[HN Gopher] Arithmetic is an underrated world-modeling technology
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Arithmetic is an underrated world-modeling technology
Author : crescit_eundo
Score : 20 points
Date : 2024-10-17 16:14 UTC (6 hours ago)
(HTM) web link (dynomight.substack.com)
(TXT) w3m dump (dynomight.substack.com)
| ddingus wrote:
| Always keep units. Indeed! I could not agree more.
|
| Long ago, as a primary school student, the move to metric, or
| Standard International units began. At first it was confusing,
| then it was all largely forgotten by many of my peers as everyone
| realized such a change was going to take a good long time(tm) to
| play out in general society.
|
| Ok fine.
|
| But for me, the most interesting thing happened to be the concept
| of units and how they help to solve problems!
|
| And so it began:
|
| Since that time, I have spent time learning about units and
| getting everyday references for them committed to memory and or
| what I can perceive to be how those units feel or look.
|
| Today, my estimates using the trusty eyecrometer (intended) are
| generally useful right along with sounds and many other basics
| that happen in life. I can assign a unit to those and to some
| degree quantify experiences.
|
| It has and will continue to be quite useful.
|
| I strongly recommend just beginning to get familiar with units of
| all kinds and use them however you can, when you can.
|
| They pay off nicely.
| samatman wrote:
| Distressingly few programming languages offer an acceptable
| implementation of units. It's a wonder we get anything done.
|
| One of the hidden gems of Julia is that it performs
| multiplication by juxtaposition, so if you define a variable
| `m`, then `2m` becomes `2 * m`. That plus overloading and
| multiple dispatch enables a rather nice library, Unitful[1],
| which does a fairly good job there.
|
| [1]: (Julia indexes by one)
| https://github.com/PainterQubits/Unitful.jl
| ddingus wrote:
| That is an interesting observation. I started out low level
| in 8 bit land. To me, units broke down to whatever close
| representation fit into 8 maybe 16 bits... But, you are
| right! A BASIC with units would have been quite useful back
| then.
|
| Would have caught a fair number of my bonehead errors.
|
| Later, moving to C and various scripting languages, I just
| sort of kept doing the same thing. Work units out old school,
| then comment whatever equations made sense in the program,
| and then do math, deciding on fixed or floating point
| depending...
|
| I will have to give Julia a look. Seems intriguing.
| Mathnerd314 wrote:
| This seems more like Fermi estimation
| (https://en.wikipedia.org/wiki/Fermi_problem). And it is
| underrated and also it is really hard. I mean, it is easy for the
| author here to say "look I threw it into Google and it worked"
| but practically I have seen many people struggle with these sorts
| of problems - they get the wrong numbers, they divide instead of
| multiply, or whatever, and the units don't really help.
| dzhang314 wrote:
| "divide instead of multiply" is _precisely_ the thing that
| units help with. If you keep track of them correctly, and you
| know the units of the result you want, then it's impossible to
| make that mistake. (Of course there are other errors that units
| don't catch, but that's a pretty large class of them gone.)
| hazbot wrote:
| I learnt this way of thinking about units in my engineering
| degree, and it is indeed incredibly powerful and I regularly use
| it.
|
| But I would classify it as "algebra" instead of "arithmetic".
| Being fluent in manipulations like
|
| 60 km/h = 60 km/h * h/3600s * 1000m/km
|
| is not a trivial modality of thought to unlock!
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