111–120 of 132 posts
Romans essentially used the same binary arithmetic computers use today for multiplication; doubling and halving. http://www.phy6.org/outreach/edu/roman.htm
And division basically works the same.
Discussed article is https://thonyc.wordpress.com/2017/02/10/the-widespread-and-p...
Nowhere as complex as it's made out to be.
I feel like the article misses the most interesting question about Roman numerals and Roman (Greek really) math. How did the numerical system influence the math that they developed and used? The Greeks were really into geometry using the compass and straight edge so they actually did a lot of math without really needing numbers at all. They viewed calculation as less worthy of mathematicians and my understanding is t…
Greek society was awash with arithmetical calculations. It wasn’t written about probably mostly because it was considered so obvious and commonplace. (Though it’s also a bit hard to say quite what was written about, since we’ve lost the vast majority of the books from the time.)
http://worrydream.com/refs/Netz%20-%20Counter%20Culture%20-%...
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> Did the Greeks (and the Romans) not develop algebra or use Arabic numerals because they weren't that into numbers as compared to geometry?
Algebra and arabic numerals really took off with the introduction of cheap paper and printed books.
It’s really hard to transmit the oral culture of skilled use of a counting board via printed book (we might call it tacit knowledge), but you can pretty straight-forwardly print out a pen-and-paper arithmetic algorithm.
In An Introduction to Mathematics (1911) Alfred North Whitehead wrote: By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and, in effect, increases the mental power of the race. Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties. Probably…
Roman numerals by and large were not used for calculating, but for recording calculations. Those calculations were done (as the very word “calculate” suggests) using pebbles or other tokens, on some kind of counting board.
The point of Roman numerals is to be as direct as possible a representation of the state of the counting board. They are a serialization format.
Think of it as the JSON (or s-expressions if you like) of the ancient world. You don’t run your algorithm by writing and rewriting JSON literals over and over with pen and paper. They are just a record; your computation is done using a different automatic tool.
When someone writes down the state of a graph structure as a big nested JSON literal, you don’t laugh at them for having a uselessly unwieldy written expression.
I have read that the uptake of Arabic numerals was actually fairly slow and fraught in Europe, but of course can't put my hands on any references. There's a reddit thread [0] that might be some of what I saw, and my wife does paleography work where she runs across books of accounts that are rendered in Roman numerals, because that's how formal accounts were prepared, even if the actual accounting was done by other me…
Earlier quoted context omitted.
Living in Japan, I became accustomed to using numbers for up to around 10,000 yen ($100USD) due to interactions at the stores and around town, but when I would hear the price of a car (1,000,000+ yen or 100 myriad yen) or a house, it would just confuse me and not register at all. It’s all just based on your personal experience, I think.
I have the same experience with German reversed way of speaking numerals, yet I speak the language fluently, including a good understanding of Swiss German as well. But reversing back the numbers into my Portuguese brain, just doesn't work after a certain size.
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This is absolutely the case for programming languages. From Haskell to Rust. Programming languages shape the way we think and reason about the problem. Sometimes it does this so well, it leaves us starring into the abyss. Facing dead on the problem domain—after all sides quests have been removed. Once you can delegate away all the busy work, you can focus on bigger and better abstractions.
Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc). Python is better.
def square(x):
return x * x
square x = x * xEarlier quoted context omitted.
Well, you can try and then you'll appreciate the difference, I am sure. Even if implemented in computer hardware, operating with Roman numerals would either be slow or take many more transistors (or both). As to why in a philosophical sense, it is because the positional system was invented specifically as a computational device, which only happened many years after people learned how write numbers down. Optimization…
We all do the same thing. Our calculators work in binary, and we only do i/o in decimal. Their calculators (slaves who pushed pebbles, calculi , around) worked in a decimal place-value system (or used egyptian/russian peasant multiplication), and only the i/o was done in roman numerals.
Earlier quoted context omitted.
I have the same experience with German reversed way of speaking numerals, yet I speak the language fluently, including a good understanding of Swiss German as well. But reversing back the numbers into my Portuguese brain, just doesn't work after a certain size.
There is (for me at least) something very deep (in the brain) regarding numerals and basic math. I am quite proficient in English, but always do arithmetic in my native Bulgarian and then have to translate the result (unlike other speech, which flows freely). And not for the lack of trying. And that is even though Bulgarian numerals do translate 1:1 to English.
When I got my math teaching credential, there were bunches of interesting historical things we learned along the way including Egyptian Fractions https://en.wikipedia.org/wiki/Egyptian_fraction Never actually used any of it so most of it has evaporated from my memory along with calculating square roots by hand, but it's nice to know at least enough to be able to look up the information if I want it.
Egyptian fractions have an interesting property that may have been useful back then. Consider the problem "How do you divide five things for eight people?" Simple - cut everything into 1/8 and give each person five. But Egyptian fractions give an even easier way. 5/8ths is 1/2 + 1/8. Divide four wholes into halves - give each person a one half. Take the unit and divide it into eights and give each person one. The ans…