@@diogorrify yes, for sure. if i were writing by the modern convention, in the final answer i'd use the subtractive notation, which also existed in Roman times, but wasn't used particularly consistently (for example, gate 44 at the Roman colosseum is written XLIIII, meaning they used both the subtractive notation and the additive notation). But for the work along the way, I'm not sure if they did anything consistently.
Subtractive notation would just be really inconvenient. Because you add right-to-left, you'd end up having to scratch out a lot of "digits" when adding up the next symbol removed the need for it.
Thank you!, your comment is what made it click to me why this algorithm works. The left column is just a way of writing the number in binary: read the rows from the bottom, the even rows are 0 and the odd rows are 1, thus representing 20 = 10100_2. Then by doubling in the right column computes the value of multiplying the right-side number in that place. This is all an elaborate way to binary multiplication!
The multiplication algorithm is interesting but I’m far more interested in their motivation for this algorithm. How did they come up with it? Did they try other algorithms earlier on?
They used an abacus. It's ironic that they were clever enough to use an abacus but not clever enough to translate it to a written place value system. It's really no great leap of imagination: Five hundred and thirty two written down our way is 532, which means two beads on the right string, three beads on the one next to it, and five beads on the one next to that. But the Romans couldn't see it. When you do written arithmetic while thinking in Arabic numerals, you're actually performing the exact same functions that are carried out on an abacus, and most of us can do it faster in our heads than on the actual machine. I struggle to understand why a user of Roman numerals in possession of an abacus didn't simply invent ten symbols to represent the possible numbers of beads on each string. I suspect they may have tried and had a nervous breakdown when one of the strings didn't have anything on it and it never occurred to them that zero could be represented by a symbol.
What’s your source for this? Did some Roman actually document their methodology and we still have it preserved or is this just a guess at one possible way they could’ve done it?
I was wondering if it is possible to do math without zero. The romans seemed to have had no problem. Since zero is often suggestive and representative of empty or nothing is it really necessary ? For continuos math, where concepts such as limits come into play I do not know. Even otherwise, if two quantities are equal, it means, they are identical, there is no difference between them, in other words their difference is zero or nil.
@wooshifgay462 Not true. I would rather not have a poor knowledge apprehension and a poor appreciation and a poor application, a poor ability, for IMHO that is true poverty.
@wooshifgay462 @wooshifgay462 Not true. I would rather not have a poor knowledge apprehension and a poor appreciation and a poor application, a poor ability, for IMHO that is true poverty.
@wooshifgay462 That which is sound in theory is also sound in practice. I have found this to be true both in theory and in practice. So that which is true science is also true philosophy. I am still right.
@wooshifgay462 There is nothing more practical than theory. Negative numbers always exist so taking their square root becomes a practical a theoretical necessity. Zero is also a practical and a theoretical necessity.
it's actually a form of binary multiplication. repeatedly dividing by 2 on the left side of table and then only keeping it when it's odd is actually another way to write the number in binary. then on the right, as we double over and over again, we're performing the binary (by 2) multiplication).
Yeah, people think this, but in fact the subtractive convention is a more modern invention. You can find it, but it was much more common to just use four symbols.
There isn't an accepted algorithm with any historical evidence, but there is a paper from 1951 that outlines what the algorithm might have looked like based on what we know. i'll try to put something together on it!
Why did you sum II with II and get IIII and not IV? You sneaky..
Just doing it the same way the ancient Romans would have :)
@@polymathematic it seems to facilitate the calculation. I’m assuming you would also avoid any prefixes like IV and XL and just write VIIII and XXXX
@@diogorrify yes, for sure. if i were writing by the modern convention, in the final answer i'd use the subtractive notation, which also existed in Roman times, but wasn't used particularly consistently (for example, gate 44 at the Roman colosseum is written XLIIII, meaning they used both the subtractive notation and the additive notation). But for the work along the way, I'm not sure if they did anything consistently.
Subtractive notation would just be really inconvenient. Because you add right-to-left, you'd end up having to scratch out a lot of "digits" when adding up the next symbol removed the need for it.
IIII and IV are interchangable and there have been examples of IIII used by Romans.
I saw an article about this years ago, and my immediate thought was, that's how I'd do binary long multiplication in machine code. Shift and add.
Thank you!, your comment is what made it click to me why this algorithm works. The left column is just a way of writing the number in binary: read the rows from the bottom, the even rows are 0 and the odd rows are 1, thus representing 20 = 10100_2. Then by doubling in the right column computes the value of multiplying the right-side number in that place.
This is all an elaborate way to binary multiplication!
This system is great, but oh my god am I glad for the modern number system
Me too!
Apparently, Romans had abacus. You can do these sort of multiplication conveniently without paper and pen using abacus.
The multiplication algorithm is interesting but I’m far more interested in their motivation for this algorithm. How did they come up with it? Did they try other algorithms earlier on?
How did the Romans perform long division?
it was hell
They used an abacus. It's ironic that they were clever enough to use an abacus but not clever enough to translate it to a written place value system. It's really no great leap of imagination: Five hundred and thirty two written down our way is 532, which means two beads on the right string, three beads on the one next to it, and five beads on the one next to that. But the Romans couldn't see it. When you do written arithmetic while thinking in Arabic numerals, you're actually performing the exact same functions that are carried out on an abacus, and most of us can do it faster in our heads than on the actual machine. I struggle to understand why a user of Roman numerals in possession of an abacus didn't simply invent ten symbols to represent the possible numbers of beads on each string. I suspect they may have tried and had a nervous breakdown when one of the strings didn't have anything on it and it never occurred to them that zero could be represented by a symbol.
What’s your source for this? Did some Roman actually document their methodology and we still have it preserved or is this just a guess at one possible way they could’ve done it?
I’m not sure about that but in Europe we use Roman numerals all the way until 14th century and their are accounting records from that period
Roman numerals were to mathematics what Internet Explorer was to the internet..
How were they able to devide
I was wondering if it is possible to do math without zero. The romans seemed to have had no problem. Since zero is often suggestive and representative of empty or nothing is it really necessary ? For continuos math, where concepts such as limits come into play I do not know. Even otherwise, if two quantities are equal, it means, they are identical, there is no difference between them, in other words their difference is zero or nil.
@wooshifgay462 Not true. I would rather not have a poor knowledge apprehension and a poor appreciation and a poor application, a poor ability, for IMHO that is true poverty.
@wooshifgay462 @wooshifgay462 Not true. I would rather not have a poor knowledge apprehension and a poor appreciation and a poor application, a poor ability, for IMHO that is true poverty.
@wooshifgay462 That which is sound in theory is also sound in practice. I have found this to be true both in theory and in practice. So that which is true science is also true philosophy. I am still right.
@wooshifgay462 There is nothing more practical than theory. Negative numbers always exist so taking their square root becomes a practical a theoretical necessity. Zero is also a practical and a theoretical necessity.
Showing work seems difficult.
lol this is basically what I do in my head
Multiply xxI by II
why does this work?
it's actually a form of binary multiplication. repeatedly dividing by 2 on the left side of table and then only keeping it when it's odd is actually another way to write the number in binary. then on the right, as we double over and over again, we're performing the binary (by 2) multiplication).
The u 500 or 5000 or 10000
IV not iiii
XL not xxxx
Yeah, people think this, but in fact the subtractive convention is a more modern invention. You can find it, but it was much more common to just use four symbols.
Wow.
I always thought 40 was XL Not XXXX
That's called subtractive notation. It's a later innovation and would be very inconvenient for mathematical purposes.
What?
After watching that, I take no pride in being of Roman descent.
no, it's really cool, you should be more proud than ever!
How did the Romans perform long division?
There isn't an accepted algorithm with any historical evidence, but there is a paper from 1951 that outlines what the algorithm might have looked like based on what we know. i'll try to put something together on it!
@@polymathematicplease do it
Tediously.