Well I just had to try it on Claude 4.0, I mean somebody has to, right? and it did a clean, if rather terse, breakdown, concluding with:
Caesar's last breath: ~0.5 liters (typical final exhale)
Total atmospheric volume: Earth's atmosphere has a mass of about 5×10^18 kg. Using the ideal gas law with average molecular weight of air (~29 g/mol), this gives roughly 4×10^44 molecules total.
Molecules in Caesar's breath: 0.5 liters at standard conditions contains about 1.3×10^22 molecules.
Your inhale: ~0.5 liters also contains about 1.3×10^22 molecules.
The fraction: Caesar's molecules represent (1.3×10^22)/(4×10^44) = 3.25×10^-23 of all atmospheric molecules.
Final answer:
(1.3×10^22) × (3.25×10^-23) ≈ 0.4 molecules
So statistically, you inhale less than one molecule from Caesar's last breath with each inhalation, but over the course of a day's breathing, you'd likely inhale several molecules that were once in his lungs as he died.
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?
That sort of estimation feels a lot easier to me than the "golf balls in a baseball stadium one" that was mentioned by the parent because it's dealing with quantities I can recall having heard before like "how many streets are there in Manhattan" rather than measurements that personally would never stick in my head like "how wide is a golf ball". I'm not sure why, but I've always been awful at making even rough estimates of units. If you gave me the diameter of a golf ball and the dimensions of the stadium, I could do some basic calculations, but even though I physically know about how large a golf ball is, I couldn't tell you whether it's more likely that its diameter is 0.5 or 1.5" (and not having looked it up, I would believe you if you told me it wasn't even within that range)! This gets worse with units I can't visualize (like weight), and when the sizes get larger than I can easy relate to; if you asked me questions like how much a car weighs or how long the Brooklyn Bridge is, I'm doubtful I'd even be within a factor of 2 more often than not.
I'm probably taking this more seriously than it was intended above, but the idea that this is some sort of proxy for "thinking" or "intelligence" feels off to me; doing the math given the size of something might be thinking or intelligence, but knowing roughly "how big" something is seems more like intuition.
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.
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.
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
That's true for most timescales, however plants and other organisms fix nitrogen in the atmosphere into biologically useful molecules so nitrogen gets cycled in and out of the atmosphere. Similar things apply for carbon dioxide and oxygen.
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.
> 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.
> 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), then...
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".
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.
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).
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.
Well I just had to try it on Claude 4.0, I mean somebody has to, right? and it did a clean, if rather terse, breakdown, concluding with:
Caesar's last breath: ~0.5 liters (typical final exhale)
Total atmospheric volume: Earth's atmosphere has a mass of about 5×10^18 kg. Using the ideal gas law with average molecular weight of air (~29 g/mol), this gives roughly 4×10^44 molecules total.
Molecules in Caesar's breath: 0.5 liters at standard conditions contains about 1.3×10^22 molecules.
Your inhale: ~0.5 liters also contains about 1.3×10^22 molecules.
The fraction: Caesar's molecules represent (1.3×10^22)/(4×10^44) = 3.25×10^-23 of all atmospheric molecules.
Final answer: (1.3×10^22) × (3.25×10^-23) ≈ 0.4 molecules
So statistically, you inhale less than one molecule from Caesar's last breath with each inhalation, but over the course of a day's breathing, you'd likely inhale several molecules that were once in his lungs as he died.
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!
This reminds me of a question from my first interview as a college grad: estimate the number of taxis in New York City. I was totally baffled by it.
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?
There are about 13,500 taxi medallions.
That sort of estimation feels a lot easier to me than the "golf balls in a baseball stadium one" that was mentioned by the parent because it's dealing with quantities I can recall having heard before like "how many streets are there in Manhattan" rather than measurements that personally would never stick in my head like "how wide is a golf ball". I'm not sure why, but I've always been awful at making even rough estimates of units. If you gave me the diameter of a golf ball and the dimensions of the stadium, I could do some basic calculations, but even though I physically know about how large a golf ball is, I couldn't tell you whether it's more likely that its diameter is 0.5 or 1.5" (and not having looked it up, I would believe you if you told me it wasn't even within that range)! This gets worse with units I can't visualize (like weight), and when the sizes get larger than I can easy relate to; if you asked me questions like how much a car weighs or how long the Brooklyn Bridge is, I'm doubtful I'd even be within a factor of 2 more often than not.
I'm probably taking this more seriously than it was intended above, but the idea that this is some sort of proxy for "thinking" or "intelligence" feels off to me; doing the math given the size of something might be thinking or intelligence, but knowing roughly "how big" something is seems more like intuition.
> How many molecules from Caesar’s last breath do we inhale with each breath we take?
> 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!
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.
A really good point.
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
Air is 1% argon (9340 ppm) and those atoms remain in the atmosphere without being chemically removed.
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...
Photosynthesis breaks up CO₂ and H₂O molecules to make O₂ and C₆H₁₂O₆ (glucose).
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.
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.
People should instead say atoms, not molecules. Or maybe even say quarks.
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).
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.
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
I don't think so — Nitrogen, the most common part of air, is stable in its most common isotope
That's true for most timescales, however plants and other organisms fix nitrogen in the atmosphere into biologically useful molecules so nitrogen gets cycled in and out of the atmosphere. Similar things apply for carbon dioxide and oxygen.
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.
Maybe you saw this story recently?: https://phys.org/news/2025-05-universe-decay-years-sooner-pr...
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 you buy into the Big Rip, then all particles in the universe (including protons and neutrons) will eventually disintegrate
Stephen Baxter wrote a short story about such. It sticks with you.
https://web.archive.org/web/20080725045740/http://www.solari...
your post made me laugh because it makes the theory sound like propaganda that is sponsored by Big Rip
Big Bang, Big Rip, Big Crush. Cosmologists like Big Things.
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.
> 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.
> 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), then...
Way to take all the fun out of it..
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?
"Obviously, many simplifying liberties were taken."
Yes, I would agree. Perhaps too many. But it's a fun exercise.
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.
Wait hang on. Is it possible the metallic taste after a flu vaccine is the saline?
i believe so, https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_dist....
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".
The dispersion assumption tends to make the estimate more rather than less conservative.
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.
we have all sorts of compounding effects.
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:
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.
Long term climate patterns are much slower than dispersion.
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).
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doesn't this assume both the external layer of the atmosphere and all of the earth to be impermeable to breath molecules?
This is sn oldie but it beautifully illustrates orders of magnitude and how many atoms there really are.
I fell for it, I thought it was καὶ σύ, τέκνον (“you too, child”), to Brutus.
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.
Super neat. Did not expect the math to work.
Well now every salad is Caesar's salad
Estimation without any attempt to quantify the distribution of each of the components of the formula doesn't give me much confidence in the result.
What? There is 10ˆ22 breaths in the atmosphere? I guess the atmosphere is huge.
i guess this also means there are around 10^23 farts in the atmosphere. a quick empirical study just showed there around 10 farts to a breath.
Empirically, my buddies' farts seem to weigh in way above 0.1 breath.
So we're also breathing Caesar's last fart.
Well, once every 10 breaths on average.
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...
> If we assume that a breath diffuses evenly throughout the atmosphere and that these molecules are preserved over time
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.
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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.