4 ms·

Actually, the duality arises from counting (there can be 0 items) and ordering (there is only a 1st item), conceptually. Which is why the year 2000 can and cann

Actually, the duality arises from counting (there can be 0 items) and ordering (there is only a 1st item), conceptually. Which is why the year 2000 can and cannot be the start of the 3rd millenium, for instance.

xeonmc 2y ago
Fun fact: the words Ordinal and Cardinal respectively derives from Ordering and Counting. So Ordinal quantities represent the ordering of coordinates and can be negative, while Cardinal quantities describes the counting of magnitudes and must be positive. You can transform between ordinal domains and cardinal domains via the logarithm/exponential function, where cardinal domains have a well-defined “absolute zero” while ordinal domains are translation-invariant.
jonahx 2y ago
I don't follow the distinction you're making. The number line is ordered and contains a 0.... The GP's explanation seems more fitting for the year 2000 ambiguity. Are you measuring completed years (celebrate millenium on NYE 2001) or are years the things happening between 0 and 1, 1 and 2, etc (celebrate on 2000, because we're already in the 2000th "gap")?
- pfortuny 2y ago
  Order as in "first, second, third", whereas counting is "none, one, two". This is not a formal distinction, it is a conceptual one for things (not mathematical models).
  - jonahx 2y ago
    Thought about this a bit more... Not sure if this is what you're saying, but the concept of "space between" I alluded to seems to arise naturally whenever you have ordered items, and vice versa. Because once you have order you have the concepts "greater than"/"less than", and once you have that you have a border between your items, and your items are between those borders. This connects back to Dijkstra's consideration of <, <=, etc....
    - pfortuny 2y ago
      Yep, same idea.
somat 2y ago
Dates and times are prime examples of modular systems that make the most sense when they start at 0. but most commonly start at 1. Think how stupid it is that the day start at 12 hours then goes back to 1 hour, at least 24 hour clocks do away with this absurdity. My personal take is that we should not let one short sighted decision 1500 years ago to mess us up and the first century covers from years 0 to 99 and the 21 century 2000 to 2099 https://madeofrome.com/how-was-it-made/how-did-we-choose-the-year-zero-or-rather-the-year-1/ https://madeofrome.com/how-was-it-made/how-did-we-choose-the... I have a database where I tried keeping once per year periodic events(like birthdays or holidays) as postgres intervals, so number_of_months:number_of_days_in_month past start of year or effectively 0 based month-day. this looks weird but solved so many calculation problems I kept it and just convert to more normal 1 based on display. and a shout out to postgres intervals, they do a heroic job at tracking months, a thankless job to program I am sure.
bmacho 2y ago
Can you elaborate? What duality, and how?

xeonmc 2y ago

Fun fact: the words Ordinal and Cardinal respectively derives from Ordering and Counting. So Ordinal quantities represent the ordering of coordinates and can be negative, while Cardinal quantities describes the counting of magnitudes and must be positive. You can transform between ordinal domains and cardinal domains via the logarithm/exponential function, where cardinal domains have a well-defined “absolute zero” while ordinal domains are translation-invariant.

jonahx 2y ago

I don't follow the distinction you're making. The number line is ordered and contains a 0.... The GP's explanation seems more fitting for the year 2000 ambiguity. Are you measuring completed years (celebrate millenium on NYE 2001) or are years the things happening between 0 and 1, 1 and 2, etc (celebrate on 2000, because we're already in the 2000th "gap")?

pfortuny 2y ago
Order as in "first, second, third", whereas counting is "none, one, two". This is not a formal distinction, it is a conceptual one for things (not mathematical models).
- jonahx 2y ago
  Thought about this a bit more... Not sure if this is what you're saying, but the concept of "space between" I alluded to seems to arise naturally whenever you have ordered items, and vice versa. Because once you have order you have the concepts "greater than"/"less than", and once you have that you have a border between your items, and your items are between those borders. This connects back to Dijkstra's consideration of <, <=, etc....
  - pfortuny 2y ago
    Yep, same idea.

somat 2y ago

Dates and times are prime examples of modular systems that make the most sense when they start at 0. but most commonly start at 1. Think how stupid it is that the day start at 12 hours then goes back to 1 hour, at least 24 hour clocks do away with this absurdity. My personal take is that we should not let one short sighted decision 1500 years ago to mess us up and the first century covers from years 0 to 99 and the 21 century 2000 to 2099 https://madeofrome.com/how-was-it-made/how-did-we-choose-the-year-zero-or-rather-the-year-1/ https://madeofrome.com/how-was-it-made/how-did-we-choose-the... I have a database where I tried keeping once per year periodic events(like birthdays or holidays) as postgres intervals, so number_of_months:number_of_days_in_month past start of year or effectively 0 based month-day. this looks weird but solved so many calculation problems I kept it and just convert to more normal 1 based on display. and a shout out to postgres intervals, they do a heroic job at tracking months, a thankless job to program I am sure.

bmacho 2y ago

Can you elaborate? What duality, and how?