September 2012 - mathfun@mailman.xmission.com

Re: [math-fun] Junk DNA allegedly isn't. Big change in standard picture of life.
by Henry Baker 07 Sep '12

07 Sep '12

I've decided that wrt "junk DNA", we're basically arguing over Sturgeon's Law: "ninety percent of everything is crap": http://en.wikipedia.org/wiki/Sturgeon%27s_Law [Sturgeon's revelation, commonly referred to as Sturgeon's law, is an adage commonly cited as "ninety percent of everything is crap." It is derived from quotations by Theodore Sturgeon, an American science fiction author: while Sturgeon coined another adage that he termed "Sturgeon's law", it is his "revelation" that is usually referred to by that term. The phrase was derived from Sturgeon's observation that while science fiction was often derided for its low quality by critics, it could be noted that the majority of examples of works in other fields could equally be seen to be of low quality and that science fiction was thus no different in that regard to other art.] --- The problem, of course, is determining _which_ 90% is crap. That's the problem posed by John Wanamaker (of Wanamaker's department store in Philadelphia): "Half the money I spend on advertising is wasted; the trouble is I don't know which half.": http://en.wikipedia.org/wiki/John_Wanamaker [Popular saying illustrating how difficult it was to reach potential customers using traditional advertising is attributed to John Wanamaker: "Half the money I spend on advertising is wasted; the trouble is I don't know which half."] --- Wanamaker's problem was solved by Potter Stewart's rule: "I know it when I see it": http://en.wikipedia.org/wiki/Potter_Stewart [To the general public, Stewart may be best known for a quotation, or a fragment thereof, from his opinion in the obscenity case of Jacobellis v. Ohio (1964). Stewart wrote in his short concurrence that "hard-core pornography" was hard to define, but that "I know it when I see it."] ----

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Re: [math-fun] gaps between primes, P2s, P3s, etc
by Warren Smith 07 Sep '12

07 Sep '12

Charles Greathouse is right (sorry) -- P2s are more common than primes by a doubly-logarithmic factor. D. A. Goldston, S.W. Graham, J. Pintz, C.Y. Yilidirm: Small gaps between primes or almost primes http://arXiv.org/abs/math.NT/0506067 proves some results on small gaps between primes and between {primes U P2's}. It is trying (but failing) to prove an infinity of twin primes exists. Chen had proved there are infinitely many primes p with p+2 being either a prime or product of two primes. I however am not interested in shrinking the smallest gaps, but rather the largest gaps. The above paper does not discuss the latter.

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Re: [math-fun] Junk DNA allegedly isn't. Big change in standard picture of life.
by Henry Baker 07 Sep '12

07 Sep '12

See point-by-point, below. At 04:54 PM 9/6/2012, Warren Smith wrote: >> From: Henry Baker <hbaker1(a)pipeline.com> >> Re biological Rube Goldberg: >> I disagree vehemently. The more I learn of DNA, RNA, proteins, signalling, >> etc., the more impressed I am. >> For example, the process of mere _copying_ of DNA operates very close to the >> thermodynamic limit -- i.e., it would be very difficult to design _any_ >> system for copying DNA that produced less waste heat than our own DNA >> copying. > >--Exactly wrong. DNA copying is done with rechecking and with use of >ATP->AMP not ADP so it can get extra certainty. In other words it >intentionally uses both extra energy and extra chemical steps. Silly me, relying on papers by Bennett, etc. Yes, there is an energy cost in doing accurate copying, but it can be made smaller by working more slowly, and not doing irreversible operations at every step. >Many biochemical reactions in fact ARE reversible (e.g. fructose <--> >glucose interconversion) and hence consume zero energy. But DNA >copying is not one of them. > >> If our DNA copying were any less thermodynamically efficient, and we >> continued to copy at the same rate, our dividing cells would fry themselves >> like a fried egg. > >--utter bull. DNA copying is a very small expenditure in human cells >compared to other stuff. > >> Most evolutionary biologists will tell you that _none_ of the DNA is truly >> "junk". The proof: if it weren't important, it would relatively quickly >> disappear after a few generations. > >--complete bull. DNA actually is expensive in bacteria and viruses, >and they have little or no junk. But in eukaryotes like us, DNA is a >tiny expenditure relatively speaking so we can afford lots of junk. >By the way, you just "proved" microsoft windows is small and compact, >not bloated. I'm certainly no fan of Microsoft or SW bloating, but the number of bits in human DNA -- on the order of 2^32 -- is incredibly small in comparison with the complexity of the human that is produced. In the near future, we'll be in a position to start randomly (or not so randomly) deleting DNA from mammals to see what the "minimal mammal" is. Of course, just like a random user of Microsoft Windows, we have no idea what insults from the past were alleviated by some particular piece of DNA. In the language of computers, we don't have access to Microsoft's "test suite", that exercises every portion of Windows to make sure that any change in one area doesn't break some other portion of Windows code. So without a _complete_ test suite, we won't be able to determine what is "junk" DNA and what isn't. The bottom line is this: there is clearly strong evolutionary pressure against carrying around too much DNA, because there appear to be very strong reasons for copying the _entire_ DNA into _every_ cell. Since this cost is borne by every single cell on every cell division, the time & energy needed to do a cell division is compromised by having to reproduce too much DNA. It is possible that this idea of having to copy the entire Microsoft Windows system onto every PC in a cluster is not optimum, but nature has so far found this strategy to be extremely robust. This definitely reduces communication costs during the organism's growth & development, and does offer the opportunity for cells--e.g., skin cells--to revert into stem cells again, as has recently been shown. >> Several biologists have proposed that complex organisms have lots of DNA as >> a form of "diagonalization": all of its siblings with less DNA didn't >> survive. This is akin to comparing the power of Turing Machines with more >> or less tape: those with "more" tape can simulate _all_ Turing Machines with >> "less" tape and do something different. > >--you are totally confused. (And if you are right re "several biologists", >they are confused too.) Basically, an organism with more bits of DNA can have more complex behavior than and organism with fewer bits of DNA, and in particular, the organism with more DNA bits can defend against any suite of attacks by organisms with fewer DNA bits. >> For example, some of our DNA encodes experiences with viruses, some of which >> may be long extinct or at least dormant. Yet if that virus suddenly shows >> up, there are at least some fraction of humans that will survive. > >--some of our DNA encodes viruses that incorporated themselves into >our DNA and are now carried along for the ride for free inside us, >where they are incurable since part of us. Yes, viruses can become part of our DNA -- there are a large number of these. But the presence of these viruses also proves that we were successful against them, else we wouldn't be around to still be carrying them. They are sort of "merit badges". They might also be seeds for useful capabilities that we are using now -- e.g., recognizing them or producing some of the proteins that they would have produced. >Further, some our DNA is "self replicating elements" which in fact >multiply WITHIN our DNA; they are "out for themselves" not you. >Somewhat like cancer but at a smaller >size and longer time scale. This is (I suspect) the main reason >closely related species have way different amounts of junk and that >much of our junk is repeating sequences. > >> Plants (which typically don't move) seem to require more DNA than animals >> (which do move). One can speculate that plants have to sit there and take >> every insult, while animals can avoid the insult by moving and even >> emigrating when necessary. > >--plants do a lot more chemistry than animals, so they need more genes >(which describe chemistry). You can't synthesize many amino acids, fats, >and vitamins you need because you lack the genes. Plants do not have that luxury. >Animals can't do photosynthesis, even though it'd clearly be beneficial if they could. I think that the jury is still out on this one. I believe that there have already been experiments showing that photosynthesis is not incompatible with being an animal. I think the big problem with animal photosynthesis is the same reason that putting solar cells on a car is a huge waste of time: there simply isn't enough surface area on a car to make enough electricity to be useful. I would imagine that animals get mutations all the time that lead in the direction of photosynthesis, but since it doesn't improve the animal's life in any way, the mutations immediately get lost. Animals that can store & utilize energy in the form of fat have a huge advantage (nearly 2:1) over the storage of energy in the form of sugars. When you're a warm-blooded mammal, whose basal metabolic rate is upwards of 50% of the animals total daily energy expenditure, fat is clearly the way to go. Energy from photosynthesis at that point is a complete joke. >--In this post I am repeating the usual bio- philosophy & refuting >weird myths posted by HB. The alleged new "it aint junk" philosophy to some extent must overthrow the old >bio philosophy, but I'd like to know what is wrong with the old arguments, because they sure mostly are not wrong.

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Re: [math-fun] non-junk DNA: junk science?
by Dave Dyer 06 Sep '12

06 Sep '12

The whole biochemistry of life is the most complex Rube Goldberg system in the known universe. Anything that doesn't break the machine completely is just carried along in the next generation of the design, and every eon or so a closet full of "junk" gets opened and a new use is found for the stuff. One of the main mechanism in evolution is accidentally duplicating a bunch of stuff, which creates spare copies that are not really need. These spares are free to become nonfunctional, and then to acquire new functions, given geologic time.

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Re: [math-fun] Continued fraction for exp(3)
by Allan Wechsler 06 Sep '12

06 Sep '12

For some reason I find this remarkable. It suggests the question: how does one go about searching for interleaved polynomial sequences? On Thu, Sep 6, 2012 at 3:53 PM, Jeffrey Shallit <shallit(a)uwaterloo.ca>wrote: > As far as I know, nothing is known. I computed thousands of partial > quotients 30 years ago, but there was no simple pattern I could detect. > > > On 9/5/12 3:17 PM, Allan Wechsler wrote: > >> What is known about the simple continued fraction expansion of exp(3)? >> Obviously we can generate it fairly easily, but I want to know if there >> are >> any known patterns or periodicities in the terms. I thought exp(3) was a >> known Hurwitz number (continued fraction consists of interleaved >> polynomials) but I can't see any obvious patterns. >> ______________________________**_________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun> >> >>

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[math-fun] Continued fraction for exp(3)
by Allan Wechsler 06 Sep '12

06 Sep '12

What is known about the simple continued fraction expansion of exp(3)? Obviously we can generate it fairly easily, but I want to know if there are any known patterns or periodicities in the terms. I thought exp(3) was a known Hurwitz number (continued fraction consists of interleaved polynomials) but I can't see any obvious patterns.

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[math-fun] non-junk DNA: junk science?
by Warren Smith 06 Sep '12

06 Sep '12

well, since some math-funners seem actually to know something about this, maybe you can answer these questions: 1. if 75% of your genome is "used" in the sense of transcribed into RNA occasionally... so what? Maybe that RNA is simply discarded, so it is not only "junk" is it "a waste" too? How do they know that RNA actually does anything important (and how do they know what percentage of it does something important)? 2. how do the "it isn't junk" advocates explain the fact that closely related species have vastly different amounts of junk? Like 10 or maybe even 100 times as much for frog A versus frog B? 3. Re that experiment with ASCII strings in your programs, a better analogy might be this. The "important" bits in your programs are those such that, if you change that bit, then your program when run, becomes greatly dysfunctional. In THAT sense, is it not still the case, that the vast majority of your DNA is unimportant? For example I think it was estimated you have about 60 point mutations versus your parental DNA, but you are fine, suggesting the important stuff is fraction 1/60 or so (or less). And if so, how do the "it isn't junk" advocates defend themselves?

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Re: [math-fun] Junk DNA allegedly isn't. Big change in standard picture of life.
by Henry Baker 06 Sep '12

06 Sep '12

When I first heard about "junk" DNA about 20-25 years ago, I did a little experiment. I computed what % of my computer programs consisted of ASCII (now UNICODE) strings. (I seem to recall that the Unix function "strings" printed out anything in a binary program that looked like an ascii string.) Voila, about the same % of my computer program was "junk" as was "junk" DNA; only a small % of my program actually transcoded into printable characters. (I'm still waiting for that midnight call from Sweden...) At 07:54 PM 9/5/2012, Michael Kleber wrote: >The Times article is pretty deceptive: anyone involved in actual biology >has known that the non-coding regions of DNA that journalists have enjoyed >calling "junk" actually has important functions. ENCODE really is a >breakthrough, but it's in understanding details of how expression-switching >mechanisms work. The deep conceptual shift to the realization that all the >rest of our DNA was actually important happened two decades ago. > >(To be clear, I'm just bashing on the journalism here; the science is incredible.) > >--Michael > >On Wed, Sep 5, 2012 at 9:43 PM, Warren Smith <warren.wds(a)gmail.com> wrote: > >> About 98% of the human genome was thought "junk." >> It was not genes (transcribed to make proteins). Humans have only about 25K genes. >> The junk often consisted of short repeating sequences. >> >> http://www.nytimes.com/2012/09/06/science/far-from-junk-dna-dark-matter-pro… >> >> NY Times today reporting on the gazillion dollar, gazillion author, ENCODE project >> claims the junk contains on the order of 4M "switches" which >> help regulate gene expression/not. It is analogous to a spaghetti-wiring circuit >> with 4M transistors, whose purpose is to control 25K real numbers. >> >> This greatly changes the whole "standard picture" of how life works. The old picture was >> few genes, each with some nearby regulatory elements, like islands in an ocean of >> useless junk DNA. The new picture is not as clear... but they claim about 50-80% >> of your DNA is "used" meaning "gets transcribed onto RNA" (but usually NOT transcribed >> further into protein) and the usage levels vary by a factor of 10^6. >> >> http://en.wikipedia.org/wiki/ENCODE >> >> http://www.ncbi.nlm.nih.gov/geo/info/ENCODE.html >> >> http://www.nature.com/nature/journal/v489/n7414/full/nature11233.html >> >> http://www.nature.com/nature/journal/v489/n7414/full/nature11247.html >> >> -- >> Warren D. Smith >> http://RangeVoting.org <-- add your endorsement (by clicking >> "endorse" as 1st step)

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[math-fun] Junk DNA allegedly isn't. Big change in standard picture of life.
by Warren Smith 06 Sep '12

06 Sep '12

About 98% of the human genome was thought "junk." It was not genes (transcribed to make proteins). Humans have only about 25K genes. The junk often consisted of short repeating sequences. http://www.nytimes.com/2012/09/06/science/far-from-junk-dna-dark-matter-pro… NY Times today reporting on the gazillion dollar, gazillion author, ENCODE project claims the junk contains on the order of 4M "switches" which help regulate gene expression/not. It is analogous to a spaghetti-wiring circuit with 4M transistors, whose purpose is to control 25K real numbers. This greatly changes the whole "standard picture" of how life works. The old picture was few genes, each with some nearby regulatory elements, like islands in an ocean of useless junk DNA. The new picture is not as clear... but they claim about 50-80% of your DNA is "used" meaning "gets transcribed onto RNA" (but usually NOT transcribed further into protein) and the usage levels vary by a factor of 10^6. http://en.wikipedia.org/wiki/ENCODE http://www.ncbi.nlm.nih.gov/geo/info/ENCODE.html http://www.nature.com/nature/journal/v489/n7414/full/nature11233.html http://www.nature.com/nature/journal/v489/n7414/full/nature11247.html -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] angoskepsis
by Bill Gosper 05 Sep '12

05 Sep '12

What happens when a plastic bucket is placed upright in a pool, as a function of how much water was in it? It's surprisingly complicated. A standard 10 qt, flat bottom bucket, density 1+ε, floated perfectly upright when empty, but leaned rapidly in proportion to the amount of added water, finally reaching a tipping point, where it sank. OtOH, it floats upright when lowered in nearly full to begin with, and eventually sinks with additional water. But when Neil tried it with a 5 gal bucket, density 1-ε, with nearly vertical sides, the rim stayed just above water at the tipping point, and it gradually righted with additional water. (And never quite sank due to its low density.) Both of these experiments were biased slightly toward tipping by the weight of the bails, but probably not significantly. The 10 qt experiment had a metal bail and needs to be repeated with more control. --rwg

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