Category talk:Dimensionless numbers
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[edit] Avogadro's number
I have removed Avogadro's number as it is not dimensionless. It is atoms per gram molecular weight or per kilogram molecular weight, so its value depends on the size of the gram in one case, or the kilogram in the other. If we used pounds or ounces, again Avogadro's number would change in value. For example, in the case of ounces, it would be the number of atoms in a number of ounces equal to the atomic weight (which, itself is dimensionless, but the ounce is not)
Pdn 05:33, 9 Mar 2005 (UTC)
More comment
I checked "mole" and I see that the kg-mole is no longer used. I actually once talked with the AIP on this. What happened was that with the transition from cgs to SI, they decided that to avoid confusion with the gram mole and kilogram mole, they would effectively eliminate the latter, which is why 0.012 kg of carbon is used, which stands for 12 grams. By that artifice, it was not necessary to change all kinds of chemical and engineering tables to a new mole based on the kg.
Yet the number is still not dimensionless! The kilogram itself is defined by a mass of a platinum-iridium bar in Sevres, France!
see
This bar can vary in its contents by absorption or desorption of moisture or gases. It is the only primary "artifact" standard left - the second is based on a vibration of a Caesium atom and the meter is based on time via the definition of the speed of light.
There are suggestions (see the above link) to replace the definition of Avogadro's number by something not dependent on an "artifact" (e.g. the bar of metal in Sevres) because an ideal standard can be recreated in any good laboratory, while to check against an artifact you have to go there (Sevres) and be allowed to access it.
So someday the number could be defined as a pure number in some sense, based on counting atoms. That has not been done. If it were done, one could still argue that the way the number was defined was based on the value of the gram or the kilogram - we're not there yet so let's leave that for future philosophers.
Pdn 06:01, 9 Mar 2005 (UTC)
[edit] is this category useful?
Isn't this a completely unnecessary page? I can come up with tons of dimensionless numbers. Euler characteristic, speed of light and whatnot. (anonymous)
Of course, pi is a dimensionless number, and so is Catalan's constant. Note that the nathematical examples are constants. But in physics and engineering, and related sciences such as astronomy and chemistry, dimensionless constants are particularly useful for describing and classifying physical behaviors. Such numbers (generally not constant from case to case) can tell you whether a fluid flow is viscous or inviscid (i.e. negligibly viscous), whether an airplane is travelling subsonic or supersonic (Mach number > 1), and a chemical example is on that page, too. Unfortunately, the majority of listed numbers are from fluid mechanics and other important cases are omitted. For example, for a rotating deformable body such as the Earth or Sun, there is a dimensionless number J2 that gives you a measure of the deformation (equatorial bulge - but for Saturn, small for the Sun). I don't have time to put in more examples like that one, but there are lots of useful ones (power factor in electric transmission theory is one) and with that page as a sort of stub, people can add more. It is very frustrating to students to run into a Peclet or Prandtl number and not find its definition easily; on the other hand it can be called a "cottage industry" to collect these and add more. Pdn 03:44, 15 Apr 2005 (UTC)
[edit] categories for dimensionless numbers
Message originally posted on User talk:SebastianHelm
Dear Mr. Helm, Glad that attention is going to those pages. I think you should restore engineering and science as categories. In engineering, the usage of dimensionless numbers reduces large families of problems that do not seem identical into single cases. It's an approach that many engineers have trouble dealing with; they will produce charts with a half dozen parallel lines that could be collapsed to one by scaling the axes. So it is educational to reference the page from engineering. In science the usage is just as important and more frequent. Unfortunately, there's an apparent (but largely fictitious) difference between pure maths constants and physical dimensionless numbers. For example, pi=3.1415926535... seems to be a mathematical constant with no dimensions, but it can be regarded as having the dimensions of inverse radians. To get a perimeter from a radius you have to measure the included angle in radians and use that value of pi I gave. If you measure the angle in degrees, you must use a constant numerically equal to pi/180, not the number just quoted. (I know this is arguable as you can define pi as the ratio of the circumference to the diameter, but for practical use it comes out as I said.) Anyway, I don't see where it hurts to leave the old categories and just add new ones, too. Pdn 14:57, 20 May 2005 (UTC)
Thank you for your nice message. I made a mistake. I had thought it were already under category:engineering via category:measurement. Also, i just realized that they are not under category:Physical quantity, and i just fixed that.
I split up my reply in two sections below. — Sebastian (talk) 19:35, 2005 May 20 (UTC)
[edit] engineering
You convinced me that it’s good if people find dimensionless numbers easily. You obviously invested more time in this area than i did so i’ll be happy with any way you see fit. Restoring the link is certainly an option.
I would like to weigh in, however, that it may not be quite at the level of most of the other categories directly under engineering. I see it this way: The introduction to category:Engineering reads “Engineering is [...]. This is accomplished through knowledge, mathematics, [...].” I don’t see how dimensionless numbers could fit in such a high level view.
How about if we created a category like "engineering tools" or so that would also include (and "demote") category:Measuring instruments, category:Tensors and category:Workstations (and category:Engineering failures – just kidding!)? This category could also hold category:measurement andcategory:Physical quantity, neither of which are currently assigned to category:engineering.
[edit] science
As for category:science: This is a big field and i don’t think it should directly include dimensionless numbers at the top level. Which other sciences unrelated to physics are you thinking of? I would think that they all should have category:Measurement and/or category:Physical quantity, so they should contain this category already.
[edit] reply
I am not really familiar with the structure of categories and subcategories in Wikipedia, so do whatever you think is best. I do not see how these numbers are related to "measurement" but evidently you do. Dimensionless numbers are very important in physics (e.g. the fine structure constant, the ratio of gravity strength to electric field strength, mass ratios of fundamental particles are essential). Being important in gas dynamics (Reynolds, Mach and similar numbers) they are important in astronomy, because most of the material in the universe is in gaseous form, and often it is stirred or shocked. I do not know much biology but I suspect there are important dimensionless numbers there. I will ask a chemist friend about chemistry - see you later Pdn 01:12, 21 May 2005 (UTC)
Thank you for your vote of confidence. If you think that the name "engineering tools" is appropriate then i will create such a category.
You're right about "measurement", i don't see a significant connection, either. It just happened to be there, and i didn't question it enough to remove it. I'll remove it now. BTW, categories are no rocket science. They are developped ad hoc, and it's very likely that if something doesn't make sense to you, it's wrong. I'd like to encourage you to be bold and get more involved with them; they offer a nice 10 km overview of our articles. Of course, that's nothing for an astrophysicist...
Biology: Well, the number 2 is very important there. ;-) Seriously, though. I don't enough about the subject to know any that are as important as the physical ones. I looked up in a biophysics book and they all are physical quantities.
chemistry: pH, solubility constant, dissociation constant. In addition, there are of course concentrations – but i assume such variable quantities aren't of interest here. — Sebastian (talk) 07:30, 2005 May 21 (UTC)
'fraid "pH" is not dimensionless at all - as I remember (from Chem 2 at Harvard, 1953) it is the negative logarithm of the hydrogen ion concentration in moles per liter. I think it's based on the common logarithm, not the natural one. So it involves moles and liters, which are based on dimensional standards. OK, a logarithm is "dimensionless" perhaps to a mathematician, but not really. It a logarithm were always dimensionless we could take the distance to the Sun, about 1.5 *10^11 meters, take its logarithm (a little over 11), and claim the distance to the Sun is dimensionless. We need to decide if a variable quantity like a concentration is a dimensionless number. If it is not then the Mach number, Reynolds number and so on also do not qualify, because they are different for different flows. Better allow concentrations in the door. I would expect that in biology the number of chromosomes, or base pairs, or something like that for a given species or individual is a dimensionless number, but I think we should not ask a biologist or chemist about any of this. We'll just have to rely on their reading Wikipedia and noticing an omission - else we'll be spread too thin.Pdn 15:30, 21 May 2005 (UTC)
You're making a good point about pH. Let's move that discussion to talk:Dimensionless number. Back to the question about categories for dimensionless numbers: I agree about biology. What do you think about chemistry? Is the relation important enough for us to include that category? I'm undecided. — Sebastian (talk) 17:45, 2005 May 21 (UTC)
[edit] Pi
I added Pi. About this one, I sure hope we don't go round and round and round and r... Bob Stein - VisiBone 22:48, 1 August 2007 (UTC)
[edit] e?
Shouldn't Euler's number e (approximately 2.71828) be here? Apparently in addition to the Euler number (physics) aka Cavitation Number. Not to be confused (!) with Euler numbers (integer series) nor Eulerian numbers (a triangular table of integers). Bob Stein - VisiBone 22:48, 1 August 2007 (UTC)
