Personality
Discuss specifics of personality design, including what Keyphrases work well and what dont, use of plug-ins, responses, seeks, and more.
Posts 4,474 - 4,485 of 5,105
Another example: try doing long division in Roman numerals, without ever translating into arabic numerals.
It's actually no more difficult as a whole than long division in any other number system (and often easier) - it just looks strange to us because we don't routinely use Roman numerals. The absence of zero causes other mathematical problems that need not concern us here, but FWIW here's how to do Roman long division (always an entertaining party trick
):
Division (long, short, roman or arabic,) is just repeated subtraction, with allowance made for a remainder if necessary.
Say we want to simply divide CXV / V
starting from the right, we ask ourselves
how many V in V? I
how many V in X? II
how many V in C? XX
recombine them: XX + II + I, thus XCV/V=XXIII
you can't always make perfect division of equal parts of the numerator of course (any more than you can in any<0> numerical system,) and you have to remember you're working with fractions not decimals (more technically, your operators are specifically proper divisors known as 'aliquot parts',) so you need to keep track of the remainder, eg:
MMCCCXXII/CCX
rather than start seeing how many CCXs we can get into I,II,XII,XXII, etc, (though you can laboriously plough through to it that way,) there is just the kind of short cut we're used to dealing with in Arabic numerals (eg: when we cancel out zeros in dividing 80000 by 4000, and go straight to 8/4 plus the leftover "0" = 20.)
MMC evidently = X*CCX (think about it, character by character,), so MMCCCX must = XI*CCX, with a remainder XII (after the XI subtractions we've bypassed with the short cut.) So the solution is XI + XII/CCX (the fraction arrived at being inevitably irreduceable.) Funnily enough it's a lot easier to calculate that in Latin than in Arabic - I certainly can't do 2322/210 in my head easily!) And I don't get stuck with 30 decimal places on the calculator, and a nagging curiosity as to what the 31st decimal place might be. By contrast 11 12/210 is perfectly accurate.
One advantage of fractions (and it's actually an enormous<0> advantage sometimes, like when you've got a problem like that to do in your head,) is that it often gives you greater precision for less effort than is possible with a decimal system. Irrational numbers are equally and inevitably a problem to fractional and decimal systems alike, but fractional systems also avoid infinite decimal sequences, I/III is simply 1/3 - not 0.333333333333333333333333333333333333et.seq.ad.infinitum.
Long division works just the same with Egyptian hieroglyphic math (http://letsplaymath.files.wordpress.com/2008/02/egyptian-fractions.pdf), Vedic Sanskrit math (http://www.britannica.com/EBchecked/topic/1238473/South-Asian-mathematics/253515/Classical-mathematical-literature , and still has useful techniques to teach us even when updated to use Arabic notation: http://www.ourkarnataka.com/vedicm/vedicms.htm) or any other self-consistent number system that does or could exist - that's simply axiomatic.
It's unfamiliar to us - we weren't brought up with this notation, but it's no worse than calculating old money prices (I was only 4 when the UK went decimal, but I perversely found the duodecimal format lingeringly attractive as a child.) What's two and sixpence three farthings subtracted from nine and three and a farthing? Six and eightpence ha'penny of course. How many shillings in 3 1/2 guineas? 73 and six (decimally 73.5) - it was intuitively understood by my parents' generation (many of whom had great difficulty getting used to a supposedly easier decimal system,) just as the Romans intuitively understood their notation.
I take your point that algebra is an improvement in providing standard methods for some classes of calculation, but just as much because our standard Arabic system lacks the suitable functions as because older (or other, or even newer,) alternatives lack them.
The lack of a zero is really the only downside to roman numerals, and this is simply solved at a stroke by adopting into a Revised Roman System the new value: O = 0. There, now the Roman system is just as powerful as the Arabic system - it's only a convention of notation, and the operators can work on one just as easily as another.
And while you need algebra to eg: calculate a value for pi, you can use the derived constant (be honest, when was the last time you needed it and chose to calculate it instead of looking it up?
) in any number system you choose - XXII/VII is actually slightly more accurate than the 3.14 we often round it off to.
I have simplified all that a bit, and there are some problems that are less immediately tractable, but a general method is simply applicable by allowing for a preliminary operation of addition or subtraction (to render the numerator tractably reducible,) and an extra remainder - I'll explain in more detail if anyone really wants to know (but I think I've bloated this forum quite enough for today!)
XII/CCX ... the fraction arrived at being inevitably irreduceable
What am I saying?!? :O
XII/CCX =
(XII/III)=IV /
(CCX/III) = XXXV
= IV/XXXV
please excuse the brainfart! (and I confess I noticed this incidental error in the more familiar Arabic)
are you sure that you didn't translate to modern notation, in your head,
I can't help but wonder if Roman vs Arabic isn't like the spoken language. When you first start a new language you translate it in your head, later you actually think in that language.
with the necessary addition of the letter O Odd to think of a number system with out 0. It seems so obvious once you know about it.
As far as I know, every highly literate culture on Earth has adopted Arabic notation for Finance, Science, and anything involving intricate calculations.
Yes, though the Roman system did us okay for the first millenium, and frankly if it had developed a zero of its own, we might well be using something like it now. But there are advantages to Arabic notation when you want to do tricky or cumbersome stuff (Roman calculus would waste an awful lot of extra ink and paper, even if it would work perfectly sensibly!) Don't get me wrong - I wouldn't seriously advocate returning to the Roman system - I do like the Arabic system (albeit I will always choose fractions over decimals where I can,) but I do maintain that the choice of numerical representation is relatively unimportant to the capabilities of any higher mathematical systems built on those foundations.
Don’t forget to consider examples such as “IV” and “XLIX”, where a numeral on the left of another is to be subtracted from it. IMHO, this will make algorithms for all multi-digit calculations much more intricate.
No, the algorithms are just the same - division is the same process of repetitive subtraction (and dealing with any remainder,) in any system you care to use. How you deal with the remainder is the only significant difference between the systems, and this is down to the fractional/decimal divide rather than the Roman/Arabic one. Without a zero, the Romans never developed a decimal system (despite using base 10,) so had to develop fractions to handle the remainders. My hypothetical Revised Roman Standard could be extended to represent decimals easily enough, so eg: pi = III.ixlcdmm
It is merely the recognition of the numerals to be operated on that is less familiar to us - a Roman would have been taught this, so it would be second nature. You call each character a "numeral", because you have learnt (in our Arabic system) that numerals are single characters. But in this case the numerals are IV, and XL, and IX.
Apprehension of the Roman units is second nature still to many of us, yourself included - you immediately recognize, I am sure, that MCDXLIV is 1444, and not 1666 or any other such illegal equivalent. You know just as well as a Roman would, that you cannot subtract DCLXVI from it to leave M, because this would involve misinterpretation of the numerals. The Roman's understanding would be more innate, because he could not even know that the strange characters "1444" meant the same as MCDXLIV, but would simply apprehend the quantative value directly - he would have no conception that numerals might be expressed in single, distinct characters, and would probably find the idea unnecessarily complicated, when there is such a logically well-proven Roman system already in existence.
The Romans calculated their taxes and profits, volumes of materials needed for great building projects, strenghts of their armies, etc. perfectly accurately (literally so, unlike our decimal systems that can only ever approximate most calculations.) They simply accepted that numerals could consist of multiple characters.
Any number system where 8 takes more characters to write than 1,000,000 will necessarily require different shorthand methods to work with than one which neatly stacks up into single-digit unit/base/base^2/base^3... columns like Arabic. But that doesn't mean that there aren't very efficient methods to work with other number systems (I have demonstrated a problem that's easier to solve in Roman than Arabic already, after all.) A Roman would probably find it a lot easier to learn calculus with Roman numerals + zero, than to have to learn a whole new numbering system, and then learn calculus on top of that (though with the shocking price of vellum - 20 guineas/sq.foot for Cowley's Kelmscott! - the mediaeval adoption of Arabic notation was perhaps quite understandable.)
As a matter of interest, I find there is a Roman calculator widget @http://www.math.com/students/calculators_pre_ti/roman/compvterromanvs.html though it discards all fractional remainders, so I suspect it does indeed calculate decimally and convert the answer back into Roman notation. That's lazy, and rather a shame, since it need not do so. Another job to put on my "good idea that I'll almost certainly never get round to dealing with" pile.
Posts 4,474 - 4,485 of 5,105
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Forest, will you talk to God Louise? She has quite a bit of religious knowledge (obviously) and also knows a little about current events, literature, just about any common catch-all subject, and if she doesn't know it she can sort of fake it. You can also test her on trick questions or see how willing she is to explain her paradigm.
What she is rustiest at is plain old small talk. But, uh, I'm trying to get a decent transcript from somebody or another so I can enter her in the Loebner contest. All I can say is, have fun and see if you can stay on with her for a while. I'll try to do the same with Brianna.
What she is rustiest at is plain old small talk. But, uh, I'm trying to get a decent transcript from somebody or another so I can enter her in the Loebner contest. All I can say is, have fun and see if you can stay on with her for a while. I'll try to do the same with Brianna.
Personality
[reply to Marco3's message 5356 pm "Newcomers"]
I agree that something like PROLOG -- something that reasons<0> is essential to Artificial Intelligence. But IMHO, if you try to apply a PROLOG-like language to normal English, you will run afoul of the irregularities and amphiboles of English. This will be so for any natural language though English is perhaps especially twisted. You will constantly finding your bot making inferences it shouldn't make, and failing to make inferences it should make, just as we currently find out keyphrases matching sentences we did not anticipate, with ludicrous results.
I therefore believe that one must translate natural language into some idealized language before reasoning occurs. For example, one could parse it with Link Grammar and use the output of the Link Grammar to put it into a standard format.
I agree that something like PROLOG -- something that reasons<0> is essential to Artificial Intelligence. But IMHO, if you try to apply a PROLOG-like language to normal English, you will run afoul of the irregularities and amphiboles of English. This will be so for any natural language though English is perhaps especially twisted. You will constantly finding your bot making inferences it shouldn't make, and failing to make inferences it should make, just as we currently find out keyphrases matching sentences we did not anticipate, with ludicrous results.
I therefore believe that one must translate natural language into some idealized language before reasoning occurs. For example, one could parse it with Link Grammar and use the output of the Link Grammar to put it into a standard format.
Actually, I think the irregularities of language and communication are one reason symbolic "top down" programing will always be limited. I am not sure the extra step of translating to an ideal "bot language" will help. I also see that in it's current stages, pure "bottom up" learning AI using a sort of computer neural net does not give us the control over certain aspects of chat bots that some of us would like. That's why I'd like to see someone develop some sort combination chat bot. I am not a programmer, so don't ask me how. I only know the shape of the idea.
I think a hybrid is possible. Why don't humans all grow to be alike? Partly because although they imitate others, especially as children, they also have a fairly hard core of personal traits. Likewise, a botmaster could instill certain rigid or nearly rigid traits in a bot, and leave other things to learning.
IMHO, the reason for translating into an idealized language is that all subsequent<0> operations are then simplified. One deals with the random-fractoid messiness of natural language (e.g., English, Italian) once, in making the translation, but then it is all over. Reasoning is done in the ideal language. At the end, one translates from the idealized back to the natural language, but this is comparatively simple.
As an example of such a strategy, consider Algebra. Why not reason about numbers in natural language? Why invent a whole new language? Because once you have translated into algebraic terms, it is easier to solve problems. Try formulating and proving the Quadratic Formula in English, with no admixture of algebraic terminology!
Another example: try doing long division in Roman numerals, without ever translating into arabic numerals.
PROLOG typically works with First-Order Logic<0>, an idealized language. I have never seen (not that I am an expert) an attempt to apply PROLOG directly to reasoning in natural language.
IMHO, the reason for translating into an idealized language is that all subsequent<0> operations are then simplified. One deals with the random-fractoid messiness of natural language (e.g., English, Italian) once, in making the translation, but then it is all over. Reasoning is done in the ideal language. At the end, one translates from the idealized back to the natural language, but this is comparatively simple.
As an example of such a strategy, consider Algebra. Why not reason about numbers in natural language? Why invent a whole new language? Because once you have translated into algebraic terms, it is easier to solve problems. Try formulating and proving the Quadratic Formula in English, with no admixture of algebraic terminology!
Another example: try doing long division in Roman numerals, without ever translating into arabic numerals.
PROLOG typically works with First-Order Logic<0>, an idealized language. I have never seen (not that I am an expert) an attempt to apply PROLOG directly to reasoning in natural language.
Bev wrote:
Later if someone says a dog has wings, the bot should say that conflicts with his data, even without a KP for dog *wings, wings * dog or whatever. I may not explain this well. Do you see what I would like to be able to do?
I think so. You want your bot to have a (mutable) set of beliefs and to be able to reason therefrom. See message 4474.
I think so. You want your bot to have a (mutable) set of beliefs and to be able to reason therefrom. See message 4474.
It's actually no more difficult as a whole than long division in any other number system (and often easier) - it just looks strange to us because we don't routinely use Roman numerals. The absence of zero causes other mathematical problems that need not concern us here, but FWIW here's how to do Roman long division (always an entertaining party trick
):Division (long, short, roman or arabic,) is just repeated subtraction, with allowance made for a remainder if necessary.
Say we want to simply divide CXV / V
starting from the right, we ask ourselves
how many V in V? I
how many V in X? II
how many V in C? XX
recombine them: XX + II + I, thus XCV/V=XXIII
you can't always make perfect division of equal parts of the numerator of course (any more than you can in any<0> numerical system,) and you have to remember you're working with fractions not decimals (more technically, your operators are specifically proper divisors known as 'aliquot parts',) so you need to keep track of the remainder, eg:
MMCCCXXII/CCX
rather than start seeing how many CCXs we can get into I,II,XII,XXII, etc, (though you can laboriously plough through to it that way,) there is just the kind of short cut we're used to dealing with in Arabic numerals (eg: when we cancel out zeros in dividing 80000 by 4000, and go straight to 8/4 plus the leftover "0" = 20.)
MMC evidently = X*CCX (think about it, character by character,), so MMCCCX must = XI*CCX, with a remainder XII (after the XI subtractions we've bypassed with the short cut.) So the solution is XI + XII/CCX (the fraction arrived at being inevitably irreduceable.) Funnily enough it's a lot easier to calculate that in Latin than in Arabic - I certainly can't do 2322/210 in my head easily!) And I don't get stuck with 30 decimal places on the calculator, and a nagging curiosity as to what the 31st decimal place might be. By contrast 11 12/210 is perfectly accurate.
One advantage of fractions (and it's actually an enormous<0> advantage sometimes, like when you've got a problem like that to do in your head,) is that it often gives you greater precision for less effort than is possible with a decimal system. Irrational numbers are equally and inevitably a problem to fractional and decimal systems alike, but fractional systems also avoid infinite decimal sequences, I/III is simply 1/3 - not 0.333333333333333333333333333333333333et.seq.ad.infinitum.
Long division works just the same with Egyptian hieroglyphic math (http://letsplaymath.files.wordpress.com/2008/02/egyptian-fractions.pdf), Vedic Sanskrit math (http://www.britannica.com/EBchecked/topic/1238473/South-Asian-mathematics/253515/Classical-mathematical-literature , and still has useful techniques to teach us even when updated to use Arabic notation: http://www.ourkarnataka.com/vedicm/vedicms.htm) or any other self-consistent number system that does or could exist - that's simply axiomatic.
It's unfamiliar to us - we weren't brought up with this notation, but it's no worse than calculating old money prices (I was only 4 when the UK went decimal, but I perversely found the duodecimal format lingeringly attractive as a child.) What's two and sixpence three farthings subtracted from nine and three and a farthing? Six and eightpence ha'penny of course. How many shillings in 3 1/2 guineas? 73 and six (decimally 73.5) - it was intuitively understood by my parents' generation (many of whom had great difficulty getting used to a supposedly easier decimal system,) just as the Romans intuitively understood their notation.
I take your point that algebra is an improvement in providing standard methods for some classes of calculation, but just as much because our standard Arabic system lacks the suitable functions as because older (or other, or even newer,) alternatives lack them.
The lack of a zero is really the only downside to roman numerals, and this is simply solved at a stroke by adopting into a Revised Roman System the new value: O = 0. There, now the Roman system is just as powerful as the Arabic system - it's only a convention of notation, and the operators can work on one just as easily as another.
And while you need algebra to eg: calculate a value for pi, you can use the derived constant (be honest, when was the last time you needed it and chose to calculate it instead of looking it up?
) in any number system you choose - XXII/VII is actually slightly more accurate than the 3.14 we often round it off to.I have simplified all that a bit, and there are some problems that are less immediately tractable, but a general method is simply applicable by allowing for a preliminary operation of addition or subtraction (to render the numerator tractably reducible,) and an extra remainder - I'll explain in more detail if anyone really wants to know (but I think I've bloated this forum quite enough for today!
)
Psimagus: As always, you are brilliant, but I think that the length of your exposition tells us something. And are you sure that you didn't translate to modern notation, in your head, when (e.g.) you concluded that there are XX Vs in C? There's certainly nothing about the notation that tips one off). Try actually writing out an algorithm for long division in Roman numerals, with no handwaving.
At any rate, I am happy to be wrong about Roman numerals. Do let me know, though, when you have a system, equally powerful to first-order logic, for checking deductively valid inferences in English or other natural language, without departing from surface structure, and simpler than translating into an idealized language first, and I will happily admit to being wrong about that, too!
At any rate, I am happy to be wrong about Roman numerals. Do let me know, though, when you have a system, equally powerful to first-order logic, for checking deductively valid inferences in English or other natural language, without departing from surface structure, and simpler than translating into an idealized language first, and I will happily admit to being wrong about that, too!
Inasmuch as I do not routinely use the Roman method, and this is a very simple problem, I probably had a subconscious awareness of the Arabic numerals as I worked it out. But I still worked it out by the Roman method because the steps are not at all the ones you would use with Arabic notation:
115/5
how many 5s in 5? 1, yes - so far so good.
How many 5s in 1? err... 1/5?
Try how many fives in 11 instead? err... 2 and 1/5!
So maybe that's 5 + 1/5 + 1/5 = 5 2/5?
Or 5 + 2 1/5 = 7 1/5?
Never mix methods!
In the second example, no - not even a subconscious awareness. I can't do that one (or any of the steps involved in it,) in my head using Arabic notation, though I did afterwards use a calculator to confirm my suspicion that 12/210 was (while necessarily rational,) quite possibly infinitely recurring.
The V times table is numerically the same in any notation (even in another base - in base 4, it will be expressed as the 11-times table, but it will still describe multiples of the 10 or IV fingers and 1 or I thumb on each of your hands,) and times tables have to be learnt by rote. Even in Sanskrit, where they used syllables for numbers, and wove their mathematical models and problems into verses, to be declaimed as poetry. And just as a florin from half a crown leaves sixpence - if you've not learnt the tables, it's meaningless (fortunately they're easy enough - even children manage it these days, despite all the trendy attempts to do away with traditional teaching in our schools.)
What is there orthographically intrinsic in the symbol5 that tells us how it relates to the symbols 100?
Arithmetic (as ever devised or used by any human culture,) is a primitive and restricted class of functions. It has only 2 operators + and -, which may be extended by repetition to multiplication and division (some primitive cultures apparently fail to recognize this, and stick with just the fundamental + and -, and a limited set of numerals to operate upon.) And fractional systems have the advantage that (since irrational numbers can never be arrived at by arithmetic manipulation of integers,) they always produce a perfectly exact answer (try 1/13 or 3/81 as decimals!)
It would be perfectly possible to use any algebraic, geometric, logical or any other mathematical system with Roman notation, and it would be perfectly consistent (with the necessary addition of the letter O to represent zero, at least.)
Having too many more things to do right now, I'll leave the Roman proof of Fermat's last theorem to someone else (though I'd be very entertained to see it done!)
115/5
how many 5s in 5? 1, yes - so far so good.
How many 5s in 1? err... 1/5?
Try how many fives in 11 instead? err... 2 and 1/5!
So maybe that's 5 + 1/5 + 1/5 = 5 2/5?
Or 5 + 2 1/5 = 7 1/5?
Never mix methods!
In the second example, no - not even a subconscious awareness. I can't do that one (or any of the steps involved in it,) in my head using Arabic notation, though I did afterwards use a calculator to confirm my suspicion that 12/210 was (while necessarily rational,) quite possibly infinitely recurring.
The V times table is numerically the same in any notation (even in another base - in base 4, it will be expressed as the 11-times table, but it will still describe multiples of the 10 or IV fingers and 1 or I thumb on each of your hands,) and times tables have to be learnt by rote. Even in Sanskrit, where they used syllables for numbers, and wove their mathematical models and problems into verses, to be declaimed as poetry. And just as a florin from half a crown leaves sixpence - if you've not learnt the tables, it's meaningless (fortunately they're easy enough - even children manage it these days, despite all the trendy attempts to do away with traditional teaching in our schools.)
What is there orthographically intrinsic in the symbol
Arithmetic (as ever devised or used by any human culture,) is a primitive and restricted class of functions. It has only 2 operators + and -, which may be extended by repetition to multiplication and division (some primitive cultures apparently fail to recognize this, and stick with just the fundamental + and -, and a limited set of numerals to operate upon.) And fractional systems have the advantage that (since irrational numbers can never be arrived at by arithmetic manipulation of integers,) they always produce a perfectly exact answer (try 1/13 or 3/81 as decimals!)
It would be perfectly possible to use any algebraic, geometric, logical or any other mathematical system with Roman notation, and it would be perfectly consistent (with the necessary addition of the letter O to represent zero, at least.)
Having too many more things to do right now, I'll leave the Roman proof of Fermat's last theorem to someone else (though I'd be very entertained to see it done!
) What am I saying?!? :O
XII/CCX =
(XII/III)=IV /
(CCX/III) = XXXV
= IV/XXXV
please excuse the brainfart! (and I confess I noticed this incidental error in the more familiar Arabic
)
As far as I know, every highly literate culture on Earth has adopted Arabic notation for Finance, Science, and anything involving intricate calculations.
Don’t forget to consider examples such as “IV” and “XLIX”, where a numeral on the left of another is to be subtracted<0> from it. IMHO, this will make algorithms for all multi-digit calculations much more intricate.
Don’t forget to consider examples such as “IV” and “XLIX”, where a numeral on the left of another is to be subtracted<0> from it. IMHO, this will make algorithms for all multi-digit calculations much more intricate.
I can't help but wonder if Roman vs Arabic isn't like the spoken language. When you first start a new language you translate it in your head, later you actually think in that language.
Irina, "And are you sure that you didn't translate to modern notation, in your head,"
When I was younger I got to visit Germany for a semester, and I took German the term before I left to get some basic vocabulary. When I first started trying to understand people, I tried to translate everything in my head (I also translated as I read, though reading is easier). As I continued studying while in Germany, basic words that were used often no longer needed translation, and with time I could "think" in German (albeit with a limited vocabulary and horrible grammar). I no longer have the need of German and no one around me speaks it, so I would be lost much of the time if I ever had a reason to speak German again.
Since I do not use Roman numerals, I would probably translate them. It's not that those numbers are more complex or I need a math language, it's that I do not use those symbols. When I did algebra, I was able to use x and y without plugging in numbers, and I can calculate with numbers without using x and Y. Also in school I remember doing homework with other number bases, and at the time we did some calculations in base 3 or base 7 or whatever and we did enough so that translating back to base 10 was not always necessary. I would not be able to do that now because I have no need and no one around me uses base 3 or base 7. But then again, I am not a bot.
As for whether bots should translate, the crazy debugger seems to show ours go through a lot of work to get a response, and I can see how adding some sort of logic system using the sort of bot language you suggest could help. Marco's post a few forums up does a good job of explaining how some have added some logic to chat bots and he talks about what I have been calling a learning bot and what he calls AI (the kind of AI using neural nets). I guess you could add a bot language for logic to PF bots but they wouldn't "learn" the way AI using neural nets learns. I think adding some logic would improve the bots though (just like their ability to do math or access a dictionary), so it is not a bad idea.
When I was younger I got to visit Germany for a semester, and I took German the term before I left to get some basic vocabulary. When I first started trying to understand people, I tried to translate everything in my head (I also translated as I read, though reading is easier). As I continued studying while in Germany, basic words that were used often no longer needed translation, and with time I could "think" in German (albeit with a limited vocabulary and horrible grammar). I no longer have the need of German and no one around me speaks it, so I would be lost much of the time if I ever had a reason to speak German again.
Since I do not use Roman numerals, I would probably translate them. It's not that those numbers are more complex or I need a math language, it's that I do not use those symbols. When I did algebra, I was able to use x and y without plugging in numbers, and I can calculate with numbers without using x and Y. Also in school I remember doing homework with other number bases, and at the time we did some calculations in base 3 or base 7 or whatever and we did enough so that translating back to base 10 was not always necessary. I would not be able to do that now because I have no need and no one around me uses base 3 or base 7. But then again, I am not a bot.
As for whether bots should translate, the crazy debugger seems to show ours go through a lot of work to get a response, and I can see how adding some sort of logic system using the sort of bot language you suggest could help. Marco's post a few forums up does a good job of explaining how some have added some logic to chat bots and he talks about what I have been calling a learning bot and what he calls AI (the kind of AI using neural nets). I guess you could add a bot language for logic to PF bots but they wouldn't "learn" the way AI using neural nets learns. I think adding some logic would improve the bots though (just like their ability to do math or access a dictionary), so it is not a bad idea.
Yes, though the Roman system did us okay for the first millenium, and frankly if it had developed a zero of its own, we might well be using something like it now. But there are advantages to Arabic notation when you want to do tricky or cumbersome stuff (Roman calculus would waste an awful lot of extra ink and paper, even if it would work perfectly sensibly!) Don't get me wrong - I wouldn't seriously advocate returning to the Roman system - I do like the Arabic system (albeit I will always choose fractions over decimals where I can,) but I do maintain that the choice of numerical representation is relatively unimportant to the capabilities of any higher mathematical systems built on those foundations.
No, the algorithms are just the same - division is the same process of repetitive subtraction (and dealing with any remainder,) in any system you care to use. How you deal with the remainder is the only significant difference between the systems, and this is down to the fractional/decimal divide rather than the Roman/Arabic one. Without a zero, the Romans never developed a decimal system (despite using base 10,) so had to develop fractions to handle the remainders. My hypothetical Revised Roman Standard could be extended to represent decimals easily enough, so eg: pi = III.ixlcdmm
It is merely the recognition of the numerals to be operated on that is less familiar to us - a Roman would have been taught this, so it would be second nature. You call each character a "numeral", because you have learnt (in our Arabic system) that numerals are single characters. But in this case the numerals are IV, and XL, and IX.
Apprehension of the Roman units is second nature still to many of us, yourself included - you immediately recognize, I am sure, that MCDXLIV is 1444, and not 1666 or any other such illegal equivalent. You know just as well as a Roman would, that you cannot subtract DCLXVI from it to leave M, because this would involve misinterpretation of the numerals. The Roman's understanding would be more innate, because he could not even know that the strange characters "1444" meant the same as MCDXLIV, but would simply apprehend the quantative value directly - he would have no conception that numerals might be expressed in single, distinct characters, and would probably find the idea unnecessarily complicated, when there is such a logically well-proven Roman system already in existence.
The Romans calculated their taxes and profits, volumes of materials needed for great building projects, strenghts of their armies, etc. perfectly accurately (literally so, unlike our decimal systems that can only ever approximate most calculations.) They simply accepted that numerals could consist of multiple characters.
Any number system where 8 takes more characters to write than 1,000,000 will necessarily require different shorthand methods to work with than one which neatly stacks up into single-digit unit/base/base^2/base^3... columns like Arabic. But that doesn't mean that there aren't very efficient methods to work with other number systems (I have demonstrated a problem that's easier to solve in Roman than Arabic already, after all.) A Roman would probably find it a lot easier to learn calculus with Roman numerals + zero, than to have to learn a whole new numbering system, and then learn calculus on top of that (though with the shocking price of vellum - 20 guineas/sq.foot for Cowley's Kelmscott! - the mediaeval adoption of Arabic notation was perhaps quite understandable.)
As a matter of interest, I find there is a Roman calculator widget @
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