Fumfer Physics 49: Evolving Mathematics, Genius at Home, and Humanizing Physics

In this interview, Scott Douglas Jacobsen and Rick Rosner discuss how mathematical definitions evolve, from the number one to prime structures and unresolved problems like twin primes. They then move into the domestic lives of intellectual giants such as Terence Tao and Edward Witten, market analysis, chartists, absent-mindedness, cognitive concerns, and why abstract physics often becomes less compelling without human stories, ending with Rosner’s reflections on long-term marriage.

Evolving Mathematical Concepts

Scott Douglas Jacobsen: I was watching an interview with Terence Tao, and he was discussing how even definitions in mathematics, perhaps in number theory, can evolve over time. Concepts as basic as one or zero may be understood differently as mathematics advances. Do you have any thoughts on that?

Rick Rosner: The more abstract and sophisticated a mathematical concept becomes, the more likely its interpretation is to evolve. Even something as intuitively simple as the number one can take on different meanings depending on the mathematical framework.

Someone deeply immersed in quantum mechanics, for example, might think about the assumptions and limitations that underlie what appears to be a straightforward concept. But in ordinary mathematics, the number one remains a remarkably stable idea.

What changes over time is not necessarily the number itself but the network of relationships and structures in which it participates. Mathematicians continually discover new properties, connections, and patterns involving numbers.

For example, prime numbers are not merely counting numbers; they also possess intricate relationships and distributions. When you remove multiples of a given prime and examine what remains, new structures emerge. This process reveals additional layers of mathematical organization.

Prime numbers occupy a particularly important role because every composite number can ultimately be factored into primes. In that sense, they form a foundational framework for the integers. Questions such as whether there are infinitely many twin primes illustrate how seemingly simple numerical concepts can lead to profound and unresolved mathematical problems.

I suspect there are deep informational principles underlying many of these patterns, although proving such ideas is another matter entirely. Mathematics continually reveals that even the most familiar concepts are embedded within far more complex structures than we initially realize.

I am sure Terence Tao knows vastly more about the number one than I do. It would be fascinating to hear him give a ninety-minute lecture on nothing but the number one.

Jacobsen: He probably could. I think he gave one lecture called The Cosmic Distance Ladder, and it was probably an hour or two long. Someone with that level of expertise certainly could.

Genius at Home

Rosner: That makes me wonder: Terence Tao has a wife and children, right?

Jacobsen: A wife and three children, yes. The same is true of Edward Witten. Terence Tao and Edward Witten are both married and have children, I think.

Rosner: All right, so these are people with extraordinarily powerful minds who spend their days doing exceptionally advanced work. Then they go home to their spouses and children. What is that household like?

At my house, if I mention that I am very smart, my wife just laughs. She knows I am intelligent, but she also sees the limited practical value of it in many day-to-day situations. She laughs because she sees me waking up from my second nap or wandering around the house in my socks. So I wonder whether, when Tao or Witten go home, it is basically the same thing. Is it just a normal family environment, like Homer and Marge and the kids, where highly abstract intellectual topics rarely come up and most conversations revolve around ordinary household matters?

I mean, the opportunities to display intellectual brilliance during dinner and while watching television afterward are fairly limited.

Investments and Practical Intelligence

There are occasional situations where analytical thinking becomes useful. For example, my wife and I discuss investments. We are older, and like many people in our generation, we have accumulated assets. It is conceivable that a highly intelligent person could apply sophisticated analysis to questions such as whether this is a good time to be invested in the stock market. Perhaps Tao or Witten would have unique insights.

In our case, I do not possess any profound mathematical framework for analyzing markets. We generally listen to a variety of commentators and analysts, then try to triangulate among their opinions. We also try to account for potential conflicts of interest.

For instance, if you invest through a mutual fund company, you can either purchase funds directly or pay an additional management fee for professional portfolio management. Those managers are often incentivized to keep your money invested because their compensation depends on assets under management. That incentive structure is worth keeping in mind.

I do not engage in elaborate mathematical forecasting techniques. Have you heard of chartists? A chartist is someone who attempts to analyze financial markets by studying the patterns formed by price movements over time. They believe that certain recurring configurations can help predict future market behavior.

Jacobsen: It is somewhat like using graph-based geometric patterns in place of formal equations.

Rosner: A graph-based predictive geometry, sure. I do not do that. I have noticed what appears to be a short-term tendency toward mean reversion in stock prices, but I have never actually analyzed it.

The simplest analysis would be to calculate the historical probability that the market rises on any given day. Since markets tend to rise over long periods, the percentage of up days is greater than 50 percent. Then you could compare that figure with the probability of an up day immediately following another up day, and the probability of an up day following a down day.

My intuition is that the probability of an up day after an up day might be somewhat lower than the overall average, while the probability of an up day after a down day might be somewhat higher. But that is just speculation on my part. I have never run the numbers.

Would Terence Tao do something like that? He certainly has the technical skills. If he became interested in a market question, or if his wife asked whether they should invest differently, he could probably write a quick program to test a hypothesis and see what the data revealed.

Then again, he might come back with a different kind of answer: that the expected return from spending time on market analysis is lower than the return from continuing the work for which he is already highly compensated. That might be the truly intelligent response.

What I wonder is whether there are highly intellectual conversations in the Tao household or the Witten household. Or are they simply ordinary families whose professional work stays at work?

Jacobsen: I suspect it varies. Idle intellectual conversations may be more likely in the Witten household because, as far as I know, Edward Witten is married to another academic. Terence Tao's wife is not a mathematician or physicist, as far as I am aware.

If that is correct, conversations in the Tao household may be more ordinary than those in the Witten household.

Absent-Mindedness and Cognitive Concerns

Rosner: Lately, Carole has been accusing me of being absent-minded because I do not always remember every detail she tells me. Part of that comes from concern. She pays close attention to signs of cognitive decline because she watched her mother experience mental deterioration, and she is aware of similar issues among friends and their spouses.

She keeps an eye on me because I am older than she is, although not dramatically older. She wants to know whether I am starting to lose my mental sharpness.

My response is that I am not experiencing cognitive decline. I also think people have a right to be absent-minded at times. Sometimes you become absorbed in your own thoughts and do not remember every detail of every conversation.

In our household, there is often an expectation that I should remember everything that has been said. Yet most of those conversations are not philosophical, scientific, or mathematical discussions of the sort one might imagine taking place among academics.

Why Physics Can Become Boring

If I try to talk to Carole about physics, which I rarely do, her response is usually, "Talk to me about something that is not boring."

I can sometimes make a scientific idea interesting for a few sentences by presenting an unexpected fact or insight. But if I continue elaborating on it, it quickly becomes boring to her.

Jacobsen: What is it about the subject that makes it boring to her?

Rosner: It seems that, beyond a certain point, which is reached fairly quickly, it becomes like discussing the Rams, the Lakers, or the Dodgers. One sentence might be interesting. For example, saying that the Dodgers have been one of the most successful teams in Major League Baseball during the twenty-first century is mildly interesting.

But if I start discussing the details, how many games the Yankees have won compared with the Dodgers, or other statistical minutiae, it quickly becomes boring.

Human Stories and Familiar Subjects

What makes sports interesting is often the human story. If there were some unusual personal rivalry between a pitcher and a batter, that would be interesting. But once you start explaining the statistical basis in great detail, how often a batter is typically hit by a pitch compared with some specific case, the conversation can quickly lose its appeal.

Physics is often similar. I could tell Carole something intriguing, such as the fact that a single photon in a quantum experiment can exhibit behavior that appears to involve multiple possible paths. That is interesting for a moment because it is counterintuitive.

People are also familiar with concepts such as Schrödinger's cat, parallel universes, and the multiverse because those ideas have become common in popular culture. The first few times someone encounters them, they seem fascinating. Eventually, however, they become clichés. Once the novelty wears off, discussing them in greater detail can become less engaging.

Recently, we have been watching Euphoria. One thing Carole pointed out was that one of the performers playing a stripper was actually a legitimate actress related to another well-known actor. That kind of behind-the-scenes detail is interesting because it provides context and a human story.

Carole and I have been together for forty years, so I have developed a fairly good sense of what she finds interesting and when a topic begins to lose her attention.

Scott Douglas Jacobsen is a blogger on Vocal with more than 200 publications on the platform. He is the Founder and Publisher of In-Sight Publishing (ISBN: 978–1–0692343; 978–1–0673505) and Editor-in-Chief of In-Sight: Interviews (ISSN: 2369–6885). He writes for International Policy Digest (ISSN: 2332–9416), The Humanist (Print: ISSN, 0018–7399; Online: ISSN, 2163–3576), Basic Income Earth Network (UK Registered Charity 1177066), Humanist Perspectives (ISSN: 1719–6337), A Further Inquiry (SubStack), Vocal, Medium, The Good Men Project, The New Enlightenment Project, The Washington Outsider, rabble.ca, and other media. His bibliography index can be found via the Jacobsen Bank at In-Sight Publishing, comprising more than 10,000 articles, interviews, and republications across more than 200 outlets. He has served in national and international leadership roles within humanist and media organizations, held several academic fellowships, and currently serves on several boards. He is a member in good standing in numerous media organizations, including the Canadian Association of Journalists, PEN Canada (CRA: 88916 2541 RR0001), Reporters Without Borders (SIREN: 343 684 221/SIRET: 343 684 221 00041/EIN: 20–0708028), and others.