[math-fun] Every breath you take
There's a popular science writing trope about how every breath you take contains atoms that were once breathed by X [or, for extra piquancy, in X's dying breath]. I think the one I saw in the late 1960s had X = Archimedes. My first question is, do any of you remember a specific source from the 1900s? (At https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone writes "Is it true that every time we take a breath of air or swallow a mouthful of water, we consume some of the atoms breathed or swallowed by Leonardo da Vinci (as I read in a children’s science book in 1960)?" but doesn't mention the source.) My second question is, what's the best writeup of this that you know? I just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last Breath", which I'm guessing will do a decent job of explaining the science. My third question is, how far back does this sort of observation go? Does it have an attributable original source? (Maybe Kean addresses this; it's a pretty thick book.) If the history of science has a subfield treating history of science popularization, and people do PhD's in it, maybe someone has tracked this trope in all its incarnations, showing how the choice of who gets to play the role of X reflects underlying cultural assumptions about significance and worth. Jim Propp
... Where did Leonardo (or X) sign the molecule he breathed? Is your question purely statistic? Best, É.
Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com> a écrit :
There's a popular science writing trope about how every breath you take contains atoms that were once breathed by X [or, for extra piquancy, in X's dying breath]. I think the one I saw in the late 1960s had X = Archimedes.
My first question is, do any of you remember a specific source from the 1900s? (At https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone writes "Is it true that every time we take a breath of air or swallow a mouthful of water, we consume some of the atoms breathed or swallowed by Leonardo da Vinci (as I read in a children’s science book in 1960)?" but doesn't mention the source.)
My second question is, what's the best writeup of this that you know? I just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last Breath", which I'm guessing will do a decent job of explaining the science.
My third question is, how far back does this sort of observation go? Does it have an attributable original source? (Maybe Kean addresses this; it's a pretty thick book.)
If the history of science has a subfield treating history of science popularization, and people do PhD's in it, maybe someone has tracked this trope in all its incarnations, showing how the choice of who gets to play the role of X reflects underlying cultural assumptions about significance and worth.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Yes, it's a statistical question (but given the magnitude of the numbers involved, one can be pretty sure in advance that the probability is either very close to 0 or very close to 1). Jim On Fri, Apr 3, 2020 at 8:07 AM Éric Angelini <bk263401@skynet.be> wrote:
... Where did Leonardo (or X) sign the molecule he breathed? Is your question purely statistic? Best, É.
Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com> a écrit :
There's a popular science writing trope about how every breath you take contains atoms that were once breathed by X [or, for extra piquancy, in X's dying breath]. I think the one I saw in the late 1960s had X = Archimedes.
My first question is, do any of you remember a specific source from the 1900s? (At https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone writes "Is it true that every time we take a breath of air or swallow a mouthful of water, we consume some of the atoms breathed or swallowed by Leonardo da Vinci (as I read in a children’s science book in 1960)?" but doesn't mention the source.)
My second question is, what's the best writeup of this that you know? I just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last Breath", which I'm guessing will do a decent job of explaining the science.
My third question is, how far back does this sort of observation go? Does it have an attributable original source? (Maybe Kean addresses this; it's a pretty thick book.)
If the history of science has a subfield treating history of science popularization, and people do PhD's in it, maybe someone has tracked this trope in all its incarnations, showing how the choice of who gets to play the role of X reflects underlying cultural assumptions about significance and worth.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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That raises the question of how big does something have to be in order to retain its identity over 500yrs? All nitrogen molecules are identical and their location spreads out per Schroedinger's equation so that one is indistinguishable from others whose wave-functions overlap. We can refer to a pen or a chair that Leonardo used, but not to an atom he breathed. Exactly, how objects gain and keep their classical character is part of the interpretation problem of quantum measurement. Brent On 4/3/2020 5:07 AM, Éric Angelini wrote:
... Where did Leonardo (or X) sign the molecule he breathed? Is your question purely statistic? Best, É.
Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com> a écrit :
There's a popular science writing trope about how every breath you take contains atoms that were once breathed by X [or, for extra piquancy, in X's dying breath]. I think the one I saw in the late 1960s had X = Archimedes.
My first question is, do any of you remember a specific source from the 1900s? (At https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone writes "Is it true that every time we take a breath of air or swallow a mouthful of water, we consume some of the atoms breathed or swallowed by Leonardo da Vinci (as I read in a children’s science book in 1960)?" but doesn't mention the source.)
My second question is, what's the best writeup of this that you know? I just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last Breath", which I'm guessing will do a decent job of explaining the science.
My third question is, how far back does this sort of observation go? Does it have an attributable original source? (Maybe Kean addresses this; it's a pretty thick book.)
If the history of science has a subfield treating history of science popularization, and people do PhD's in it, maybe someone has tracked this trope in all its incarnations, showing how the choice of who gets to play the role of X reflects underlying cultural assumptions about significance and worth.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Interesting point! One certainly can't "tag" a nitrogen atom and see where it ends up later. Nonetheless, my understanding is that the classical approximation to quantum physics is sufficiently close (and the natural decay of nitrogen nuclei sufficiently slow) that nitrogen atoms have a well-defined identity over human time-scales (even though nitrogen MOLECULES don't because of chemical processes). Am I wrong? Jim On Fri, Apr 3, 2020 at 3:03 PM Brent Meeker via math-fun < math-fun@mailman.xmission.com> wrote:
That raises the question of how big does something have to be in order to retain its identity over 500yrs? All nitrogen molecules are identical and their location spreads out per Schroedinger's equation so that one is indistinguishable from others whose wave-functions overlap. We can refer to a pen or a chair that Leonardo used, but not to an atom he breathed. Exactly, how objects gain and keep their classical character is part of the interpretation problem of quantum measurement.
Brent
On 4/3/2020 5:07 AM, Éric Angelini wrote:
... Where did Leonardo (or X) sign the molecule he breathed? Is your question purely statistic? Best, É.
Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com> a écrit :
There's a popular science writing trope about how every breath you take contains atoms that were once breathed by X [or, for extra piquancy, in X's dying breath]. I think the one I saw in the late 1960s had X = Archimedes.
My first question is, do any of you remember a specific source from the 1900s? (At https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone writes "Is it true that every time we take a breath of air or swallow a mouthful of water, we consume some of the atoms breathed or swallowed by Leonardo da Vinci (as I read in a children’s science book in 1960)?" but doesn't mention the source.)
My second question is, what's the best writeup of this that you know? I just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last Breath", which I'm guessing will do a decent job of explaining the science.
My third question is, how far back does this sort of observation go? Does it have an attributable original source? (Maybe Kean addresses this; it's a pretty thick book.)
If the history of science has a subfield treating history of science popularization, and people do PhD's in it, maybe someone has tracked this trope in all its incarnations, showing how the choice of who gets to play the role of X reflects underlying cultural assumptions about significance and worth.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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how big does something have to be in order
to retain its identity over 500yrs?
... ahem -- I thought this debate was over since... at least the ship of Theseus! https://en.m.wikipedia.org/wiki/Ship_of_Theseus Our oldest (mine, yours) cell is 7 years old... Identity is not well defined (in general), it is a social construction, as we know. à+ É. Catapulté de mon aPhone Le 3 avr. 2020 à 21:42, James Propp <jamespropp@gmail.com> a écrit :
how big does something have to be in order to retain its identity over 500yrs?
You maybe right, although it's hard to do a useful calculation. If you imagine an N2 molecule localized (to it's own diameter) in the left nostril of Leonardo on his death bed 501 years ago, and you treat is as one massive particle (i.e. ignore degrees of freedom other than center-of-mass motion) then you can estimate that the uncertainty of its position will expand at 140m/s. So the uncertainty in it's position will exceed the mean-free-path (68e-9 m) in 500 nanoseconds; which I think is rough estimate of how long you could track a single molecule. Brent On 4/3/2020 12:42 PM, James Propp wrote:
Interesting point! One certainly can't "tag" a nitrogen atom and see where it ends up later. Nonetheless, my understanding is that the classical approximation to quantum physics is sufficiently close (and the natural decay of nitrogen nuclei sufficiently slow) that nitrogen atoms have a well-defined identity over human time-scales (even though nitrogen MOLECULES don't because of chemical processes). Am I wrong?
Jim
On Fri, Apr 3, 2020 at 3:03 PM Brent Meeker via math-fun <math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com>> wrote:
That raises the question of how big does something have to be in order to retain its identity over 500yrs? All nitrogen molecules are identical and their location spreads out per Schroedinger's equation so that one is indistinguishable from others whose wave-functions overlap. We can refer to a pen or a chair that Leonardo used, but not to an atom he breathed. Exactly, how objects gain and keep their classical character is part of the interpretation problem of quantum measurement.
Brent
On 4/3/2020 5:07 AM, Éric Angelini wrote: > ... Where did Leonardo (or X) sign the molecule he breathed? > Is your question purely statistic? > Best, > É. > > > >> Le 3 avril 2020 à 13:49, James Propp <jamespropp@gmail.com <mailto:jamespropp@gmail.com>> a écrit : >> >> >> There's a popular science writing trope about how every breath you take >> contains atoms that were once breathed by X [or, for extra piquancy, in X's >> dying breath]. I think the one I saw in the late 1960s had X = Archimedes. >> >> My first question is, do any of you remember a specific source from the >> 1900s? (At >> https://www.newscientist.com/article/mg15020308-500-the-last-word/ someone >> writes "Is it true that every time we take a breath of air or swallow a >> mouthful of water, we consume some of the atoms breathed or swallowed by >> Leonardo da Vinci (as I read in a children’s science book in 1960)?" but >> doesn't mention the source.) >> >> My second question is, what's the best writeup of this that you know? I >> just borrowed (in e-book form) Sam Kean's recent book "Caesar's Last >> Breath", which I'm guessing will do a decent job of explaining the science. >> >> My third question is, how far back does this sort of observation go? Does >> it have an attributable original source? (Maybe Kean addresses this; it's a >> pretty thick book.) >> >> If the history of science has a subfield treating history of science >> popularization, and people do PhD's in it, maybe someone has tracked this >> trope in all its incarnations, showing how the choice of who gets to play >> the role of X reflects underlying cultural assumptions about significance >> and worth. >> >> Jim Propp >> _______________________________________________ >> math-fun mailing list >> math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com> >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com> > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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There are different isotopes of nitrogen, with 2 particularly common: N-14 (~99.6%) and N-15 (~0.4%). Nitrogen molecules N2 have 3 versions with these 2 isotopes. So nitrogen isn't terribly interesting. Carbon is far more interesting, due to its ability to form complex molecules and solids (diamond, nanotubes, etc.). C-12 (~98.9%) and C-13 (~1.1%) are stable isotopes. Benzene, with 6 carbons, can have O(2^6) forms with different carbon isotopes (forget the hydrogen isotopes). Math geeks: exactly how many different benzene rings are there using C-12, C-13, H-1 ? Clearly, in order to retain "identity" for a long period of time, a diamond crystal would seem to be pretty decent for a larger object. One could conceivably "read out" this identity by utilizing some sort of laser configuration that could tweak a single atom in the crystal in order to determine its mass. A question I've asked here before, but never found a satisfying answer to, is "At a given absolute temperature T, what is the half-life before 2 carbon atoms exchange places in a diamond lattice?" Given quantum mechanics, such an exchange is possible, but presumably highly unlikely. Is such a time period longer or shorter than the time for a C-12 or C-13 atom to decay into non-carbon ? At 12:02 PM 4/3/2020, Brent Meeker via math-fun wrote:
That raises the question of how big does something have to be in order to retain its identity over 500yrs?
All nitrogen molecules are identical and their location spreads out per Schroedinger's equation so that one is indistinguishable from others whose wave-functions overlap.
We can refer to a pen or a chair that Leonardo used, but not to an atom he breathed.
Exactly, how objects gain and keep their classical character is part of the interpretation problem of quantum measurement.
Brent
On 4/3/2020 5:07 AM, Ãric Angelini wrote:
... Where did Leonardo (or X) sign the molecule he breathed?
The Oxford Dictionary of Quotations suggests James Jeans (1877-1946), English astronomer, physicist, and mathematician: "If we assume that the last breath of, say, Julius Caesar has by now become thoroughly scattered through the atmosphere, then the chances are that each of us inhales one molecule of it with every breath we take." An Introduction to the Kinetic Theory of Gases (1940).
"The Oxford Dictionary of Quotations suggests James Jeans ..." I believe J.E. Littlewood mentioned Jeans in the Mathematical Gazette in 1948 and this was included in his 1953 A Mathematician's Miscellany. From here infection would have been widespread.
participants (6)
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Brent Meeker -
Hans Havermann -
Henry Baker -
James Propp -
Éric Angelini -
Éric Angelini