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Comment by saalweachter | Hacker News Reader

It's a shame that we entered the era of precision a century or so before we got some good science.

We could have chosen so many different, cooler distance units than "one ten-millionth the distance between the North Pole and the equator, on a line passing through Paris". We could have chosen 1 nano-lightsecond! We could have chosen the wavelength of the hydrogen line! We had options, but we didn't even know them in 1800.

Avogadro's number is about 3% off from 24!. Instead of defining our mole as the number of carbon-12 atoms equal in weight to 12 cubes of water each one-billionth the distance between the North Pole and the equator, on a line passing through Paris, on a side, we could have defined it as 4!!! Imagine telling that to aliens when explaining our standard units, they'd be so jealous they'd convert on the spot.

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More importantly, we missed a real opportunity to switch to a base-12 number system.

Now we have to wait for the French to have another revolution.

Liberté, égalité, duodecimilité!

And for people to start growing 6 fingers per hand instead of 5

Duodecimal also has a connection to counting on your fingers.

You've got twelve finger bones/joints. Move your thumb from one to the next as you increment your count.

Bampf, base twelve, no extra fingers needed.

Instead of having Avogadro's number at all, chemists could just count using numbers like we do for everything else. We already have the prefixes to make 10^+/-24 easy. No need to re-define it, just stop using it.

It's nothing more than a conversion factor between two parallel unit systems that somehow both coexist within SI.

Avogadro's number is for making calculations including weight simpler. If I have x grams of carbon how many grams of oxygen I need to burn it all. And then how many grams of carbon dioxide I end up with.

Value is somewhat arbitrary. And could also be tied to some other isotope. It is really about the ratios between all the elements including their isotopes. Picking carbon and there of isotope C-12, and saying this is exactly 12 grams is not unreasonable selection.

And now that we actually know how big particles are, we could work the other direction [if restandarizing an industrialized civilization wasn't impossible] -- pick an arbitrary number of particles that is a nice number for some reason or another (eg, 4!!), take the simplest thing that has mass (monatomic hydrogen), and declare your unit of mass to be equal to 4!! hydrogen atoms.

Sure, it's not easy for a primitive scientist to take a box of an exact number of hydrogen atoms and weigh them, but any advanced civilization should know exactly what a hydrogen atom masses.

That system would last only as long as nobody wanted any more precision than you could get from measuring hydrogen atoms. Then they're do what they've always done and redefine it to something uglier but which can be measured more accurately.

> any advanced civilization should know exactly what a hydrogen atom masses.

Nobody can know that exactly. Just giving it a name isn't the same as knowing it. We already have a name for it - "the mass of a hydrogen atom".

There's a validity to your criticism that I'm not enough of a domain expert to really dismiss, but also --

We're already like, really good at measuring the mass of atoms. We know the hydrogen atom's mass to ten or eleven significant figures, something like one part in ten billion. It's not the most precise measurement we have, those are at around one part in a trillion or so, but it's still pretty darn good.

Are you suggesting we're already good enough at measuring the mass of atoms and no further precision will ever be needed? Otherwise, your statement would have been equally valid 100 years ago by just taking some significant figures off.

By the way, 4!! ~= N_A was a funny surprise! If you were starting from scratch though, you could make it even simpler and define the unit of mass to be 1e27 times the mass of a hydrogen atom which is 1.7 kg. But again, you might find some other more accurate way and have to redefine it to include an ugly conversion factor just to get practical work done in some high-precision future world.

Factorials are a base-independent way to make large numbers. You could go 10^27 or 10^25 or some other random power of ten, but why powers of ten over powers of two? And then once you choose a base, why 10^27 versus 10^25 versus 10^24? Which makes one the more natural choice than another?

On the other hand, once you choose factorials over exponents, and furthermore, double-factorials, there's really only one option. 3!! is is 720, which is not really much of anything, in the grand scheme of things. 5!! is something like 7e198, which is probably more than there is of anything in the universe, or at least, in the known universe. 4!! is the only double-factorial which is a useful number of particles.

The more annoying thing is that mass and electric charge are so far apart. If you were starting from scratch, it'd be really cool to have 1 number-unit of something be the mass unit, and 1 number-unit of electrons be the charge-unit. But 4!! electrons is like 100,000 coulombs, which is just a lot. 2^64 electrons is more like 3 coulombs, which is more workable, but 2^64 daltons is only around 30 migrograms, which is a helluva mass unit if roughly human-sized is the scale of most intelligent life forms.

(Incidentally, powers of two have an even closer coincidence to Avogadro's number -- 2^79 is within half a percent of N_A. But 79 is such an ugly number -- there's nothing particularly elegant about 10^1001111.)

Re: measurement, we're presumably going to get better at measuring the mass of a hydrogen atom over time. We might even eventually be able to calculate it from first principles (which is really just saying we might be able to establish an exact relationship between the mass of a proton, electron and various physical constants; according to a random search, a 2008 paper was able to calculate the mass of a nucleon within about 3% of experimental results, which isn't great accuracy wise but is still pretty interesting).

(Aside #2: You could also pick a larger particle to try to bridge the gap between mass and charge. The Higgs Boson, for instance, masses around 130x the hydrogen atom.)

Good point about being natural rather than tied to base 10. Though natural conflicts with human convenience and ultimately is is for humans. Even more natural could be using the same unit for mass and energy, and make it dimensionless!

2^64 daltons (30 micrograms) is already about 2 gigajoules.

4!! photons -- specifically the 21cm photons corresponding to the hydrogen line [which, speaking of precision, we have the frequency of that down to around 1 part in ten trillion] -- is about 0.6 Joules.

So 4!! hydrogen atoms gets you about 1 gram, 4!! H-I photons gets you about 0.6 Joules, and the wavelength of the H-I photon is around 21 cm.

It all seems a bit marginal. Nobody actually uses the definitions to measure anything anyway, least of all by hand or memory, so it's not going to make anything more convenient having fewer digits in the still-arbitrary conversion factors.

Let me try to do it without Avogadro's number approximately:

  m_oxygen / m_carbon = (n_oxygen * A_oxygen) / (n_carbon * A_carbon)
  m_oxygen = x * (2 * 16) / (1 * 12)
  = 2.7 x

and more accurately:

  m_oxygen / m_carbon = n_oxygen * m_oxygen / n_carbon * m_carbon
  m_oxygen = x * (2 * 26.567 yg) / (1 * 19.945 yg)
  = 2.664 x

Can you do it more easily using Avogadro's number?

Where did you get the A_oxygen and A_carbon in first part?

Take the same calculation, use 12,01 for carbon and 16,00 for oxygen. Values in one reference book, get 2,66444629475 or the 2,644.

Avogadro's number is just number of atoms in the mole. Making atomic masses sensible numbers.

Carbon dioxide is actually relatively bad example as both values are close to integers. Chloride with atomic mass 35,45 starts to be more reasonable example where you have pretty simple number.

As shown dealing with very small numbers like counting together masses of neutrons, protons and electrons and then removing binding energy gets very tiny numbers. Which make calculations more error prone or even complex to do by hand. Using atomic masses which include Avogadro's number makes it much simpler process.

Those are the mass numbers from the periodic table which are exact integers and chemists probably know in their heads.

If you have to look up a 4-digit number, it's not easier to look up or use 12.01 u instead of 19.95 yg, especially with higher atomic masses where they're less integer-like, as you say. But using u involves more conceptual complexity because you're mixing two different mass units (u and g) in the same calculation. That's the part that's hard to do in your head. Chemistry students often struggle with this whole concept, which comes with a whole parallel collection of formulas and quantities to work with the alternative mass unit. They more easily understand SI prefixes which is just reusing an existing well-known concept.

You don't need to struggle with doin math on very tiny numbers any more than electrical engineers have to struggle with picofarads and nanoseconds.

Avogadro's constant or number makes things relatively simple as you can treat 1 gram as 1 u and just work in moles. You have 100 grams of something, divide that by u or g and get number of moles of stuff. If you need to add something to react with, just multiply the number you just calculated with u of other stuff and get a minimum amount you need in grams.

It really doesn't matter that you have 6.02214097×10^23 things of something. Moles, grams and atomic units really only matter. You never go to yoctograms(btw defined in 1991). But instead deal with numbers above 1. Which is doable calculating by hand even. Avogadro is there just to tie 1 atomic mass unit to 1 gram.

Technically you could do it all on kilo, hecto, deka, deci, milli, micro moles... Depending on scale you work. As long as you keep it constant... In the end it is just moving the deciman point in the weight.

Can you write out a specific calculation using Avogadro's number/moles/u/etc. so I can do the same without those and see if it's actually any easier?

"treat 1 gram as 1 u and just work in moles"

Surely that's no easier than treating 1 gram as 1 yocto-gram and just working in yotta-things.

> You never go to yoctograms

You can and it's both as easy as moles to work with and conceptually simpler. That's why I'm saying we don't need all the Avogadro's number stuff since we do already have yg even if nobody uses it.

Just to be clear, I'm talking about how it could be done. You seem to be talking about how it is done. I'm not denying how people actually use it, just pointing out that it's a giant needlessly-complicated historical legacy.

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