Oct 30th MSL Teleconference

 

src: nasajpl

 

  At Tuesday's teleconference the MSL project scientists discussed the results of the first xray diffraction measurements made on another body of the solar system. Using xray diffraction equipment that had been reduced from the size of a refrigerator on Earth to that of a shoe box for the mission they were able to capture the diffraction pattern of finely divided particles to determine the minerals present. The minerals were basaltic and similar to feldspar, pyroxene and olivine. The particles are believed to be a mixture of blown in dust and local particles along with volcanic glasses and their weathered products. telecon images and related press release

 

Earthquake Convictions in Italy 2

 

  The plots in the last blog may not be admissible as evidence against the individuals charged with wrong doing since they assume facts not in evidence at the time the statements were made, specifically, the existence and time of the M6.3 earthquake. Here is a new set of plots using averaging intervals of 1/3 of the anomalistic month of 27.55 days. They start at the beginning of 2002 and the time scale is in Julian years of 365.25 days.

 

 

 

 

 

  There doesn't appear to be much to indicate that a major earthquake is imminent. There is a decrease in the frequency of earthquakes in an interval of time and some low level earthquakes are missing. The pattern of the total energy of the earthquakes in an interval for several years before the earthquake doesn't appear to change much. The nonuniformity could be interpreted as statistical fluctuations as might be the increase in the average energy with fewer earthquakes per interval. With lower numbers one can expect greater fluctuations in the average. What may be abnormal is the low level of earthquake activity immediately prior to the time of the major earthquake which I have referred to elsewhere as a "lull." Another oddity is the disappearance of low level earthquakes which might indicate that the faults have locked up some. It's still difficult to point to anything that says there will be a major earthquake soon.

 

  Supplemental (Oct 28): One should probably ask if the absence of earthquakes below M2.5 from mid 2004 onward was due to a change in earthquake activity or a change in monitoring them. Would a global network charged with monitoring earthquakes worldwide reduce the sensitivity of a seismograph when there are a large number of local earthquakes or would they reduce the number reported to the system? The explanation might be relevant to the case.

 

Earthquake Convictions in Italy

 

  Six scientists and a former government official were found guilty in an Italian regional court on October 22 for making "inaccurate, incomplete and contradictory" statements prior the the magnitude 6.3 earthquake in Aquila on April 6, 2009. I downloaded the data for the earthquakes with magnitudes greater than 2.0 from the beginning of 2002 to just prior to the M6.3 earthquake and within 1 degree in latitude and longitude of l'Aquila. The distribution of the earthquakes in latitude and longitude can be seen in the map below.

 

 

  An analysis of the data produced the following plots as a function of 30 day months prior the the earthquake. The frequency of earthquakes decreased while the total energy released per month remained fairly constant. The average energy per earthquake showed some spikes just before the major earthquake but these spikes occur when there are relatively few earthquakes. One would have to look at the sequence of earthquakes over a much longer period of time to decide if this record was atypical. But the pattern of the energy released does appear to become more periodic towards the end of the plot.

 

 

 

 

Modified Galton Board: The Go - No Go Problem

 

  The Galton board is used to illustrate how one can arrive at a normal distribution using a natural process. To see how this works we can use a modified model of the Galton board which is more general in nature.

 

 Consider the simple two event mechanism to the left. In each interval of time the device can either advance one step to the right or not advance. If p is the probability of advance then q=1-p is the probability of no advance since these are the only two possible events.

 

 The number of paths to a point in the tree to the left is a Bernouli coefficient. The probability of reaching a point on a line after n intervals is a binomial distribution.

Binomial Distribution

 

 For p=3/4 the average distribution of 1024 objects after n intervals of time is shown to the left. One would expect the results of an actual experiment to deviate slightly.

 

The Oct 18th Teleconference

 

src: NASAJPL [ustream]

 

  At this afternoon's MSL teleconference Robin Cook and John Grotzinger reported that the activities were going well. The first two scoops were discarded and didn't make it to Chemin due to concerns about possible contamination by spacecraft debris since some bright specks were spotted in the scoop trenches. It was concluded the these specks were indiginous Martian material since they were about the same size as the other grains in the trench. The third scoop was placed on the observation tray to be checked out prior to sending it to Chemin. The sample consisted of a light toned fine grained component along with some larger dark specks that was spread horizontally on the tray. [see telecon images] Grotzinger also said that MSL reported just before the teleconference that the third scoop did make it to Chemin. He said the light toned material on the tray may have whited out.

 

  The saturation problem happens when all the RGB values for a pixel are greater than or equal to 255, which is the upper bound for the value, as a result of high photon counts. When all three components have this value the pixel appears to be white in color.

 

  These first scoops are being used to remove the remains of contaminants from Earth. Sand is being used to scrub the sampling and transfer apparatus. The sand has a very large surface area and the amount of contaminants present can be reduced through contact with the sand and subsequently discarding the it.

 

Coated Granules

src: MSL Raw Images

This Sol 69 MAHLI image shows that the coating on the surface granules does not cover the entire granule. The interior of the granule looks like it might be a saltation particle. A possible explanation is that a layer of saltation particles collected at this location on top of a small sand drift and the fine powder coated them later. In a dust storm one would expect a light fine powder to be airborn the longest. Electrostatic or intermolecular forces might be what made them adhere together. On the surface light might play a role in breaking chemical bonds permitting new ones to form between adjacent particles. On Earth dampness helps things cling together.

A Close-up of the Bright Object

src: MSL multimedia

  Curiosity managed to get a close-up of the mysterious bright object that was spotted in an Oct 7th image with the MAHLI hand imager. The small granules present appear to be of the same material as the sand or electrostatically coated.

Galton - Selected Works on Heredity

  Here is a list of selected works by Galton on the normal distribution and the heredity of physical traits along with their dates. They can be found at galton.org. Galton also made use of the error ellipse which is discussed in more detail in the appendices.

Typical Laws of Heredity (Feb 9, 1877)
Proceedings Royal Institution of Great Britain Volume 8

Regression towards mediocracy in hereditary stature p. 246 (June 9, 1885)
  mentions J. Hamilton Dickson p. 255 (with figures)
Journal of the Anthropological Institute of Great Britain Volume 15

President's Address (1885)
Reports of the Meetings of the British Association for the Advancement of Science Volume 55

Family Likeness of Stature (January 21, 1886)
  appendix by J. D. Hamilton Dickson (with figures)
Proceedings of the Royal Society of London Volume 40 p. 42

President's Address p. 489 (Annual General Meeting, January 26, 1886)
Journal of the Anthropological Institute of Great Britain Volume 15

Co-relations and their measurements (December 20, 1888)
Proceedings of the Royal Society of London Volume 45

Natural Inheritance 1894
  Appendix B, Problems by J. D. Hamilton Dickson
  reprinted from Proc. Royal Soc., No. 242, 1886, p. 63 (no figures)

Airy's Theory of Errors

 

  The intellectual capital needed to calculate the means, moduli (scaling units) and quartiles in the last blog can be found in Airy, Theory of Errors of Observations (1875). The work appeared just before the start of Galton's series of publications on the normal distribution and heredity. Here is an index of the relevant sections.

 

  §3 Law of probability, frequency of errors

 

    mean error #24-6, p. 18f

 

    squares of errors #27, p. 20

 

    quartile #28-9, p. 22-3

 

  §9, mean error, error of mean square #60-1, p. 45-8

 

  §11, sum of weighted error #68, p.53

 

  Airy's Theory of Errors also discusses solving for errors and "minimum squares" in §13, #87, p. 71f which are related to regression.

 

Galton's Use Of The Normal Distribution

 

 

   Francis Galton wrote a number of papers in which he used the normal distribution in the study of human inheritance. The most mathematically complete paper appears to be Family Likeness in Stature, published in the Proceedings of the Royal Society of London, Volume 40, pages 42-73. The publication is dated January 21, 1886. The work seems to have been done with the assistance of J. D. Hamilton Dickson who was a tutor at St. Peter's College in Cambridge. Part of this paper is available in the collected papers at galton.org but part of the appendix and the tables at the end seem to be missing. The data for the inheritance of stature is from the Record of Family Faculties. I've been going over the mathematics used in the paper and have found a simple way to calculate Galton's measure of the deviation from the mean for the normal distributions. Column A in the table above contains a distribution of heights for the population in general and two sets of brothers. One can convert the frequencies in the tables to probilities by dividing by the sum of the columns. Multiplying the heights by the probabilities and adding gives the average height for each column. One can also calculate the standard deviation for each column and convert this to something like a scale height which can be used to determine the dimensionless parameter t. Galton uses the cumulative probability distribution analysis and quartile distances to characterize the spread of the distributions. For each distribution Galton found that the quartile distance qH = 1.7 inches. In general the height H = mH + t sH. An explanation of the terms can be found in the simplified Mathcad calculation seen below.

 

 

  A better name for the scaling unit that Galton used might be "scale deviation". Computing the probabilites for one inch intervals and multiplying by the sum of each A column one gets these fits.

 

 

 

 

  Supplemental (Oct 13): The calculation was intended to give a simple estimate of the scaling unit. One could get technical about the precise definition of standard deviation and the difference of estimated, expected and observed deviations. For one data point the observed deviation might be taken as zero but the standard deviation would be infinite.

 

  Supplemental (Oct 15): The table above is from the Google eBook edition of the Proceedings of the Royal Society that was cited.

 

2012 Nobel Prize for Literature

 

src: thenobelprize

 

  Earlier today the 2012 Nobel Prize for Literature was awarded to the Chinese writer Mo Yan "who with hallucinatory realism merges folk tales, history and the contemporary".

 

Oct 11 Teleconference

 

src: Curiosity Cam - ustream

 

  Today's MSL teleconference discussed the chemical composition of some of the rocks recently tested at Gale Crater with the main focus on Jake Matijevic. The images for the conference can be found on the NASA MSL telecon page and at the MSL Image Gallery. The rock Jake Matijevic was found to be have high concentrations of sodium, magnesium, aluminum and silicon and was a new type found on Mars. The closest rocks on Earth are found on the ocean floors. The process of their formation is referred to as alkalic. A melt such as that in a volcano can lose material through solidification which alters the composition of the melt leading to higher concentrations of some minerals. Water is also dissolved in the melt like cabon dioxide is dissolved in the liquid of a cola drink. The process was compared to the traditional method of producing cider. The cider is repeatedly frozen and the ice crystals are removed. The liquid remaining has a higher concentration of alcohol. Related geological processes are igneous differentiation, fractional crystalization and partial melting. It is difficult to deduce more about the conditions that led to the rock's formation since it is not known if it is part of a local rockbed or if it was relocated by meteor impact. The teleconference also discussed the first effort at decontamination of sample collection system and monitoring of the process.

 

2012 Nobel Prize for Chemistry

 

  The Nobel Committee announced today that Robert J. Lefkowitz and Brian K. Kobilka are the recipients of the 2012 Nobel Prize for Chemistry "for studies of G-protein-coupled receptors." These receptors are located in the cell membrane and enable the cell to detect chemical messengers and respond to them. They are part of the mechanism which allows the cells of the body to communicate with each other.

 

  Supplemental (Oct 11): The video of the announcement is now available at thenobelprize on YouTube.

 

2012 Nobel Prize for Physics

 

src: thenobelprize

 

  The Nobel Committee announced today that the 2012 Nobel Prize for Physics goes to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems." Both researchers have done work on Quantum Optics which is concerned with the interaction between light and matter. Some articles on their work:

 

  Wineland Awarded 2007 National Medal of Science

 

  Quantum Logic Clock (NIST)

 

  Decoherence of quantum superpositions...

 

  Reversible Decoherence of a Mesoscopic Superposition of Field States

 

2012 Nobel Prize for Physiology or Medicine

 

src: thenobelprize

 

  Today the Nobel Committee announced the recipients for the 2012 Nobel prize for Physiology or Medicine. They are Sir John B. Gurdon and Shinya Yamanaka. The prize was awarded for showing that genetic material from mature cells could be transferred into an egg subsequently developed into complete organisms and that this could also accomplish by reprogramming individual cells.

 

Curiosity's First Scoopful of Mars

 

src: mslnews

 

  On Sol 61 Curiosity captured a MastCam video of the scoop vibrating a sample of from one of the drifts at Rocknest. Here are some more images.

 

 

src: MSL Raw Images

 

Oct 4 Teleconference & Close-up Images Of A "Ripple"

 

  The MSL Oct 4 telecon dwelt on the plans for the next couple of weeks at the Rocknest site to scoop material from a "sandbox" there. The sampling system first needs to be purged and cleaned of contaminants by doing a number of trial runs through it. The process will be more closely monitored initially to verify the proper functioning of the system. The caption for the conference image with the wheel impression on one of the drifts refers to it as a ripple. The Sol 58 MAHLI close-ups shows that the ripples consist of a crusty coarse grain layer resting on top of a more sandy one. The coarser grains may be saltation particles.

 

 

 

 

  Supplemental (Oct 5): A zastryga, Russian заструга, is an inanimate object. It is fixed in place. There are other things like bow waves that are relatively fixed in place that fit in a more general class with similar attributes. Tags may be useful in identifying them.

 

Avoiding Misnomers

 

  The driftlike objects that I have named "zastrugi" illustrate the problem that we can have in naming something new to our experience. They may look like something we have seen before but occur elsewhere. The problem is one of identity. Are the objects the same? For biologists the problem is quite complicated and their nomenclature system is the solution that they have come up with. The objects most closely related are included in the same species. They are the same kind of objects. Other objects with roughly similar properties are grouped together as a genus. More distantly related objects form families and orders. To properly name something we need a classification system and a set of rules for making the identifications. Sometimes a genus takes the name of one of its members as in the case of vulpes vulpes, the red fox or lynx lynx, the European lynx. I use the name "zastruga" for the objects found on Mars in this broader sense since the Russians say it can refer to sand and gravel spurs in addition to shaped snow drifts. So if we wish we can use the name for a group of objects that is zastruga-like. Often we use the indefinite article to indicate membership is a class. For example we could say, "Felix is a cat," and, "Wolf is a dog."

 

  In this context what can be said about the "alluvial fan"? The word "fan" indicates a diverging deposit of some sort. The adjective "alluvial" indicates the active agent was water. If wind was the active agent we might say that it is an "aeolian fan". In the case of "talus cone" there is no active agent except gravity. In each case there is a slope that the particles of the deposit distribute themselves over in a manner similar to the way balls move down Galton's board. I used "cascade" as the general term for the field that particles travel over.

 

  As we explore Mars and the other planets it is likely we will encounter things outside our normal experience the scientists need to come up with a general procedure or set of guidelines or precedents to follow in coming up with new names and in identifying what is what. A classification system may prove to be the best approach to the problem.

 

A Fragile Zastruga

 

 

 The "zastrugi" don't seem to be able to take much weight as this Sol 56 anaglyph shows but the sides of the depression left by one of Curiosity's wheels didn't collapse as one would expect loose dry sand to do.

 

Zastrugi

 

  Some of the drifts in these Sol 55 anaglyphs look a like zastrugi. I use red and cyan for these anaglyphs and set green to their average to add more gray because of the problem with ghost images of the large drift. It helped a little both eyes still see some of complementary color.