Re: [math-fun] Diamonds for dopes
Veit Elser <ve10@cornell.edu> wrote:
Not sure what?s driving this discussion, or the fascination with carbon isotopes, ...
Perhaps it's slightly off-topic here, but I for one find it fascinating because it could hold all the world's knowledge (books, journals, movies, TV shows, newspapers, web pages, databases, letters, emails, security videos, genomes, paintings, etc.) in a crystal smaller than an ant, a crystal that should last for at least billions of years even with no special storage precautions. The longevity of the world's information is currently a major concern, everything from nitrate-based movie films from the early 20th century to computer tapes and diskettes from the late 20th century. Not to mention much older stuff. Henry Baker <hbaker1@pipeline.com> wrote:
Although I don't know enough quantum physics to do the calculation, my gut still tells me that the probability of exchanging an adjacent C12 for a C13 nucleus is non-negligible.
My gut tells me otherwise. :-) How do you think it would happen? Thermally? Without disrupting the extremely rigid lattice? Each carbon atom is at the center of a regular tetrahedron, with a covalent bond at each vertex. In general, the Arrehenius equation predicts reaction times of much more than trillions of years when applied at absolute temperatures that are small fractions of the temperatures at which the reaction proceeds at a reasonable rate. Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions. It could happen, but for diamond to spontaneously turn into graphite is far more likely -- and has never been observed, even though most natural diamonds are billions of years old. None of this has anything to do with *electron* delocalization, but there's little of that too. Pure diamond is an excellent electrical insulator, with a breakdown voltage of more than a million volts per millimeter. (It's a good conductor of heat, but that's due to phonons, not electrons.)
So I would guess that the probability of an adjacent C12<->C13 exchange would be dramatically improved with 100x atmospheric pressure, and floating on top of molten tungsten at 6500-7000 degrees F.
I agree. Of course the lattice would cease to exist first.
So the real question is: what is the falloff in exchange probability as we lower the temperature from 3500F to 100F ?
Apply the Arrhenius equation to find out.
On Mon, Jun 6, 2016 at 7:31 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:
Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions.
Actually, you just need to have a neutron tunnel from one nucleus to the other across the barrier. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
If we're going to store the entirety of human history & culture in a diamond lattice, it makes sense to ensure that the info won't degrade for a while, at least! "Diamonds are Forever!" Who could have ever doubted it? Here's some organizations that would be interested: https://archive.org/about/ http://longnow.org/ BTW, suppose that some civilization has *already* encoded its information in diamond & sent it Fed Ex (via meteorite drone) to Earth. Why are we wasting time with SETI instead of reading every diamond we find? Also, BTW, it looks like DNA data storage may be a lot closer to hand than C12/C13 diamond storage. Is there a way to somehow crystallize & stabilize DNA at room temp (or higher) for stable data storage over thousands of years? Alternatively, is there an error-correcting information coding scheme for DNA that "heals" itself automatically against evolutionary pressures so that we could store the DNA info in real biologic organisms -- e.g., bristlecone pines ? https://en.wikipedia.org/wiki/List_of_longest-living_organisms Perhaps some of this "noncoding DNA" is *already* a message from the past -- e.g., intelligent dinosaurs that were destroyed 65Mya. At 07:31 PM 6/6/2016, Keith F. Lynch wrote:
The longevity of the world's information is currently a major concern, everything from nitrate-based movie films from the early 20th century to computer tapes and diskettes from the late 20th century. Not to mention much older stuff.
Henry Baker <hbaker1@pipeline.com> wrote:
Although I don't know enough quantum physics to do the calculation, my gut still tells me that the probability of exchanging an adjacent C12 for a C13 nucleus is non-negligible.
My gut tells me otherwise. :-) How do you think it would happen?
Thermally? Without disrupting the extremely rigid lattice? Each carbon atom is at the center of a regular tetrahedron, with a covalent bond at each vertex. In general, the Arrehenius equation predicts reaction times of much more than trillions of years when applied at absolute temperatures that are small fractions of the temperatures at which the reaction proceeds at a reasonable rate.
Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions. It could happen, but for diamond to spontaneously turn into graphite is far more likely -- and has never been observed, even though most natural diamonds are billions of years old.
As long as we are considering the possibility of storing information in crystal lattices, we should spend a little time thinking about whether diamond is really the optimal medium. There are lots of kinds of crystals, after all. Perhaps we should prefer kinds where the relevant atoms are more easily distinguished than C12 and C13? Or kinds where the bits are bigger, and thus easier to engineer? DNA gives one possible idea: what about a three-dimensional polymer whose units are one of 256 different roughly-cubical "triple amino acids"? I'm imagining something with a COOH on three faces, and an NH2 on the opposite three faces, and somewhere in the middle a C-R group, with R having one of 256 values. (Or 2. Or 8. You know what I mean.) My overall point is that we have the freedom to choose a medium to suit ourselves, and diamond might not be the best. On Tue, Jun 7, 2016 at 10:33 AM, Henry Baker <hbaker1@pipeline.com> wrote:
If we're going to store the entirety of human history & culture in a diamond lattice, it makes sense to ensure that the info won't degrade for a while, at least!
"Diamonds are Forever!" Who could have ever doubted it?
Here's some organizations that would be interested:
BTW, suppose that some civilization has *already* encoded its information in diamond & sent it Fed Ex (via meteorite drone) to Earth. Why are we wasting time with SETI instead of reading every diamond we find?
Also, BTW, it looks like DNA data storage may be a lot closer to hand than C12/C13 diamond storage. Is there a way to somehow crystallize & stabilize DNA at room temp (or higher) for stable data storage over thousands of years?
Alternatively, is there an error-correcting information coding scheme for DNA that "heals" itself automatically against evolutionary pressures so that we could store the DNA info in real biologic organisms -- e.g., bristlecone pines ?
https://en.wikipedia.org/wiki/List_of_longest-living_organisms
Perhaps some of this "noncoding DNA" is *already* a message from the past -- e.g., intelligent dinosaurs that were destroyed 65Mya.
At 07:31 PM 6/6/2016, Keith F. Lynch wrote:
The longevity of the world's information is currently a major concern, everything from nitrate-based movie films from the early 20th century to computer tapes and diskettes from the late 20th century. Not to mention much older stuff.
Henry Baker <hbaker1@pipeline.com> wrote:
Although I don't know enough quantum physics to do the calculation, my gut still tells me that the probability of exchanging an adjacent C12 for a C13 nucleus is non-negligible.
My gut tells me otherwise. :-) How do you think it would happen?
Thermally? Without disrupting the extremely rigid lattice? Each carbon atom is at the center of a regular tetrahedron, with a covalent bond at each vertex. In general, the Arrehenius equation predicts reaction times of much more than trillions of years when applied at absolute temperatures that are small fractions of the temperatures at which the reaction proceeds at a reasonable rate.
Quantum tunneling? The distance between the centers of adjacent atoms in a diamond is 1.54E-10 meters. That's 57,000 times the 2.7E-15 meter radius of a carbon nucleus. And for it to happen, two nuclei would have to simultaneously tunnel into each other's positions. It could happen, but for diamond to spontaneously turn into graphite is far more likely -- and has never been observed, even though most natural diamonds are billions of years old.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
="Henry Baker" <hbaker1@pipeline.com> Perhaps some of this "noncoding DNA" is *already* a message from the past -- e.g., intelligent dinosaurs that were destroyed 65Mya.
See John Walker's 1989 short story, "We'll Return, After This Message" http://www.fourmilab.ch/documents/sftriple/gpic.html It's quite an amusing read from our vantage of 2016. ''Every human who'd turned his eyes skyward wondering, "Are we alone?" had been carrying the answer, all along, in every cell of his body.'' He makes the point that *coding* DNA is actually the better choice: ''Whoever wove that Message into our DNA meant it to last until we figured out how to read it‹it's built inextricably into the protein expression mechanism so any organism with a corrupted copy won't be viable. It's obvious in retrospect. If a visitor wants to leave a message, why not make it a self-reproducing, error-correcting message that any sentient race would stumble upon as soon as they undertook to reverse engineer their own design?'' Jellies Are Forever?
participants (5)
-
Allan Wechsler -
Henry Baker -
Keith F. Lynch -
Marc LeBrun -
Mike Stay