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1 Ångström = 1e-10 m

11.5 mÅ = 1.15e-12 m

That’s a mind boggling measurement.

My chemistry professor told me 10 Ångström is about how long your fingernails grow in the time it takes to say "10 Ångström"
I just did the math, and it looks like this is correct!

Assuming 2.5mm per month (quick google search), that's 2.5e+7 angstrom/month

Divide by the number of seconds in a month (30 * 24 * 3600) and you get about 10 angstroms per second. It takes about 1 second to say 10 angstroms. Very cool!

Now that's just the type of knowledge my brain loves to collect and store in its useless information department (and it's pretty full already). Useless? Well perhaps not. But one thing's certain I'll never forget the fact.

Incidentally, it's worth remembering we owe the beginnings of this story to August Kekulé's remarkable insight-benzene's structure and the snake swallowing its tail. That too is also unforgettable information (but likely more useful, methinks).

Share some of your useless knowledge with us!
Ha! And where to start and or what topic with which to begin? You've no idea how potentially dangerous tempting me like that really is (I'd be immediately banned from HN for server overloading)!

Take a look at my reply to alliao. Can you imagine thousands of pages like that? Not likely. I'm far from being the brightest spark on the block but I'm smart enough to know I'd be chased off in a greased lightning sprint.

...But you've seeded an idea, some of it could be used as a substitute for Vogon poetry (shame on you).

Honi soit qui mal y pense.

;-)

there's a Japanese phrase for it.. まめちしき literally translates to bean knowledge. It quite a nice image though, little beans which may end up sprouting and connecting with others to form a web of knowledge somehow, someday
Sorry for not acknowledging your post earlier but I simply forgot. Anyway, thank you for that little gem of wisdom; I've already 'noted' it in my mind's useless info dept. :-)

It's an excellent metaphor because that's what happens. Over the years I've noted many times that some facts (even seemingly irrelevant ones) in one field can play an important role in me understanding a concept in a totally different (and often unrelated) one. The trouble is that I've never had a photographic memory so all too frequently when I encounter something new then I can be left thinking 'now I recognize that from something I've come across previously but where?'. It's a nuisance but I put it down to my brain's 'garbage collection mechanism' being overly efficient.

Sometimes it's also a burden especially when you can't mentally discard or turn off an old 'connection' as it can become annoying. Here's an example you might appreciate. It's well known fact there's a propensity for English language speakers to steal words from other languages then incorporate them effortlessly into English as if they'd always been there—simply because the foreign imports sound fashionable or posh—and that this practice happens even when well-known and perfectly adequate English words or phrases exist. The trouble is that inevitably they never take the time or effort to pronounce these imports correctly. (Right, it's no wonder English is such a bastard language).

When in Japan years ago I learned to pronounce tsu - つ, ツ - perhaps not perfectly but likely better than many Westerners/English speakers do who have never been there. Nowadays, the transliteration of the Japanese word ツナミ is more commonly used in English than its original native counterpart! Unfortunately, the trouble is that almost no native English speaker takes the time or effort to pronounce tsu correctly even though the Latin characters provide a reasonable facsimile of/guide to its correct pronunciation (even those who've much better diction than me—BBC announcers for instance—usually make a mess of it).

Thus, whenever I hear a slurred-out overly-long tsu it inevitably grates with me. If I'd never learned the correct Japanese pronunciation, which, given that I'm a native English speaker (thus it's essentially useless information), then I could be blissfully ignorant of the fact just like everyone else. ;-)

No doubt, having provided the phrase 'まめちしき', you are also aware of the difficulty we native English speakers have in pronouncing tsu. I often wonder what the Japanese think of us given that we're so efficient at mashing up their language and that we don't give a damn about doing so. It annoys me is that we've the hide and arrogance to adopt the word ツナミ then just mangle its pronunciation. In my opinion adopting and incorporating a word from another language and being insensitive or oblivious to its cultural significance is both rude and indicates ignorance. (Here, I make a distinction between incorporating a word into another language and say those who are learning another language and who are having difficulty in pronouncing words in that newly-acquired language).

BTW, I don't want to give you the impression that I'm fluent in Japanese as I'm not. Some decades ago, I worked in Japan for a short while but I was never there long enough to acquire an adequate understanding of the language let alone gain fluency. Also, I'm aware that I've a mixture of hiragana and katakana here (kanji is too complicated for me to deal with here). One curiosity I've never quite figured out (except perhaps that it's traditional), which is to ask why a certain formalism seems to have been adopted in the naming of Japanese cities. Why do cities and towns [seemingly] nearly always use kanji for their names (and not hiragana ...

Note that the length of the C-C bound is ~1.3Å and the length of the C-H is ~1.0Å, so te corrections is like .5%.
The paper is really about the difference between C-H and C-D. Also it uses a physical method (Raman) and statistical approaches that will need to be reproduced to make sure it was not just an artifact of the method.
Knowing very little about chemistry and physics, I always enjoy learning the names of new measurements.

Milliangstroms? Lmao great name.

Yes, it's a great name like millimetres of mercury (mmHg), kilotons of TNT, light-years, etc. /s

But seriously, SI already has appropriate units for these quantities. Milliangstroms should be converted to picometres, millimetres of mercury should be converted to kilopascals, kilotons of TNT should be converted to terajoules, and light-years should be converted to petametres.

How is 1 light year = 1 petameter?
They're not. We're saying the non-SI unit of light years shouldn't be used over something like petameter. Just multiply the "light year" measurement by .9461 and you're set. Or, ideally, just measure in SI units to begin with? The US is the holdout here and for no good reason
How long does it take for light to travel petameter vs how long did it take to travel that light year? The light year is something people can relate to
I for one welcome the idea of measuring time in lightpetametres ;)

(that's about 38.6 days for the curious)

The problem is with what a year is, which is arbitrary to begin with, but worse still, a year is not constant. The momentum of every planet is affected by the gravity of every other planet, leading to fluctuations in solar orbital speed, which means a full orbit is likely never the same period as the previous or subsequent orbit. Maybe these fluctuations are small, but light travels so fast that over long distances it is sure to be significant. Thus the definition of a light year is defined as the distance light travels in a Julian year, 365.25 days, but this just pushes the error down to a different measure, because days are not constant either. Since the speed of light actually is constant, maybe we should define years and days by the speed of light instead of vice versa.
Of course, there's also the problem that a light year is only relevant to someone from Earth. A light year for a Neptunian would be drastically longer, let alone someone extra-solar system to us
Shush pedant and relate to things with the rest of us using stuff we already understand
The US isn't the holdout. Astronomers everywhere use light years and parsecs. Particle physicists everywhere use barns. Chemists everywhere use Angstroms.
Astronomers also use angstroms when refering to the filters used for solar observations.

Just because they're pretty, here's a link to the SDO gallery: https://sdo.gsfc.nasa.gov/gallery/main

Also, the SDO takes an image through each filter as it rotates through the filter wheel, IIRC, it takes 15 minutes to rotate through them all. They are then made available for each filter at different resolutions. Being the hacker-ish type, I wrote a script to use curl to download the image sequences for chosen filter/framesize for the sun's full rotation to create a one day timelapse.

And if used literally, parsecs (parallax arc-second) should have smaller values the father away something is!
'everyone should use the units I want them to use and not the commonly used ones'
This is a disingenuous argument. Do you not see the problems with using application-specific units? They are jargon and don't form a coherent system.

When you have a jumble of units, it is hard to relate them. If an acre of land gets an inch of rain, how many gallons of water is that? If you did this in millimetres, metres, and cubic metres, it is easy.

If your car's motor is rated in horsepower but electricity is measured in kilowatts, how do you compare those?

What about fitting copies of a product measured in ounces in a shipping container measured in short tons?

Typesetting measured in points, but paper measured in inches?

Fitting metalwork done in mils but woodwork done in binary-fraction inches in a house measured in feet?

The list goes on and on. It's easy to say "but my domain is special and deserves its own units". It's much harder to resist and say no, there is a perfectly suitable unit with power-of-1000 prefixes to use in your application.

There are an infinite number of possible coherent unit systems, all of them totally arbitrary. Why should any system be preferred over the rest?
Because mathing in one is much easier by orders of magnitude (pun intended) in one system.
OK, but why choose any one system over any others? Why chose base 10 over base 2? Why choose the current definition of the meter as opposed to some other length?
>kilotons of TNT should be converted to terajoules

I disagree with this one. A ton of TNT is much more easily understood vs some measurement of energy that no normal human has any capacity of understanding.

Also, milliangstroms vs picometers. if you are already using angstroms, then dividing it by milli makes sense.

I doubt a typical person can describe the effect of one ton of TNT with any accuracy. I'll give it a try though: 2 meter deep and 6 meter wide crater in typical soil, death due to shockwave out to 150m, death likely due to shrapnel out to 300m, buildings destroyed out to 300m, audible from 10 km.

From here: https://unsaferguard.org/un-saferguard/blast-damage-estimati...

26 meters fatal distance, 83 or 142 meters buildings destroyed

My estimates are more appropriate for a 20-30 ton explosion, it seems.

You think the typical person can tell the effect of whatever value in terajoules would be? At least the typical person would know that dynamite/TNT is an explosive causing damage and that can be extrapolated in one's mind the effect of 1000 tons of TNT would be much larger and so forth.
No, the point is can't do it with kilotons otherwise. but at least terajoules are consistent with other units of energy. If there's no familiar reference point then why use random units?
This is a bad argument. Units exist to make things easier to communicate, using lightyears or kilotons makes perfect sense for contexts where they convey more information directly than petameters or terajoules. Especially since the conversions aren't exactly difficult to remember for anyone who needs them.

Here the use of milliangstroms easily conveys the information that bond lengths are measured in angstroms and thus this is a very small correction, picometers would not convey that to anyone not already familiar with typical bond lengths.

Turn this around: How many people have seen the speed of light, even for a second? How many people have seen a kiloton of TNT being blasted? You're only advocating for these units because they are commonly reported in the media and are thus familiar - at least in print, not in physical experience.

Angstroms are needless jargon because nanometres already cover roughly the same scale. Do you want to go back to the bad old days when every town had its own definition of feet and pounds, and consumers were routinely cheated through the use of confusing and obfuscated units?

People haven't seen the speed of light, but they have an understanding of the fact that it's the maximum possible speed. Similarly, while people haven't seen a kiloton of TNT being blasted, they can easily visualize what a kiloton of TNT is and understand what that means.

Your claim that I'm only advocating these units because they're common in media is ignoring the fact that these are also very common as formal units in their respective fields. Another great example is AU, no one has seen what 1AU exactly is, but everyone can intuitively understand that 5AU means 5x further from the Sun than the Earth is, 0.74 terameters conveys absolutely nothing on its own and even for someone who is aware that 1AU=0.15 terameters, it takes a bit of extra mental effort to obtain the same information while not really adding anything because '1AU=0.15 terameters' is fundamental knowledge in the field anyway.

This is not going back to the old days of units for two big reasons, they have important meaning within their field and there is widespread knowledge of conversion factors. Normalized units are also very popular in physics as they simplify the math and are more intuitive due to being directly tied to physical properties.

Hell, even going back to the old metric vs imperial debate, there were very good benefits to the imperial system back when calculators were rare as multiples of 12s were more convenient to divide in the most common fractions (2, 3, 4, 6). Even now our clocks are based on those multiples due to their convenience for general use.

Angstroms stick around in chemistry and biochemistry because they're approximately the length of a carbon-hydrogen bond (~1.09Å), and therefore easy to reason about and talk about.

Saying 1.09e-10 meters is fine, I guess, but it's a lot easier and more intuitive to think in terms of units of CH (plus 10%), especially when you're talking about more than one.

Remembering that CH is about 1Å and CC is about 1.5Å is such a basic approximation that it's become universal.

Angstroms are like cm - we could express everything as 10x mm or even 1/100 m, when you are deep in the subject matter having intuitive units facilitates communication by abstracting the 100pm or 0.1 to an A is helpful as that is the order of magnitude that covalent bonds exist within

eg Bohr radius is roughly half an angstrom and width of H2 gas is just under 3A

By expressing them in pm they actually lose some context as then they're all just numbers.

Daltons is a similar concept that springs to mind

Except for kilopascals, sometimes, none of the other things is even something physicists (or chemists or engineers) use regularly. Nanometers, angstroms, and femtometers are much more commonly found in the jargon.

You’re being pedantic, and incorrectly so at that.

If you want to know a little more about benzene, it is also known as a "Kekule Structure."

It is also called a "resonant structure" as the double bonds are said to flip in the ring of carbon atoms.

...or, at least, that was what I heard in high school organic chemistry. That was a very long time ago, and interpretations might have changed.

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

They don't exactly flip. It's more like each bond is on average 1.5 electrons. You'll often see it drawn as a hexagon with a small circle in the middle.
It's not that the bonds are flipping, but rather that each bond is kind of half a C-C single bond and half a C=C double bond--more of an average 1½ bond. This makes a lot more sense when you start getting into full-blown molecular orbital theory.
aka superposition?
That's something I wondered too, but I doubt it. The model used to explain benzene's bonds superficially sounds like superposition, and I can't really speak about the electrons involved (way too complex for me to even imagine), but when you look at the nuclei involved, it sounds implausible that the superposition of irregularly-positioned nuclei results in regularly-positioned nuclei. Implausible because they are too heavy and therefore localized.

But that's my layman's knowledge. I'd like to be corrected!

I can see why you might think this. It is a quantum mechanical effect, but it has nothing to do with the main quantum mechanical effect everyone knows about (superposition).

Superposition of two states is not preserved by measurement: it's more akin to a (complex, not real) probability you'll find the system of one of the states.

By contrast, resonant bonds are a real mixing of the two states: you don't observe the carbon-carbon bonds in a benzene molecule as either being a single bond or a double bond, you observe them as a uniform bond that's somewhere between a single bond and a double bond (e.g., bond length). Treating such things as a weighted average of various resonance structures is a usable approximation that allows you to predict the structure of more molecules without having to dive deep into molecular orbital theory.

I’m curious will this new knowledge will lead to new discoveries which might not have been possible due to working with the incorrect lengths in calculations?
It is an example of a new technique being used on a common chemical with an eye towards using it on other chemicals once the technique is proven.

‘And as this technique can be applied to highly symmetric molecules, it opens the door to the characterisation of many chemically important species like polycyclic aromatic hydrocarbons.’ - a researcher quoted in the article

So ... I'm guessing chemistry wasn't really sensitive to the difference, except in whatever few "edge cases" prompted this re-examination?
> milliangstroms

There is a perfectly sensible nearby SI unit called the picometre (pm). 10 mÅ = 1 pm. https://en.wikipedia.org/wiki/Picometre

Yes, while the ångström is often used for bond lengths, I've only heard of picometers used for smaller lengths.
ok but 'milliangstroms' immediately conveys a sense of relative error
Same as "mils" for thousands of an inch. It's actually wildly popular in the US.
Mils are a terrible compromise. On the one hand, they acknowledge that dividing by 1000 is useful and that it's easier to work on a linear scale instead of mixed units and fractions. On the other hand, it stubbornly clings onto the inch instead of embracing the millimetre or micrometre.

As a side note, I heard of carpenters who work in decimal feet. Yeah, that's great, adding yet another option to the mix. Everyone else talks in feet and inches.

When every measure around is on the same unity, you use that as your base unity.

If you are designing a large steel piece for milling, you will write a length of 1000mm, not 1m.

1m and 1000mm are not the same length.

1000mm and 1.000m are the same length.

Pretty close. If they added an additional zero to make 1.0000 meters they would be the same number of significant figures technically. But it's all convention. I've been in classes where 1.000 would be 4 significant figures.

> 120.0000 consists of six significant figures (1, 2, and the four subsequent zeroes) except for the last zero If the resolution is to 0.001.

1.000 has 4 significant figures. Absent other context, 1000 has 1.
When arguing convention, everyone is right, and everyone is wrong.
You're right that I'm remembering my sig-fig rules wrong, but you're not entirely right:

> Zeros to the right of the last non-zero digit (trailing zeros) in a number with the decimal point are significant if they are within the measurement or reporting resolution.

> 1.200 has four significant figures (1, 2, 0, and 0) if they are allowed by the measurement resolution.

and

> Trailing zeros in an integer may or may not be significant, depending on the measurement or reporting resolution.

So my first example "1m and 1000mm" actually might be the same length, depending on if those zeros are significant or not which has not been clearly communicated.

My second example "1000mm and 1.000m" is also ambiguous, since 1.000m is clear(ish) about its sig-figs, while 1000mm is not. I suppose I could have written "1000. mm"

Best solution imo would probably be:

- something that actually specified the error: 1m ± 0.0001m

- or using words to indicate what's meant: "exactly 1000mm"

The classic solution to this ambiguity is to always use scientific notation.

The sig figs in 1.0E3mm, 1E3mm, or 1.000000E3mm are unambiguous.

the only thing significant figures seem to be optimizing for is debate about the right way to use significant figures

in my experience, it’s always better to eschew them entirely and simply write an explicit error margin

Well, you wouldn't write 1.000m on it either.

That one would certainly lead to you getting something other than you are trying to design. Unless the machinist misreads it, or it gets assigned to that one machinist that likes searching people out and talking to them.

I don’t think this is correct.

1000.0 mm would be the same as 1.000m (or is it 1.0000?).

1000m has ambiguous sig figs.

The wikipedia article https://en.wikipedia.org/wiki/Angstrom has some historical context: 'In the late 19th century, spectroscopists adopted 10^−10 of a metre as a convenient unit (...). However, they soon realized that the definition of the metre at the time, based on a material artifact, was not accurate enough for their work. So, around 1907 they defined their own unit of length, which they called "Ångström", based on the wavelength of a specific spectral line. It was only in 1960, when the metre was redefined in the same way, that the angstrom became again equal to 10^−10 meter.'
Makes me wonder if this will result in any computational chemistry projects needing to be reworked.
I don’t think it’s likely. A well implemented ab initio calculation will include geometry optimization.

It’s possible that some forcefield constants will need to be tweaked in MD jobs, but this is a really small change in the bond length.

(comment deleted)
Title is cringe:

> Benzene’s bond lengths corrected

First, passive voice should not be used when avoidable.

Second, the bond lengths are fine. It's the measurement that was wrong.