Peter Thiel Shares his Insights

Source: Medium, Apr 2015
<via the Mercatus Center, George Washington University>

TYLER COWEN: Then if you have to make a prediction, which breakthrough in particular will get us out of the stagnation? What’s your pick?

PETER THIEL: I still think there are — probably the most natural ones are all these things that are at the boundary of information technology on atoms, of bits and atoms.

I think the most natural hope is that information technology starts to broaden out and starts to impact this world of atoms.

We need to ask, what is it about our society where those of us who do not suffer from Asperger’s are at some massive disadvantage because we will be talked out of our interesting, original, creative ideas before they are even fully formed?

We’ll notice that’s a little bit too weird, that’s a little bit too strange. Maybe I’ll just go ahead and open the restaurant that I’ve been talking about, that everyone else can understand and agree with, or do something extremely safe and conventional, and therefore hypercompetitive, and probably not that great as an idea.

… that’s probably not how the system really changes. It probably will be changed by some idiosyncratic people who have really strong convictions, and are over time, able to convince more people of them. But whether this means that we have more or less change is hard to evaluate. It always comes from these somewhat nonconventional channels.

a lot of what you’re looking for, are these almost Zen-like opposites. You want people who are both really stubborn and really open-minded. That’s a little bit contradictory. You want people who are idiosyncratic and really different, but then who can work well together in teams. And so, this is again, maybe not 180 degrees opposite, but like 175 degrees.

think the technology and science questions are ones that I find very interesting. I think they are somewhat more measurable than a lot of the qualitative social ones.

A lot of what I end up doing is somewhat serendipitous. You talk with a lot of interesting people. You try to figure out what are some great technologies, great entrepreneurs to work with in different ways.

That’s how you end up getting very interesting perspectives, and how you change your mind on things. The overarching agenda is always to try to figure out some way to get out of the stagnation by literally helping people to start companies that will change the world.

AUDIENCE MEMBER: You talk about vertical progress versus horizontal progress. I’m wondering, how does one create vertical progress? Do you have any tips for doing that?

PETER THIEL: There’s no straightforward formula for innovation. It’s much easier to do horizontal progress, which I describe as globalization, copying things that work going from one to n, versus vertical progress, technology, doing new things, going from zero to one.

Globalization, I think there is actually a formula. You can copy what’s working, try to mechanically apply it. There’s something scientific about globalization. There’s something deeply unscientific about the history of technology itself.

Science starts with the number two, whereas every moment in the history of science, technology, business, I believe, happens only once. The next Mark Zuckerberg won’t start a social network, the next Larry Page won’t start a search engine.

It’s always some idiosyncratic thing. It’s good to be passionate about something that you are good at, that other people are not doing. If you get those three things lined up, that’s a very good start.

AUDIENCE MEMBER: In order to go from zero to one in a nonprofit organization, or a political advocacy group, what would one have to do? What would be a key differentiator, or angle, to approach with it?

PETER THIEL: The contrarian business question is what are great businesses no one has started, the contrarian investor question is what great investments does nobody like — the contrarian nonprofit question is what great causes are deeply unpopular? This is how I always deflect requests for money, is I ask people, “Why is your cause popular? Why is your cause unpopular?” Because I only want to fund unpopular causes. I assume popular causes are funded relatively well. Relative to good, unpopular causes.

If you are able to push unpopular causes, that’s very good. Then, the Zen-like problem, the paradox, is that you have a lot of impact, if you are able to push a good, worthwhile, but unpopular cause. The Zen paradox, is that it’s very hard to market it and get money to do it.

Always having a counterfactual sense of mission is important. If we weren’t doing this, nobody else in the world would be doing this. To the extent that’s not true, you want to make that more true. Maybe it’s a spectrum, but you want to always tilt more in that direction.

Running Can Make You Smarter

Source:  NYTimes, Jul 2016

our brains appear to function better when they are awash in cathepsin B and we make more cathepsin B when we exercise, says Henriette van Praag, an investigator at the National Institute on Aging at the N.I.H. who oversaw this study.

McDonalds @ Johor Bahru City Square


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Mathematical Patterns in/of the Universe

Source: Quanta magazine, Feb 2013

Subatomic particles have little to do with decentralized bus systems. But in the years since the odd coupling was discovered, the same pattern has turned up in other unrelated settings. Scientists now believe the widespread phenomenon, known as “universality,” stems from an underlying connection to mathematics, and it is helping them to model complex systems from the Internet to Earth’s climate.

The red pattern exhibits a precise balance of randomness and regularity known as “universality,” which has been observed in the spectra of many complex, correlated systems. In this spectrum, a mathematical formula called the “correlation function” gives the exact probability of finding two lines spaced a given distance apart.

Universality is thought to arise when a system is very complex, consisting of many parts that strongly interact with each other to generate a spectrum. The pattern emerges in the spectrum of a random matrix, for example, because the matrix elements all enter into the calculation of that spectrum. But random matrices are merely “toy systems” that are of interest because they can be rigorously studied, while also being rich enough to model real-world systems, Vu said. Universality is much more widespread. Wigner’s hypothesis (named after Eugene Wigner, the physicist who discovered universality in atomic spectra) asserts that all complex, correlated systems exhibit universality, from a crystal lattice to the Internet.

The more complex a system is, the more robust its universality should be, said László Erdös of the University of Munich, one of Yau’s collaborators. “This is because we believe that universality is the typical behavior.”

“It may happen that it is not a matrix that lies at the core of both Wigner’s universality and the zeta function, but some other, yet undiscovered, mathematical structure,” Erdös said. “Wigner matrices and zeta functions may then just be different representations of this structure.”

Many mathematicians are searching for the answer, with no guarantee that there is one. “Nobody imagined that the buses in Cuernavaca would turn out to be an example of this. Nobody imagined that the zeroes of the zeta function would be another example,” Dyson said. “The beauty of science is it’s completely unpredictable, and so everything useful comes out of surprises.”

Peter Scholze: deep connections between number theory and geometry.

Source: Quanta, Jun 2016

The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry.

his unnerving ability to see deep into the nature of mathematical phenomena. Unlike many mathematicians, he often starts not with a particular problem he wants to solve, but with some elusive concept that he wants to understand for its own sake.

As Scholze burrowed into the proof, he became captivated by the mathematical objects involved — structures called modular forms and elliptic curves that mysteriously unify disparate areas of number theory, algebra, geometry and analysis. Reading about the kinds of objects involved was perhaps even more fascinating than the problem itself, he said.

Scholze’s mathematical tastes were taking shape. Today, he still gravitates toward problems that have their roots in basic equations about whole numbers. Those very tangible roots make even esoteric mathematical structures feel concrete to him. “I’m interested in arithmetic, in the end,” he said. He’s happiest, he said, when his abstract constructions lead him back around to small discoveries about ordinary whole numbers.

Scholze avoids getting tangled in the jungle vines by forcing himself to fly above them: As when he was in college, he prefers to work without writing anything down. That means that he must formulate his ideas in the cleanest way possible, he said. “You have only some kind of limited capacity in your head, so you can’t do too complicated things.”

In the middle of the 20th century, mathematicians discovered an astonishing link between reciprocity laws and what seemed like an entirely different subject: the “hyperbolic” geometry of patterns such as M.C. Escher’s famousangel-devil tilings of a disk. This link is a core part of the “Langlands program,” a collection of interconnected conjectures and theorems about the relationship between number theory, geometry and analysis. When these conjectures can be proved, they are often enormously powerful: For instance, the proof of Fermat’s Last Theorem boiled down to solving one small (but highly nontrivial) section of the Langlands program.

Mathematicians have gradually become aware that the Langlands program extends far beyond the hyperbolic disk; it can also be studied in higher-dimensional hyperbolic spaces and a variety of other contexts. Now, Scholze has shown how to extend the Langlands program to a wide range of structures in “hyperbolic three-space” — a three-dimensional analogue of the hyperbolic disk — and beyond. By constructing a perfectoid version of hyperbolic three-space, Scholze has discovered an entirely new suite of reciprocity laws.

Soap Foam as a Rose – Kanebo Evita

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Ramanujan’s Puzzles

Source: Quanta Magazine, Jul 2016

The work that Ramanujan did in his brief professional life a century ago has spawned whole new areas of mathematical investigation, kept top mathematicians busy for their whole professional lives, and is finding applications in computer science, string theory, and the mathematical basis of black hole physics.

The mathematician Mark Kac divided all geniuses into two types: “ordinary” geniuses, who make you feel that you could have done what they did if you were say, a hundred times smarter, and “magical geniuses,” the working of whose minds is, for all intents and purposes, incomprehensible. There is no doubt that Srinivas Ramanujan was a magical genius, one of the greatest of all time. Just looking at any of his almost 4,000 original results can inspire a feeling of bewilderment and awe even in professional mathematicians: What kind of mind can dream up exotic gems like these?

Ramanujan indeed had preternatural insights into infinity: he was a consummate bridge builder between the finite and the infinite, finding ways to represent numbers in the form of infinite series, infinite sums and products, infinite integrals, and infinite continued fractions, an area in which, in the words of Hardy, his mastery was “beyond that of any mathematician in the world.”

What if Ramanujan had modern calculating tools?

Ramanujan, like many other great mathematical geniuses such as Gauss, loved to play with specific cases, which he then built into general results. These geniuses did prodigious calculations by hand — Ramanujan used chalk on slate in his early days, erasing intermediate results with his elbow.

Steven Wolfram has conjectured that if Ramanujan had modern calculating tools like Mathematica, “he would have been quite an adventurergoing out into the mathematical universe and finding all sorts of strange and wonderful things, then using his intuition and aesthetic sense to see what fits together and what to study further.” What do you think?