3 ms·
> This here desk I have here is about 1.7 times as long as it is wide. No inches or centimeters required. But you are using units. Your unit is the width of y
by bj0 11y ago
> This here desk I have here is about 1.7 times as long as it is wide. No inches or centimeters required.
But you are using units. Your unit is the width of your desk. If it were a different width but the same length, your measurement would be different.
- kazinator 11y agoSo tell me, how large is my desk? Note that the aspect ratio lets us say things like: "these two desks have the same aspect ratio". The "desk widths" interpretation of aspect ratio precludes this useful sentence from having semantics. The aspect ratio 1.7 has a life of its own, independently of that desk.
- bobcostas55 11y agoLet's say the width of your desk is denoted by "w". The length is then 1.7w. The aspect ratio is dimensionless because it is = 1.7w/1w. w/w = dimensionless. But you still used a unit, w, to make the measurement in the first place.
- contravariant 11y agoHe could have measured the angle of the desk's diagonal makes with the longer side, that would give him tan(w/l), no inches or centimetres required. You do need radians, but that's not a unit in the same way a 'meter' is, you don't need any kind of reference to know how much, say, 1 pi radians is. For most intents and purposes angles are unitless.
- kazinator 11y agoThat is inescapable for any quantity whatsoever that we extract from nature. In dimensionless quantities, the units just canceled out. Amperes divided by amperes, or whatever. See root comment. I do not have to specify the units that I used when I quote the aspect ratio, or the method that I used.
- contravariant 11y agoSo, if he measured the width and height again, using different units, would he get a different answer?