I Was Taught That Boys Need Girls And Girls Need Boys; You Say That's Not True

I am not a biologist. In this world of 8 billion people, not all are men or women, where a man has XY chromosomes and a woman has XX chromosomes.

When fraternal twins are conceived, these two balls of cells may clump together, and one person develops. Such a human chimera may have a mixture of cells that are both XX and XY.

The SRY gene may cross over from a Y to an X chromosome. And so some men may grow up with XX chromosomes.

Klinefelter syndrome occurs in men with XXY chromosomes. Men can also have XYY or XYYY chromosomes. Women can have XXX chromosomes.

But genetics is not destiny. A long road is traversed in growing up. Sports, such as the Olympics, is about finding exceptional people who can delight us with their performances. Caster Semenya is one example, who apparently is a woman with androgen insensitivity. As I understand it, she is only one case in which the International Olympic Committee has wrong-footed itself.

In Las Salinas, in the Dominican Republic, some girls grow up to be men. Basically, some physical developments that occurred for me in the womb occur there during puberty. For some reason, this condition is more common there than elsewhere.

This post is inspired by sad current events in the United States. I have tried to concentrate above on biology. One can read Flannery O'Connor to get a Catholic sensibility on another possible complication. Deidre McCloskey is an economist who has an interesting memoir. Judith Butler supposedly is clearer in lecturing or talking about the complexities of gender than she is in her writing.

Selected References

• Judith Butler. 1990. Gender Trouble.
• Anne Fausto-Sterling. 2000. Sexing the Body: Gender Politics and the Construction of Sexuality.
• Deidre McCloskey. 1999. Crossing: A Memoir.
• Flannery O'Connor. 1955. A temple of the holy ghost.

Some Stories About Math And Science

I find certain stories of achievements in mathematics and science intriguing. In some of those I select, much that came before was overthrown. At any rate, these are stories about creations of the human mind that are tough to wrap your head around. I only claim to understand the last story.

Fermat's last theorem lacked a proof for three and a half centuries. When he first saw the theorem as a school boy, Andrew Wiles decided he was going to be a mathematican when he grew up and prove it. And he did.

I have written about the classification of finite simple groups before.

The twentieth century saw some amazing results in logic, set theory, and model theory. Gödel's incompleteness theorem, computability, the axiom of choice, the (generalized) continuum hypothesis, and the Löwenheim-Skolem theorem are very puzzling topics. Perhaps the question of the truth of the continuum hypothesis is, after last year, closer to being solved, whatever that might mean. As I understand it, both the assertion and denial of the continuum hypothesis are consistent with the axioms of Zermelo Fraenkel set theory. So its resolution would take agreement on additional axioms. Apparently, David Asperó and Ralf Schindler showed last year that one such proposed axiom implied another. I doubt I will ever understand this. I suppose perplexity at how maths mean goes back to, at least, the invention of non-Euclidean geometry.

In physics, quantum mechanics and the theory of relativity provide amazement. Their very existence is a surprise. Newtonian mechanics seemed to be the most empirically well-confirmed theory in all of science. Then, in the first couple of decades of the twentieth century, Newton was shown to be incorrect in his basic picture of the universe. At least, this is something like how Karl Popper saw it. Relativity has the surprising implication that time travel is possible in a rotating universe. Gödel showed this when he wanted to provide something for a festschrift for his friend Albert Einstein. I gather Bell's theorem shows that quantum mechanics and a limitation imposed by general relativity cannot both be right. I gather that Bell has been experimentally verified by astronomers looking at radiation passing through gravitational lenses formed from intermediate galaxies.

Political economy provides at least one story like the above. I refer to Sraffa's disproof of marginalism half a century ago.

References

• David Asperó and Ralf Schindler. 2021. MM⁺ implies (*).
• J. S. Bell. 1964. On the Einstein Podolsky Rosen paradox. Physics 1(3): 195-200.
• Stephen Budiansky. 2021. Journey to the Edge of Reason: The Life of Kurt Gödel W. W. Norton.
• Paul J. Cohen. 1963. The independence of the continuum hypothesis IProceedings of the U.S. National Academy of Sciences 50(6):1143-1148.
• Paul Cohen. 1964. The independence of the continuum hypothesis IIProceedings of the U.S. National Academy of Sciences 51(1):105-110.
• Torkel Franzen. 2005. Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. Peters.
• Kurt Gödel. 1936. On formally undecidable propositions of Principia Mathematica and related systems I. Monatsheft für Mathematik und Physik 38:173-198.
• Kurt Gödel. 1938. Consistency-proof for the generalized continuum-hypothesis. Proceedings of the U.S. National Academy of Sciences 25: 220-224.
• Kurt Gödel. 1940. The consistency of the axiom of choice and the generalized continuum hypothesis with the axioms of set theory. Annals of Mathematic Studies 3.
• Kurt Gödel. 1949. An example of a new type of cosmological solutions of Einstein's field equations of gravitation. Review of Modern Physics 21: 447-450.
• Joel David Hamkins. 2011. The set-theoretic multiverse
• Morris Kline. 1982. Mathematics: The Loss of Certainty. Oxford University Press.
• Calvin Leung et al. 2018. Astronomical random numbers for quantum foundations experiments
• Edwin E. Moise. 1963. Elementary Geometry from an Advanced Standpoint. Addison-Wesley.
• Piero Sraffa. 1960. Production of Commodities by Means of Commodities: A Prelude to a Critique of Economic Theory. Cambridge University Press.
• Robert A. Wilson. 2009. The Finite Simple Groups. Springer.

Easy To Be Hard

Young Children Policing Group Members

This post presents examples of psychologists inducing stress in experimental subjects, some showing why we need Institutional Review Boards (IRBs). Some of the older studies involved so much suffering that experimental subjects suffered Post-Traumatic Stress Disorder (PTSD). I recall that at the end of the 1976 movie, The Tenth Level, about the Milgram experiment, starring William Shatner, the scientists are discussing what they would do if they were experimental subjects. Would they refuse to torture others? And one says to Shatner/Milgram something like, "It seems to me, you have already been tested and failed."

• Yudkin, Van Bavel, and Rhodes: Almost the only somewhat happy story here. Toddlers are willing to close a fun slide, for themselves, to punish another child for misbehavior. The experiment illustrates costly third-party punishment.
• Stanford prison experiment: A sample of college students are randomly divided up into pretend guards and prisoners. The guards quickly begin abusing the prisoners.
• Jane Ellliot experiments: In order to understand segregation and prejudice, divides a class of school children into blue eyes and brown eyes. The blue eyes sit at the front and treated well; the brown eyes sit at the back and are badly treated. The next Monday, the situation is reversed. Quickly, the well-treated act as if they believe they are superior and the others inferior.
• Robber's Cave experiment: A somewhat happy ending, I guess. Boys divided up into two competitive groups at summer camp quickly disdain one another. Given a problem that requires cooperation with the other group, they will work together.
• Milgram experiment: Given an authority figure telling them that this is experiment on negative re-inforcement for learning, people are willing to increase electric shocks past the point of torture. Some refused.
• Gibson and Walk experiment: As far as the baby is concerned, they are crawling over the edge of a cliff on air. Tests whether caution about heights is inherent. More about individual psychology than most of the rest in this list.
• Asch experiment: On conformity. Subject goes last in a group noting which line was the same length as the a standard. The subject does not realize the rest are part of the experiment. Many were willing to go along with the obvious falsehood all the others said.
• Little Albert experiment: A baby is conditioned, as with Pavlov's dogs, to be terrified of a white rat, rabbit, dog, and a sealskin coat. More about individual psychology than most of the rest in this list.

Randomized Control Trials (RCTs) provide a rigorous methodology, albeit they can present problems of generalization and external validity. Not all of the above are RCTs. They do illustrate that designing ethical RCTs can be difficult. I expect the above list of amazingly mostly abusive studies, even in psychology can be extended.

References

• Yudkin, Danial A., Jay J. Van Bavel, and Marjorie Rhodes (2019). Young children police group members at personal cost. Journal of Experimental Psychology.
• Haney, C., W. C. Banks, and P. G. Zimbardo (1973). A study of prisoners and guards in a simulated prison. Naval Research Review 30: 4-17.
• Muzafer Sherif (1966). In Common Predicament: Social Psychology of Intergroup Conflict and Cooperation Houghton Miffin.
• Milgram, Stanley (1963). Behavioral study of obedience. Journal of Abnormal Social Psychology 67: 371-378.
• Gibson, E. J. and R. D. Walk (1960).Visual Cliff. Scientific American April.
• Asch, Solomon E. (1955). Opinions and social pressure. Scientific American November.
• Watson, John B. and Rosalie Rayner (1920). Conditioned emotional reactions. Journal of Experimental Psychology 3(1): 1-14.

Frugal Science

Carolyn Kormann has an article, Through the Looking Glass, in this week's New Yorker. This article profiles Manu Prakash, a biophysicist at Stanford and his invention of the Foldscope. The Foldscope is a small, foldable microscope, with the case made of paper. It is an example of frugal science. Prakash hopes to make these microscopes widely available to people in third world countries. One impact might be that residents in, say, African countries will be more conscious of disease-causing micro-organisms, since they can now see such. But, it is not clear to me, what the overall impact of this project might be.

Frugal science reminds me somewhat of E.F. Schumacher's "appropriate technology". It seems to me that in the last few years I've read articles about people developing new stoves and toilets without water targeted to have very low cost and for distribution among the global poor. (THose links are the result of googling now - not where I first read about them.) It seems to me solar power now gives isolated communities a capability to have power without being hooked up to an extensive infrastructure. I like to look for hopeful stories.

Humans And Other Animals

Figure 1: Chapuchin Monkeys, Our Cousins

What do we think about generalizations, validated partly with experiments with non-human animals, for economics?

Nicholas Georgescu-Roegen is an economist widely admired by heterodox economists. He quit the American Economic Association in response to their flagship publication, the American Economic Review, publishing articles on, if I recall correctly, pigeons. Researchers were trying to demonstrate that properly trained pigeons had downward-sloping demand curves. I gather they wanted to show income effects and substitution effects, as well, with these laboratory experiments.

On the other hand, are we not supportive of behavioral economists undermining utility theory? I am thinking of controlled experiments that demonstrate people do not conform to the axioms of preference theory. And some of these experiments, as illustrated in the YouTube video linked above, extend beyond humans.

I have a suggestion to resolve such a tension. One might want to treat investigations of humans as a naturalistic enterprise. If so, one would not want to impose an a priori boundary on the different constituents of minds. Whether some species of animals has some sense of self, expectations of the future, primitive languages, or what not should be found by empirical investigation. On the other hand, activities that depend on the existence of social institutions cannot be expected to be found in animals not embedded in any society. And demand curves, if they were to exist, would only arise in specific market institutions.

Reference

• Philip Mirowski (1994). The realms of the Natural, in Natural Images in Economic Thought (ed. by P. Mirowski), Cambridge University Press.

Weird Science III

I guess this is part of a series in which I describe oddities upon which I have stumbled. Here I focus on two phenomena in the measurement of gravity. Perhaps the theory of general relativity is wrong. (The link goes to an explanation of a different problem in physics). Of course, much more prosaic explanations are possible.

Maurice Allais, the recently dead "Nobel" laureate in economics, experimented with a paraconical pendulum during the 1950s. He discovered the Allais effect, which is a variation in the behavior of a pendulum during an eclipse. The plane of the pendulum rotated approximately ten degrees during the eclipse and then returned to the previously pattern. A number of scientists have tried to replicate this and similar effects with various experimental equipment during various eclipses. Some succeeded in replication and some failed. Allais’ explanation, apparently, was to revive the 19th century concept of the aether and argue that space is anisotropic.

Pioneers 10 and 11 were launched in 1972 and 1973, respectively. NASA was still in communication with them after they had passed beyond the orbit of Pluto and were more than 20 Astronomical Units away from the sun. (An AU is the average distance from the Earth to the sun.) Pioneers 10 and 11 have an anomalous acceleration towards the sun of an order of magnitude of 10^-7 centimeters per square seconds. In other words, as they move away from the sun, they are very slowly slowing down more than can be accounted for under the current (relativistic) understanding of gravity. Pioneers 10 and 11 are moving away from the sun at a rate of approximately 12 kilometers per second. (It dawned on me while writing the above that I am no longer sure how many planets are in our solar system.)

References

• Maurice Allais (1986). "The Concepts of Surplus and Loss and the Reformulation of the Theories of Stable General Equilibrium and Maximum Efficiency", in Foundations of Economics (edited by Mauro Baranzini and Roberto Scazzieri), Basil Blackwell.
• John D. Anderson et al. (1998) "Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration", arXiv:gr-qc/9808081v2 (1 October)
• John D. Anderson et al. (2005) "Study of the Anomalous Acceleration of Pioneer 10 and 11", arXiv:gr-qc/0104064v5 (10 March)
• Gibor Basri and Michael E. Brown (2006) "Planetesimals to Brown Dwarfs: What is a Planet?", Ann. Rev. Earth Planet. Sci., V. 34: pp. 193-216
• M. E. Brown, C. A. Trujillo, and D. L. Rabinowitz (2005) "Discovery of a Planetary-Sized Object in the Scattered Kuiper Belt", The Astrophysical Journal, 635: L97-L100, (10 December)
• Chris P. Duif (2004) "A Review of Conventional Explanations of Anomalous Observations during Solar Eclipses", arXiv:gr-qc/0408023 v5 (31 December)

Weird Science II

A bit from Avatar reminds me of Ursula K. LeGuin's "Vaster Than Empires and More Slow", a short story republished in her collection The Wind's Twelve Quarters (1975). LeGuin postulates a world in which nodes in tree roots act like synapses. The plant life is one sentience. Maybe even vines and spores partake in it. As before, a cultural work reminds me of some science:

• The longest lived thing is arguably Pando, a grove of aspens in Utah that seems to be one plant, connected at the roots and propagating through runners like strawberries or mrytle.
• Or maybe it is an instance of the fungus Armillaria bulbosa in Oregon.

A Wikipedia article lists other such organisms, for what it's worth. (The references in this post are reminders for me to look up sometime.)

O Brave New World That Has Such Bacteria In It

The BioBricks Foundation (BBF) has Request For Comments (RFCs), just like the Internet Engineering Task Force (IETF). They have a BioBrick language, a graphical language, and are working on an RDF-based framework for a synthetic biology ontology. (The Resource Description Framework (RDF) is a standard for the semantic web.)

BBF is using this this computer science technology and organizational structure to create "standard biological parts" that "encode basic biological functions". The goal is to enable biological engineers to "program living organisms in the same way a computer scientist can program a computer".

(Hat Tip to Michael Specter's New Yorker 28 September 2009 article.)

Weird Science

I'm not sure I had heard of the Voynich Manuscript before this xkcd cartoon. But it did remind me of a couple of other artifacts whose existence I think extremely curious:

• The Antikythera Mechanism is a mechanical computer for calculating astronomical positions, and it dates from classical Greece.
• Piri Reis map dates, maybe, from before the Europeans had explored the New World, but yet shows the coast of South America and Anartica under the ice sheet.
• The Nazca lines are a series of drawings on a plateau in Peru dating from before Columbus and that make the most sense when viewed from the air.

It's Herd Behavior, Uh Huh, It's Evolution, Baby

Anybody interested in institutional economics should be interested in evolutionary theory, a theory that I can stand to learn more about. The interest in evolution among institutionalists goes back to Veblen. A more-or-less mid twentieth expression of interest can be seen in Ayres's biography of Thomas Huxley, also known as "Charles Darwin's bulldog". Geoffrey Hodgson is a current institutialist interested in evolution. What evolves in economies? I suggest organizational forms, business processes, and technology, at least.

I never saw anything interesting when operating Tierra on my old computer. Perhaps I understand neither the assembly language nor the visualization well-enough. Or perhaps I should have designed experiments and let it operate for more generations. I was never into Core Wars either. John Conway's Game of Life was more my speed. I don't seem to have executables for any of these for my OS X Macintosh.

But I think Thearling and Ray (1994) describe a neat idea. In Tierra, programs composed of machine instructions reproduce, perhaps with mutations. Memory is not protected, and programs can overwrite one another's code. An ability to more successfully protect one's own code and data and overwrite others is selected for.

One can do repeatable experiments with a computer program. Each generation can be saved, and the simulation can be rerun from any point in time, with random number generators restarted with new seeds. Lenski et al (2003) report such experiments with Avida, a computer simulation much like Tierra. In Avida, evolving computer programs collect energy to run their code. Programs that can do advanced logical operators are more fit. Lenski et al show that the evolution of a complex feature may depend on the prior evolutionary history of an organism providing the potential of the last few steps, even if previous mutations do not increase fitness.

I was surprised to find last week not only that repeatable experiments with evolution have been performed on simulations, but that Richard Lenski has been performing such a repeatable experiment on real-world organisms - namely, E. Coli - since 1988. (I must have missed Carl Zimmer's article, of 26 June 2008 in The New York Times, on the Long Term Evolution Experiment (LTEE).) Anyway, Blount, Borland, and Lenski's 2008 article reports on recent results.

In the LTEE, populations of each generation are isolated in a solution containing glucose for the E. Coli to eat. The isolated solution, I guess, acts like the simulated core memory in Tierra. And the E. Coli of any generation and evolutionary history can be frozen and restarted, just as an image of the computer core memory in a simulation run can be saved and reloaded. One run yielded a mutation that seems to have surprised Linski. This mutation allows the E. Coli to thrive on citrate, whatever that is, in the solution even "under oxic conditions". The ability to sample previous generations and look at other isolated population histories starting from the same initial conditions allows Linski and his colleagues to understand something about this mutation even before genetic sequencing. It is not the result of a single gene mutating, but is dependent on prior mutations in the history. These prior mutations may not have increased fitness themselves, but prepared the E. Coli to become dramatically more well-adapted for their specific environment after a couple more mutations. History matters.

References

• Ayres, Clarence (1932) Huxley, W. W. Norton
• Blount, Zachary D., Christina Z. Borland, and Richard E. Lenski (2008) "Historical Contingency and the Evolution of a Key Innovation in an Experimental Population of Escherichia Coli", Proceedings of the National Academy of Sciences V. 105, N. 23 (June 10): 7899-7906
• Hodgson, Geoffrey (2008), "Interview" Revue de la Régulation (January)
• Lenski, Richard E., Charles Ofria, Robert T. Pennock and Christoph Adaml (2003) "The Evolutionary Origin of Complex Features", Nature, V. 423 (8 May): 139-144
• Thearling, Kurt and Thomas S. Ray (1994) "Evolving Multi-celluar Artificial Life, Artificial Life IV, MIT Press