Everything is Entangled

This paper will be available tomorrow at the link.

http://arxiv.org/abs/1205.1584 

Everything is Entangled 

Roman V. Buniy, Stephen D.H. Hsu 

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other -- the reduced density matrix describing any pair is likely to be separable.

From the introduction:

Ergodicity and properties of typical pure states 

When two particles interact, their quantum states generally become entangled. Further interaction with other particles spreads the entanglement far and wide. Subsequent local manipulations of separated particles cannot, in the absence of quantum communication, undo the entanglement. We know from big bang cosmology that our universe was in thermal equilibrium at early times, and we believe, due to the uniformity of the cosmic microwave background, that regions which today are out of causal contact were once in equilibrium with each other. Below we show that these simple observations allow us to characterize many aspects of cosmological entanglement. 

We will utilize the properties of typical pure states in quantum mechanics. These are states which dominate the Hilbert measure. The ergodic theorem proved by von Neumann implies that under Schrodinger evolution most systems spend almost all their time in typical states. Indeed, systems in thermal equilibrium have nearly maximal entropy and hence must be typical. Typical states are maximally entangled (see below) and the approach to equilibrium can be thought of in terms of the spread of entanglement. ...

Professor Buniy in action! (Working on this research.)

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The truth about venture capital

The excerpt below is from the Kauffman Foundation's report on venture investing. I'd like to see a similar report for hedge and private equity funds. If you believe in efficient markets and rational sophisticated investors (i.e., pension funds, endowments, the super wealthy), you have to explain why they continue to invest in underperforming asset classes and pay exorbitant fees. My explanation is that apes are not smart. Alpha is hard to detect and it's easier to believe a story (narrative sales pitch) than the numbers (esp. if the numbers are hard to obtain or require a bit of brainpower to interpret). Financial services are incorrectly priced, both by sophisticated investors, and by society. Via Ben Lorica.

EXECUTIVE SUMMARY 

Venture capital (VC) has delivered poor returns for more than a decade. VC returns haven’t significantly outperformed the public market since the late 1990s, and, since 1997, less cash has been returned to investors than has been invested in VC. Speculation among industry insiders is that the VC model is broken, despite occasional high-profile successes like Groupon, Zynga, LinkedIn, and Facebook in recent years. 

The Kauffman Foundation investment team analyzed our twenty-year history of venture investing experience in nearly 100 VC funds with some of the most notable and exclusive partnership “brands” and concluded that the Limited Partner (LP) investment model is broken. Limited Partners—foundations, endowments, and state pension fund—invest too much capital in underperforming venture capital funds on frequently mis-aligned terms. 

Our research suggests that investors like us succumb time and again to narrative fallacies, a well-studied behavioral finance bias. We found in our own portfolio that: 

 Only twenty of 100 venture funds generated returns that beat a public-market equivalent by more than 3 percent annually, and half of those began investing prior to 1995.

 The majority of funds—sixty-two out of 100—failed to exceed returns available from the public markets, after fees and carry were paid. 

 There is not consistent evidence of a J-curve in venture investing since 1997; the typical Kauffman Foundation venture fund reported peak internal rates of return (IRRs) and investment multiples early in a fund’s life (while still in the typical sixty-month investment period), followed by serial fundraising in month twenty-seven. 

 Only four of thirty venture capital funds with committed capital of more than $400 million delivered returns better than those available from a publicly traded small cap common stock index. 

 Of eighty-eight venture funds in our sample, sixty-six failed to deliver expected venture rates of return in the first twenty-seven months (prior to serial fundraises). The cumulative effect of fees, carry, and the uneven nature of venture investing ultimately left us with sixty-nine funds (78 percent) that did not achieve returns sufficient to reward us for patient, expensive, longterm investing. 

Investment committees and trustees should shoulder blame for the broken LP investment model, as they have created the conditions for the chronic misallocation of capital. ...

See earlier post How to run a hedge fund.

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NRC physics ranking by research output

I was pleasantly surprised by the recent NRC rankings of physics departments. In the research output ranking, UO did quite well. NRC uses a sophisticated statistical method that gives a range of possible outcomes.

In the list below I would say MIT and Stanford deserve higher ratings, and UO is (alas) ranked higher than it deserves. Once you get beyond the top 10 or so physics departments, there are many good programs across the country, and it's hard to differentiate between them.

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Exceptional Cognitive Ability: The Phenotype

Participants in the previous discussion thread may be interested in David Lubinski's paper Exceptional Cognitive Ability: The Phenotype. The individuals in this study were identified through gifted programs, and tested at the top 1% level (i.e., for their age) on at least one section (M,V) of the SAT, administered by age 13. The highest group scored above the 1 in 10,000 level. The longitudinal study reveals interesting differences in life outcomes within this group of gifted individuals.

See also related posts.

In the figure below A refers to participants with terminal Bachelor's or Master's degrees, B to doctorate recipients (note little dots denoting JDs and MDs), C to tenured faculty at US universities, and D to patent holders or authors of important literary works.

From the discussion at the end of the paper:

There does not appear to be an ‘‘ability threshold’’ (i.e., a point at which, say, beyond an IQ of 115 or 120, more ability does not matter). Although other things like ambition and opportunity clearly matter, more ability is better. The data also suggest the importance of going beyond general ability level when characterizing exceptional phenotypes, because specific abilities add nuance to predictions across different domains of talent development. Differential ability pattern, in this case verbal relative to mathematical ability and vice versa, are differentially related to accomplishments that draw on different intellectual strengths. Exceptional cognitive abilities do appear to be involved in creative expression, or ‘‘abstract noegenesis’’ (Spearman and Jones, 1950). That these abilities are readily detectable at age 12 is especially noteworthy.

This figure, describing the same study population, may also be of interest:

Earlier discussion:

Scores are normalized in units of SDs. The vertical axis is V, the horizontal axis is M, and the length of the arrow reflects spatial ability: pointing to the right means above the group average, to the left means below average; note the arrow for business majors should be twice as long as indicated but there was not enough space on the diagram. The spatial score is obviously correlated with the M score. Upper right = high V, high M (e.g., physical science) Upper left = high V, lower M (e.g., humanities, social science) Lower left = lower V, lower M (e.g., business, law) Lower right = lower V, high M (e.g., math, engineering, CS)

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Jensen on g and genius

I found the excerpt below in the comments here.

Mega Questions for Renowned Psychologist Dr._Arthur R. Jensen - Interview by Christopher Michael Langan and Dr. Gina LoSasso and members of the Mega Foundation, Mega Society East and Ultranet 

Question #1: 

Christopher Langan for the Mega Foundation: It is reported that one of this century’s greatest physicists, Nobelist Richard Feynman, had an IQ of 125 or so. Yet, a careful reading of his work reveals amazing powers of concentration and analysis…powers of thought far in excess of those suggested by a z score of well under two standard deviations above the population mean. Could this be evidence that something might be wrong with the way intelligence is tested? Could it mean that early crystallization of intelligence, or specialization of intelligence in a specific set of (sub-g) factors – i.e., a narrow investment of g based on a lopsided combination of opportunity and proclivity - might put it beyond the reach of g-loaded tests weak in those specific factors, leading to deceptive results?

Arthur Jensen: I don’t take anecdotal report of the IQs of famous persons at all seriously. They are often fictitious and are used to make a point - typically a put-down of IQ test and the whole idea that individual differences in intelligence can be ranked or measured. James Watson once claimed an IQ of 115; the daughter of another very famous Nobelist claimed that her father would absolutely “flunk” any IQ test. It’s all ridiculous. 

Furthermore, the outstanding feature of any famous and accomplished person, especially a reputed genius, such as Feynman, is never their level of g (or their IQ), but some special talent and some other traits (e.g., zeal, persistence). Outstanding achievements(s) depend on these other qualities besides high intelligence. The special talents, such as mathematical musical, artistic, literary, or any other of the various “multiple intelligences” that have been mentioned by Howard Gardner and others are more salient in the achievements of geniuses than is their typically high level of g. Most very high-IQ people, of course, are not recognized as geniuses, because they haven’t any very outstanding creative achievements to their credit. However, there is a threshold property of IQ, or g, below which few if any individuals are even able to develop high-level complex talents or become known for socially significant intellectual or artistic achievements. This bare minimum threshold is probably somewhere between about +1.5 sigma and +2 sigma from the population mean on highly g-loaded tests. 

Childhood IQs that are at least above this threshold can also be misleading. There are two famous scientific geniuses, both Nobelists in physics, whose childhood IQs are very well authenticated to have been in the mid-130s. They are on record and were tested by none other than Lewis Terman himself, in his search for subjects in his well-known study of gifted children with IQs of 140 or above on the Stanford-Binet intelligence test. Although these two boys were brought to Terman’s attention because they were mathematical prodigies, they failed by a few IQ points to meet the one and only criterion (IQ > 139) for inclusion in Terman’s study. Although Terman was impressed by them, as a good scientist he had to exclude them from his sample of high-IQ kids. Yet none of the 1,500+ subjects in the study ever won a Nobel Prize or has a biography in the Encyclopedia Britannica as these two fellows did. Not only were they gifted mathematically, they had a combination of other traits without which they probably would not have become generally recognized as scientific and inventive geniuses. So-called intelligence tests, or IQ, are not intended to assess these special abilities unrelated to IQ or any other traits involved in outstanding achievement. It would be undesirable for IQ tests to attempt to do so, as it would be undesirable for a clinical thermometer to measure not just temperature but some combination of temperature, blood count, metabolic rate, etc. A good IQ test attempts to estimate the g factor, which isn’t a mixture, but a distillate of the one factor (i.e., a unitary source of individual differences variance) that is common to all cognitive tests, however diverse. 

I have had personal encounters with three Nobelists in science, including Feynman, who attended a lecture I gave at Cal Tech and later discussed it with me. He, like the other two Nobelists I’ve known (Francis Crick and William Shockley), not only came across as extremely sharp, especially in mathematical reasoning, but they were also rather obsessive about making sure they thoroughly understood the topic under immediate discussion. They at times transformed my verbal statements into graphical or mathematical forms and relationships. Two of these men knew each other very well and often discussed problems with each other. Each thought the other was very smart. I got a chance to test one of these Nobelists with Terman’s Concept Mastery Test, which was developed to test the Terman gifted group as adults, and he obtained an exceptionally high score even compared to the Terman group all with IQ > 139 and a mean of 152. 

I have written an essay relevant to this whole question: “Giftedness and genius: Crucial differences.” In C. P. Benbow & D. Lubinski (Eds.) Intellectual Talent: Psychometric and Social Issues, pp. 393-411. Baltimore: Johns Hopkins University Press.

See here for data relevant to this topic and the discussion in the comments.

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Theory and experiment

From the autobiography Alvarez: Adventures of a Physicist. See also Alvarez quotes, and related posts.

Chapter 4: I learned about the discovery of nuclear fission in the Berkeley campus barbershop one morning in late January 1939, while my hair was being cut. Buried on an inside page of the Chronicle was a story from Washington reporting Bohr's announcement that German chemists had split the uranium atom by bombarding it with neutrons. I stopped the barber in mid-snip and ran all the way to the Rad Lab to spread the word. The first person I saw was my graduate student Phil Abelson. I knew the news would shock him. "I have something terribly important to tell you," I said. "I think you should lie down on the table." Phil sensed my seriousness and complied. I told him what I had read. He was stunned; he realized immediately, as I had before, that he was within days of making the same discovery himself. 

... I tracked down Oppenheimer working with his entourage in his bullpen in LeConte Hall. He instantly pronounced the reaction impossible and proceeded to prove mathematically to everyone in the room that someone must have made a mistake. The next day Ken Green and I demonstrated the reaction. I invited Robert over to see [it] ... In less than 15 minutes he not only agreed that the reaction was authentic but also speculated that in the process extra neutrons would boil off that could be used to split more uranium atoms and thereby generate power or make bombs. It was amazing to see how rapidly his mind worked, and he came to the right conclusions. His response demonstrated the scientific ethic at its best. When we proved that his previous position was untenable, he accepted the evidence with good grace, and without looking back he immediately turned to examining where the new knowledge might lead.

This short passage illustrates many aspects of science: the role of luck, the convergence of different avenues of investigation, the overconfidence of theorists and the supremacy of experiments in discerning reality, the startling reach of a powerful mind.

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Risk taking and innovation: lawyers and art history majors

At least the incentives and cultural support for risk taking are better in the US than in other countries.

NYTimes ... In a competitive market, all that’s left are the truly hard puzzles. And they require extraordinary resources. While we often hear about the greatest successes — penicillin, the iPhone — we rarely hear about the countless failures and the people and companies who financed them. 

A central problem with the U.S. economy, he told me, is finding a way to get more people to look for solutions despite these terrible odds of success. Conard’s solution is simple. Society benefits if the successful risk takers get a lot of money. For proof, he looks to the market. At a nearby table we saw three young people with plaid shirts and floppy hair. For all we know, they may have been plotting the next generation’s Twitter, but Conard felt sure they were merely lounging on the sidelines. “What are they doing, sitting here, having a coffee at 2:30?” he asked. “I’m sure those guys are college-educated.” Conard, who occasionally flashed a mean streak during our talks, started calling the group “art-history majors,” his derisive term for pretty much anyone who was lucky enough to be born with the talent and opportunity to join the risk-taking, innovation-hunting mechanism but who chose instead a less competitive life. In Conard’s mind, this includes, surprisingly, people like lawyers, who opt for stable professions that don’t maximize their wealth-creating potential. He said the only way to persuade these “art-history majors” to join the fiercely competitive economic mechanism is to tempt them with extraordinary payoffs.

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