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How did anyone do math in Roman numerals? (2017)

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Re: How did anyone do math in Roman numerals? (2017)

#101

Post by blub »

avindroth wrote: post #97
blub wrote: post #72

Earlier quoted context omitted.

Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc). Python is better.

You had to learn 0,1,2,3, etc. at some point. The thing with notation is that it takes time to learn, but it proves profoundly useful over time. The benefit of notation integrated over your career outweighs the adoption costs. Arabic numbers are like this (no child immediately ‘groks’ Arabic numbers), and Haskell notation is making the same case. Haskell abbreviates abstract structures so that they become fluid. If f…

You have to remember the context in order to understand my reply. Here it is once again "It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilisation advances by extending the number of important operations which we can perform without thinking about them."

First of all programming without thinking about it (i.e. instinctively) is arguably not even possible. But let's be generous and assume that it is somehow.

Are you seriously trying to argue that it's possible to program in a complex programming language which not only requires types, but almost requires encoding complex relationships in them without involving the "higher faculties of the brain"? This is such an extraordinary claim that it requires evidence to even consider it.

Re: How did anyone do math in Roman numerals? (2017)

#102

Post by blub »

d2v wrote: post #86
blub wrote: post #72

Earlier quoted context omitted.

Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc). Python is better.

Types in Haskell are generally used to describe the structure of the data. Defining a type in Haskell is like writing documentation and a test all in one. I can mentally offload certain concerns to the compiler, which will tell me whether or not the shape of the data in my head matches the code I'm writing. I pretty frequently use the compiler to guide my development, especially with a tool ghcid, which gives instant…

That's not relevant unless you can do all of the above instinctively and without involving the higher faculties of the brain.

Re: How did anyone do math in Roman numerals? (2017)

#103

Post by blub »

dependenttypes wrote: post #95
blub wrote: post #72

Earlier quoted context omitted.

Both Haskell and Rust are poor examples because one has to focus more on the notation (i.e. types, declarations, etc). Python is better.

In python you have to focus more on the debugging where this run-time type-error came from. Also, Haskell has type inference unlike the other two.

Python merely allows you to program quite close to a state where you focus on the problem and less on the infrastructure and syntax required to solve the problem. At least in exploratory phases and when working with smaller pieces of code.

Other languages almost always require more thinking and design upfront, even when doing exploratory programming.

Re: How did anyone do math in Roman numerals? (2017)

#104

Post by philwelch »

d2v wrote: post #78
philwelch wrote: post #62

Earlier quoted context omitted.

Adding Roman numerals, at least, isn’t hard. If it was I doubt Roman numerals would have ever lasted. Arabic is still, in my opinion, easier to add—from the perspective of a lifetime spent exclusively doing arithmetic in Arabic numerals—but it’s not much easier until you’ve memorized all 50 unique sums of one-digit numbers. Multiplication, though, that’s the real difference maker.

This is only tangentially related, but until now I never really thought about how I sum single digit numbers, but it's not by having memorized all combinations. I'd say I have all combinations that sum to 10 or less memorized, which adds up to 25 unique combos (plus the rule that number + 0 = number). If I can tell it sums to more than 10, I break it up mentally into [larger number] + [smaller number] = [larger numbe…

Honestly I feel like I do the same thing when I think about it, but it’s so well cached that whenever my brain sees 5+7 or 7+5, I simultaneously think “12”, forget the specific order, and imagine 5+5=10 with 2 overflow all at once and I can’t honestly tell you which concept arrives first.

And yeah, you can get by with less memorization and more counting, but eh...either you’re taught not to do that or you do enough arithmetic that your brain just caches the whole table eventually anyway.

Re: How did anyone do math in Roman numerals? (2017)

#105

Post by DNied »

MaxBarraclough wrote: post #99
DNied wrote: post #34

Earlier quoted context omitted.

> look what the world achieved after it left roman numerals behind. Look what the world achieved after we started wearing button shirts.

Perhaps it would be expressed better as Look at what mathematics achieved after it left Roman numerals behind .

Nope. Still an unproven correlation.

Re: How did anyone do math in Roman numerals? (2017)

#106

Post by Grustaf »

shultays wrote: post #27
Grustaf wrote: post #14

Why would it be significantly harder than using some other system of numerals?

They probably had algorithms for it, but even then it sounds challenging. Addition sounds easy and works mostly like how we do base 10 addition. I imagine they would first go for sub 5 part which is a bit exceptional and had to be manually. And then start grouping letters together like we do and create carries if they reach the next letter. Subtraction sounds harder. It sounds close enough to our base 10 system but b…

How numbers are written down does not necessarily correspond to how you do calculations. Given that 499 was called 499 I’m pretty sure they thought in base 10, so subtracting 1 from 500 would be trivial. Writing it down took a few more symbols but so what?

Re: How did anyone do math in Roman numerals? (2017)

#107

Post by sn41 »

jbit wrote: post #59
sn41 wrote: post #58

It is well-known that the place-value system introduced into Europe from India via the Arabs played an invaluable role in modern arithmetic. But, if you read the "Sand Reckoner" by Archimedes, what he lays out are the rudiments of a place-value system. He essentially describes the modern notation, but not rules for addition, subtraction, multiplication and division using this notation. Another tidbit: if you see the…

I'd never heard of this documentary, so I took a look. I assume you meant "The Bit Player"? ( https://www.imdb.com/title/tt5015534/ ). It looks interesting, and it's on Amazon prime video so I'll give it a watch. Thanks!

Sorry, you are right.

Re: How did anyone do math in Roman numerals? (2017)

#108

Post by Xelbair »

ThrustVectoring wrote: post #66
rland wrote: post #64

Earlier quoted context omitted.

I wonder if arabic numerals really are the best system. Too much inertia is invested in them now but I wonder if a yet easier representation exists. For example, I know that there was a brief push to use quaternions in physics.

Base 12 is likely better than base 10. Twelve is the number of phalanges on your hand that you can touch with your thumb, so if that counting system had caught on and stuck we'd likely have a better base for divisibility.

if you add tip of the finger you can easily work in base 16.

Re: How did anyone do math in Roman numerals? (2017)

#109

Post by dependenttypes »

blub wrote: post #103
dependenttypes wrote: post #95

Earlier quoted context omitted.

In python you have to focus more on the debugging where this run-time type-error came from. Also, Haskell has type inference unlike the other two.

Python merely allows you to program quite close to a state where you focus on the problem and less on the infrastructure and syntax required to solve the problem. At least in exploratory phases and when working with smaller pieces of code. Other languages almost always require more thinking and design upfront, even when doing exploratory programming.

> and less on the infrastructure and syntax required to solve the problem

I do not think that this is true for python any more than it is true for haskell for example.

Re: How did anyone do math in Roman numerals? (2017)

#110

Post by qtplatypus »

crazygringo wrote: post #37
Sharlin wrote: post #31

Earlier quoted context omitted.

But that's the thing about Roman numerals: you don't need a placeholder number to represent empty columns. And for "what is XVI subtracted from XVI" they could just use a word meaning "nothing", such as nihil or nihilum . The need for the concept of zero as we understand it really only arises together with a place-value system.

Thanks for explaining that clearly. I've always been so baffled by people who claim that some society didn't have a concept for zero, as if "inventing" zero marks some major advance in intelligence. Every culture has a concept of "nothing" which works for zero. The ancient Greeks debated over whether nothing was a number or not, but that's just a semantic splitting of hairs. At some point a symbol for nothing becomes…

Is zero a number isn’t just a semantic splitting of hairs but has an important outcome. If zero is a number then you can do arithmetic to it. In particular having the concept of zero as a number that you can do maths with is a prerequisite for algebra.
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