Physicist, Startup Founder, Blogger, Dad

Sunday, December 31, 2017

Happy New Year 2018

Greetings from the Central Coast of California! I've been spending part of the holiday working with the kids on their swimming. Hope to get both of them qualified for the Michigan middle school state championship meet :-)

It's hard to beat sunshine, palm trees, and an outdoor pool in December!

On the beach, New Year's Day :-)

A brief exposition on the nature of tides:

Friday, December 29, 2017

The Bonfire of the Black Public Intellectual Vanities: Economist Glenn Loury on Ta Nehisi Coates and Cornell West

Glenn Loury is Merton P. Stoltz Professor of the Social Sciences, Department of Economics, Brown University. John McWhorter is Associate Professor of English and Comparative Literature at Columbia University, where he teaches linguistics, American studies, philosophy, and music history.

(Video will start at 20:50 but the entire conversation is worth a listen.)
[20:50] ... I'm talking about 65 or 70 percent of kids born to unmarried women. You can't tell me that that doesn't matter. It matters. There could be many explanations for it, but don't try to ignore that fact. Development, the test scores? This whole edifice that we'd built of Diversity and Inclusion, it's founded on a lie, John. Because the issue is performance and the Asians have demonstrated that. The facts are so palpable that it amazes me that people can't look at them. The Asians have demonstrated -- these are people who are second generation descendants; people were born 10,000 miles from here -- it [the USA] is an open society. African-American under-representation is a reflection of African-American under-development. Now, we can go into the historical reasons for that. If the issue is who is to blame ... plenty enough blame to go around. But the fundamental imperative is to enhance the development and that won't happen unless you acknowledge the absence of it. The test scores reflect an inadequate acquisition of functional and cognitive capacities essential to functioning in the modern world and the gaps are enormous etcetera...
Now Loury gets really worked up:
[23:50] ... the Afro Studies hustle ... the avoidance of the necessity of failure against standards in order for the standards to be meaningful and for the kind of disciplines and capacities that constitute excellence to be honed and developed. It's a shell game. It's a lie, ok. That's what I'm saying. Just say that the jails are full of black people means that the criminal justice system is racist and to leave it at that when the bodies pile up in Chicago and elsewhere. To talk about Diversity / Inclusion is the way of legitimating and institutionalizing a deferential and racist withholding of judgment from African-American people to perform at the level of excellence at a place like MIT or Caltech or Brown or Columbia or Yale requires. I mean, I'm really really angry about this because people are being dishonest about this in the interest of a Coon Show, John, a Coon Show -- that's what we're talking about ...
More at [25:17] The Bonfire of the Black Public Intellectual Vanities. See earlier post Talking Ta-Nehisi Coates, Seriously?

See also Loury's Kenneth Arrow Lecture, Department of Economics, Columbia University: Persistent Racial Inequality in the US: An Economic Theorist’s Account (PDF).

Monday, December 25, 2017

Peace on Earth, Good Will to Men 2017

For years, when asked what I wanted for Christmas, I've been replying: Peace On Earth, Good Will To All Men :-)

No one ever seems to recognize that this comes from the bible, Luke 2.14 to be precise!

Linus said it best in A Charlie Brown Christmas:
And there were in the same country shepherds abiding in the field, keeping watch over their flock by night.

And, lo, the angel of the Lord came upon them, and the glory of the Lord shone round about them: and they were sore afraid.

And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.

For unto you is born this day in the city of David a Saviour, which is Christ the Lord.

And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger.

And suddenly there was with the angel a multitude of the heavenly host praising God, and saying,

Glory to God in the highest, and on earth peace, good will toward men.

Merry Christmas!

Two years ago today I shared the following story on this blog: Nativity 2050

For an update, see The Future is Here: Genomic Prediction in MIT Technology Review

And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.
Mary was born in the twenties, when the tests were new and still primitive. Her mother had frozen a dozen eggs, from which came Mary and her sister Elizabeth. Mary had her father's long frame, brown eyes, and friendly demeanor. She was clever, but Elizabeth was the really brainy one. Both were healthy and strong and free from inherited disease. All this her parents knew from the tests -- performed on DNA taken from a few cells of each embryo. The reports came via email, from GP Inc., by way of the fertility doctor. Dad used to joke that Mary and Elizabeth were the pick of the litter, but never mentioned what happened to the other fertilized eggs.

Now Mary and Joe were ready for their first child. The choices were dizzying. Fortunately, Elizabeth had been through the same process just the year before, and referred them to her genetic engineer, a friend from Harvard. Joe was a bit reluctant about bleeding edge edits, but Mary had a feeling the GP engineer was right -- their son had the potential to be truly special, with just the right tweaks ...
See also [1], [2], and [3].

Tuesday, December 19, 2017

Low SES does not decrease heritability of cognitive ability (N=300k)

These researchers, from Stanford, Northwestern, and the University of Florida, analyze a large population of twins and siblings (~24k twins and ~300k children in total, born 1994-2002 in Florida). They find no evidence of SES (Socio-Economic Status) moderation of genetic influence on test scores (i.e., cognitive ability). The figure above shows the usual pattern of lower pairwise correlations in test performance between non-identical twins and ordinary sibs, consistent with strong heritability. (In figure, ICC = Intraclass Correlation = ratio of between-pair variance to total variance; SS/OS = Same/Opposite Sex.) The researchers find, via further analysis (see below), that lower SES does not decrease heritability. No large GxE effect at low SES.

Earlier work by Turkheimer and collaborators (with much smaller sample size) suggested that low SES can drastically reduce the genetic heritability of intelligence. Their result has been widely publicized, but over time evidence is accumulating against it.

Note that Economics Nobelist James J. Heckman is the editor at PNAS who handled this paper. Heckman is an expert statistician and one of the most highly cited researchers in the area of childhood education and human capital. He was also a vocal critic of The Bell Curve, but seems (now) to accept the validity of general intelligence as a construct, its heritability, and the difficulty of increasing intelligence through environmental intervention. He tends to focus on other, more trainable, factors that influence life success, such as (my interpretation) Conscientiousness, Rule Following, Pro-Sociality, etc. ("non-cognitive skills").
Socioeconomic status and genetic influences on cognitive development
PNAS doi: 10.1073/pnas.1708491114

A prominent hypothesis in the study of intelligence is that genetic influences on cognitive abilities are larger for children raised in more advantaged environments. Evidence to date has been mixed, with some indication that the hypothesized pattern may hold in the United States but not elsewhere. We conducted the largest study to date using matched birth and school administrative records from the socioeconomically diverse state of Florida, and we did not find evidence for the hypothesis.

Accurate understanding of environmental moderation of genetic influences is vital to advancing the science of cognitive development as well as for designing interventions. One widely reported idea is increasing genetic influence on cognition for children raised in higher socioeconomic status (SES) families, including recent proposals that the pattern is a particularly US phenomenon. We used matched birth and school records from Florida siblings and twins born in 1994–2002 to provide the largest, most population-diverse consideration of this hypothesis to date. We found no evidence of SES moderation of genetic influence on test scores, suggesting that articulating gene-environment interactions for cognition is more complex and elusive than previously supposed.
From the paper. Note SS/OS = Same/Opposite Sex, SES = Socio-Economic Status.
First, Turkheimer and Horn indicate that “the between-pair variance of MZ pairs decreases in poor environments” (ref. 21, p. 63). Contrary to this relationship, we found that the between-pair variance of SS twins is actually lowest in the highest SES families. Given that SS twins are a relatively equal combination of MZ and DZ twins, one possibility is that a pattern supporting the hypothesis among MZ SS twins is masked by an even stronger pattern in the opposite direction among DZ SS twins. However, Fig. 3 shows that corresponding results for OS twins (all of whom are DZ) give no indication of such a pattern. Between-pair variances in achievement test scores for high-school educated parents of OS twins are higher in all cases than it is for parents without a high school diploma.

Second, Turkheimer and Horn report that “the within-pair variance of MZ twin pairs increases at lower levels of SES: poverty appears to have the effect of making MZ twins more different from each other” (ref. 21, p. 61). We would therefore expect in our data that the within-pair variance for SS twins whose mother did not graduate from high school would be higher than the variance for SS twins whose mother has a high school diploma. However, this is not the case in any of the SS twin comparisons shown in Fig. 3.
Via SSC -- thanks, Scott!

Added remarks about context and broader implications: This paper does not exclude SES effects on intelligence. Rather, it excludes a hypothesis (big nonlinear effect at low SES; GxE!) that has been widely discussed: In good environments individuals can achieve their full genetic potential, and consequently measured heritability is high. However, in bad environments individuals don't achieve their full genetic potential, and (perhaps) do not even realize the full effect of beneficial genetic variants, so heritability is much reduced. This reasonable sounding hypothesis is not supported by the Florida data, suggesting that genetic influence is similarly strong in both high and low SES families.

Now, just how strong is this genetic influence? Many large studies have been conducted on populations of twins (raised together and apart), adoptees (who end up resembling their biological parents much more than the adoptive parents who raised them), and ordinary siblings. The results suggest very high heritability of adult intelligence -- broad sense heritability may be as high as ~0.8!
Wikipedia: Recent twin and adoption studies suggest that while the effect of the shared family environment is substantial in early childhood, it becomes quite small by late adolescence. These findings suggest that differences in the life styles of families whatever their importance may be for many aspects of children's lives make little long-term difference for the skills measured by intelligence tests.

Monday, December 18, 2017

Quantum Computing near a Tipping Point?

I received an email from a physicist colleague suggesting that we might be near a "tipping point" in quantum computation. I've sort of followed quantum computation and quantum information as an outsider for about 20 years now, but haven't been paying close attention recently because it seems that practical general purpose quantum computers are still quite distant. Furthermore, I am turned off by the constant hype in the technology press...

But perhaps my opinion is due for an update? I know some real quantum computing people read this blog, so I welcome comments.

Here's part of what I wrote back:
I'm not sure what is meant by "tipping point" -- I don't think we know yet what qubit technology can be scaled to the point of making Shor's Algorithm feasible. The threat to classical cryptography is still very far off -- you need millions* of qubits and the adversary can always just increase the key length; the tradeoffs are likely to be in favor of the classical method for a long time.

Noisy quantum simulators of the type Preskill talks about might be almost possible (first envisioned by Feynman in the Caltech class he gave in the 1980s: Limits to Computation). These are scientifically very interesting but I am not sure that there will be practical applications for some time.

* This is from distant memory so might not be quite right. The number of ideal qubits needed would be a lot less, but with imperfect qubits/gates and quantum error-correction, etc., I seem to remember a result like this. Perhaps millions is the number of gates, not qubits? (See here.)
These are the Preskill slides I mentioned -- highly recommended. John Preskill is the Feynman Professor of Theoretical Physics at Caltech :-)

Here's a summary of current and near-term hardware capability:

Thursday, December 14, 2017

100 Billionaires In Beijing Alone

Real talk from former Australian Prime Minister Paul Keating on the strategic outlook for Australia in Asia, the rise of China, and the likely future military balance of power in the Pacific region.

More from the Australian strategic viewpoint. Balance of power in the Western Pacific.

From the YouTube transcript:
29:18 [Eventually... Total] Chinese GDP is twice as large as America's so the idea that this great massive economy is going to be a strategic client of the United States that they are kept in line by the US 7th fleet that the US 7th fleet controls its coasts six miles off the ... territorial sea is of course nonsense but this is what the Pivot was all about. This is what Hillary Clinton and Barrack Obama's Pivot was all about was about the reestablishment of US power...

... you know it's simply unreal and if we try and become remain party to that piece of nonsense you know... that's not to say we don't need the US strategically in Asia as a balancing and conciliating power we do, but if we are party to the nonsense that we will line up for the United States to maintain its strategic hegemony in Asia over China we must have troubles...

Wednesday, December 13, 2017

Nature, Nurture, and Invention: analysis of Finnish data

What is the dominant causal mechanism for the results shown above? Is it that better family environments experienced by affluent children make them more likely to invent later in life? Is it that higher income fathers tend to pass on better genes (e.g., for cognitive ability) to their children? Obviously the explanation has important implications for social policy and for models of how the world works.

The authors of the paper below have access to patent, income, education, and military IQ records in Finland. (All males are subject to conscription.) By looking at brothers who are close in age but differ in IQ score, they can estimate the relative importance of common family environment (such as family income level or parental education level, which affect both brothers) versus the IQ difference itself. Their results suggest that cognitive ability has a stronger effect than shared family environment. Again, if one just looks at probability of invention versus family income or SES (see graph), one might mistakenly conclude that family environment is the main cause of increased likelihood of earning a patent later in life. In fact, higher family SES is also correlated to superior genetic endowments which can be passed on to the children.
The Social Origins of Inventors
Philippe Aghion, Ufuk Akcigit, Ari Hyytinen, Otto Toivanen
NBER Working Paper No. 24110
December 2017

In this paper we merge three datasets - individual income data, patenting data, and IQ data - to analyze the determinants of an individual's probability of inventing. We find that: (i) parental income matters even after controlling for other background variables and for IQ, yet the estimated impact of parental income is greatly diminished once parental education and the individual's IQ are controlled for; (ii) IQ has both a direct effect on the probability of inventing an indirect impact through education. The effect of IQ is larger for inventors than for medical doctors or lawyers. The impact of IQ is robust to controlling for unobserved family characteristics by focusing on potential inventors with brothers close in age. We also provide evidence on the importance of social family interactions, by looking at biological versus non-biological parents. Finally, we find a positive and significant interaction effect between IQ and father income, which suggests a misallocation of talents to innovation.
From the paper:
... IQ has both a direct effect on the probability of inventing which is almost five times as large as that of having a high-income father, and an indirect effect through education ...

... an R-squared decomposition shows that IQ matters more than all family background variables combined; moreover, IQ has both a direct and an indirect impact through education on the probability of inventing, and finally the impact of IQ is larger and more convex for inventors than for medical doctors or lawyers. Third, to address the potential endogeneity of IQ, we focused on potential inventors with brothers close in age. This allowed us to control for family-specific time-invariant unobservables. We showed that the effect of visuospatial IQ on the probability of inventing is maintained when adding these controls.

More on the close brothers analysis (p.24).
We look at the effect of an IQ differential between the individual and close brother(s) born at most three years apart.16 This allows us to include family fixed effects and thereby control for family-level time-invariant unobservables, such as genes shared by siblings, parenting style, and fixed family resources. Table 4 shows the results from the regression with family-fixed effects. The first column shows the baseline OLS results using the sample on brothers born at most three years apart. Notice that we include a dummy for the individual being the first born son in the family to account for birth-order effects. The second column shows the results from a regression where we introduce family fixed effects. We lose other parental characteristics than income due to their time-invariant nature.17 The main finding in Table 4 is that the coefficients on "IQ 91-95" and "IQ 96-100" [ these are percentiles, not IQ scores ] in Column 2 (i.e. when we perform the regression with family fixed effects) are the same as in the OLS Column 1. This suggests that these coefficients capture an effect of IQ on the probability of inventing which is largely independent of unobserved family background characteristics, as otherwise the OLS coefficients would be biased and different from the fixed effects estimates.

Note Added: Finland is generally more egalitarian than the US, both in terms of wealth distribution and access to education. But the probability of invention vs family income graph is qualitatively similar in both countries (see Fig 1 in the paper). The figure below is from recent US data; compare to the Finland figure at top.

Thanks to some discussion (see comments) I noticed that in the Finnish data the probability of invention seems to saturate at high incomes (see top figure, red circle), whereas it continues to rise strongly at top IQ scores (middle figure above; also perhaps in the US data above?). It would be interesting to explore this in more detail...

Friday, December 08, 2017

Recursive Cortical Networks: data efficient computer vision

Will knowledge from neuroscience inform the design of better AIs (neural nets)? These results from startup Vicarious AI suggest that the answer is yes! (See also this company blog post describing the research.)

It has often been remarked that evolved biological systems (e.g., a baby) can learn much faster and using much less data than existing artificial neural nets. Significant improvements in AI are almost certainly within reach...

Thanks to reader and former UO Physics colleague Raghuveer Parthasarathy for a pointer to this paper!
A generative vision model that trains with high data efficiency and breaks text-based CAPTCHAs

Science 08 Dec 2017: Vol. 358, Issue 6368, eaag2612
DOI: 10.1126/science.aag2612

Compositionality, generalization, and learning from a few examples are among the hallmarks of human intelligence. CAPTCHAs (Completely Automated Public Turing test to tell Computers and Humans Apart), images used by websites to block automated interactions, are examples of problems that are easy for people but difficult for computers. CAPTCHAs add clutter and crowd letters together to create a chicken-and-egg problem for algorithmic classifiers—the classifiers work well for characters that have been segmented out, but segmenting requires an understanding of the characters, which may be rendered in a combinatorial number of ways. CAPTCHAs also demonstrate human data efficiency: A recent deep-learning approach for parsing one specific CAPTCHA style required millions of labeled examples, whereas humans solve new styles without explicit training.

By drawing inspiration from systems neuroscience, we introduce recursive cortical network (RCN), a probabilistic generative model for vision in which message-passing–based inference handles recognition, segmentation, and reasoning in a unified manner. RCN learns with very little training data and fundamentally breaks the defense of modern text-based CAPTCHAs by generatively segmenting characters. In addition, RCN outperforms deep neural networks on a variety of benchmarks while being orders of magnitude more data-efficient.

Modern deep neural networks resemble the feed-forward hierarchy of simple and complex cells in the neocortex. Neuroscience has postulated computational roles for lateral and feedback connections, segregated contour and surface representations, and border-ownership coding observed in the visual cortex, yet these features are not commonly used by deep neural nets. We hypothesized that systematically incorporating these findings into a new model could lead to higher data efficiency and generalization. Structured probabilistic models provide a natural framework for incorporating prior knowledge, and belief propagation (BP) is an inference algorithm that can match the cortical computational speed. The representational choices in RCN were determined by investigating the computational underpinnings of neuroscience data under the constraint that accurate inference should be possible using BP.

RCN was effective in breaking a wide variety of CAPTCHAs with very little training data and without using CAPTCHA-specific heuristics. By comparison, a convolutional neural network required a 50,000-fold larger training set and was less robust to perturbations to the input. Similar results are shown on one- and few-shot MNIST (modified National Institute of Standards and Technology handwritten digit data set) classification, where RCN was significantly more robust to clutter introduced during testing. As a generative model, RCN outperformed neural network models when tested on noisy and cluttered examples and generated realistic samples from one-shot training of handwritten characters. RCN also proved to be effective at an occlusion reasoning task that required identifying the precise relationships between characters at multiple points of overlap. On a standard benchmark for parsing text in natural scenes, RCN outperformed state-of-the-art deep-learning methods while requiring 300-fold less training data.

Our work demonstrates that structured probabilistic models that incorporate inductive biases from neuroscience can lead to robust, generalizable machine learning models that learn with high data efficiency. In addition, our model’s effectiveness in breaking text-based CAPTCHAs with very little training data suggests that websites should seek more robust mechanisms for detecting automated interactions.

Wednesday, December 06, 2017

AlphaZero: learns via self-play, surpasses best humans and machines at chess

AlphaZero taught itself chess through 4 hours of self-play, surpassing the best humans and the best (old-style) chess programs in the world.
Chess24: 20 years after DeepBlue defeated Garry Kasparov in a match, chess players have awoken to a new revolution. The AlphaZero algorithm developed by Google and DeepMind took just four hours of playing against itself to synthesise the chess knowledge of one and a half millennium and reach a level where it not only surpassed humans but crushed the reigning World Computer Champion Stockfish 28 wins to 0 in a 100-game match. All the brilliant stratagems and refinements that human programmers used to build chess engines have been outdone, and like Go players we can only marvel at a wholly new approach to the game. ...
ArXiv preprint:
Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm

The game of chess is the most widely-studied domain in the history of artificial intelligence. The strongest programs are based on a combination of sophisticated search techniques, domain-specific adaptations, and handcrafted evaluation functions that have been refined by human experts over several decades. In contrast, the AlphaGo Zero program recently achieved superhuman performance in the game of Go, by tabula rasa reinforcement learning from games of self-play. In this paper, we generalise this approach into a single AlphaZero algorithm that can achieve, tabula rasa, superhuman performance in many challenging domains. Starting from random play, and given no domain knowledge except the game rules, AlphaZero achieved within 24 hours a superhuman level of play in the games of chess and shogi (Japanese chess) as well as Go, and convincingly defeated a world-champion program in each case.
Finally, we analysed the chess knowledge discovered by AlphaZero. Table 2 analyses the most common human openings (those played more than 100,000 times in an online database of human chess games (1)). Each of these openings is independently discovered and played frequently by AlphaZero during self-play training. When starting from each human opening, AlphaZero convincingly defeated Stockfish, suggesting that it has indeed mastered a wide spectrum of chess play.

Tuesday, December 05, 2017

How Europe lost its tech companies

Some perspectives from a Berlin tech guy who has also worked in China.

To some extent Europe is like the Midwest of the US: a source of human capital for SV and other places. Europe and the Midwest have strong universities and produce talented individuals, but lack a mature tech ecosystem which includes access to venture funding, exits (acquisition by big established companies), and a culture of risk taking and innovation.

See also The next Silicon Valley? (another German guy):
My meeting in Beijing with Hugo Barra, who runs all international expansion for Xiaomi — the cool smartphone maker and highest-valued startup in China, at around $45 billion or so — was scheduled for 11 pm, but got delayed because of other meetings, so it started at midnight. (Hugo had a flight to catch at 6:30 am after that.)

In China, there is a company work culture at startups that's called 9/9/6. It means that regular work hours for most employees are from 9 am to 9 pm, six days a week. If you thought Silicon Valley has intense work hours, think again.

For founders and top executives, it's often 9/11/6.5. That's probably not very efficient and useful (who's good as a leader when they're always tired and don't know their kids?) but totally common.

Teams get locked up in hotels for weeks before a product launch, where they only work, sleep and work out, to drive 100 percent focus without distractions and make the launch date. And while I don't think long hours are any measure of productivity, I was amazed by the enormous hunger and drive. ...

Sunday, December 03, 2017

Big Ed

Today I came across a recent interview with Ed Witten in Quanta Magazine. The article has some nice photos like the one above. I was struck by the following quote from Witten ("It from Qubit!"):
When I was a beginning grad student, they had a series of lectures by faculty members to the new students about theoretical research, and one of the people who gave such a lecture was Wheeler. He drew a picture on the blackboard of the universe visualized as an eye looking at itself. I had no idea what he was talking about. It’s obvious to me in hindsight that he was explaining what it meant to talk about quantum mechanics when the observer is part of the quantum system. I imagine there is something we don’t understand about that.  [ Italics mine ]
The picture he refers to is reproduced below.

This question has been of interest to me since I was first exposed to quantum mechanics, although I put it off for a long time because quantum foundations is not considered a respectable area by most physicists! Of course it should be obvious that if quantum mechanics is to be a universal theory of nature, then observers like ourselves can't help but be part of the (big) quantum system.

See related posts Feynman and Everett, Schwinger on Quantum Foundations, Gell-Man on Quantum Foundations, and Weinberg on Quantum Foundations.

Here's a similar figure, meant to represent the perspective of an observer inside the wavefunction of the universe (which evolves deterministically and unitarily; the degrees of freedom of the observer's mind are part of the Hilbert space of Psi; time runs vertically and Psi evolves into exp(-iHT) Psi while we are "inside" :-). The figure was drawn on the whiteboard of my University of Oregon office and persisted there for a year or more. I doubt any visitors (other than perhaps one special grad student) understood what it was about.

For some powerful Witten anecdotes like the one below, see here. (If you don't know who Ed Witten is this should clarify things a bit!)
I met him in Boston in 1977, when I was getting interested in the connection between physics and mathematics. I attended a meeting, and there was this young chap with the older guys. We started talking, and after a few minutes I realized that the younger guy was much smarter than the old guys. He understood all the mathematics I was talking about, so I started paying attention to him. That was Witten. And I’ve kept in touch with him ever since.

In 2001, he invited me to Caltech, where he was a visiting professor. I felt like a graduate student again. Every morning I would walk into the department, I’d go to see Witten, and we’d talk for an hour or so. He’d give me my homework. I’d go away and spend the next 23 hours trying to catch up. Meanwhile, he’d go off and do half a dozen other things. We had a very intense collaboration. It was an incredible experience because it was like working with a brilliant supervisor. I mean, he knew all the answers before I got them. If we ever argued, he was right and I was wrong. It was embarrassing!

(Fields Medalist Michael Atiyah, on what it was like to collaborate with Witten)
The closest thing I have read to a personal intellectual history of Witten is his essay Adventures in Physics and Math, which I highly recommend. The essay addresses some common questions, such as What was Ed like as a kid? How did he choose a career in Physics? How does he know so much Mathematics? For example,
At about age 11, I was presented with some relatively advanced math books. My father is a theoretical physicist and he introduced me to calculus. For a while, math was my passion. My parents, however, were reluctant to push me too far, too fast with math (as they saw it) and so it was a long time after that before I was exposed to any math that was really more advanced than basic calculus. I am not sure in hindsight whether their attitude was best or not.
A great video, suggested by a commenter:

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