Personality
Discuss specifics of personality design, including what Keyphrases work well and what dont, use of plug-ins, responses, seeks, and more.
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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.
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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
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 @
Well, I hereby agree to disagree about the advantages (or lack thereof) of arabic numeration over Roman.
Bev writes:
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.
1. It may be that such a bot wouldn't learn the way<0> that neural nets learn, but that doesn't mean they can't learn<0>. They could learn, for example, by making inductive inferences.
2. I see no reason why a bot with an inner idealized language could not have neural nets as part of its design. In that case it could (to some extent) learn the way neural nets do.
3. My impression is that neural nets have been very good indeed at learning perceptual recognition, but not so good at higher cognitive functions. In the 60's, using computers that had incredibly tiny memories and horribly slow clocks by today's standards, researchers made AI programs, based on symbol manipulation, that could (e.g.) solve differential equations, evaluate complex integrals, and solve logic problems. They preformed better than humans, even mathematicians, at these tasks. I have never heard of neural nets learning to do this sort of thing. But then, I am by no means current with this field; can someone bring me up to date?
4. Minsky and Papert wrote a book, "Perceptrons," purporting to show mathematically that there were certain kinds of problems that neural nets (= perceptrons) could not solve, by their very nature, but that symbol-manipulating programs could solve. Has this claim been refuted?
For me the upshot is this:
Given my present beliefs, if I were to design a robot today, I would make it a hybrid, using neural nets for learning perception and motor co-ordination, and symbolic processing for higher cognitive functions.
Bev writes:
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.
2. I see no reason why a bot with an inner idealized language could not have neural nets as part of its design. In that case it could (to some extent) learn the way neural nets do.
3. My impression is that neural nets have been very good indeed at learning perceptual recognition, but not so good at higher cognitive functions. In the 60's, using computers that had incredibly tiny memories and horribly slow clocks by today's standards, researchers made AI programs, based on symbol manipulation, that could (e.g.) solve differential equations, evaluate complex integrals, and solve logic problems. They preformed better than humans, even mathematicians, at these tasks. I have never heard of neural nets learning to do this sort of thing. But then, I am by no means current with this field; can someone bring me up to date?
4. Minsky and Papert wrote a book, "Perceptrons," purporting to show mathematically that there were certain kinds of problems that neural nets (= perceptrons) could not solve, by their very nature, but that symbol-manipulating programs could solve. Has this claim been refuted?
For me the upshot is this:
Given my present beliefs, if I were to design a robot today, I would make it a hybrid, using neural nets for learning perception and motor co-ordination, and symbolic processing for higher cognitive functions.
Suppose you wished to teach someone to solve linear equations. The student has never heard of linear equations before. Which way would you prefer do it?
1.
Write a new linear equation on the board and look expectantly at the student. If the student writes the correct solution, give him a piece of candy. If he fails to do so, give him a mild electric shock. Continue until he almost always gives the right answer.
2. Explain the notation of the relevant part of Algebra, its syntax and meaning. Give methods for solving various types of linear equations, starting with simple ones and working up to more complex ones. give examples frequently and give exercises frequently. Reward or punish the student for answers only when you are sure that he has the conceptual tools to answer the question correctly without having to be a genius. In fact, don't even ask<0> him a question unless you are sure of this.
1.
Write a new linear equation on the board and look expectantly at the student. If the student writes the correct solution, give him a piece of candy. If he fails to do so, give him a mild electric shock. Continue until he almost always gives the right answer.
2. Explain the notation of the relevant part of Algebra, its syntax and meaning. Give methods for solving various types of linear equations, starting with simple ones and working up to more complex ones. give examples frequently and give exercises frequently. Reward or punish the student for answers only when you are sure that he has the conceptual tools to answer the question correctly without having to be a genius. In fact, don't even ask<0> him a question unless you are sure of this.
What do you think about a mad personality sometimes you are mad but then sometimes you are happy or even sad. But then there is no doubt every time someone is bound to mess everything up all over again!!
I need friends and I will continue to post these things as well!!:O
I need friends and I will continue to post these things as well!!:O
Irina, I agree that computer neural nets are also limited in some ways (especially in their current state of development). However, I will mention that I strongly object to BOTH models of education you describe though I will refrain from boring you with the details.
Oh, please, Bev, bore me with the details! Or are you just going to give me an electric shock when I get it wrong?
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