Spirit, Already Dead

On January 26th, 2274 Mars days into the mission, NASA declared Spirit a 'stationary research station', expected to stay operational for several more months until the dust buildup on its solar panels forces a final shutdown.

If the Spirit rover is just a little robot crawling around on a little red planet somewhere, then why are we so sad that it is dying? The rover is certainly easy to anthropomorphize, but I think there is more to it. The spectrum of sentient to insentient, is just that a spectrum. When we speak of these concepts we make subtle judgments through the connotation of our words. For example is the robot going to die, or is it going to shutdown? On some level it must be alive, or, at least it was.

The Entropy of the Universe

First, what is entropy? Is it a philosophers dream?

"Acqua Alta - L'amnésie contagieuse de l'amante religieuse." by jef safi

The chaos is not a shapeless state, or a confused and inert mixing, but rather the place of a plastic and dynamic becoming... Philosophy, science and art are "drawing plans" on the chaos, they are the three chords. Philosophy on its plane of immanence of ideas and concepts, science on its plane of consistency of variables and functives, and art on its plane of composition of affects and percepts." -Gilles Deleuze, Qu'est-ce que la philosophie?

That was about as quantitative as dancing about architecture. Let us define entropy as a measurement of disorder in a system. The entropy of a system can be defined as proportional to (the natural log of) the number of microstates corresponding to the observed system macrostate. Entropy is usually defined by big S.

Where Ω is the number of accessible microstates and where k_B = 1.381×10⁻²³ J K⁻¹ (through out the rest of this post k will represent Boltzmann constant and K the unit of Kelvin) is the Boltzmann constant in units of Joules per Kelvin. Entropy has always intrigued me so when I saw this paper on entropy of the entire Universe I was delighted.

A Larger Estimate of the Entropy of the Universe

Authors: Chas Egan, Charles Lineweaver

Abstract: Using recent measurements of the supermassive black hole mass function we find that supermassive black holes are the largest contributor to the entropy of the observable Universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable Universe is correspondingly higher, and is S_obs = 3.1×10¹⁰⁴ k. We calculate the entropy of the current cosmic event horizon to be S_CEH = 2.6±0.3×10¹²² k, dwarfing the entropy of its interior, S_{CEH int}= 1.2×10¹⁰³ k. We make the first tentative estimate of the entropy of dark matter within the observable Universe, S_dm = 10^88±1 k. We highlight several caveats pertaining to these estimates and make recommendations for future work.

Entropy is important in the Universe because it is inexorably linked to the arrow of time and understanding why the Universe began in such a low entropy state, namely the big bang, is an open question (considering the anthropic explanation unsatisfactory or at least not fully quantitative). A better quantifiable question that we can answer is the current total value of entropy in our Universe and the constituent contributions from major astrophysical phenomena. The authors explain that the increase of the entropy budget of our Universe is associated with all irreversible process including gravitational clustering, accretion disks, supernovae, stellar fusion, terrestrial weather, chemical, geological and biological processes. The authors have assumed a flat Universe with standard cosmological parameters (Ω_k=0, h=.705, Ω_b = 0.0224, Ω_m= 0.136 and T_cmb=2.725 K) and applied the second law of thermodynamics to the determine the entropy contribution of the most dominate processes in the entropy budget. The exact volume of the Universe is the dominating error in some of the estimates. In fact the entire definition of the volume of the Universe is questionable. In the case of the observable Universe we are considering a volume with a moving boundary in which matter or information may flow in and out, however we may attempt to dispel this concern that our system is not closed because as the authors state, 'the system is effectively isolated because large-scale homogeneity and isotropy imply no net flows of entropy into or out of the comoving volume'. In the appendix of the paper they explain how to calculate the volume of the Universe in a very simple manner if you are familiar with cosmography. The volume of the observable Universe is 3.65×10⁸⁰ m³ or s 43.2×10⁴ glyr³.

Figure 1 from the paper illustrates the particle and cosmic event horizons. At the origin on the x-axis is a vertical dashed line representing our galaxy. In the top panel the x-axis is the comoving distance, x=D/a where a is the cosmic scale factor. In the bottom panel the x-axis is the proper distance D. The region inside the particle horizon is the observable Universe. The comoving volume that corresponds to the observable Universe today is filled grey.

The largest contributor to the entropy budget of our Universe is super massive black holes (BH or SMBH). In the Schwarzchild case:

where , G is the gravitational constant, h (or rather h-bar) is Planck's constant, c is the speed of light, A is area, and M is mass. The largest contributor to the entropy of the Universe besides SMBH is certainly the cosmic microwave background which can be calculated succinctly using the equation of blackbody from Kolb and Turner (1990):

Where Tγ is the photon temperature and g_γ is the number of photon spin states, namely 2. The results for all phenomena in the entropy budget considered are tabulated in the table below:

Table 1 from the paper. The bracketed numbers refer to previous literature references.

It was interesting to hear the discussion on neutrino and graviton entropy. The total entropy of the neutrino background is a little tricky to compute because the neutrino entropy cannot be calculated directly because the temperature of the cosmic neutrino background has not been measured (to young scientists out there, go measure it and report back for a guaranteed Noble Prize). Additionally, infall of neutrinos into nonlinear structure with significant gravitational potentials may alter the neutrino entropy and the authors see this as possible future work. Then there is the relic graviton radiation, and its entropy contribution which is again insignificant compared to SMBH, but it is interesting to note that by reversing the relationship between the current graviton temperature and photon temperature it may enable, 'calculating the number of relativistic degrees of freedom at the Planck time using future measurements of the graviton background temperature'. Dark matter is the final twist. The authors present the first ever tentative estimates by interpreting it as a weakly-interacting superpartner to conclude its contribution is minimal.

Ultimately the entire entropy budget is dominated by black holes and critically the masses of black holes in our Universe. Entropy increases when gravitons are produced. The contribution of super massive black holes to entropy comes from the production of gravitons. Take for example, not a black hole, but another extreme gravitational system of two black holes or neutron stars inspiralling towards each other; gravitational waves are emitted from the system extracting orbital energy and therefore entropy allowing the system to contract. The authors find the BH entropy to be the dominating factor and larger by at least an order of magnitude compared to previous estimates which have different BH initial mass functions (IMF). Indeed the flaw in any work that attempts to make estimates of populations of stars, galaxies, or BHs faces the issue of ambiguous IMFs for the objects. The primary source of uncertainty that I perceive here is the lack of understanding of the IMF. Regardless if anyone was wondering what the entropy of the observable Universe is, and I know I was, it is 3.1×10¹⁰⁴ k .

References:

Chas A. Egan, & Charles H. Lineweaver (2010). A Larger Estimate of the Entropy of the Universe ApJ arXiv: 0909.3983v3

The Limits of Cosmology

Amedeo Balbi on The Limits of Cosmology

When attempting to discuss what a certain discipline can or cannot know, one should keep in mind, as a cautionary tale, the famous case of philosopher Auguste Comte. Writing in the first half of the nineteenth century, he stated that astronomers would never be able to ascertain the chemical composition of celestial objects. However, only a few decades after Comte’s prediction, Kirchhoff founded spectroscopy and managed to identify chemical elements in the atmosphere of the Sun.
    Cosmology is arguably one of mankind’s boldest enterprises. It tries to scientifically understand the origin, evolution and structure of the universe as a whole. In doing so, it has to rely on a certain set of observational data (what we see of the cosmos) whose collection cannot be repeated under different conditions; furthermore, it has to interpret such data according to a set of physical laws whose validity was mostly assessed in laboratories on Earth. Most cosmology is based on extrapolations of known physics to uncertain territories, and on indirect evidence derived from the behaviour of the part of the universe we can observe. We happen to live in the golden age of cosmology—for the first time in the history of mankind we are able to scientifically describe the overall structure of the universe. However, to some extent, it is surprising that we have managed to make some sense of the universe at all. Continued...

This essay is one of the winners from FQXi's contest on What Is Ultimately Possible in Physics?

Perceiving Itself

Through our eyes, the universe is perceiving itself.

Quote from Alan Watts. Art by Viktor Timofeev.

IceCube

The IceCube Neutrino Observatory is currently under construction in Antarctica. It is a pretty nifty project and this animated video by Casey O'hara is well worth watching for an explanation of the IceCube concept. It is light on the science, but it is delight because it explains neutrinos with Legos, breakfast cereal, and otter pops! I will have to post about IceCube again when they catch a neutrino.

The Moon, where the Helium-3 from the Sun is

Moon is a 2009 science fiction film about astronaut Sam Bell who is the solitary worker on the moon. Sam is at the end of a three-year stint on the Moon so the film begins as if it was the denouement of another quieter story. When an accident occurs Sam suddenly meets himself for the first time.

I am adept at finding flaws in science fiction films, but Moon nails a lot of science as well as could be expected. The most incredulous point about the film for me was the lack of a radio array on the far side of the moon, I mean why else would we go to the moon? There is a very good and scientifically feasible answer for this. The movie begins, as you can see above with the first seven minutes of the film, with a commercial by Lunar Industries:

There was a time when energy was dirty word, when turning on your light was a hard choice. Cities in brown out, food shortages, cars burning fuel to run, but that was the past, where are we now? How did we make the world so much better? Make deserts bloom? Right now we're the largest producer of fusion energy in the world. The energy of the sun trapped in rock harvested by machine from the far side of the moon. Today we deliever enough clean burning helium-3 to supply the energy needs of nearly 70% of the planet. Who would have thought all the energy we ever needed, right above our heads? The power of the moon, the power of our future.

When I saw this at the beginning of the film I was delighted that they had based the story on a kernel of truthful science. The energy source they are gathering from the moon is Helium-3 (³He), but they aren't exactly burning it for fuel as they say. Helium-3 is a light isotope of helium with two protons and one neutron which is suitable as a fusion fuel. I have done some research into the literature to determine just how feasible this ³He mining on the moon is with two specific questions in mind. Why use ³He? Why go to the moon?

An advanced fusion reactor would combine ³He and deuterium (²H) in a fusion reaction to produce a helium-4 nucleus (⁴He) and a high-energy proton. Energy is released as charged particles and that is what powers the world in this science fiction vision of the future. ³He fuel offers some advantages over other types of fusion fuel because it is efficient and because less radioactive byproducts are produced (it is often stated or assumed that fusion power does not create any dangerous materials, but in reality the reactor housing can become radioactively activated and remain so for a number of years. However, the time scale on which it remains active is comparable to human lifetimes and is overall not as dangerous as the byproducts of fission reactors). ³He is very scarce on earth. It is possible to manufacture ³He on earth though the neutron bombardment of certain elemental targets which results in tritium, which then decays to ³He with a half-life of 12 years. This is a complicated, dangerous and inefficient process so other sources would be required to make ³He a viable fusion fuel.

The cosmological abundance of ³He is paltry, but its abundance and chemical evolution is of interest to astronomers because it can be a tracer of various stellar phenomena so it has been studied for many years. The primordial cosmological ratio of ³He to ⁴He is ~1.4 × 10 ^-6, however this abundance can be thousands of times greater in the solar wind. The solar wind is primarily protium traveling at a velocity of ~450 km/s with a flux of ~6 × 10 ¹⁰  ions/(m² s). Of this flux there is ~4% He which has an unusually high ratio of ³He to ⁴He of ~480 atomic parts per million (Heber V. 2003). ³He should be abundant on the moon's surface of regolith where it has been deposited by solar wind over billions of years.  Hence, we could go to the moon and mine it. However, to gather enough fuel to power the earth at current energy consumption rates more than one Space Shuttle load and the processing of 4 million tons of regolith per week, on the lunar surface, would be necessary. Further, to really nail the science here I cite Fa and Jin who state:

The [lunar] inventory of ³He is estimated as 6.50×10⁸ kg, where 3.72×10⁸ kg is for the lunar nearside and 2.78×10⁸ kg is for the lunar far side.

There is a bounty of lunar fuel available, but I wouldn't place my base on 'the far side of the moon' as Lunar Industries states they have done because it would be cold, there is less ³He, and it would be, well, lonely. In conclusion I have found the academic literature validates the idea that Helium from the moon could power terrestrial fusion reactors one day.

Apparently Sam Bell is working alone on the moon to cut costs for the company. In order to mine the necessary amounts of ³He with minimal overhead costs Lunar Industries has chosen a one man job; and based on the size of the lunar regolith harvesters seen in the movie 4 million tons processed per week would not be unfeasible. As the movie continues themes of alienation and societal deception emerge. I have discussed some science that the film never divulges, but in fact, the film never even mentions anything about ³He or the reasons why any of this is going on again. This is a strong point for the film which actually raises deep philosophical questions, which I could dive into, but I don't want to spoil it for anyone. It is a great film and not the craziest science, really:

Online resources:
Mining the Moon from Popular Mechanics
Lunar ³He and Fusion power by J. Santarius
Non-Lunar  ³He Resources by L. Wittenberg
Moon for Sale from the BBC

References:

FA, W., & JIN, Y. (2007). Quantitative estimation of helium-3 spatial distribution in the lunar regolith layer Icarus, 190 (1), 15-23 DOI: 10.1016/j.icarus.2007.03.014

Heber, V., Baur, H., & Wieler, R. (2003). Helium in Lunar Samples Analyzed by High‐Resolution Stepwise Etching: Implications for the Temporal Constancy of Solar Wind Isotopic Composition The Astrophysical Journal, 597 (1), 602-614 DOI: 10.1086/378402

Can Religion Explain Prosociality and Can Science Explain Religion?

Today, a philosophical diversion on the evolution of religion. Specifically I was thinking about the metaphorical evolution of religion and the Darwinian evolution of the human mind with a predisposition to the mystical. I was reminded about this topic and a Science article from some time ago when I saw a review for The Evolution of God a new book by Robert Right. My thesis on the topic is that as long as religion infers a survival advantage upon a group then evolution will select individuals whose minds are wired to be religious; or as society changes rapidly religion itself will evolve in a cultural respect. In this recent NYRB article Can Science Explain Religion? Allen Orr reviews Right's book with positive and critical remarks, an excerpt:

 In The Evolution of God, he [Right] both surveys the history of religion and, more important, offers a new theory to explain why this history unfolded as it did.

According to Wright's theory, although religion may seem otherworldly—a realm of revelation and spirituality—its history has, like that of much else, been driven by mundane "facts on the ground." Religion, that is, changes through time primarily because it responds to changing circumstances in the real world: economics, politics, and war. Wright thus offers what he emphasizes is a materialist account of religion. As he further emphasizes, the ways in which religion responds to the world make sense. Like organisms, religions respond adaptively to the world.

More formally, Wright argues that religious responses to reality are generally explained by game theory and evolutionary psychology, the subjects of his previous books. Subtle aspects of the human mind, he claims, were shaped by Darwinian natural selection to allow us to recognize and take advantage of certain social situations. The most important of these—and the centerpiece of Wright's theory—are what game theorists call non-zero-sum interactions. Unlike zero-sum games, wherein one player's gain is another player's loss, in some games both players can win; hence "non-zero-sum." The classic example is economic trade. In a free market, trade occurs when both parties benefit from exchange (otherwise they wouldn't engage in it).

Again, this theory doesn't seem new at all. It is, to my perspective, obvious that religion co-evolved with early humans precisely because religious tendencies in a society inferred an evolutionary advantage upon the group. Wright's basic theory is that due to historical circumstance the optimal strategy suggested by game theory has moved religion towards tolerance and conciliation. Religion changed its fundamental tenants throughout history in order that it would continue to instill advantages on its society. So, then this leads to the question, does religion and the church as an institution encourage prosociality or is it a self-serving system?

The Good Samaritan [painting by Jacopo Bassano, d. 1592, copyright 2006, The National Gallery, London]

Modern society has developed into a complex system in which people must work together. A cynical perspective is that people work together only in exchange for money or services with the ultimate goal of only helping themselves. There is nothing altruistic about the interactions. Yet, altruism is rampant. Another person helping another person with no aim other than to help can be described as a prosocial act. Prosociallity is defined as the quality of being beneficial to all parties and consistent with community laws and norms. Psychologists and evolutionary psychologists are seeking the answers as to why people engage in prosocial behavior, even at a cost to themselves in certain cases. Norenzayan and Shariff explain the issue in The Origin and Evolution of Religious Prosociality (Science 2008, a link to the article on the Science website is here. The Science link to the article will not be available to those who do not have a Science subscription. You would expect that an article about prosociality would be available to all in line with its prosocial topic, but that's situational irony for you. The direct link to the PDF posted above was from the author's web page and it may not be stable). The article abstract:

We examine empirical evidence for religious prosociality, the hypothesis that religions facilitate costly behaviors that benefit other people. Although sociological surveys reveal an association between self-reports of religiosity and prosociality, experiments measuring religiosity and actual prosocial behavior suggest that this association emerges primarily in contexts where reputational concerns are heightened. Experimentally induced religious thoughts reduce rates of cheating and increase altruistic behavior among anonymous strangers. Experiments demonstrate an association between apparent profession of religious devotion and greater trust. Cross-cultural evidence suggests an association between the cultural presence of morally concerned deities and large group size in humans. We synthesize converging evidence from various fields for religious prosociality, address its specific boundary conditions, and point to unresolved questions and novel predictions.

The authors run various experiments to determine in what situations people exhibit prosocial behavior. For example they ask when the average person would stop to help someone fallen on the sidewalk. Would a religious individual be more inclined to help that same fallen person, just as in the bible parable the good Samaritan? In the authors own words:

In several behavioral studies, researchers failed to find any reliable association between religiosity and prosocial tendencies. In the classic “Good Samaritan” experiment (22), for example, researchers staged an anonymous situation modeled after the Biblical parable—a man was lying on a sidewalk appearing to be sick and in need of assistance (Fig. 1, image above). Participants varying in religiousness were led to pass by this victim (actually a research confederate) on their way to complete their participation in a study. Unobtrusively recorded offers of help showed no relation with religiosity in this anonymous context (22). Only a situational variable whether participants were told to rush or take their time—produced differences in helping rates. Other behavioral studies, however, have found reliable associations between religiosity and prosociality, but under limited conditions. In one study (23), researchers compared levels of cooperation and coordination between secular and religious kibbutzim in Israel. In this economic game, two members of the same kibbutz who remained anonymous to each other were given access to an envelope with a certain amount of money. Each participant simultaneously decided how much money to withdraw from the envelope and keep. Players only kept the money they requested if the sum of the requests did not exceed the total amount in the envelope. If it did, the players received nothing. The results showed that, controlling for relevant predictors, systematically less money was withdrawn in the religious kibbutzim than in the secular ones (23).

In the conclusion the authors of this study on prosicoalty find evidence that prosociality is a bounded phenomenon. It more likely to be exhibited in situations where it helps in maintaining a favorable social reputation within the ingroup. It seems that evolution has enforced this self-serving ingroup behavior in some cases and evolution has also enforced purely altruistic behavior in other cases. The human mind certainly doesn't evolve on human time scales so it is up to religious groups to evolve their beliefs. Hopefully religious groups can continue to move towards tolerance, but in the meanwhile atheists will wonder why we need religion to move forward at all.


References:

Norenzayan A, & Shariff AF (2008). The origin and evolution of religious prosociality. Science (New York, N.Y.), 322 (5898), 58-62 PMID: 18832637

Tricks, Tricks, Tricks to remember

How to remember everything? I am not particularly keen on historical facts, but in order to remember various physical constants I recall historical dates:

The Cosmic Microwave Background: The CMB surface of last scattering occured at approximatley 1066 which is the year that historians consdier the begining of the Middle Ages (the years just prior being the late Dark Ages). Historically 1066 was the year of the Battle of Hastings and the ensuing Norman conquest of England. In the case of cosmology 1066 coresponds to the begining of the cosmological dark ages.

The mass ratio of a proton to an electron: The actual ratio of a proton to electron mass is 1836.153. The Battle of the Alamo was 1836. This trick works best if you are from Texas.




Euler's number: e is 2.7 1828 1828 I wrote it with the spaces between the 1828's because many people remember the 2.7.  And 1828 is one year after Beethoven died. This trick works best if you know your classical composers.




This memory trick using historical dates seems strange even to me; if anything the physical constants actually helped me remember the history dates, but either way I remembered. Memory tricks can be powerful tools. For example you can memorize nearly 4000 digits of π with a mnemonic technique, but the most powerful memory enhancing approach is certainly the method of loci.

Be sure and watch the second part that teaches you the link memory technique.

New Planet Discovered 400 Light Years Away From Public's Interest

The Kepler team has just announced their first results on the discovery and confirmation of five new exoplanets. The news barely made a splash so it reminded me of an old Onion article, New Planet Discovered 400 Light Years Away From Public's Interest. I can't help but think that this is all too true. Now to be fair none of the new exoplanets are particularly interesting as they aren't in the habitable zone and have very short periods. However, this news from Kepler is proof that the satellite is working as planned so in the future we can expect some much more exciting finds.

Star Count

How many stars are in the sky? There are actually only a couple thousand stars you can see with your eye on even on the clearest nights. It is estimated there are some 10¹¹ stars in our own Milky Way and perhaps some 10¹⁰ galaxies within our horizon. That makes 10²¹ stars in the universe a good first guess.