How does something like `let y: Time = 1 year` work? Does it take into consideration the idea of leap years and leap seconds, counting a single year as 365.2422 days[0]? Or does it count as 365 days?
I got curious and installed the CLI tool[1] and found that it does indeed account for leap second / leap years:
I feel like that’s unit confusion. Converting from year to day should require you to specify what calendar year you’re in to resolve the ambiguity. Otherwise I set an alarm for today + 1 year and things are off by 6 hours.
Time is nasty because there’s lots of overloaded concepts and bugs hide in the implicit conversions between meanings.
I’m also kinda curious what the underlying type is. Is it a double or do they use arbitrary precision math and take the perf hit.
> I feel like that’s unit confusion. Converting from year to day should require you to specify what calendar year you’re in to resolve the ambiguity.
A year has two meanings - a calendar year, with all the leap days and seconds and timezones, or a duration of time. The latter is still useful, e.g. when someone states that Proxima Centauri is 4.2 light-years away, they don't want to deal with leap-days.
Decent time libraries have separate ways to deal with durations and dates.
Per 400 years, there is one leap day every 4 years (100 leap days), except when the year is divisible by 100 (so we overcounted by 4 and there are 100 – 4 = 96 leap days), except when the year is divisible by 400 (so we need to add that day back and arrive at 100 – 4 + 1 = 97). This gives us 97/400 = 0·2425.
The tropical year is about 365·24219 days long, but that's not relevant to timekeeping.
How does Numbat infer the type/unit for operations that involve transcendental functions like the trigonometric functions and the natural logarithm? How about for exponents that are not integers (rational or irrational)?
I've seen from to time some empirical equations that result to this. Usually, it's just hand-waved away and the non-integer units are ignored or dropped when the transcendental function is evaluated. I guess the trivial answer is probably add an extra factor with a value of 1 with the reciprocal units to result to the said type 1 for dimensionless units?
the issue is that each column and each row of a matrix can have different units. worse, gauss-jordan elimination chooses which rows to operate on dynamically. there is eventually a solution to this problem in c++ far down the comments thread
i don't see anything in https://numbat.dev/doc/type-system.html about aggregate types such as vectors, matrices, maps, arrays, lists, trees, records, etc., though it does have a suggestively named scalar type. i wonder how it handles this sort of thing
No, we do not have aggregate types in Numbat yet. But it is definitely something I would like to support.
Note that it is possible to construct a type system solution to this problem (vectors/matrices with non-uniform units). A colleague of mine has an excellent talk on this: https://www.youtube.com/watch?v=SLSTS-EvOx4
By 'Scalar', in the document you referenced, we mean a dimensionless quantity. Not a scalar in the scalar-vector-matrix-tensor sense. Maybe I should rethink that notation.
Interesting article... though to be honest, I'm not sure I buy the premise.
In the article, he states: "Let's call the matrix of all (xi 1) `X` and let's call the vector of all yi `Y`", and then states that the units of `X` are (m 1).
But if you instead say the units of `X` are just m, the "1" is in units "m", then the problem goes away, the whole matrix has the same units ("m"), and everything works fine.
I'll be honest in that I've never thought of a matrix having multiple units per column... and I can't think of any example where you aren't just putting the units in the wrong place. Let me know if you have a concrete example that might work.
If you multiply by a transform where the first entry is 1, the second entry is d/dx, the third entry is d^2/dx^2, etc. You will get a different unit for each entry of the vector.
Also most of economics consists of linear systems with non homogeneous units. The first entry could be bushels of wheat, the next demand for steel, etc.
i hadn't thought of it either before auditing an introductory numerical methods class, but in retrospect the page i linked does explain this, repeatedly, in the comments; i just didn't understand it at the time
I looked at Frink quite a bit and I agree that it looks cool. But as far as I can tell, it does not have a static type system. At least it's not based on physical dimensions.
Still reading the article, and really intrigued by and love this idea. But can I just say that I find this intro extremely well written. I feel like the writer is reading my thought process almost. Wvery time I start to form questions about decisions made in the language, it seems to answer them one or two paragraphs later. I feel like this is incredibly rare and yet incredibly important in an intro piece. Nicely done on the author['s]/[s'] part.
If the author is around, I notice in the README you mention the GNU units program, which I use quite a bit. I'm curious if you've made any notable divergences from it?
I don't think we diverge from units on purpose anywhere, but I am probably not very familiar with its syntax, to be honest. I did however look at its huge collection of units and checked if there were any important units missing. I think we have a pretty comprehensive list of units that are supported by now in Numbat [1].
Readit News
I got curious and installed the CLI tool[1] and found that it does indeed account for leap second / leap years:
>>> let jahr: Time = 1 year
>>> let tage: Time = jahr -> days
>>> tage
References:0: https://museum.seiko.co.jp/en/knowledge/story_01/
1: https://numbat.dev/doc/cli-installation.html
Time is nasty because there’s lots of overloaded concepts and bugs hide in the implicit conversions between meanings.
I’m also kinda curious what the underlying type is. Is it a double or do they use arbitrary precision math and take the perf hit.
A year has two meanings - a calendar year, with all the leap days and seconds and timezones, or a duration of time. The latter is still useful, e.g. when someone states that Proxima Centauri is 4.2 light-years away, they don't want to deal with leap-days.
Decent time libraries have separate ways to deal with durations and dates.
Per 400 years, there is one leap day every 4 years (100 leap days), except when the year is divisible by 100 (so we overcounted by 4 and there are 100 – 4 = 96 leap days), except when the year is divisible by 400 (so we need to add that day back and arrive at 100 – 4 + 1 = 97). This gives us 97/400 = 0·2425.
The tropical year is about 365·24219 days long, but that's not relevant to timekeeping.
Yes. This is also how it is defined: https://github.com/sharkdp/numbat/blob/ba9e97b1fbf6353d24695...
The calculation above is showing a rounded result (6 significant digits by default).
I've seen from to time some empirical equations that result to this. Usually, it's just hand-waved away and the non-integer units are ignored or dropped when the transcendental function is evaluated. I guess the trivial answer is probably add an extra factor with a value of 1 with the reciprocal units to result to the said type 1 for dimensionless units?
[1]: https://numbat.dev
the issue is that each column and each row of a matrix can have different units. worse, gauss-jordan elimination chooses which rows to operate on dynamically. there is eventually a solution to this problem in c++ far down the comments thread
i don't see anything in https://numbat.dev/doc/type-system.html about aggregate types such as vectors, matrices, maps, arrays, lists, trees, records, etc., though it does have a suggestively named scalar type. i wonder how it handles this sort of thing
Note that it is possible to construct a type system solution to this problem (vectors/matrices with non-uniform units). A colleague of mine has an excellent talk on this: https://www.youtube.com/watch?v=SLSTS-EvOx4
By 'Scalar', in the document you referenced, we mean a dimensionless quantity. Not a scalar in the scalar-vector-matrix-tensor sense. Maybe I should rethink that notation.
i know it's possible (even in c++ apparently) but so far it seems difficult
In the article, he states: "Let's call the matrix of all (xi 1) `X` and let's call the vector of all yi `Y`", and then states that the units of `X` are (m 1).
But if you instead say the units of `X` are just m, the "1" is in units "m", then the problem goes away, the whole matrix has the same units ("m"), and everything works fine.
I'll be honest in that I've never thought of a matrix having multiple units per column... and I can't think of any example where you aren't just putting the units in the wrong place. Let me know if you have a concrete example that might work.
Also most of economics consists of linear systems with non homogeneous units. The first entry could be bushels of wheat, the next demand for steel, etc.
basically it's very very common
And it is not open source.
If the author is around, I notice in the README you mention the GNU units program, which I use quite a bit. I'm curious if you've made any notable divergences from it?
I don't think we diverge from units on purpose anywhere, but I am probably not very familiar with its syntax, to be honest. I did however look at its huge collection of units and checked if there were any important units missing. I think we have a pretty comprehensive list of units that are supported by now in Numbat [1].
[1] https://numbat.dev/doc/list-units.html