Hacker News Reader

Comment by Koshkin | Hacker News Reader

Too many digits… TL;DR: .5 MeV and .9 GeV, respectively.

I prefer to use the same unit for all numbers because it makes the comparison easier. The bound of mass of the neutrino is really low. Using M and G hides it.

I was going to write:

> For comparison, the mass of an electron is approximately 500,000 eV and the mass of a proton is 900,000,000 eV.

But all the numbers I wrote are measured experimentally. Both values have a lot of experimentally measured digits! I only removed the part that overlaps with the uncertainty, because the notation with parenthesis is somewhat confusing.

> I prefer to use the same unit for all numbers because it makes the comparison easier.

Thank you; this is a style guideline I wish more writers would adopt.

Alternatively, you can use exponential notation to compare numbers of very different sizes while writing them similarly and using the same unit.

Yeah. The point is keeping the units consistent.

511 keV and 938 MeV would have been much clearer than a distinction via comma/point like in 510,998 -> . <- 950 eV and 938,272 -> , <- 088 eV.

I agree that the coma/point distinction is confusing. Also, I'd like to cut all the numbers in the same digit, but the next digit of the proton is too dubious.

What about this version:

> [an upper bound of 0.9 eV] For comparison, the mass of an electron is approximately 510998.9 eV and the mass of a proton is 938272088.0 eV.

I would just round to the nearest eV and keep the commas.

> the mass of an electron is approximately 510,999 eV and the mass of a proton is 938,272,088 eV.

This reads best to me.

I know we're just bikeshedding now, but

  neutrino:           0. 8 eV/c^2
  electron:     510 000. 0 eV/c^2
  proton:   940 000 000. 0 eV/c^2

(Note: neutrino mass is given as the upper limit.)

The first value has one, the others two significant figures in this example. The decimal point is also giving a false sense of certainty when used like this. You can find more about significant figures at Wikipedia:

https://en.m.wikipedia.org/wiki/Significant_figures

Yes, I know about significant figures. In fact, I considered adding a note about sig figs before deciding it was too minor of a nitpick to elaborate on. Elsewhere in this thread, people have already listed these masses to much greater precision than almost anyone needs (including me, a practicing physicist); obviously people can infer I'm rounding from context.

Of course, if you were to present the masses this way without context, you should add a note about rounding.

I find that significantly less clear.

In fact, I find it so unintuitive that I didn't even notice the units changed and thought you'd made a mistake in magnitude before I finished your sentence and I went back.

Comparisons should always be done in like units.

In contrast to some sibling comments, I think using the same unit is a great idea. It’s just that long numbers with commas are a bit hard to read. At least I think 511 keV and 938 000 keV would have been another clear way to present those numbers.

Writing out the digits gives a more visceral impression of the difference in weight, from roughly one, to a six-digit number, to a nine-digit number.

That's what the GP wrote. Their electron value has a decimal point before the last three digits. The GP values are approximately 510 keV and 938 MeV.

Reply on news.ycombinator.com