Purely empirical observation, in my own life, make no claim as to humanity/society/etc.:
It's interesting how often fermi estimation problems are used as proxy's for "intelligence". Something like: 'let's assess how well "they can think" - how many golf balls fit in a baseball stadium?' etc.
Often, doing well in these kinds of problems can more than makeup for a lack of specific knowledge in something someone is interested in assessing!
I’ll simplify for manhattan and extrapolate for the four outer boroughs. Ten avenues, a hundred streets. A thousand blocks? One cab per block? One thousand cabs in manhattan? 5,000 total?
I found it weirdly hard to Google an answer on this. Firstly, rates are given in terms of decays per second instead of in half-life which would be more relevant for our purposes. Secondly, it seems to be well studied in the interstellar medium than in atmospheric conditions.
Anyway, the most relevant measurements I could find [0] say photodisassociation of N2 in the interstellar medium happens at a rate of approximately 10^-10 s^-1 - i.e. every 10 billion seconds on average.
Caesar died about 60 billion seconds ago [1] so at that rate, many of the molecules would still be alive.
However, we don't live in the interstellar medium. By interstellar standards, we pretty much live on the surface of the sun. The average point in the ISM is maybe 2 light years from the nearest star [2] but we are only 10^-5 ly away. They're all the same photons, but radiation intensity diminishes with the square of the distance, so our nitrogen molecules should disassociate every 1 second instead. If that's true, Caesar's last breath had its last surviving molecules persist for only a minute or two after Caesar himself.
True, but I think that only occurs in the upper atmosphere and at a very low rate. Atmospheric N2 is also converted by bacteria into ammonia, which is absorbed by plants. And lightning oxidizes N2, as do combustion engines. I'm not sure if all those different reactions add up to a significant fraction, though. It might be true that most of the N2 molecules from Caesar's time still exist.
isnt the half life of most types of molecules in air far shorter than 2k years? maybe i am nitpicking, but would it not be more to correct to say we are breathing the same atoms as those in caesers last breath?
edit: itchy trigger finger, think i subconsciously wanted to be the first to comment. it is stated quite early that molecules preservation is assumed. still think it would be more correct and just as interesting to discuss atoms, not molecules.
edit 2: quick research has taught me that nitrogen gas, n2, and naturally occurring isotopes do not even have a half life. they do not radioactively decay. til.
I have seen the similar assertion "some of the water molecules you drank today were once part of a dinosaur", which is false because water molecules do not last very long when in liquid phase (they continuously swap protons, turning into hydronium ions and back).
The O-O and N-N bonds are much stronger than H-O bonds, but there are still atmospheric processes that can break them. For instance, O2 undergoes photodissociation under ultraviolet light and recombines into O3 ozone, and N2 likely also undergoes photodissociation. And obviously, the fact that living beings breathe O2...
The atmosphere is estimated to have ~830PgC worth of CO₂, and plants are estimated to photosynthesize ~120PgC worth of CO₂ every year, so a given molecule would have 14% chance to be broken down in a year. The probability to survive for 2000 years would be around 1e-60.
Of course, CO₂ contents of the atmosphere have varied over the last 2000 years, and not all CO₂ is produced into or consumed from the atmosphere (it can be dissolved in surface water, etc).
EDIT: since there's much more O₂ than CO₂ in the atmosphere, a given O₂ molecule has a 8% chance to not be broken down by respiration over 2000 years.
Why quarks? There are untold bazillions of those inside each proton, and there's no quark conservation law (rather than conservation of (for example) isospin and strangeness, but only under electromagnetism not under weak interactions, so quark counts get furiously complex in bigger nuclei).
For a single proton, though, one always measures (with available measurement technology) a small excess of quarks: two excess up quarks and one excess down quark. That the valence quark model of hadrons works is weird. Who ordered that?
The excess quarks are not "the same" quarks every time you probe your carefully selected and isolated and cold sample proton. Indeed, today's valence quarks in your pet proton are not guaranteed to exist tomorrow, even if the proton stays trapped -- particle creation and annihilation are furious inside, and there are all sorts of other disturbances of quarks that go on in there.
Why atoms? While much calmer, there's still plenty of crazy stuff happening in atoms -- even a neutral hydrogen atom has a bunch of photons and positrons and excess electrons floating around "inside", with an energy fraction proportional to the fine structure constant and with no guarantees that they were there yesterday. Is it the "same" atom at that level? Also, for most of the hydrogen in an exhalation, it probably will be in and out of various electron-swapping configurations over the years. Water gets pretty crazy with its ions, for example.
What's the 'half-life' you're thinking of? Your basic gas molecules will last a lot longer than 2k years short of being involved in some reaction or another. And a lot of these reactions aren't that easy in atmospheric conditions- e.g. pulling nitrogen out of the atmosphere https://en.wikipedia.org/wiki/Nitrogen_cycle
> would it not be more to correct to say we are breathing the same atoms as those in caesers last breath?
You may be right, but according to quantum mechanics, you can't really meaningfully talk about the "same" atoms, or any particles, because they don't have identities. There was a particle here, now there's a particle there, but we can't say exactly where it was at all the times in between, and it may not have been at any particular place: its amplitudes may have passed through two doors at once.
indeed it seems so, i thought all atoms (except hydrogen) had some kind of decay. i thought so called stable atoms still had half-lives of 10^{very large number} years.
Also, bismuth was once thought to be the most massive "fully" stable element, but turns out does decay with a half life of 10^19 years, compared to the universe's age of ~10^10 years.
Neutrons decay into a proton/electron pair after 15 minutes when not part of a nucleus.
Protons appear to be fully stable for any practical considerations, however they might decay after 10^30 years.
In this scenario, you can think of a reaction as terminating a molecule's life. So if there's a 50% chance that an H2O (or CO2) molecule reacts in a certain period, that could be its half-life time.
If we're talking about these kinds of scales, N2 molecules are not stable because there's a non-zero probability for the atoms to fuse into a heavier element through tunneling. And this will release more than enough energy to break the chemical bonds, of course.
How many breaths do I have to take, to pull in an oxygen atom that used to be part of a dinosaur, and was also in Caesar’s last breath? Could we turn this number into a unit of measure, so we can name it the…Caesaur? Caesarasaur?
But do the molecules really disperse like that? The molecules were all in Caesar's mouth before he released them in his last breath. Is the movement of molecules such that they are now, roughly 2000 years later, about equally spread around the Earth? Is there more of them in Rome? In Italy? In the norther hemisphere?
Not gas dispersion, but it's crazy how fast some compounds can disperse in the human circulatory system when introduced by IV. If you've ever had IV saline flush you may know that metallic taste that seems to show up in your mouth almost instantly.
Similarly, there is a sensation from Adenosine for chemical cardioversion that creates a hot flushing feeling inside your body as it spreads, and it's quite the sensation to feel it going from your chest down to your extremities in a few seconds.
2k years is a long time for gas dispersion in such a "small" volume as the earth's atmosphere. early weather behaviour probably affected the distribution unevenly, but by now it should be relatively evenly distributed across the globe. no more or less in rome or italy. this is, however, as we say in sweden, a "guy's guess".
It depends where you are. If you live in Italy, assuming dispersion makes the estimate more conservative (ie the assumption that it has dispersed means there is less of caesar's breath near you than the alternative) but if you live in Australia, it is less conservative (ie dispersion favours there being caesar breath near you).
I think the contention is that I don't have an intuition for how molecules actually disperse, but I do know that general climate trends certainly aren't "random dispersion".
Ex - we see consistent, long term, patterns in weather that make it unlikely that this dispersion is anything close to "ideal gas in a chamber" style dispersion.
Further - we have all sorts of compounding effects. Ex - atmospheric escape is a real thing, plants do nitrogen fixation, hydrogen and oxygen can be bound up in the oceans, etc...
Maybe 2000 years is enough time for real random dispersion, maybe it's not. But it's a huge assumption baked into this that doesn't feel especially reasonable to me.
All we have is this:
>If we assume that a breath diffuses evenly throughout the atmosphere and that these molecules are preserved over time (a reasonable assumption—nitrogen is relatively inert)
Which... I challenge is likely not a particularly reasonable assumption to base this on.
It's still an atmosphere mostly made of nitrogen, on a scale vastly exceeding 2000 years.
I don't have an intuition for how molecules actually disperse, but I do know that general climate trends certainly aren't "random dispersion".
Big volcano eruptions make for pretty sunsets across the world. Nuclear testing fallout is detectable in everything since atmospheric nuclear testing began. Everywhere we find the K-P boundary, we find iridium. The counter-assumption (which may well be true!) is the counter-intuitive one.
The jetstream moves north and south over the US in somewhat predictable ways each year. But the molecules in the jetstream never stop flowing, and the jetstream tends to diverge after it reaches the Atlantic ocean. Sometimes it does another tight lap around the artic circle, sometimes it veers down towards Africa, sometimes it splits and goes both ways:
The jetstream blows at around 110 mph, and Earth's circumference at mid-northern latitudes is around 12500 miles, so it takes 12500/110=114 hours or just under 5 days for the jets to complete a lap around the planet, assuming we choose a molecule that doesn't take a diverging path on that lap. That's 73 laps per year, so 2000 years is nearly 150,000 times that the faster parts of the atmosphere have circled the globe, twisting, breaking, and reconnecting paths the whole time.
technically, the diminutive τεκνίον would be more appropriate in this context. Teknon was more formal, and in its colloquial usage was used commonly in the stereotyped phrase "women and children", which in the ancient world was a symbol of low social status. The diminuative would indicate a different usage, more affectionate, friendly, etc.
Well actually, air molecules (N2, O2) are indistinguishable. This means that they are fundamentally interchangeable with each other and it’s not well defined what ”same” molecules mean. You can’t label the individual molecules.
It’s of course possible to track a single molecule if you really try hard. But this hasn’t been done since Caesar's time and the molecules have mixed. Even if we knew the exact state of the universe right now and could play back time perfectly it would be impossible to say that some particular molecules were part of his last breath.
It's interesting how often fermi estimation problems are used as proxy's for "intelligence". Something like: 'let's assess how well "they can think" - how many golf balls fit in a baseball stadium?' etc.
Often, doing well in these kinds of problems can more than makeup for a lack of specific knowledge in something someone is interested in assessing!
There are about 13,500 taxi medallions.
> If we assume that ... these molecules are preserved over time (a reasonable assumption—nitrogen is relatively inert),
But they are not inert. Single UV photon can break single N2 molecule bond.
Elemental N is highly reactive and will form new N2 molecule pretty fast, but that is NEW and different molecule!
N2 is not stable over period of 2000 years under constant exposure to solar UV radiation!
So what's the rate of this photodisassociation?
I found it weirdly hard to Google an answer on this. Firstly, rates are given in terms of decays per second instead of in half-life which would be more relevant for our purposes. Secondly, it seems to be well studied in the interstellar medium than in atmospheric conditions.
Anyway, the most relevant measurements I could find [0] say photodisassociation of N2 in the interstellar medium happens at a rate of approximately 10^-10 s^-1 - i.e. every 10 billion seconds on average.
Caesar died about 60 billion seconds ago [1] so at that rate, many of the molecules would still be alive.
However, we don't live in the interstellar medium. By interstellar standards, we pretty much live on the surface of the sun. The average point in the ISM is maybe 2 light years from the nearest star [2] but we are only 10^-5 ly away. They're all the same photons, but radiation intensity diminishes with the square of the distance, so our nitrogen molecules should disassociate every 1 second instead. If that's true, Caesar's last breath had its last surviving molecules persist for only a minute or two after Caesar himself.
[0] https://www.aanda.org/articles/aa/full_html/2013/07/aa20625-... https://www.aanda.org/articles/aa/full_html/2013/07/aa20625-...
[1] https://math.answers.com/math-and-arithmetic/How_many_second...
[2] https://www.livescience.com/space/how-far-apart-are-stars
edit: itchy trigger finger, think i subconsciously wanted to be the first to comment. it is stated quite early that molecules preservation is assumed. still think it would be more correct and just as interesting to discuss atoms, not molecules.
edit 2: quick research has taught me that nitrogen gas, n2, and naturally occurring isotopes do not even have a half life. they do not radioactively decay. til.
The O-O and N-N bonds are much stronger than H-O bonds, but there are still atmospheric processes that can break them. For instance, O2 undergoes photodissociation under ultraviolet light and recombines into O3 ozone, and N2 likely also undergoes photodissociation. And obviously, the fact that living beings breathe O2...
I don't know how often the average water CO₂/H₂O molecule gets dismantled this way, but there can't be many left since 44 BC.
Of course, CO₂ contents of the atmosphere have varied over the last 2000 years, and not all CO₂ is produced into or consumed from the atmosphere (it can be dissolved in surface water, etc).
EDIT: since there's much more O₂ than CO₂ in the atmosphere, a given O₂ molecule has a 8% chance to not be broken down by respiration over 2000 years.
https://profmattstrassler.com/articles-and-posts/largehadron...
For a single proton, though, one always measures (with available measurement technology) a small excess of quarks: two excess up quarks and one excess down quark. That the valence quark model of hadrons works is weird. Who ordered that?
The excess quarks are not "the same" quarks every time you probe your carefully selected and isolated and cold sample proton. Indeed, today's valence quarks in your pet proton are not guaranteed to exist tomorrow, even if the proton stays trapped -- particle creation and annihilation are furious inside, and there are all sorts of other disturbances of quarks that go on in there.
Why atoms? While much calmer, there's still plenty of crazy stuff happening in atoms -- even a neutral hydrogen atom has a bunch of photons and positrons and excess electrons floating around "inside", with an energy fraction proportional to the fine structure constant and with no guarantees that they were there yesterday. Is it the "same" atom at that level? Also, for most of the hydrogen in an exhalation, it probably will be in and out of various electron-swapping configurations over the years. Water gets pretty crazy with its ions, for example.
You may be right, but according to quantum mechanics, you can't really meaningfully talk about the "same" atoms, or any particles, because they don't have identities. There was a particle here, now there's a particle there, but we can't say exactly where it was at all the times in between, and it may not have been at any particular place: its amplitudes may have passed through two doors at once.
Also, bismuth was once thought to be the most massive "fully" stable element, but turns out does decay with a half life of 10^19 years, compared to the universe's age of ~10^10 years.
Neutrons decay into a proton/electron pair after 15 minutes when not part of a nucleus.
Protons appear to be fully stable for any practical considerations, however they might decay after 10^30 years.
Yes, I would agree. Perhaps too many. But it's a fun exercise.
Similarly, there is a sensation from Adenosine for chemical cardioversion that creates a hot flushing feeling inside your body as it spreads, and it's quite the sensation to feel it going from your chest down to your extremities in a few seconds.
2k years is a long time for gas dispersion in such a "small" volume as the earth's atmosphere. early weather behaviour probably affected the distribution unevenly, but by now it should be relatively evenly distributed across the globe. no more or less in rome or italy. this is, however, as we say in sweden, a "guy's guess".
Ex - we see consistent, long term, patterns in weather that make it unlikely that this dispersion is anything close to "ideal gas in a chamber" style dispersion.
Further - we have all sorts of compounding effects. Ex - atmospheric escape is a real thing, plants do nitrogen fixation, hydrogen and oxygen can be bound up in the oceans, etc...
Maybe 2000 years is enough time for real random dispersion, maybe it's not. But it's a huge assumption baked into this that doesn't feel especially reasonable to me.
All we have is this:
>If we assume that a breath diffuses evenly throughout the atmosphere and that these molecules are preserved over time (a reasonable assumption—nitrogen is relatively inert)
Which... I challenge is likely not a particularly reasonable assumption to base this on.
It's still an atmosphere mostly made of nitrogen, on a scale vastly exceeding 2000 years.
I don't have an intuition for how molecules actually disperse, but I do know that general climate trends certainly aren't "random dispersion".
Big volcano eruptions make for pretty sunsets across the world. Nuclear testing fallout is detectable in everything since atmospheric nuclear testing began. Everywhere we find the K-P boundary, we find iridium. The counter-assumption (which may well be true!) is the counter-intuitive one.
https://en.wikipedia.org/wiki/File:Aerial_Superhighway.ogv
The jetstream blows at around 110 mph, and Earth's circumference at mid-northern latitudes is around 12500 miles, so it takes 12500/110=114 hours or just under 5 days for the jets to complete a lap around the planet, assuming we choose a molecule that doesn't take a diverging path on that lap. That's 73 laps per year, so 2000 years is nearly 150,000 times that the faster parts of the atmosphere have circled the globe, twisting, breaking, and reconnecting paths the whole time.
But on the other 9 breaths, you get to breath quite a lot of his other farts... So... your breath is really never Caesar-fart-free.
But as a consolation, most of humanity will breath your farts on every breath, so...
In other words, let’s hand-wave away the most interesting part of the question, and then come up with a trivial answer to whatever’s left.
It’s of course possible to track a single molecule if you really try hard. But this hasn’t been done since Caesar's time and the molecules have mixed. Even if we knew the exact state of the universe right now and could play back time perfectly it would be impossible to say that some particular molecules were part of his last breath.