00:00 - 15:0015:00 - 00:00

12:02 AM
@antimony Take a look at the no-cloning theorem.

1 hour later…
1:19 AM
ahh danke

4 hours later…
5:20 AM
@DanielSank What you are describing is basically a stochastic process, like in Brownian motion. You can derive in such situations the fluctuation-dissipation theorem, that relates friction to noise as you said, like the one derived by Einstein. If I understand correctly, you are saying that in QM this relation is already "given".

5:51 AM
@Feynman_00 Yep.
Exactly. I'm saying that if you are diligent to represent all parts of a system as quantum degrees of freedom, there's no escaping fluctuation-dissipation.

5 hours later…
11:11 AM

1 hour later…
12:29 PM
It seems that there was a change in relativity theory about fifty years ago that involved starting to avoid the concept of relativistic mass, and saying that there is only one kind of mass, and it is invariant, and mass does not vary with speed.

You can define a lot of mathematical objects in a theory
You can indeed define relativistic mass if you so choose
But the concept tends to confuse people learning about it more than help them

Furthermore, it seems that a lot of people don't find out about this, and it is my contention that the reason is that people tend not to realize that the word "mass" unadorned, is being used in a new sense by professional relativists.
Did Einstein mistakenly create the concept of relativistic mass, then?
@Slereah
Or did Einstein not care about learners?

I mean it is not a mistake
You can define it if you so wish
But it is not as useful a concept as you would think

It's my contention that most people with an opinion about it are unaware that relativity has moved on. I myself had an incredibly tough time finding out about this. I even talked with an expert on relativity who simply insisted that a photon does not have mass and could not explain to my satisfaction why it was so. Finally, I found out using the internet, especially SE (Stack Exchange, not Street Epistemology :) )
Said expert was in real life.

As also discussed in this question, every professional relativist should be aware of this

12:42 PM
it is a complex question because both "photon" and "mass" are ambiguous terms

How so?

A physicist who took an intro course to GR but otherwise is not really doing anything with GR might not be

Well what do you think photon and mass mean

@MatthewChristopherBartsh Einstein wrote one book that he considered appropriate for high school learners.

I have been reading GR for over a decade and I have never read any book by Einstein

12:45 PM
Mass curves spacetime and is a form of energy. A photon is a particle of electromagnetic radiation.

By modern standards reading Einstein for GR is like reading Euclid for geometry
@MatthewChristopherBartsh What is a particle

Both possibly correct but underspecified definitions. What does "mass curves spacetime" mean? How does one compute it? What is a "particle of radiation"?

I do miss the era when you could just pretend particles were little marbles

Einstein wrote a book for the layman. It was in English. I was appalled at how badly written it was.

indeed

12:47 PM
I much preferred "Relativity Visualized" by LC Epstein.

I think that was the 16th century idea
Mechanism, as it was called

Ive read the special relativity book by Einstein some years ago by i didnt find it particularly enlightening

Einstein was grappling with a weird new theory

Of course not, most of the early texts about a new subject in physics are pretty terrible in the pedagogical sense if you look at them with a few decades of hindsight

While I am thankful I don't think it's particularly helpful now

12:49 PM
A particle is a small lump.

also not terribly specific, but definitely wrong for a photon, a photon doesn't even have a proper position, see physics.stackexchange.com/a/463454/50583

@ShikiRyougi It looses something in the numerous editions and translations

@user4539917 How do you know? Do you speak German? Have you read the original?

And that "something" is readability in English

12:51 PM
Also maybe even then everything sounded weirdly Swiss
@ACuriousMind does Einstein sound particularly Swiss to you

You didn't let me finish my post.
nvm

Didn't Einstein know how to write English?

"The essence of Pure Mechanism is (a) a single kind of stuff, all of whose parts are exactly alike except for differences of position and motion; (b) a single fundamental kind of change, viz, change of position. Imposed on this there may of course be changes of a higher order, e.g., changes of velocity, of acceleration, and so on; (c) a single elementary causal law, according to which particles influence each other by pairs; and (d) a single and simple principle of composition, according to which

I be more much smarter then einstein.

Those were simpler times

12:55 PM
@Slereah no, but he wasn't Swiss and grew up in Munich, so that's not a big surprise :P

no point in denying that fact.

Ach

@MatthewChristopherBartsh sure, but his native language was German and at his time German was still a major language of the sciences
so most of his works - especially the earlier ones - are originally German

"An electronic theory of matter departs to some extent from this ideal. In the first place, it has to assume at present that there are two ultimately different kinds of particle, viz., protons and electrons."
Electricity ruined physics

So was his thesis.
(I think)

12:57 PM
@user4539917 My point is that the readability might not be there in the original either and I don't know how you would know unless you've read the original

btw, what do you think of this definition of a particle: a wave-packet with well-defined energy

what's a "wave packet"? :P
and why does it need a well-defined energy?

@ACuriousMind good point

This comedy routine of defining what a particle is can go on for hours

is a particle suddenly not a particle just because there's some slight uncertainty about its energy?

12:58 PM
and after a while people will start bringing out Malament's theorem or other weird things

at the end of the day "a particle" is the thing that makes "click" in something we've decided to call particle detector :P

I was talking about the book that I read. It was in English, and I can't remember whether it was translated from German, but I don't think so. The author was Einstein, and it was aimed explicitly at the layman. It gave me the impression that Einstein didn't understand his own theory very well.

you can of course say what states correspond to that in a particular physical theory

@ACuriousMind What if you just wired it wrong though

Im not sure what a wave-packet is supposed to mean, but I think it just refers to its wavefunction

1:00 PM
@ACuriousMind

I wonder if you could write a book arguing what particles are going from Democritus to today

@MatthewChristopherBartsh You probably mean this which was indeed originally German

as an extended such conversation

What were all of the CSEducators pings for?

Galileo style

1:01 PM
@Nat what do you mean?

@ACuriousMind Someone's pinging SE.ComputerScienceEducators to come visit this room.

Hi Professor @Buffy
Welcome

@Nat that looks like trolling to me, then
raise a flag on CSEducators, nothing I can do about it from here, sadly

Weird

@ACuriousMind That looks plausible.

1:03 PM
trolling

Yeah, it seemed strange enough to take a look.

Democritus was a wise man

I'd like you guys thoughts on whether it would be a good idea to make it easier for people to find out that the word "mass" is being used in a very different way by relativists than fifty years ago.
*guys'

the problem is that mass refers to a variety of things

1:06 PM
Go on.

@MatthewChristopherBartsh not sure how much easier we could make it other than having a highly upvoted question about that (which we already have) and all modern textbooks refraining from using mass in that way

Even the basic classical notion you have two senses at least

You have mass as inertia (how hard it is to change an object's momentum)
and you have gravitational mass (what gravitational force that object projects onto other objects)
Not even getting into things like effective mass, still classically, because for instance you do not feel as much gravity from Earth as you should because of centrifugal force

@ACuriousMind What do mean by "in that way"?

1:09 PM
@MatthewChristopherBartsh I mean "for relativistic mass", i.e. as a concept that increases with speed

I thought inertia was the same thing as "gravitational mass"
@Slereah

...in order to say that they are the same you first need two definitions that are not just the same by definition

they are also different to check experimentally

"inertial=gravitational" mass is an actual statement about physics, not something that's just true by definition

You do not measure inertial mass and gravitational mass the same way
But it turns out that they are proportional
If you have an object with a given inertial and gravitational mass, if you consider an object with twice the inertial mass, it has twice the gravitational mass

1:12 PM
@MatthewChristopherBartsh because of equivalence principle

@ACuriousMind I don't think that would help those who already think mass increases with speed, and in any case, not all of those will have even heard of "relativistic mass".

@Slereah proportional? arent the same?

@MatthewChristopherBartsh sorry, you've lost me

What does it mean for two physical quantities to be the same

I'm saying that no modern textbook talks about mass increasing with speed (except as a historical aside)
the only way you end up thinking that is if you read bad pop-sci or outdated books

1:13 PM
Do you think that the temperature of an object and the length of the column of a thermometer are the same

@Slereah to have the same value i suppose

Well how do you compare two values like that
Gravitational mass you measure by for instance looking at a scale, measuring the gravitational force on a set mass

and we can't do anything about outdated books and I've long given up the fight against bad pop-sci, so I don't know what else you want to do here :P

like the compression of a spring for instance

@MatthewChristopherBartsh Translating concepts from earlier works seems like a largely historical issue. And perhaps context-dependent, since stuff from the pre-internet days would presumably be fragmented.

1:15 PM
Inertial mass, you measure by subjecting different objects to the same force
and looking at how they move

you measure the inertial mass and then the gravitational mass and you compare them i suppose

it's not trivial work to compare those two things
Well how do you measure those things?

I have no idea how to actually measure them :p

If you're right, then most of pop-sci is bad. And it seems to me that people don't know which books are outdated. For example, L C Epstein's Relativity Visualized has always enjoyed a good reputation, but it says that mass increases with speed. And nearly every physicist that isn't a pro relativist thinks that.

yes, most pop sci is bad
also, yes, most people don't really understand relativity

1:17 PM
Your experimental data are 1) A given mass in the gravitational field of object A or B caused the scale's spring to compress a certain distance 2) Subjecting object A or B to the same force, they have gone a certain distance in a certain amount of time

neither of these is news :P

You can't compare those two quantities directly

:61526101

brb im coming back a bit later

and it's not as if thinking "mass increases with speed" is that bad of a pop sci take, really - there's nothing inherently wrong with it, it just becomes a problem if you then confuse that meaning of "mass" with other meanings of "mass"

1:19 PM
Seems like the easiest way to learn a topic would be to just learn it. Guessing that "pop-sci" is mostly about folks who want to do less than the minimum; that that might backfire seems like it'd be hard to avoid.

and that's just when you're considering classical mechanics where mass is mostly just two things
and it doesn't do weird things like mess with the flow of time
Theoretical physics is fun and all but you have to remember once in a while that those refer to real phenomenon in the end :p
And you have to try to remember what those are

@ACuriousMind My view is that it is an important problem, and to remedy it, relativists should substitute "rest mass" for "mass" in their writing and speaking, and m subscript naught for "m" in their equations. What do you think?

compared to all the other terrible things pop sci tries to teach people about e.g. quantum theory, I'm really not all that concerned about a few people going about their lives thinking in terms of relativistic mass :P

Otherwise you're gonna start thinking that every quantity is the same because they are connected by some equation

@MatthewChristopherBartsh in contexts where there is danger of confusion, that's precisely what people do!

1:22 PM
@ACuriousMind The problem is people waste time debating whether mass increases with speed, and don't realize that relavists are using new definition of mass that neither of them knows about, perhaps.

I think it's maybe useful to try to think of objects as having properties rather than thinking of those properties as objects themselves
There isn't an object called mass
mass is just a property objects can have

@MatthewChristopherBartsh I have seen no evidence of such debates.

@ACuriousMind Ditto.

Every time this has come up in actual discussions I've had, someone says "We really just mean 'rest mass' when we say 'mass'" and the person that was confused goes "oh, okay then"

@ACuriousMind I've debated whether a photon has mass.

1:24 PM
I can debate that issue for days but unfortunately the people who will usually bring up such issue just see E = mc^2 and think this is all there is to it

@MatthewChristopherBartsh Isn't that considered an open question?

They just see symbols on paper and decide that such is the world
Basically magic

How is it an open question?

See above
What is a photon, what is mass

:61526220

1:26 PM
and how do you check
If you hit light with a little hammer it will certainly not change its speed
But the issue is a bit more complex usually

When I debated it, I took the position that since it was agreed that a photon has energy, and that energy has mass, a photon must have mass.

Although I guess a solar sail is basically hitting light with a little hammer
"energy has mass" does not mean anything unfortunately
Energy isn't an object
it's just a property an object can have

But the relativity expert (not a pro relativist though) just insisted that it was not that simple, but couldn't say why to my satisfaction.

Might as well say "blue has green"

honestly, that just sounds to me like you talked to the wrong "expert" :P

1:29 PM
And yet, according to relativists, my interlocutor was correct.

Or one that couldn't be bothered

@Nat and yes, it is technically an open question because experiments of course can only measure upper bounds on the (rest) mass

What level are these discussions at? Like, are you a PhD physicist talking to folks at a conference, or are you chatting with folks on reddit?

Well he was a very smart guy, a pro physicist, and had make software simulating relativity.

it is entirely possible that the photon has a vanishingly small mass that just so happens to be so small that none of our experiments so far has detected it
but in practice that's what we mean when we say that we're certain it's massless :P

1:30 PM
You can check this fun Feynman quote for the experimental side of it :
7

For most parameters, it is often impossible to differentiate them being a certain value from being extremely close to that value. Even if you finally have an experiment precise enough to differentiate, you could always then ask "What if the difference is even smaller!" In the context of special r...

A physicist I met by chance.
:61526282

Physicists can often agree on the idealistic basics. For example, sure, a photon can often be thought of as "massless", in a theoretical sense. And that's what we'd tend to tell students in class.
Once you get into theoretical stuff, then it gets messy. And probably not really productive for popularization.

Hell even in experimental stuff it gets messy :p
Photons never go at light speed experimentally
For a variety of reasons
Mass doesn't even really mean much of the same thing for a localized object and a wave
For wavelike things it's gonna do things like dispersion
This is what giving light an effective mass does
It's not quite the same as holding a brick in your hand

@Nat But the fact is that relativity is hugely interesting to many people, including me, and therefore it will continue to be popularized. The question then becomes how can it be done better? Also it isn't just laymen who are confused because they don't know about the meaning change of unadorned "mass" in relativity, it's also most physics graduates, which means most physics teachers.
I think a big help would be for relativists to substitute the phrase "rest mass" form "mass" in their speech and m sub naught for "m" in their equations. In addition, the following terms would be shunned: "relativistic mass", "invariant mass", and most importantly, unadorned "mass". What would be the downside?
*from
*for
not from

@MatthewChristopherBartsh Popularization seems like it's not really productive, almost by-definition. I mean, if there's an easy way to learn a topic for real, then that's not "popularization" -- it seems like stuff is called "popularization" when it falls short of that mark.

1:44 PM
Popularization has its role but it's mostly to get people interested in the topic
It's not usually very good as an educational tool
But by now a lot of popular science stuff has basically stopped being taught by physicist but still has a life of its own

And physics teachers are also mostly ignorant of the meaning change.
From what I gather, the old meaning of mass in relativity is still being taught by most physics teachers, including at degree level. It is only if a student takes a deep course in relativity that they find out about it, and are often shocked and stunned.

Dunno what to tell ya about an alleged meaning-change. I mean, language can be pretty heavily fragmented; for example, what's a "molecule"?
We kinda infer what someone means based on context.

True, but the context doesn't help much with "mass" in relativity.

Sure, if you're just considering "relativity" like it's a singular context. But surely folks discuss it in all sorts of different ways; word-meanings would seem related to the specific contexts in which they'd be used.
Don't get me wrong, it annoys me when folks use the word "molecule" to imply that something must be polyatomic, pseudo-stable, and uncharged, but that's how some folks write it in some contexts.
And that's even what I'd use the word to mean, when talking which such folks in such contexts. As much as I think the concept is silly.

@Nat The meaning change is well-established, or so it seems. See physics.stackexchange.com/questions/133376/…

1:56 PM
@MatthewChristopherBartsh There're preferred definitions that folks may tend to favor, but part of being conversational is learning to pick up on others' language and engaging them through it, even if they're not employing conventions that you'd tend to favor.

It's like trying to define what the word "love" means~

By which I mean, I'm not sure what problem you're trying to address because, even if folks do vary their definitions in some contexts, that'd seem like a normal enough thing that people are used to dealing with anyway.

There is a psychiatric symptom called clanging where people think that two words that sound the same are related
This is what people do with "mass"

@Slereah Why bring up Catholic religious services?

Why do you think they called Higgs the god particle

2:03 PM
@Nat The problem is that many people including most physics graduates and physics teachers are confused unnecessarily about relativity and this causes time spent thinking about it to be wasted. There are a lot of misunderstandings and disagreements about relativity due to ignorance of the fact that relativists are using the word "mass" in a new way.

@MatthewChristopherBartsh If most students/teachers were confused about such things, it'd seem like students would be failing a lot of tests/quizzes/homework/etc..
Actually, sorry.. what's a "graduate" here? Do you just mean anyone with a Bachelor's degree in Physics?
Or do you mean folks doing graduate-level work in Physics, e.g. as part of a Master's or/and Ph.D.?
Because if you're talking about folks who just got a Bachelor's in Physics, then graduated and went into another profession, then, sure, that might not be too surprising.

@Nat I guess I mean by "graduate" anyone with a bachelor's degree in physics from a decent university.

the level of knowledge of people with Bachelor's (and even Master's) degrees is so variable as to that being a really broad category

@MatthewChristopherBartsh Ahhh okay, that might be the issue: a lot of Bachelor's degree programs don't really require students to get a firm understanding of relativity.

@MatthewChristopherBartsh I guess the main thing I don't understand is why you think so many people are "wasting their time" with this
I would expect people who have no professional need to engage with GR on this level to...not think about it at all, really

2:11 PM
@Nat From what I can gather, a lot of uni text books teach that mass increases with speed, which contradicts what the relativists are teaching.

conversely, the few people who do want to think about this should really be good enough at research to figure this out - this is far from the only place in physics where different words can mean different things in different contexts!

@Slereah Aah! I see! So yes you cant compare them directly. I didnt know that... Does that mean that inertial and gravitational mass are fundamentally different properties? Furthermore, how can we deduce the equivalence principle experimentally? If we cant compare them directly then it seems impossible to explicitly find that the two masses are equal...

@MatthewChristopherBartsh a lot of uni text books also teach Newtonian gravity :P

@MatthewChristopherBartsh Do you have an example of such a textbook to illustrate the issue?

you need to look at the level and intent of these books

2:13 PM
The same way that you can deduce that two different properties are linked together
You check for various objects and look at them
The big equivalence principle experiment was the Eotvos experiment
Just lots and lots of checking the gravitational and inertial mass of various objects
of different shapes, composition, size and mass

@Nat I myself had to spend a huge amount of time and energy, and wrongly told several physics graduates as well as many other people that they were suffering from a misconception in thinking that a photon had no mass. I was incredibly lucky to find out that I was wrong.

and within experimental error, if the ratio of two inertial mass is a given value, the ratio of gravitational mass is also that value
We identify those two notions and call it mass and give it the same dimension, which is maybe a bit of a confusing thing
but that's true of a lot of quantities
Just have to keep in mind that the properties of an object being "the same" depend on the model you're using

@ACuriousMind The word "mass" in relativity seems to be unique in hard science, in terms of how confusing it is, and how few people are even aware of the problem.

@MatthewChristopherBartsh So you made an incorrect claim about "mass" based on a misunderstanding you had about the term, and you're concerned that this error came from an incorrect definition you picked up from a textbook?

Not really

2:17 PM
@MatthewChristopherBartsh try 'power' in ordinary high school physics, for one

Plenty of terms in physics are very overloaded with different meanings

really confusing to a lot of people because the technical definition of 'power' does not really correspond to its much broader colloquial meaning

You just don't necessarily hear about it

@Nat I never did an explicit course on relativity in my bachelors for example. The only relativity I knew was from classical mechanics which was also an optional course

all the "dimensional" words in physics come from thousands of years ago for the most part
It's hard to have them make sense in the context of modern physics
Calling something the same thing people use to weigh bags of grain may not be ideal in quantum mechanics

2:21 PM
other example: what exactly does the term "wave" mean? Something that solves "the wave equation"? Which wave equation do you mean? Does it have to a have a medium? (people disagreeing about this gave us the ether!) Is a quantum wavefunction "a wave"?

@ShikiRyougi Likewise, I think Relativity might've been briefly reviewed in a required course that surveyed "modern" physics, but I don't think they required any classes that really went into Relativity beyond tangents in E&M and such.

What's a field
there is no wheat in there

A field's where you write your info down on a form.

physics is full of historical accidents of terminology, but you can't really change established terminology since everyone would still have to learn the old usage to understand anything written before the change

2:22 PM
μᾶζα

Or it's a location where an object stores data in object-oriented programming.

How much bread is in a photon

@Slereah depends on what you mean by "literally"

I mean literally literally
as it is written in The Literature

@Nat I learned that mass increased with speed when I was a small kid. I deduced as a young man that a photon must have mass and for years after wrongly dismissed any book, person, TV program, or website that disagreed, never finding out from any of them (until I came to SE a year or two ago) that the disagreement was caused by a matter of semantics. The relativists it seems started using "mass" in a new sense, and didn't do a good job of telling the rest of the world about it.

2:26 PM
@MatthewChristopherBartsh Maybe you learned that momentum increased with speed, rather than mass? And maybe "mass" was used as an informal synonym for momentum?

@Slereah That might have been the case in ancient greek, but it no longer has that meaning.

@Nat The world probably bears some responsibility for listening well, I assume. The world is what it is, but relativists, could change their terminology, and that is what I am proposing.

Sorta like how "weight" and "mass" are sometimes used as informal synonyms?

I am an ancient greek
@Nat Yes

You are greek?

2:28 PM
@Slereah What I mean is that maza comes from massein, meaning "to knead", so "literally" a maza is more like "something kneaded", which of course usually was bread

Here I am

no, that's why it's massless

You probably indeed know more ancient greek than I do, I hated the class in school

electrons like a good massage (what do you think that word comes from? ;), though

@MatthewChristopherBartsh Dunno what to tell ya. I mean, if folks do run into problems, they can fix it, as you might be fixing your own terminology. But a lot of folks just aren't having problems with what you're talking about. I mean, I can't recall ever having seen anyone confuse stuff like that.

2:31 PM
@Nat In physics weight is a force, and mass isn't. Weight is measured in newtons and mass in kilograms. A lot of layman are very confused because outside of physics, the word "weight" is used to mean mass. So people think that something in space is weightless, and thus conclude that it has no inertia. But in this case, any physics graduate, and any good high school student knows the difference, and can explain it.

Light isn't even that well localized so it's pretty hard to even talk about its inertia
Plus since we're talking about light in a vacuum, a thing that does not actually exist, it's pretty hard to test for

@MatthewChristopherBartsh See, I think the problem here is the part where you dismiss for years a plethora of people who disagree with you without ever realizing the problem must be that you're misunderstanding them rather than all of these people being extremely obviously wrong

@Slereah When light hits a piece of dust in space it transfers momentum to it, and propels it in some cases right out of the solar system. You can use a sail made of reflective material to fly around the solar system in principle.

that's the ultimate bad faith assumption - that everyone else is really stupid - and the better a priori explanation is always that there must be some sort of misunderstanding

@MatthewChristopherBartsh True, but only relevant if you have the relation between momentum and mass!

2:37 PM
and I'd argue that if you had tried to engage with these materials rather than dismissing them you should have realized that because I find it impossible that not one of these materials actually wrote down their definition of mass as invariant mass ($m^2 = E^2 - \vec p^2$ or $m^2 = p^2$ are really pretty common equations)

@ACuriousMind I probably could have been a bit more open minded or patient, or a better listener, but OTOH none of those people even knew about the meaning change, and that is an atrocious situation. I dismissed them (their positions not as people) because they had no strong arguments, which was because of their own ignorance.
@ACuriousMind I didn't think everyone was stupid. I thought L C Epstein was brilliant. And so did/does everyone else it seems. But now it seems that he didn't know about (or kept quiet about) what had been going in relativity research for the last fifty years. He wasn't totally wrong, it seems, but he was out of date with no excuse (except maybe that even he was unable to find out the truth).
@ACuriousMind As I see it, relativists have done a terrible job of letting people know that they mean something quite different by "mass" from what Einstein meant.
@ACuriousMind Yes. Reading Einstein is highly damaging for your relativity, in the absence of someone to point out the pitfalls.
@ACuriousMind Who knew? I say that unironically.

not sure what the last 2 messages are replies to
but anyway: I think you're right that the world would be a better place if every word had an unambiguous meaning and science communication can definitely improve in many respects but I think you're wrong that a lot of other people have the same amount of problems with this particular pitfall :P

@ACuriousMind I think this will convince you: physics.stackexchange.com/questions/133376/…

I linked that Q&A a while ago myself :P
I'm not saying no one is confused about this, I'm saying for most people this just a case of someone telling them "we're talking about rest mass" five minutes later and that's the end of the confusion

@ACuriousMind Worst one is flux
Took me a while to find out radiometers where using it to mean "flux density"

2:52 PM
oh, omitting "density" is a far broader phenomenon
many "Lagrangians" are actually "Lagrangian densities", for instance
i thought you were going to talk about how the flux of fields has nothing to do with soldering :P

or thinking that water has a density of 1 kg/L

@ACuriousMind Im gonna agree with that, I dont find it such a big deal even though i was also confused about this till today :))
Its a small misunderstanding easily solved

I think the confusion was that radiometers refer to flux as radiant energy, and flux density as flux
I dunno it's been a while but it was a big mess

also those chemists are giving a dimension to counting things
pretty weird

Moles in general seems convoluted when you could just give a name to the order of magnitude

2:58 PM