3 ms·

I think of it the other way around - dimensional analysis of units is a special case of a type system. Two units of different measures cannot be added/subtracte

I think of it the other way around - dimensional analysis of units is a special case of a type system. Two units of different measures cannot be added/subtracted with one another. Units of the same measure (e.g. length: cm, in) are trivially convertible via a scalar factor (e.g. 2.54 cm/in), and units of different measures (e.g. length: m, time: s) can be multiplied/divided to get a new unit of measure (speed: m/s), although some such units might have no practical use.

cb321 5y ago
Dimensional analysis of units is absolutely a special case (I said "primordial example") of type systems. Proof: "constrained operations" and "notional objects" are very limited/somewhat concrete - "additive/comparative/conversion-y" and "measured things". Modern notions abstract both ideas. This is, however, not unimportant (not to suggest I think @10000truths said so, exactly). In educational settings one usually wants to begin with the most familiar examples and then generalize. { Why, this probably even applies to greats like Russell. :-) } Further, in attributional settings, giving general names/notions to things is often less seminal than the things one is naming. (Both are often worthy of attention, but I tend to push back when "namers get all the credit".) There is probably no single, famous big name like Russell to attach to the idea of units of measure/standard conversion/comparison. There may be a King of Olden Times who beheaded those who didn't follow his particular "system" when taxing crop growing areas or converting area to expected weights or volumes of grain/etc. ;-) In some ways the very idea of "money" itself incorporates standardized exchange/comparison within it. Money itself is taken to be pre-historic [1], though there may have been a few original "coins"/tokens of money. Little tick marks in clay ledgers may have been the first and we can be fairly sure even before all the spice trade/wars that not all crops/goods were deemed equal/additive unconverted. On the contrary, money was useful specifically to help convert. [1] https://en.wikipedia.org/wiki/History_of_money https://en.wikipedia.org/wiki/History_of_money
HPsquared 5y ago
Perhaps the fundamental dimension (mass, length, time etc.) could be considered as the 'abstract base class', with the specific units (meters, feet...) being derived classes.
- cb321 5y ago
  Perhaps. The https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem and Lord Rayleigh's refined ideas on units of measure predated Russell's work. These ideas also include at least 1 abstract-to-specialized transform like @HPSquared suggests. Probably it was >1 transform in the sense that (Mass, Length, Time) are conventional not fundamental. Following up on that ">1" requires a bit of explanation. Particle physics gets by with "natural" units where basically everything is rational powers of one base unit (MeV|energy|whatnot). SI units want like 7 or 8 or 9 base dimensions to avoid fractional powers (kind of a losing game since as soon as you have an equation with varying integer powers on either side fractional powers resurface). Rayleigh may have used different English words than "abstract base class" or "type" (maybe "kind", "sort", etc.), but physicists definitely had "type ideas" more abstract and formally symbolic than the units of measure your grandma knew for recipes - before Russell said anything about them. I am not sure Planck was the first to realize the "pick how many base dimensions you want" tricks - seems like Rayleigh or even earlier may have been, but in 1899 Planck published (before Russell's 1903 Doctrine of Types) a very abstract system of units such that major constants are 1.0 and dimensionless [1]. That level of conceptual abstraction (dimensionality - at least 1 more than just concrete vs abstract) also clearly predated Russell - but maybe only by a decade or two. It seems to me uncontentious that physics/physicists were in a very abstract type theory headspace with regard to units of measure before Russell published that appendix. The only point of debate would be "Does it count or did Russell abstract it so much further as to count as a fundamentally different thing?" While I am no Russell biographer, it would be unsurprising to me if he was inspired either implicitly or even very explicitly by such "just earlier than him" happenings in physics like Planck units. These units famously "make physics look more like pure math" which does not seem like something Russell would have failed to notice. As an "error catching mechanism" like types in programming languages, units function exactly the same way as programming types - just with the person as a compiler "doing their own checksum" to make sure they don't add apples & oranges. Calculation by hand was the predominant kind of computation at the time. So this is all coherent. At least "along the history of ideas arc" leading to programming language types, there may be great abstracters, but I doubt credit can be given to one person like TFA article tries to except maybe as an ambassador/evangelist/namer/maaaaybe first abstractor. (Not trying to suggest realizing the importance of something doesn't matter, but more make people realize how much this particular line of thought is almost as prehistoric as numbers themselves/quantification itself.) Anyway, I find units for mass, speed, time, etc. useful in explaining types (and checksums) to non-programmers. Maybe you will, too. [1] https://en.wikipedia.org/wiki/Planck_units https://en.wikipedia.org/wiki/Planck_units
ithinkso 5y ago
> and units of different measures (e.g. length: m, time: s) A nitpick but those are also related by a simple scalar factor (the speed of light)

cb321 5y ago

Dimensional analysis of units is absolutely a special case (I said "primordial example") of type systems. Proof: "constrained operations" and "notional objects" are very limited/somewhat concrete - "additive/comparative/conversion-y" and "measured things". Modern notions abstract both ideas. This is, however, not unimportant (not to suggest I think @10000truths said so, exactly). In educational settings one usually wants to begin with the most familiar examples and then generalize. { Why, this probably even applies to greats like Russell. :-) } Further, in attributional settings, giving general names/notions to things is often less seminal than the things one is naming. (Both are often worthy of attention, but I tend to push back when "namers get all the credit".) There is probably no single, famous big name like Russell to attach to the idea of units of measure/standard conversion/comparison. There may be a King of Olden Times who beheaded those who didn't follow his particular "system" when taxing crop growing areas or converting area to expected weights or volumes of grain/etc. ;-) In some ways the very idea of "money" itself incorporates standardized exchange/comparison within it. Money itself is taken to be pre-historic [1], though there may have been a few original "coins"/tokens of money. Little tick marks in clay ledgers may have been the first and we can be fairly sure even before all the spice trade/wars that not all crops/goods were deemed equal/additive unconverted. On the contrary, money was useful specifically to help convert. [1] https://en.wikipedia.org/wiki/History_of_money https://en.wikipedia.org/wiki/History_of_money

HPsquared 5y ago

Perhaps the fundamental dimension (mass, length, time etc.) could be considered as the 'abstract base class', with the specific units (meters, feet...) being derived classes.

cb321 5y ago
Perhaps. The https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem and Lord Rayleigh's refined ideas on units of measure predated Russell's work. These ideas also include at least 1 abstract-to-specialized transform like @HPSquared suggests. Probably it was >1 transform in the sense that (Mass, Length, Time) are conventional not fundamental. Following up on that ">1" requires a bit of explanation. Particle physics gets by with "natural" units where basically everything is rational powers of one base unit (MeV|energy|whatnot). SI units want like 7 or 8 or 9 base dimensions to avoid fractional powers (kind of a losing game since as soon as you have an equation with varying integer powers on either side fractional powers resurface). Rayleigh may have used different English words than "abstract base class" or "type" (maybe "kind", "sort", etc.), but physicists definitely had "type ideas" more abstract and formally symbolic than the units of measure your grandma knew for recipes - before Russell said anything about them. I am not sure Planck was the first to realize the "pick how many base dimensions you want" tricks - seems like Rayleigh or even earlier may have been, but in 1899 Planck published (before Russell's 1903 Doctrine of Types) a very abstract system of units such that major constants are 1.0 and dimensionless [1]. That level of conceptual abstraction (dimensionality - at least 1 more than just concrete vs abstract) also clearly predated Russell - but maybe only by a decade or two. It seems to me uncontentious that physics/physicists were in a very abstract type theory headspace with regard to units of measure before Russell published that appendix. The only point of debate would be "Does it count or did Russell abstract it so much further as to count as a fundamentally different thing?" While I am no Russell biographer, it would be unsurprising to me if he was inspired either implicitly or even very explicitly by such "just earlier than him" happenings in physics like Planck units. These units famously "make physics look more like pure math" which does not seem like something Russell would have failed to notice. As an "error catching mechanism" like types in programming languages, units function exactly the same way as programming types - just with the person as a compiler "doing their own checksum" to make sure they don't add apples & oranges. Calculation by hand was the predominant kind of computation at the time. So this is all coherent. At least "along the history of ideas arc" leading to programming language types, there may be great abstracters, but I doubt credit can be given to one person like TFA article tries to except maybe as an ambassador/evangelist/namer/maaaaybe first abstractor. (Not trying to suggest realizing the importance of something doesn't matter, but more make people realize how much this particular line of thought is almost as prehistoric as numbers themselves/quantification itself.) Anyway, I find units for mass, speed, time, etc. useful in explaining types (and checksums) to non-programmers. Maybe you will, too. [1] https://en.wikipedia.org/wiki/Planck_units https://en.wikipedia.org/wiki/Planck_units

ithinkso 5y ago

> and units of different measures (e.g. length: m, time: s) A nitpick but those are also related by a simple scalar factor (the speed of light)