8 ms·

I've often felt it to be helpful to treat dimensionless quantities as a smell that the dimensions might be too unspecific. 12 meters / 3 meters is just a unitle

• TeMPOraL 5y ago
  On a related note, I've been dealing with some process chemistry recently, and I've noticed that a lot of dimensionless quantities that are ratios retain their original units - I've seen many cases of units like e.g. [kg/kg]. Not sure what's the reasoning behind this, but I suppose this prevents mixing up [kg/kg] with [m/m] and other unrelated ratios.
  • jimmaswell 5y ago
    If it's something like milligrams of X per gram of Y I think it's generally better to just write it like (mg X)/(g Y)
  • gerdesj 5y ago
    If you are having snags with dimensionless ratios in chemistry, why not talk to any half competent cook/chef? They don't piss about like that! The reason your quantities (LMT etc) are dimensionless is because you need to bake a decent cake or mix a cocktail and get a grip 8) I am being flippant but I don't think that mixing kilos and meters in any unlikely ratio is likely to end well. They tend to become quite forceful if not mixed carefully.
    • rendall 5y ago
      Well done. Jokes and puns aren't appreciated on HN, but I see what you did there.
      • lupire 5y ago
        What were the jokes and puns?
        • rendall 5y ago
          OP was being silly, and kg m / s^2 is a measure of force, so you have to mix them carefully or they might act forcefully.
      • gerdesj 5y ago
        "Jokes and puns aren't appreciated on HN" You have to pick your time(zone) when deploying them. I generally find that GMT/UTC >=+6 is when a sense of humour failure generally kicks in. At +8 it relents a bit when en_AU kicks in and is reinforced at +11 by en_NZ.
        • rendall 5y ago
          Worst downvotes I ever got, in response to a fellow from Google expressing a very uncontroversial opinion and then making it clear it was only his own opinion, I wrote: "Hi Jim, this is Chet from HR. Let's have a chat on Monday." Even my "Sorry, bad joke. I'm not 'Chet' and I don't work at 'Google HR'" response got downvotes. Many, many responses hating on Google HR in particular and HR in general.
    • TeMPOraL 5y ago
      > If you are having snags with dimensionless ratios in chemistry, why not talk to any half competent cook/chef? They don't piss about like that! I don't! Also, doing this would go against my belief that I already mentioned on HN several times - that the difference between process chemistry and cooking is that the former actually cares about the quality of outcome ;).
  • nradov 5y ago
    It's useful to distinguish between mass ratios versus volume ratios. Some materials can vary in density depending on how they're packed or compressed.
  • talaketu 5y ago
    Or, in electrical engineering, "power factor" and the distinction between kVA and kW.
    • henrikeh 5y ago
      And in communication theory / information theory there is spectral efficiency, which is 1/s/Hz (rate over bandwidth. Sometimes given in bits, sometimes in symbols)
  • jzwinck 5y ago
    This commonplace in liquor stores and pharmacies: concentration by volume is v/v and by weight is w/w. https://www.bode-science-center.com/center/hand-hygiene/hand-disinfection/detail-hand-disinfection/article/ethanol-concentration-table-what-is-the-percentage-by-volume-or-weight.html https://www.bode-science-center.com/center/hand-hygiene/hand...
• jobigoud 5y ago
  Yeah it's always a normalization to the denominator.
• elcritch 5y ago
  We had a physics prof infamous for "randomly" regrouping a bunch of constants into a new unitless (or just combined) constant. Except he never explained it; a new "α'" would just appear and bunch of old constants were gone! It was frustrating at first, but then we discovered how handy it was to do and our cohort nicknamed the "method" after him. It was common to ask each other 'did you "Rebka-tize" that term here?'.
  • mhh__ 5y ago
    That kind of trick is honestly the reason why I don't like reading engineering textbooks. A physicists prose is usually better, sure, but I'm not very good at reading so that doesn't bother me: What I can't stand is cumbersome notation, which many mathematical (i.e. FEM) engineering books I've read suffer from immensely.
• digikata 5y ago
  Sometimes they're well established and provide very useful characterizations that tie into physical behavior. For examples Reynolds numbers and Mach numbers in aerodynamics are quantities that can tell you immediately what kind of flight dynamics range you're dealing with.
• deleted 5y ago
  [deleted]
• sidpatil 5y ago
  > 12 meters east / 3 meters north is a much more interesting 4 units-east-per-unit-north. Wouldn't it make more sense to describe those distances as vectors instead of overloading their dimensions?
• smingo 5y ago
  There is this Erlang unit, for the number of simultaneous calls a telecommunication system can handle. https://en.wikipedia.org/wiki/Erlang_(unit) https://en.wikipedia.org/wiki/Erlang_(unit) It's dimensionless, because it multiplies the rate that calls are initiated by the average length of a call: 'calls / second' by 'seconds / call'. Dimensionless. But that makes little sense - we're measuring the number of simultaneous calls. It gets reflected in buffers, circuits, sockets, channels allocated, etc. It would be better to consider 'call starts / second' as the rate at which calls are initiated, and the average 'call.seconds / call start', which when multiplies gives the more sensible unit 'call'. Or simpler: just measure the average length in seconds. So we have so many 'calls / second' initiated, and the average length is so many 'seconds', which when multiplied again gives a unit of 'call'.
  • beerandt 5y ago
    You don't have to always reduce units if it makes sense not to. Like saying a foundation footing has 27-ft^3/ft of concrete.
  • resonantjacket5 5y ago
    Agreed, though I'd interpret it slightly different. Like if I said 100 cars per hour and each car needs 30 seconds of spacing per car the units don't cancel out because they are physically taking up space for the "30 seconds of spacing per car." I'd say the same applies in this case. It'd be more "calls/sec" times "active phone * sec/calls". Though I guess for "call" in your case or "active phone" the industry has chosen 'Erlang' a bit recursively.
• wyager 5y ago
  You should be using a dimensionless vector. Dimensionless numbers are the opposite of a smell - they are the most pristine, fresh quantities you can get in physics. You usually want to express everything you possibly can in a dimensionless way. It tends to make the math a lot simpler and to punch to the heart of the problem.
  • awill88 5y ago
    You talk about math like it’s poetry … can it really be that artistic of a practice? I suppose that’s how I view writing software.. What is an example of dimensionless numbers?
    • deleted 5y ago
      [deleted]
    • wyager 5y ago
      I would put dimensionality more in the purview of physics than pure math, and at that point it might be more reverse engineering than poetry. Fine structure constant, quantum phase, angles, e, pi are all dimensionless.
• bobbylarrybobby 5y ago
  Same thing with radians (a "dimensionless" unit) -- angle is the ratio of two lengths, arc length/radius, so technically dimensionless, but those two lengths are not of the same thing. I always felt more comfortable saying "pi radians" rather than just "pi" because radians feel like a real unit in the same way that units-east-per-unit-north do. I wonder if there's been any study into when it's ok to cancel two of the same unit and when it's better to leave it as a ratio of two quantities with the same unit but describing different dimensions. Is there a way to make this notion precise?
• feoren 5y ago
  Units are to calculations as Types are to code. They help prevent a large class of common errors. If your types aren't consistent, you know your code is wrong. If your units aren't consistent, you know your calculation is wrong. Just like there can be stronger and weaker type systems, there can be stronger and weaker unit systems. Stronger unit systems catch a larger class of errors. I commonly catch errors nobody else sees because I use a stronger unit system than they do, which is amended with generics ("kg of what?"). Just like you said: a unitless quantity is weak; ppm doesn't help you catch errors very well. It could be mg/kg or µL/L, and it matters when you start canceling ratios. But you can take it further: mg<constituent>/kg<soil>. When you start throwing in soil density and molecular mass, it's very easy to come up with examples that "pass" the standard dimensional analysis but "fail" your advanced unit checker. You can look like a wizard by detecting errors in equations completely outside of your field of expertise. Once you realize that there can be as many unit-systems as type-systems and the only criterion for a good vs. bad unit system is how well it catches errors, the purists who try to enforce their physics textbook's view of units will look really silly to you. The only problem is that you start arguing with them about whether specific gravity is really unitless or not (it's more helpful to say it's not), and they immediately decide you must be a moron because that's not what their textbook says. Oh well. You're getting the right answer, and they're not.
  • lordnacho 5y ago
    This is the most insightful comment I've read today. Ties up a number of thoughts I've had while explaining this to my kid. You're right that there's a choice about how strongly typed your unit system is. Another useful tidbit is if your formula has a log or an exp, the arg needs to be dimensionless.
    • feoren 5y ago
      > Another useful tidbit is if your formula has a log or an exp, the arg needs to be dimensionless. I have cognitive dissonance about that. I understand that if you look at the Taylor series of Exp(x), you're clearly adding terms containing 1, x, x^2, x^3, etc., and that it doesn't make sense to add a meter to a square meter to a cubic meter and so forth. So therefore Exp(1m) doesn't/shouldn't make sense. But on the other hand, I can come up with examples that seem to make sense, but seem "dimensionful". Is a bit dimensionless? Because it certainly makes sense to consider 2^(32 bits) and 2^(4 bytes). Yet bits are deeply related to entropy and might even be considered a unit of energy. Are we sure they're dimensionless? What is a "square bit" anyway? I can also define "specific meters" to be the length of an object divided by the length of a 1-meter-long stick. This value is now dimensionless, so it should be OK to exponentiate it, correct? Am I cheating? How? Or I should be allowed to take Log(7 mg/kg) because mg/kg is dimensionless. But this should equal Log(7 mg) - Log(1 kg), which I'm not allowed to do. What gives? Again I come back to: is this actually helping me catch errors in my calculation? I'm honestly not sure here.
• omegalulw 5y ago
  What's a use case for "units-east-per-unit-north"? Proportions of a room? Call it 3:2 or whatever, makes perfect sense. A direction? Use an angle. Like some other commenter said having to deal with "units-east-per-unit-north" is like code smell.
  • lupire 5y ago
    why use an ambiguous unit when you have a precise unit? radians and ratios require a zero axis. The code smell is when the uniy is missing.
• anonytrary 5y ago
  12m east / 3m north does not make any sense, since vector division is undefined. You might be thinking about the derivative which has no units in this case.
  • lupire 5y ago
    You're missing the point. The units are useful because they express direction.
  • OscarCunningham 5y ago
    You can divide by a vector of a 1-dimensional vector space, which is all units really are. https://oscarcunningham.com/4/dividing-by-a-vector/ https://oscarcunningham.com/4/dividing-by-a-vector/
    • anonytrary 5y ago
      How is that relevant here? We're talking about a two dimensional vector space (hence "east", "north").
      • OscarCunningham 5y ago
        Since we've chosen a basis of the vector space (east, north) we can think of it as two 1-dimensional vector spaces. So we're dividing meters east by meters north.
• ctdonath 5y ago
  Hence the genius of E=mc^2 in that the units did line up but nobody would accept the obvious, until Einstein.
  • teddyh 5y ago
    𝐸=𝑚𝑐²
  • Armisael16 5y ago
    Everyone was perfectly willing to multiply mass by the square of a velocity: KE = 1/2mv^2 It wasn’t at all obvious that removing the 1/2 and using c as your velocity would be meaningful.