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Talk:Orders of magnitude

For suggestions of new chains:

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Table of contents


  • Suggestion: The individual size pages should probably all have a link back to this overview.
  • Resolution: Not clear, but most of the size pages have one anyway.

  • Suggestion: Add a column of examples for each order of magnitude.
  • Resolution: Added, then removed.
  • Discussion

  • Suggestions for new chains:
    • A comparison of times would also be nice. --AxelBoldt Resolution: Done.
    • dimensionless numbers, like the number of stars in the Galaxy, the number of cells in the human body, and the largest known prime, the population of various countries and cities.
    • speeds (m/s = mps) of light, sound in various materials, ..., running animals, etc.
    • Add frequencies (Hz) for light, radio, sound, etc.
    • Add power, since many of the energy entries are really just "so much power" over "so much time". -- John Owens... hey, why are you looking at me like that?
  • Resolution: No major objections to these new chain ideas; not done because no-one's been willing to do the grunt work yet.

  • Further discussion not organized.

Sorry but this bit of Wiki just doesn't do the business for me. I know that I should put the effort in to sort it but I just don't have the confidence to replace all this stuff. Could we get some more views?
What "bit of Wiki" do you mean exactly? What do you think needs sorting? What do you think needs replacing? You solicit views about what exactly? --AxelBoldt

I generally agree that this page, while already very useful, needs work.
There seem to be two differing views going on here, concept and preciseness. I'm not convinced that the concept of scale is all that difficult to grasp, except when dealing with very large or very small and even then perhaps we're only providing a list of nice facts (grains of sand in a teaspoon v sahara). Conversely exactly what kind of day and precisely how many seconds it has doesn't matter when dealing with scale because the detail is irrelevant except to a scientist who already understands this stuff anyway?

I revert to my original question of the purpose of this all is, except that it creates a lot of pages? -Rjstott

Name of this page

First, why is this list of different units of measurement on a page called "orders of magnitude"? The latter does not mean "units of measurement." Why not put it on a units of measurement[?] (or better, listing of units of measurement[?]) page?

I'm not sure that "listing of units of measurement" would be more appropriate. We already have SI unit and conversion of units, and all units are listed there. "Meter" is a unit of length, but 100m, 1000m, 10000m are not. I believe they are often called "orders of magnitude of length".

What we could do though is to break this list up and put the length part on length, the mass part on mass etc., under a headline of "orders of magnitude of length" or similar. That however would lose the connection between different units, such as the connection between length and time given by the speed of light. Maybe we should do both: put it on length, together with nice examples for every order of magnitude, and keep it here as a general reference table. --AxelBoldt

Second, there are names like 1e-15 m. For someone who wants to know what "1e-15 m" means, in the article, we are told: "To help compare different orders of magnitudes this page lists lengths between 10-15 m and 10-14 m." This isn't very helpful for someone who doesn't know what "1e-15 m" means in the first place. For instance, what does that mean, using decimal places? Yes, any well-educated person knows how to figure it out; but a Wikipedia article about X, remember, is always for the benefit of a (perhaps theoretical) person who doesn't know much at all about X.

Larry, I changed 1e-15 m to be hopefully more informative in this regard. What do you think of that style? Also, these pages are not intended to be linked without an alias to a particular measure like [[1e-15 m|20 millionths of an angstrom]], so I do not think we need worry too much about the page names per se. --Eob

Third, I generally agree with the person who said (somewhere) that the titles of these articles could perhaps be stated in more clearly recognizable words and numbers, without symbols, e.g.: 1,000,000,000 meters[?] (or metres, if you insist). What's wrong with that, at least with the magnitudes close to 1?

Fourth, I think the simplest, single examples should be given for each unit of measurement at each order of magnitude. Again, the whole point here is not to make a pretty table but to make concepts clear to people who do not understand them. If we need several tables, grand, let's make them.

In general, try to bear in mind that our task here is to make concepts as simple as possible--it is not to build a merely pretty-and-clever system of webpages. Prettiness and cleverness are good but must be entirely subsumed under the task of making concepts clear to those who do not have them. --LMS

I disagree with the absolute mish-mash of units being used in this table. I replaced angstroms with nanometres, and gave microns their SI name (micrometres), but it still has four different units being used to measure distances (metres, nanometres, astronomical units and light years). Similarly, for time it has seconds, days, years, etc., for volumes it has cubic metres and litres, for mass grams, kilograms and tonnes, for energy joules and electron volts... the whole idea of "orders of magnitude" would be clearer if a single unit is used throughout. -- SJK

My intent was to use at each scale the units that is used most commonly (by scientists and technologists) at that scale. I think, using units appropriate to the scale gives a better intuitive sense of the orders of magnitude. As regards Angstrom, my understanding is that in the 10-10m range scientists in a lot of fields use that unit a lot (if not mostly). Similarly, I think "micron" is more familiar than "micrometre". --Eob

Column Layout of this page

Moved this from "TalkAboutExampleColumn":

I think the example column should be placed immediately after the column of dimensions that it's an example of. As it is now, it's unclear what dimension things in the example column are an example of; for example, is the Sun an example of something that is 109m in diameter, or is it an example of something with an area of 1018m2? This gets even more confusing when mass is considered as well. I'll move it over and see if it looks okay.

There, fixed. If everybody hates this, revert it; otherwise I'm going to add empty example columns for the other measurements as well for future expansion. :)

Hmmm, I think having an example for every unit might clutter up the table too much. My intention of lining things up in rows the way I did was to show a general sense of order of magnitude of objects that have "normal" densities (within an order of magnitude of water at 1000 kg/m3). But perhaps this is not appropriate as things like sub-atomic particles and galaxies have densities that are much-much bigger or smaller. So perhaps on reconsideration we should try to keep the table clean and not put examples columns, but just have people link down to the pages to see the examples. --Eob

Hi 129.128.164.xxx, thanks for entering all those examples, but I think that now the table is getting too cluttered up and some of the examples are not in the individual pages. I suggest we do get rid of the examples column and move them to the individual pages. That way they will be more useful in other pages that link to those pages. --Eob

Heh. Sorry, got a bit carried away and wasn't reading Talk updates while I worked. :) I was getting those examples off of http://math.ucr.edu/home/baez/distances for the most part, if you want more precice measurements. I think it'd be good to have at least a few examples scattered throughout the range of this table, however; otherwise the measurements are just meaningless numbers. - BD, from a public terminal

Here is my reasons for not including examples in the table:
    1. I think the table should be as clean as possible. This will become particularly important if we add columns for time, temperature, pressure, etc.
    2. The formatting on this table is tricky because of the use of HTML tables. Many people will have problems editing it if we are going to keep on adding examples. (In fact some of the recent edits had bad HTML which might have caused problems with some browsers.) I think that it should be more like the periodic table which does not get modified very often once it is set up.
    3. Having the same info in two places would make it hard to maintain.

The table would be a lot more fun if there was an example of something of that size at each order of magnitude, sort of the equivalent of the Eames film or this link Quarks to Quasars (http://www.wordwizz.com/pwrsof10.htm). Ortolan88

Yes that is pretty neat. How might this be done though? --mav

Well (A) we could link a couple of these animations (there's more than one kicking around) and (B) simply add an example at each size: fox is 10 times bigger than a rat is 10 times bigger than a cockroach is 10 times bigger than a lentil is 10 times bigger than whatever a lentil is 10 times bigger than, etc, till we got all the way down and all the way up. Ortolan88

It's a good idea. It might bloat the table a bit, depends on how many columns we add. It might be better to keep this main table as is, and put a more interesting versions on volume, length, area etc. For that matter, I can see why 1g, 1cm, 1cm^2 share a row, but why 1 picosecond? -- Tarquin

here (http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index) is an example (you'll need to allow Java to view it though). --KQ

Tarquin wrote: I can see why 1g, 1cm, 1cm^2 share a row, but why 1 picosecond? -- Tarquin

Read the article: 1 ps is the time it takes light to go 1 cm (give or take a factor of 3).

Personally, I don't think that this is a good idea. For a table like this, we should stick to Earth sized relationships between units. Plus, our factors will be much closer to 1; it's no coincidence that the density of water and the strength of Earth's gravitation field are both nearly round multiples of SI units at Earth's surface. We already set the density of water to 1 (as a physicist would put it), but then we set the speed of light to 1. I say that instead, we should set the strength of Earth's gravitational field to 1. We can even add a Force column that gives the weight of an object with a certain mass, on Earth's surface.

A more radical idea: Since the Energy column serves only to store measurements in electron volts, which are used just as often as a measurement of mass, remove the Energy column and stick the electron volts into the mass column in the places where they're typically used. As anybody that groks special relativity can tell you, rest mass and rest energy are different names for precisely the same thing. (BTW, I've only ever see "electron volt" abbreviated as "eV", never "E V" as on the temp page. Was somebody trigger happy with the search and replace?)

A typical row:

Time Length Area Volume Mass Force
1 s 1 dm 100 cm² 1 L 1 kg 10 N

All human sized, because this is a human sized row.

So what is the relationship between a second and a decimetre? Make a pendulum clock out of a decimetre stick and see for yourself ^_^. — Toby 15:21 Aug 24, 2002 (PDT)

the old pages The old-style names redirects still exist; IMO they should be deleted. I doubt they are Google material, so they're not really useful, and may even confuse. -- Tarquin

Even though I usually hate deleting redirects I think that in this case their existence will lead to more confusion than anything else. This shouldn't be too big of a deal for those outside of Wikipedia since these pages haven't been used that much. In the end all links will be changed to the new syntax. The second best solution would be to create redirects for all major valid alternatives so that most everything works. --mav

What can be gained by deleting the redirects? Isn't the whole idea to make linking easy? Forcing people to check every time which convention of the day we currently prefer for orders-of-magnitude pages seems to be counterproductive. All reasonable conventions should continue to work. AxelBoldt

The way it is now there are three ways to links to many but not all of the orders of mag articles. We must therefore either create redirects so that each orders of mag article can be linked in a few different ways or we delete the current redirects. Either way works for me -- although since many orders of mag article have yet to be written, it is a bit much to ask that each person making a new one has to create several redirects. I guess that's why we have Wikipediaholics like me... If nobody else does it, I will. --mav

I agree with Axel. Whenever I create a page, I always try to think of likely alternative names for redirects. I think that it's just good policy to make linking easy. We have naming conventions, not linking conventions. (My smart-ass quote for the day ^_^.) BTW, I guess that I'm going to work on some order of time magnitude pages soon. — Toby 05:14 Sep 19, 2002 (UTC)

Next Steps Now the the existing orders of mag articles and templates are moved to their new (hopefully semi-permanent) homes I now propose the format for each should be something similar to 1 E-10 m. In this entry I am using the SI prefix before the SI primary unit as the primary way to express the unit. In this case that is nanometres and picometres. Non-standard metric units, in this case the Angstrom, would be within the comparisons list along with non-SI units. SI prefixes will be able to go fairly high (1 E24) and fairly low (1 E-24) and should cover most everything. What does everybody else think? --mav

Sounds good. Though I'm confused about " 225 pm (0.33 nm) ". I think having another number in parentheses on each line is a little heavy on the eye. On several pages, I've put all the "unit conversions" and "pure geometric" stuff in an indented list: see 1 E6 mē. -- Tarquin 10:33 Oct 6, 2002 (UTC)

I agree - there is no reason to have two SI units right next to each other. That was a left-over from the previous version of the article in which Angstroms were the primary unit and nm were in parens. It should be * 225 pm (0.225 nm) to be factually correct -- yet another artifact of my hasty conversions. -- mav

It occurs to me that we should never say something like "5 E 22 m" in an article's text, since printed material says "5 × 1022 m" when it's capable — and HTML has been thus capable since the days of Netscape 2. Note that this doesn't affect article titles, which can't handle superscripts; "E" notation is standard in a superscriptless environment. But it does mean that we won't have free links like "5 E22 m[?]". — Toby 16:07 Oct 28, 2002 (UTC)

I've noticed that sometimes when people edit articles containing the superscript-2 character (as opposed to its HTML encoding, 2 or ²) it seems to automatically get translated into a normal 2 by their browsers (it's either that or they reflexively change it into a normal character, an understandable reaction IMO :). I think all area pages of the form 1 E14 m² should have redirects from the associated 1 E14 m2 page. Bryan

I've spotted this particular browser bug very occasionally on other occasions. It's an argument for always using the HTML character entity (ampersand) encoding, instead of the Latin-1 character directly. Although I agree that redirects of this sort are very wise, note that it's quite possible to make a link using them ([[1 E14 m²]] = 1 E14 m²). — Toby 14:24 Nov 17, 2002 (UTC)

One note, though: The &sup2; looks much better typographically than <sup>2</sup> since at least on my browser the first one does not add extra leading but the second one adds one extra half blank line which is quite disturbing. So for m² I would suggest using the HTML character form.

One other thing: Has anyone ever seen the Mm unit outside of Wikipedia? I have not, so I suggest we use 103 km instead. -- Egil 09:40 Mar 23, 2003 (UTC)

Once: http://hem.fyristorg.com/ojarnef/fys/metric-units-comp.txt It's been a while since I read it, but I seem to remember this guy doesn't like scientific notation very much, and would like to see some extra prefixes added so that we can write Planck's constant as 0.105 vJ·s. I think we should go with 103 km. -- Tim Starling 22:56 Mar 23, 2003 (UTC)

Google gives a reasonable amount of hits for megameter, most of which refer to some astronomical instrument but many of which refer to the unit. The correct SI spelling only gets about 200 hits. It's not a very common unit over here, but then, I never saw centilitres until I went to France, and then they were everywhere.

I've made a template for orders of magnitude; if I'm mistaken and one already exists, I'd love a pointer to it. -- JohnOwens 08:05 Mar 26, 2003 (UTC)

Nice work! It's been ages since I've done any work on these entries and I'm glad they haven't been forgotten. --mav

I'm noticing that, admittedly, a lot of the examples I'm using for energy are really just an amount of power over an arbitrary period of time. So register your objections here, if any, or a power column gets added in a couple of days. -- JohnOwens 23:41 Mar 27, 2003 (UTC)

Is there any reason to include entries below 1_E-19_m? It serves no purpose other than adding confusion, as fas as I can see. When/if science enters this realm, the table can always be extended. -- Egil 07:38 Mar 31, 2003 (UTC)

Well Planck's length is at 1 E-35 m... I don't see how it would be confusing to fill the gap between that and measurable lengths. --mav

Sure, but what are you going to fill it with? Other than just '10n' over and over again. -- John Owens

Agreed. The entire point of the sub-articles for various orders of magnitude is that you can compare things of the same magnitude. 15 empty articles between 10-19 and 10-35 does not serve any purpose... -- Egil 08:28 Mar 31, 2003 (UTC)

It suddenly struck me: For very high masses and energy levels, it would make a lot of sense to make articles covering thousands instead of tens, wouldn't it? I've done it for high temperatures, and it seems to make sense. -- Egil 06:56 Apr 1, 2003 (UTC)

I would thus suggest making articles for thousands for other extremes too. Also, just like years are used for long durations and light years for long distances, I would suggest using kWh for energy levels above 106 J. That would make it easier for people to relate to and understand these energy levels. -- Egil 07:43 Apr 3, 2003 (UTC)


STOP adding arbritary prefixes to SI units. PLEASE only use prefixes that are in common, scientific, use. Constructions like Zettaseconds and Megameter are just that, constructions. They are not commonly understood, add only confusion, and additionally makes what is supposed to be an encyclopedia look like a product of some juvenile word game. -- Egil 13:15 Apr 1, 2003 (UTC)

On the other hand, just a decade ago, you could have said much the same about the prefix "giga", and nowadays it's very commonly used, although almost entirely in the area of computer storage (I sometimes see it used with Watts, too). -- John Owens 22:51 Apr 1, 2003 (UTC)

Yes, giga and tera has been in common use for watt, watt hours and electron volts for as long as I can remember.
But the important issue is: The encyclopedia should reflect the current state of affairs, not seek to introduce new and unknown terms. For an influential encyclopedia there might be an aspect of a sort of Heisenberg uncertainty principle, obviously. -- Egil

Are you aware of the following entry Magnitude comparison? Can you find a better title (my proposal is too long: Order of magnitude comparisons of distance[?])? -- looxix 23:14 Apr 19, 2003 (UTC)

Order of magnitude - length maybe? Just move Magnitude comparison to whatever title you want. -- Tarquin 09:07 Apr 20, 2003 (UTC)

Is the Order of magnitude - length really required? It seems like duplicated information and effort to me. -- Egil 14:33 Apr 24, 2003 (UTC)

Agreed, all the different dimensions have their links up in the top section. I'll take that one out, but I think it might be nicer to have them in a list format instead; I'll see if that can be worked in nicely while I'm at it. -- John Owens 15:25 Apr 24, 2003 (UTC)
Oops - Order of magnitude - length is actually a different page than Orders of magnitude (length). :p Now I'm not so sure what to do about that link. -- John Owens 15:28 Apr 24, 2003 (UTC)

Order of magnitude for frequency

I frankly don't see the need for these, because they are merely expressing the same property as time. I suggest all (now open) magnitude of Hz be redirected to the relevant times. As I test I've redirected 1 E6 Hz to 1 E-7 s (not -6, because of the decade greater or equal convention). -- Egil 14:49 May 2, 2003 (UTC)

While you're at it, why don't you get rid of area and volume, since they're physically the same as length?

I'm not serious, by the way. The point is that T ≠ T-1. It's perfectly reasonable to have periodic phenomena listed on one page and one-shot phenomena listed on another. Not only is the phrase "shortwave radiation has a cycle time of 0.1μs (10MHz)" horribly counterintuitive and at odds with the terminology of the general public, it's dimensionally dubious. -- Tim Starling 07:36 May 8, 2003 (UTC)

I'm not really with you on the area and length. The reciprocal of frequency is wavvelength, and they are often treated similarily (even on the scale of your radio). For me it made sense to make the Hz links point somewhere, and I still think it is nice to combine them. Perhaps a short introductory sentence that explains the connection would help? -- Egil 06:13 May 9, 2003 (UTC)

Area is the same as length in that you could say on 1 E3 m:
  • a square with sides 1.4km has the same area as Monaco
Converting from Hz to s requires a little bit of rhetoric and some dimensional manipulation, just like m2 → m.

When I wrote my comment, I thought you were actually merging pre-existing Hz pages with s pages. I'm content now, but I'd be happier if someone would write Hz pages. I'm not going to do it myself because I think trivia lists are a waste of time. Please ignore my backseat driving :)

I don't think an introductory sentence explaining the connection is necessary. -- Tim Starling 10:23 19 May 2003 (UTC)

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