääbo (1955- ): Cousins in the Cave.

The story that they are telling is of a grand transition that occurred about fifty thousand years ago, when the driving force of evolution changed from biology to culture, and the direction changed from diversification to unification of species. The understanding of this story can perhaps help us to deal more wisely with our responsibilities as stewards of our planet.

Reuben Hersh: 1927-2020

Reuben Hersh
[1.21.20]

REUBEN HERSH, (1927-2020), was professor emeritus at the University of New Mexico, Albuquerque. He was the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh was the co-author (with Philip J. Davis) of The Mathematical Experience and Descartes' Dream, which won the National Book Award in 1983, and author of What is Mathematics, Really?

He advocated for what he called a "humanist" philosophy of mathematics, opposed to both Platonism (so-called "realism") and its rivals nominalism/fictionalism/formalism. He held that mathematics is real, and its reality is social-cultural-historical, located in the shared thoughts of those who learn it, teach it, and create it. His article "The Kingdom of Math is Within You" (a chapter in his Experiencing Mathematics, 2014) explains how mathematicians' proofs compel agreement, even when they are inadequate as formal logic.​ 

[February 10, 1997]

What is mathematics? It's neither physical nor mental, it's social. It's part of culture. It's part of history. It's like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That's what math is.

For mathematician Reuben Hersh, mathematics has existence or reality only as part of human culture. Despite its seeming timelessness and infallibility, it is a social-cultural-historic phenomenon. He takes the long view. He thinks a lot about the ancient problems. What are numbers? What are triangles, squares and circles? What are infinite sets? What is the fourth dimension? What is the meaning and nature of mathematics?

In so doing he explains and criticizes current and past theories of the nature of mathematics. His main purpose is to confront philosophical problems: In what sense do mathematical objects exist? How can we have knowledge of them? Why do mathematicians think mathematical entities exist forever, independent of human action and knowledge?

REUBEN HERSH: What is a number? Like, what is two? Or even three? This is sort of a kindergarten question, and of course a kindergarten kid would answer like this: (raising three fingers), or two (raising two fingers). That's a good answer and a bad answer. 

Pages

Subscribe to RSS - Conversations