Re:Roman Finger Counting
by npunt on Friday May 15, 2020 @03:12AM
(#23189733)
I imagine there's a natural gravitational pull toward base 10 from having fingers, and throughout prehistory and early civilization occasionally systems deviated to suit certain purposes (like sibling comment about even divisibility of 60) but usually came back to using 10. We've always needed to count, been smart enough to count, and had 10 fingers readily accessible to count, so I wouldn't count that theory out :)
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I think the biggest strength of base 10 is not hand-counting (the OP and the Babylonian/Chinese base-12 method are both superior in that regard), but ease of performing pen-and-paper operations. You can literally teach a 6-year-old to multiply huge numbers effortlessly.
Re:Roman Finger Counting
by laszlokorte on Friday May 15, 2020 @05:31AM
(#23190378)
Couldnt you do the same using two additional digits? Say binary and hexedicmal arithmetic are as easy as decimal if you substract the bias of being used to decimal.
If you use any other base for writing numbers down, it's just as easy to perform pen-and-paper operations. The only problem with larger bases is that the multiplication tables increase quadratically. Whereas a base-10 multiplication table has 100 entries, a base-16 table already has 256 entries.
>a base-10 multiplication table has 100 entries
Not quite! You can safely ignore identities (0, 1, and 10 itself) so you only have 8 numbers in your table. And multiplication is commutative so you only need 8+7+6... (= (8+1)(8/2) as per Gauss) = 36 entries.
Base 16 would have (14+1)(14/2) = 105 entries. So proportional to base-10, actually slightly harder than you said.
Re:Roman Finger Counting
by curiousllama on Friday May 15, 2020 @10:06AM
(#23192320)
The classic - detailed correction followed by "but yea you're totally right anyway" lmao
A fine demonstration how "basically correct in two sentences" is better than "technically correct in five sentences" in most situations.
This video convinced me that base 6 would be even better for simple pen-and-paper math, as well as just about everything else: https://youtu.be/qID2B4MK7Y0