Re: The Seventh Step 1 (Numbers and Notations)
On 12 Feb 2009, at 18:17, John Mikes wrote: My present inserts in Italics - some parts of the posts erased for brevity John On Thu, Feb 12, 2009 at 10:32 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 11 Feb 2009, at 23:46, John Mikes wrote: (...) Not that if I see 'I' that means 1, but if I see 'III' that does not mean 3 to me, it means 111. You have to teach first what those funny 'figures' (3,7,etc.) mean. I don't have to do that. If you follow the thread, you will even understand why I cannot do that. The existence and nature of numbers as well as our understanding of it will remain a mystery. But assuming comp (and thus the numbers), we can understand why this is a necessary mystery. It is part of the unbridgeable gap which has to remain if we want to remain bot scientist and consistent. JM: like a religion? The religion of the mystic, perhaps. But like consciousness (true but you can't prove it), which can be seen has an elementary mystical state already. Surely John, you can sole the problem of extending the sequence I II III ... That is the mystery. Later we will see that the ... is even necessarily ambiguous, but then we (the humans) can progress. If you teach: III and III mean 3 and 7, then you said nothing, just named them. I said nothing indeed, but I did not even name them. If you look carefully. Obviously by 7 I was referring to the meaning I am supposing you already know. Br: That was my point. To talk on notation. I just hope people understand enough the number so that if I ask them to give me 3 euros, they will not give me two or four. JM: now you swithch to quantity. I did not switch. Cardinal numbers (and natural number are both cardinal and ordinal numbers) are the elementary quanta of quantities. BR: Later we will axiomatize the theory of numbers. But I prefer to wait to be sure people understand the notion of number before axiomatizing. If I do the axiomatization too early, some people will believe I am rigorously defining the numbers, but this is a grave error. I will axiomatize the number to reason about them and to interview machines about the numbers. JM: interviewing machines is no evasion of the topic. Axiomatizing in my vocabulary means to invent some unreal statement that justifies the otherwise not justified theory. I don't fight it in this case: with your numbers it may be (excusably) needed. Numbers are as mysterius as consciousness and time. That is why mathematicians does not even try. But wait for the next thread, I will give a definition of numbers (which sometimes makes some mathematician believed we have a definition). But it will not be a definition, just a representation in term of another notion, av- ctually the notion of set. of course the notion of set is richer and even less definable than numbers. JM: can't wait for your definition. Set is introduced? a many looking like a one? with lots of characteristics hidden? A table of 9 loose letters is no 'set' by itself. I am hesitating but I think I will do it. The order of the presentation is not easy to decide. Thanks for your cannot wait. Asap! No content meant. Quantity???(vs. number?) (...) [to: Romans...] Br: decimal? Without zero there is no position based notation for the number. JM: I consider a decimal system as more than just positioned numbers The Romans emphsised the exceptional role of 10 (X) 100 (C) 1000(M) (even if I play down V,L,D as auxilieries) yes but a position notation emphasize the role of position. The Romans like the Greeks were a bit crazy about the Decade. Best regards, Bruno (...) I think your teaching is fine, but one has to know it before learning it. And: as a nun said to a friend when she had questions 'upon thinking': you should not think, you should believe. (...) Your teachings made an enjoyable reading, thank you. I confess: I did not count the 'I'-s just believed that there are 2009 of them. It is not magical, in other calendar-countings the year has quite different number of 'I'-s. (...) Br: Thanks for those kind and funny remarks and questions, Best, Bruno JM:I take it lightly John M On Wed, Feb 11, 2009 at 1:01 PM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Kim, I told you that to grasp the seventh step we have to do some little amount of math. Now math is a bit like consciousness or time, we know very well what it is, but we cannot really define it, and such an encompassing definition can depend on the philosophical view you can have on the mathematical reality. So, if I try to be precise enough so that the math will be applicable, not just on the seventh step, but also on the 8th step and eventually for the sketch of the AUDA, that is the arithmetical translation of the universal dovetailer argument, I am tempted by
Re: The Seventh Step 1 (Numbers and Notations)
On 11 Feb 2009, at 23:46, John Mikes wrote:
Dear Bruno, just lightening up a bit...you know that I graduated
already from 2nd yr grade school so I have an open mind criticizing
high science.
Not that if I see 'I' that means 1, but if I see 'III' that does
not mean 3 to me, it means 111. You have to teach first what those
funny 'figures' (3,7,etc.) mean.
I don't have to do that. If you follow the thread, you will even
understand why I cannot do that. The existence and nature of numbers
as well as our understanding of it will remain a mystery. But assuming
comp (and thus the numbers), we can understand why this is a necessary
mystery. It is part of the unbridgeable gap which has to remain if we
want to remain bot scientist and consistent.
If you teach: III and III mean 3 and 7, then you said
nothing, just named them.
That was my point. To talk on notation. I just hope people understand
enough the number so that if I ask them to give me 3 euros, they will
not give me two or four.
Later we will axiomatize the theory of numbers. But I prefer to wait
to be sure people understand the notion of number before axiomatizing.
If I do the axiomatization too early, some people will believe I am
rigorously defining the numbers, but this is a grave error. I will
axiomatize the number to reason about them and to interview machines
about the numbers.
Numbers are as mysterius as consciousness and time. That is why
mathematicians does not even try. But wait for the next thread, I will
give a definition of numbers (which sometimes makes some mathematician
believed we have a definition). But it will not be a definition, just
a representation in term of another notion, av-ctually the notion of
set. of course the notion of set is richer and even less definable
than numbers.
No content meant. Quantity???(vs. number?)
Having 10 digits on 2 hands is the 2nd mental evolutionary step
after recognizing 5 digits on 1 hand, which was the earlier stage
(among others old Hungarians had that and a folks music in
pentatonic scale). The 'ancient' computer-folks have ony 2 digits on
their mind, Yin and Yang (0 and 1) and voila they made lots of
marvels from this simplified system already. (You have that). And
the French? with quatrevingtdix for nonante? XC is not XX-XX-XX-XX-
X - Romans still recognizing the '5' as a basic tenet (V, L, D,) as
cornerstones in their number system.
Also your digital 0,9,8,7,6 and then 5,4,3,2,1 was trouble in
ancient Rome..
The Romans had no zero, yet used a (quasi) decimal system.
decimal? Without zero there is no position based notation for the
number.
However they did not write rather IV and then for 9: IX
anticipating V and X as the next one. They also subtracted 4 from 7
as counting backwards: like 7,6,5,4, which made 7-4=4 in all
calendar countings which was based on the subtraction of day-numbers
from the next 'fix' day in the month. Can you figure the
consequences of this in paying interest (or taxes?)
(That may be the reason why Muslims are banned from counting
interest).
I think your teaching is fine, but one has to know it before
learning it.
And: as a nun said to a friend when she had questions 'upon
thinking': you should not think, you should believe.
About the 12 digital creation: In J.Cohen - J.Stewart ('Chaos' and
'Reality') the Zarathustran 'aliens' had an 8 based thinking
(octimal) as best and perfect. Well, 10 gives a prime after one
halfing, 12 after two, 8 after 3. I think there were 12 digit
creatures but failed. 10 proved practical - maybe not because of the
decimal as best mathematical system. It just survived...
Your teachings made an enjoyable reading, thank you. I confess: I
did not count the 'I'-s just believed that there are 2009 of them.
It is not magical, in other calendar-countings the year has quite
different number of 'I'-s.
If I should ask a question: how would one note 1 billion on the
planet of centipeds with 8 fingers on all 100 feet? (Don't answer,
please). (Q2: which billion? the 1000M or the MM?)
Thanks for those kind and funny remarks and questions,
Best,
Bruno
John M
On Wed, Feb 11, 2009 at 1:01 PM, Bruno Marchal marc...@ulb.ac.be
wrote:
Hi Kim,
I told you that to grasp the seventh step we have to do some little
amount of math.
Now math is a bit like consciousness or time, we know very well what
it is, but we cannot really define it, and such an encompassing
definition can depend on the philosophical view you can have on the
mathematical reality.
So, if I try to be precise enough so that the math will be applicable,
not just on the seventh step, but also on the 8th step and eventually
for the sketch of the AUDA, that is the arithmetical translation of
the universal dovetailer argument, I am tempted by providing the
philosophical clues, deducible from the
Re: The Seventh Step 1 (Numbers and Notations)
I'm sorry but I can't resist to paste this short conversation between Lord Blackadder and his servant Baldrick. Maybe you know this british blackadder comedy. If you teach: III and III mean 3 and 7, then you said nothing, just named them. That was my point. To talk on notation. I just hope people understand enough the number so that if I ask them to give me 3 euros, they will not give me two or four. - Baldrick, if I have 2 beans and then I add 2 more beans, what do I have? - Some beans. - Yes... and no. Let's try again shall we? I have 2 beans, then I add 2 more beans. What does that make? - A very small casserole. - Baldrick, the ape creatures of the Indus have mastered this. Now try again. 1, 2, 3, 4. So how many are there? - 3 - What?! - And that one. - 3.. and that one. So if I add that 1 to the 3 what will I have? - Oh! Some beans. - Yes.. To you Baldrick the renaissance was just something that happened to other people wasn't it? mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: The Seventh Step 1 (Numbers and Notations)
My present inserts in Italics - some parts of the posts erased for brevity John On Thu, Feb 12, 2009 at 10:32 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 11 Feb 2009, at 23:46, John Mikes wrote: (...) Not that if I see 'I' that means 1, but if I see 'III' that does not mean 3 to me, it means 111. You have to teach first what those funny 'figures' (3,7,etc.) mean. I don't have to do that. If you follow the thread, you will even understand why I cannot do that. *The existence and nature of numbers as well as our understanding of it will remain a mystery.* But assuming comp (and thus the numbers), we can understand why this is a necessary mystery. It is part of the unbridgeable gap which has to remain if we want to remain bot scientist and consistent. *JM: * *like a religion?* If you teach: III and III mean 3 and 7, then you said nothing, just named them. Br: That was my point. To talk on notation. I just hope people understand enough the number so that if I ask them to give me 3 euros, they will not give me two or four. *JM:* *now you swithch to quantity.* BR: Later we will axiomatize the theory of numbers. But I prefer to wait to be sure people understand the notion of number before axiomatizing. If I do the axiomatization too early, some people will believe I am rigorously defining the numbers, but this is a grave error. I will axiomatize the number to reason about them and to interview machines about the numbers. ** *JM: interviewing machines is no evasion of the topic. Axiomatizing in my vocabulary means to invent some unreal statement that justifies the otherwise not justified theory. I don't fight it in this case: with your numbers it may be (excusably) needed.* Numbers are as mysterius as consciousness and time. That is why mathematicians does not even try. But wait for the next thread, *I will give a definition of numbers* (which sometimes makes some mathematician believed we have a definition). But it will not be a definition, just a representation in term of another notion, av-ctually the notion of set. of course the notion of set is richer and even less definable than numbers. *JM: can't wait for your definition. Set is introduced? a many looking like a one? with lots of characteristics hidden? A table of 9 loose letters is no 'set' **by itself. * ** No content meant. Quantity???(vs. number?) (...) [to: Romans...] Br: decimal? Without zero there is no position based notation for the number. *JM: I consider a decimal system as more than just positioned numbers* *The Romans emphsised the exceptional role of 10 (X) 100 (C) 1000(M) (even if I play down V,L,D as auxilieries)* (...) I think your teaching is fine, but one has to know it before learning it. And: as a nun said to a friend when she had questions 'upon thinking': you should not think, you should believe. (...) Your teachings made an enjoyable reading, thank you. I confess: I did not count the 'I'-s just believed that there are 2009 of them. It is not magical, in other calendar-countings the year has quite different number of 'I'-s. (...) Br: Thanks for those kind and funny remarks and questions, Best, Bruno *JM:I take it lightly* *John M* On Wed, Feb 11, 2009 at 1:01 PM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Kim, I told you that to grasp the seventh step we have to do some little amount of math. Now math is a bit like consciousness or time, we know very well what it is, but we cannot really define it, and such an encompassing definition can depend on the philosophical view you can have on the mathematical reality. So, if I try to be precise enough so that the math will be applicable, not just on the seventh step, but also on the 8th step and eventually for the sketch of the AUDA, that is the arithmetical translation of the universal dovetailer argument, I am tempted by providing the philosophical clues, deducible from the comp hypothesis, for the introduction to math. But I realize that this would entail philosophical discussion right at the beginning, and that would give to you the feeling that, well, elementary math is something very difficult, which is NOT the case. The truth is that philosophy of elementary math is difficult. So I have change my mind, and we will do a bit of math. Simply. It is far best to have a practice of math before getting involved in more subtle discussion, even if we will not been able to hide those subtleties when applying the math to the foundation of physics and cognition. I propose to you a shortcut to the seventh step. It is not a thorough introduction to math. Yet it starts from the very basic things. Let us begin. What I explain here is standard, except for the notations, and this for mailing technical reason. I guess you have heard about the Natural Numbers, also called Positive Integers. By default, when I use the word number, it
The Seventh Step 1 (Numbers and Notations)
Hi Kim, I told you that to grasp the seventh step we have to do some little amount of math. Now math is a bit like consciousness or time, we know very well what it is, but we cannot really define it, and such an encompassing definition can depend on the philosophical view you can have on the mathematical reality. So, if I try to be precise enough so that the math will be applicable, not just on the seventh step, but also on the 8th step and eventually for the sketch of the AUDA, that is the arithmetical translation of the universal dovetailer argument, I am tempted by providing the philosophical clues, deducible from the comp hypothesis, for the introduction to math. But I realize that this would entail philosophical discussion right at the beginning, and that would give to you the feeling that, well, elementary math is something very difficult, which is NOT the case. The truth is that philosophy of elementary math is difficult. So I have change my mind, and we will do a bit of math. Simply. It is far best to have a practice of math before getting involved in more subtle discussion, even if we will not been able to hide those subtleties when applying the math to the foundation of physics and cognition. I propose to you a shortcut to the seventh step. It is not a thorough introduction to math. Yet it starts from the very basic things. Let us begin. What I explain here is standard, except for the notations, and this for mailing technical reason. I guess you have heard about the Natural Numbers, also called Positive Integers. By default, when I use the word number, it will mean I am meaning the natural number. I guess you agree with the statement that 0 is equal to the number of occurrence of the letter y in the word spelling. OK? Then you have the number 1, 2, 3, 4, etc. OK? They are respectively equal to the number of stroke in I, II, III, , etc. OK? Of course the number four is not equal to . But the string, or sequence of symbols is a good notation for the number four. The notation is good in the sense that it is quasi self-explaining. To see what number is denoted by a string like III: just count the strokes. OK? If that stroke sequences are conceptually good for describing the numbers, it happens that it is horrible for using them, and you are probably used to the much more modern positional notation for the number. If I ask you which year we are. You will not answer me that we are in the year I You will most probably tell me that we are in the year 2009. Is that not a bit magical? The explanation of that miracle relies in the very ingenuous way we can use our hands to count on our fingers or digits. We put 0 on a little finger, and then 1 on the next up to 4, and then we use the other hand to continue with 5 on the thumb, 6, then 7, then 8, then 9 on the last right fingers. Unfortunately we lack
Re: The Seventh Step 1 (Numbers and Notations)
Dear Bruno, just lightening up a bit...you know that I graduated already
from 2nd yr grade school so I have an open mind criticizing high science.
Not that if I see 'I' that means 1, but if I see 'III' that does not mean
3 to me, it means 111. You have to teach first what those funny 'figures'
(3,7,etc.) mean. If you teach: III and III mean 3 and 7, then you
said nothing, just named them. No content meant. Quantity???(vs. number?)
Having 10 digits on 2 hands is the 2nd mental evolutionary step after
recognizing 5 digits on 1 hand, which was the earlier stage (among others
old Hungarians had that and a folks music in pentatonic scale). The
'ancient' computer-folks have ony 2 digits on their mind, Yin and Yang (0
and 1) and voila they made lots of marvels from this simplified system
already. (You have that). And the French? with quatrevingtdix for nonante?
XC is not XX-XX-XX-XX-X - Romans still recognizing the '5' as a basic tenet
(V, L, D,) as cornerstones in their number system.
Also your digital 0,9,8,7,6 and then 5,4,3,2,1 was trouble in ancient Rome..
The Romans had no zero, yet used a (quasi) decimal system. However they did
not write rather IV and then for 9: IX anticipating V and X as the next
one. They also subtracted 4 from 7 as counting backwards: like 7,6,5,4,
which made 7-4=4 in all calendar countings which was based on the
subtraction of day-numbers from the next 'fix' day in the month. Can you
figure the consequences of this in paying interest (or taxes?)
(That may be the reason why Muslims are banned from counting interest).
I think your teaching is fine, but one has to know it before learning it.
And: as a nun said to a friend when she had questions 'upon thinking': you
should not think, you should believe.
About the 12 digital creation: In J.Cohen - J.Stewart ('Chaos' and
'Reality') the Zarathustran 'aliens' had an 8 based thinking (octimal) as
best and perfect. Well, 10 gives a prime after one halfing, 12 after two, 8
after 3. I think there were 12 digit creatures but failed. 10 proved
practical - maybe not because of the decimal as best mathematical system. It
just survived...
Your teachings made an enjoyable reading, thank you. I confess: I did not
count the 'I'-s just believed that there are 2009 of them. It is not
magical, in other calendar-countings the year has quite different number of
'I'-s.
If I should ask a question: how would one note 1 billion on the planet of
centipeds with 8 fingers on all 100 feet? (Don't answer, please). (Q2: which
billion? the 1000M or the MM?)
John M
On Wed, Feb 11, 2009 at 1:01 PM, Bruno Marchal marc...@ulb.ac.be wrote:
Hi Kim,
I told you that to grasp the seventh step we have to do some little
amount of math.
Now math is a bit like consciousness or time, we know very well what
it is, but we cannot really define it, and such an encompassing
definition can depend on the philosophical view you can have on the
mathematical reality.
So, if I try to be precise enough so that the math will be applicable,
not just on the seventh step, but also on the 8th step and eventually
for the sketch of the AUDA, that is the arithmetical translation of
the universal dovetailer argument, I am tempted by providing the
philosophical clues, deducible from the comp hypothesis, for the
introduction to math.
But I realize that this would entail philosophical discussion right at
the beginning, and that would give to you the feeling that, well,
elementary math is something very difficult, which is NOT the case.
The truth is that philosophy of elementary math is difficult.
So I have change my mind, and we will do a bit of math. Simply. It is
far best to have a practice of math before getting involved in more
subtle discussion, even if we will not been able to hide those
subtleties when applying the math to the foundation of physics and
cognition.
I propose to you a shortcut to the seventh step. It is not a thorough
introduction to math. Yet it starts from the very basic things.
Let us begin. What I explain here is standard, except for the
notations, and this for mailing technical reason.
I guess you have heard about the Natural Numbers, also called Positive
Integers. By default, when I use the word number, it will mean I am
meaning the natural number.
I guess you agree with the statement that 0 is equal to the number of
occurrence of the letter y in the word spelling. OK?
Then you have the number 1, 2, 3, 4, etc. OK? They are respectively
equal to the number of stroke in I, II, III, , etc. OK?
Of course the number four is not equal to . But the string, or
sequence of symbols is a good notation for the number four. The
notation is good in the sense that it is quasi self-explaining. To see
what number is denoted by a string like III: just count the
strokes. OK?
If that stroke sequences are conceptually good for describing the
numbers, it happens that it is horrible for using them, and
