> 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
UV breakdown doesn't appear as a significant source in http://nmsp.cals.cornell.edu/publications/factsheets/factshe... although lightning does. So, if this mechanism is operating at a significant scale in Earth's atmosphere, it's escaped the attention of the scientists who specialize in the terrestrial nitrogen cycle, which seems implausible.
The ozone layer blocks around 99% of UV light [0], the earth about 50%. That's two orders of magnitude accounted for, but even a dissociation rate of every few hours seems too fast.
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.
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.
The ability to estimate within an order of magnitude or within 2X is vastly more valuable, and beyond being able to have a sense of whether the "official" answer is likely accurate or off by orders of magnitude.
During most of the process of designing anything in or that touches the physical world, you are using rough figures.
Taking time to get the fully accurate and precise answer for every question is a waste of time as you don't need that many decimals of precision to move forward. Every decimal of precision in the answer takes more time and there are MANY of those questions, so being 100% accurate in every answer does not scale.
Of course, when it gets to the end of the process, the accuracy & precision requirements increase, but the emphasis needs to be placed where needed, not everywhere.
Plus, you are not going to find the "official" and accurate number of golf balls in the particular school bus you want to model. You'll find some vaguely similar answer or set of sub-answers, so sure, those will be fully accurate and precise, but THEN you must take those as inputs for your estimate, and we're back to the skill of estimating being most critical.
Being able to estimate and do sound back-of-the-envelope calculations is the far more critical skill, at least on any team I'm building.
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.
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.
https://web.archive.org/web/20080725045740/http://www.solari...
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.
Yes, I would agree. Perhaps too many. But it's a fun exercise.
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.
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.
In simple terms cellular respiration involves
Sugar molecules (C6H12O6) reacting with oxygen molecules (O2) to produce Carbon Dioxide (CO2) and Water (H20).
Now a common misconception folks have from school is that the oxygen “turns into” carbon dioxide. This isn’t true. What actually happens is that the Hydrogen atoms from the sugar molecule eventually combine with the Oxygen molecule to produce water. The water is generated from hydrogen being accepted by the oxygen molecule. The carbon dioxide is what remains of the sugar molecules once the hydrogen has been removed.
Of course there are many steps in this process but this is broadly how cells generate energy. As you can see this process leads to the creation of molecules and the destruction of others.
Now let’s move away from the cell and towards the lungs more broadly.
During the act of breathing we breath in many molecules. Most of what we breath in is Nitrogen molecules which are inert and don’t do anything. We also breath many other molecules including oxygen, water, etc. Now not all the oxygen molecules we breath in enter the blood stream. Some will be expired out. When we breath out we also breath out those newly created carbon dioxide molecules I mentioned.
(It actually gets even more complicated because some of those carbon dioxide molecules get converted into other molecules that get removed through the urine).
Furthermore some of those water molecules that are created by our cells are also in the breath that we expire. It is important to keep the lungs moist. The breath we inspire is more humid than what we inspire. But it gets even more complicated. Because some of those water molecules being expired are created by our cells but others enter the body from the water we drink. Some of the water molecules our cells create leave in the urine or through our skin or through feces and some of those water molecules that leave from those areas are also those that enter the body from the water we drink.
So Caesar’s last breath happened thousands of years ago right? And we have countless animals and countless plants in all that time creating molecules and destroying them. Given all these animals and plants I would say that it stands to reason that these molecules either don’t exist or may no longer be in gaseous form.
And remember the nitrogen molecules I mentioned earlier? They are inert in our lungs but not inert in other parts of nature.
Anyway the point I’m making is that this question is more complicated because it’s doubtful a large chunk of Caesar’s Last breath’s molecules even exist anymore.
Way to take all the fun out of it..
A thing I'd like to know is how big the non-atmospheric reservoirs of nitrogen are. When nitrogen is "fixed" out of the atmosphere and into an ocean or a pile of bat guano, how long before it cycles back into the atmosphere, on average? A hundred years? A hundred million years? I'm pretty sure it's in that range because nitrate rocks are rare but used to support most of global agriculture, but I don't have a good idea of where it is in that range.
The total mass we are dealing with is far larger than the Earth's atmosphere.
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.