December 2014 - mathfun@mailman.xmission.com

[math-fun] 2015 with the other six digits
by Eric Angelini 24 Dec '14

24 Dec '14

Hello Math-funsters, what could be an economic way to get 2015 with the six other digits [3,4,6,7,8,9] and the usual signs [=,+,-,x,:,^,...]? Best, É. Catapulté de mon aPhone

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[math-fun] life on mars(?)
by Warren D Smith 21 Dec '14

21 Dec '14

To reply to Baker, it seems to me if there was widespread microbial life on Mars once, it'd still be there now. Do you believe that if Earth lost most of its atmosphere, its oceans, and became cold -- but gradually over a billion years -- that would extinguish all life? I do not. First, there actually were several "snowball Earth" eras where the whole planet was frozen over about 700 M years ago for around 20 M years or more. The equator in that era was as cold as modern-day Antarctica. Second, the so-called "deep biosphere" (estimated to contain anywhere from 1% to over 50% of all earth's biomass) would be virtually unaffected. And that is without any Darwinian adaption needed at all. With adaption, it gets more speculative, but there's a big free energy source on Mars with (1) the sun and (2) perchlorates near surface, and that's plenty of incentive for adaption to try to use it, with the deep biosphere providing a continually available reservoir of safeguarded life that can keep trying to find the right adaptions to handle the surface, no matter what. Hence: it still seems to me that the widespread unused surface perchlorates on Mars are a strong argument that (1) there is no life and (2) never was any. Why isn't everybody saying that? I can make some highly disparaging guesses related to (a) their psychology and (b) the fact they all want to keep the myth alive to get funding. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] The first 1000 billion digits of pi in color
by Simon Plouffe 20 Dec '14

20 Dec '14

Hello, I made an experiment with the first 1000 billion digits of Pi, http://plouffe.fr/piat1000billion/ each image is 10000x10000 and there are 10000 images. Each digits -> gray scale image -> colorized result. The choice of colors is simple ; random. The combined image size is 1000 billion pixels. I could only put the first 220 billion digits on the page because of space. I am working now on finding a site for the rest of the images. caution : the page is huge, 10000 thumbnails. Best regards. Simon Plouffe

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[math-fun] Life on Mars? Latest grist
by Bill Gosper 19 Dec '14

19 Dec '14

WDS>1. The Curiosity rover detected time-varying methane concentration in Mars atmosphere, changing by factor>10 over a several-month period. They claim the usual "background" level is about 0.7+-0.25 parts per billion, but it has gone as high as 7.2+-2.1 ppb at least locally near Curiosity (these are 95% confidence intervals). Earth based telescope observations have been claimed to see Mars-wide changes in methane, spiking as high as 60 ppb. To put this in perspective, the total amount of methane (at background level) in the whole Mars atmosphere, is about 200 metric tons. Meanwhile the total amount in the Earth's atmosphere at any time is about 500,000,000 metric tons. 2. Also, it found chlorobenzene in a mudstone rock sample (something like dried clay). Chlorobenzene is the most abundant organic found in that sample (as well as the most complex; several chloro-alkanes were also found) with concentrations between 150 and 300 parts per billion. Chlorobenzene does not occur naturally on Earth but is present in pollution. <WDS Presumably there are microorganisms in the harshest terrestrial deserts. Could Curiosity detect these? I'm guessing the methane is primordial. It's looking really glum for life on Mars. --rwg

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Re: [math-fun] life on mars(?)
by Henry Baker 19 Dec '14

19 Dec '14

At 11:25 AM 12/19/2014, Warren D Smith wrote: >>Looking glum for life on Mars. > >--actually, here's what seems to me a pretty convincing argument there >is not life on Mars! > > From Wikipedia "Perchlorate": I'm more interested in previous life on Mars. The early Solar system was a pretty chaotic place, and it would appear that some oxygen-generating life forms got started on Earth within the first 1-1.5 billion years. Do to the celestial chaos, there were likely a large number of significant meteor impact events as big or bigger than the one on Earth 65 million years ago. So IMHO it is highly likely that we will eventually find traces (likely dead) of early Earth organisms on Mars. The next question is whether early Mars could sustain life or not; I think that that question is still unanswered. But even if early Mars could sustain life, I would think that if Mars is dead now, then it was probably dead 65 million years ago, as well, so we might also still find traces of 65 million-year-old Earth life on Mars. If Mars developed life prior to Earth, then unless Mars life was transported to Earth and became Earth life, then Mars life could be substantially different from Earth life -- e.g., perhaps mirror-imaged proteins (50% probability), etc.

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Re: [math-fun] life on mars(?)
by Warren D Smith 19 Dec '14

19 Dec '14

>Looking glum for life on Mars. --actually, here's what seems to me a pretty convincing argument there is not life on Mars! >From Wikipedia "Perchlorate": BIOLOGY: Over 40 phylogenetically and metabolically diverse microorganisms capable of growth via perchlorate reduction have been isolated since 1996. Most originate from the Proteobacteria but others include the Firmicutes, Moorella perchloratireducens and Sporomusa sp., and the archaeon Archaeoglobus fulgidus.[10][11] With the exception of A. fulgidus, all known microbes that grow via perchlorate reduction utilize the enzymes perchlorate reductase and chlorite dismutase, which collectively take perchlorate to innocuous chloride.[10] In the process, free oxygen (O2) is generated and this is one of only a handful of biological processes to generate oxygen aside from photosynthesis.[10] Apparently that research was prompted by perchlorate pollution of water now being a major problem caused by irresponsible rocket manufacturers. Well damn, I did not know that. So if there were microbes on Mars, they'd be crazy not to utilize this excellent free energy source of all those perchlorates lying around constituting about 0.6 weight percent of all Martian rocks/dirt. Which therefore would no longer be lying around. (Same way they aren't available in Nature here on Earth... except in Chilean nitrate deposits...) So there are not Mars microbes, QED.

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Re: [math-fun] Mars and convexity
by Warren D Smith 19 Dec '14

19 Dec '14

To RCS & Baker: As far as I understood, they thought the chlorobenzene was probably real, not due to contamination & processing, because they'd tested other rocks too and not seen it. But I do not know. Mars evidently pretty weird place with perchlorate all over. Perchlorates and chlorates would never survive on Earth for geological time scales. Didn't they already know about the perchlorates from previous (viking) lander? (And I must say I find the notion of using perchlorate as rocket fuel on Earth, disturbing for pollution reasons.) Robert Zubrin in some amusing book proposed a plan to travel to mars with a big hydrogen tank, then from martian CO2 synthesize methane and oxygen as fuel you would then use to take off & return to Earth. His ship carried a nuclear reactor to mars for power. He actually built & tested a chemical reactor to carry out the methane synthesis. To Latto: A = [-x/2, x/2], B = [2,3] the intersection of A with B is 0, then a linear function of x, then 1. Oh, I see, the last two parts are convex, but not the first two parts. Well, I guess I was only thinking of the function of x starting at the least x for which we get a nonzero volume. You & Veit both made some interesting suggestions about good conjectures, but I do not know their answers.

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[math-fun] Dick Clark's Malibu retreat sells for $ 10^6*2^4/3^2
by Henry Baker 18 Dec '14

18 Dec '14

FYI -- "Dick Clark's Malibu retreat sells for a significant sum: $1,777,777". What a bizarre number! 1.7777... = 16/9 = cfdisrep([1,1,3,2]). Note that the aspect ratio of modern HDTV's is 16:9, but to my knowledge, all of Dick Clark's shows were 4:3. http://www.latimes.com/business/realestate/hot-property/la-fi-hotprop-dick-…

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[math-fun] Distinguishing cause from effect using observational data
by Henry Baker 18 Dec '14

18 Dec '14

FYI -- Perhaps this article has some bearing on WDS's questions: http://science.slashdot.org/story/14/12/18/1810221/cause-and-effect-how-a-r… Statisticians have long thought it impossible to tell cause and effect apart using observational data. The problem is to take two sets of measurements that are correlated, say X and Y, and to find out if X caused Y or Y caused X. That's straightforward with a controlled experiment in which one variable can be held constant to see how this influences the other. Take for example, a correlation between wind speed and the rotation speed of a wind turbine. Observational data gives no clue about cause and effect but an experiment that holds the wind speed constant while measuring the speed of the turbine, and vice versa, would soon give an answer. But in the last couple of years, statisticians have developed a technique that can tease apart cause and effect from the observational data alone. It is based on the idea that any set of measurements always contain noise. However, the noise in the cause variable can influence the effect but not the other way round. So the noise in the effect dataset is always more complex than the noise in the cause dataset. The new statistical test, known as the additive noise model, is designed to find this asymmetry. Now statisticians have tested the model on 88 sets of cause-and-effect data, ranging from altitude and temperature measurements at German weather stations to the correlation between rent and a partment size in student accommodation. The results suggest that the additive noise model can tease apart cause and effect correctly in up to 80 per cent of the cases (provided there are no confounding factors or selection effects). That's a useful new trick in a statistician's armoury, particularly in areas of science where controlled experiments are expensive, unethical or practically impossible. http://arxiv.org/abs/1412.3773 Distinguishing cause from effect using observational data: methods and benchmarks Joris M. Mooij, Jonas Peters, Dominik Janzing, Jakob Zscheischler, Bernhard SchÃ¶lkopf (Submitted on 11 Dec 2014) The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y . This was often considered to be impossible. Nevertheless, several approaches for addressing this bivariate causal discovery problem were proposed recently. In this paper, we present the benchmark data set CauseEffectPairs that consists of 88 different "cause-effect pairs" selected from 31 datasets from various domains. We evaluated the performance of several bivariate causal discovery methods on these real-world benchmark data and on artificially simulated data. Our empirical results provide evidence that additive-noise methods are indeed able to distinguish cause from effect using only purely observational data. In addition, we prove consistency of the additive-noise method proposed by Hoyer et al. ( 2009).

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Re: [math-fun] Life on Mars? Latest grist
by Henry Baker 18 Dec '14

18 Dec '14

At 10:18 PM 12/17/2014, rcs(a)xmission.com wrote: >The article pointed out that perchlorate ClO4- is common on the Mars' surface, Hmmm... This gives us half of a good solid rocket fuel: https://en.wikipedia.org/wiki/Ammonium_perchlorate_composite_propellant SpaceX claims to have picked methane as a rocket fuel because they want to go to Mars, and there's methane on Mars. https://en.wikipedia.org/wiki/Raptor_%28rocket_engine%29

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