# What is Complementary Logic

1. Jan 20, 2004

### Organic

2. Jan 20, 2004

### master_coda

Well, the biggest problem seems to be that you don't actually provide any kind of logic system. You just state the results you think your logic can provide.

This has been a general theme of your posts on complimentary logic. You continue to make statements like "Complimentary Logic can be used to do this". Until we see what comp logic is, we don't know what it can do. And all your attempts do define it so far have involved you invoking other undefined terms.

"associations between opposite concepts" may be a valid statement in English, but it is not a valid mathematical one. The English meaning of this sentance is too vague and nebulous. "Opposite" in particular is difficult to define mathematically. And you can't use existing math to define your concepts either, since math is based on logic you don't want to use.

Also, I should point out that a form of logic with no contradictions doesn't seem to be particularly useful. Contradictions help us determine which of our assumptions are good, and which are bad. If we get a contradiction, it means we made a bad assumption.

Thus it seems to me that if a logical system is unable to derive contradictions from bad assumptions, then it's doubtful it can derive tautologies from good assumptions. And that's kind of the whole point of logic, at least as far as math is concerned.

3. Jan 21, 2004

### Organic

Hi master_coda,

If we find efficient methods to explore and use a vary complex structural and dynamical real time phenomena, then very powerful models can become an actual realty.

This is a very dangerous state if the gap between our moral level and our technological level is too big.

Therefore I think that powerful language like Mathematics has to include the developer|development relations as natural part of it.

Maybe CL point of view is in the right way to this goal, because it first of all based on the idea of associations between opposite things, that naturally destroying each other by association.

If we learn how to develop methods that can help us to communicate with each other in non-distractive ways, I think maybe we will be able to survive the power of future’s technology.

More than that:

I think one of the beautiful things in open systems is not to find THE SOLUTION to something, but to find solutions by active participation through non-destructive communication.

By this attitude i think we always tuning ourselves in real time.

Because Complementary Logic is an open system by nature (and by saying this I mean that any of its results is under the lows of probability that can be clearly shown here:
http://www.geocities.com/complement...ry/Identity.pdf ) then any moment is the time to choose if we survive our choices or not.

Moral conclusions based on CL can be found here:

http://www.geocities.com/complementarytheory/Moral.pdf

Shortly speaking, any decision is based on our abilities to destroy or construct our system.

The answer to this dilemma cannot fully found in the limits of the examined system simply because of the fact that we always can destroy what we can explore.

CL solution to this dilemma is real time participation through communication between opposite things, by discovering their abilities to complement each other to something which its quality is more valuable then any one of them alone.

I think that not be aware to the potential destructive power of mathematics language, by disconnect it from the real world complexity, this is the big problem of Boolean-Logic, and nobody else but us is going to pay for it.

What do you think?

(Please be aware that Boolean Logic and Fuzzy Logic are private cases of CL).

Last edited: Jan 21, 2004
4. Jan 21, 2004

### master_coda

None of what you posted is relevant, because you still haven't addressed my main point, which is that you haven't actually provided us with a system of logic yet. All of your posts have been assertions about what you can do with your logic, and why you think it's better than traditional logic. But without the actual logic system, those claims don't have any relevance.

If you came here claiming to have a design for a spaceship that could travel faster than light, but refused to give a detailed or precise explaination of how it worked, then it wouldn't matter how important you thought your discovery was, or what you thought you could do with it.

I'm also more convinced than ever that your logic has nothing to do with math. You seem unable to grasp that concept that math has nothing to do with the real world by design. That isn't because the real world is unimportant or irrelevant, but because there are already other fields in philosophy and science that deal with the real world.

If you want to study how logic relates to the real world, go study the fields in philosophy that deal with how logic relates to the real world.

5. Jan 21, 2004

### Organic

master_coda,

First, BL and ZL are private cases in CL:
http://www.geocities.com/complementarytheory/BFinC.pdf

But CL has the built-in ability to deal with non-linearity, by connecting in a coherent way concepts like symmetry-degree that related to information’s clarity-degree.

where I construct the natural number by complementary associations between its integral side (its sum) and its differential side (some finite collection of 1’s).

Through this attitude addition and multiplication are complementary operations.

Show me how can you do that by using Boolean Logic.

Last edited: Jan 21, 2004
6. Jan 21, 2004

### master_coda

It can deal with non-linearity? Wow. And all these years I've been wasting my time with traditional logic. Of course, since traditional logic can handle non-linearity, wasted is probably the wrong word. Unless by non-linearity you mean "something I made up and I'm not telling you the definition of".

You also mention that you can construct the natural numbers with CT. But your construction has non-commutative multiplication. So it can't be the natural numbers, because the natural numbers have commutative multiplication.

Bragging about a construction of N with non-commutative multiplication is like bragging about building a car with no brakes. A car is supposed to have brakes. And the natural numbers are supposed to have commutative multiplication. So your construction has failed to accomplish its goals.

As for addition and multiplication being "complimentary", I don't really see how that is so. You've managed to make up other operations and have said they're complimentary, but those operations have little to do with any existing definitions of addition and multiplication.

And you've hardly shown why your goals are worthwhile. All you've done is make up a goal that you think math can't accomplish and said "that should be the goal of math". The fact that math fails to accomplish vague goals that you've made up on the spot is hardly remarkable. Pick any field of science or philosophy, and I can make up a goal that the field has failed at.

Finally, my point still remains...you have yet to do anything but make assertions about what CL can do. Saying "BL and ZL are private cases in CL" doesn't mean anything until you tell us what CL is, and stop telling us about all the wonderful things you think CL will accomplish.

And note: a picture is not a definition. A picture may "be worth a 1000 words", but those words are usually vague and ambiguous. Simply churning out pages and pages of assertions and pictures is something anybody can do if they have a lot of time on their hands. It's more impressive if you can produce a single page of precise, unambiguous content.

7. Jan 21, 2004

### Organic

master_coda,

You don't read to understand what I write for example:

I wrote:

"But CL has the built-in ability to deal with non-linearity, by connecting in a coherent way concepts like symmetry-degree that related to information’s clarity-degree."

You cut the first line of it and then run to show me how smart you are.

If you read all of it then you will see that I am talking about non-linearity which is based on the ability to connent in a coherent way concepts like symmetry-degree that related to information’s clarity-degree.

If you look at:
http://www.geocities.com/complementarytheory/ET.pdf

But if you want to understand someone's point of view then please ask specific questions about something that you don’t understand in ET.pdf and please stop giving me general lecturers about what is Math how Math should be and so on.

About non-commutative and commutative multiplication, let me tell you a secret, commutative multiplication is a private case of non-commutative multiplication because of this reason:

Commutative point of view can see only the quantitative property of the natural number, but the non-commutative point of view can see both structural and quantitative properties of the natural number.

Also what you call natural number is only the private case of an ET with no redundancy and no uncertainty.

For me the Natural number is what I call ET.

My pictures in ET.pdf are precise and rigorous exactly like any mathematical definition.

If you don't think so it means that you understand my pictures and in this case take one of my pictures and show me why it is not precise and rigorous as mathematical definition should be.

Thank you.

Organic

Last edited: Jan 21, 2004
8. Jan 21, 2004

### master_coda

You've been asked many specific questions in the past. You've been asked to define terms without using more undefined terms. You've been asked to prove your assertions. You've been asked to provide the rules of the your "complimentary logic". And you've done none of these things.

As for telling you how math is...if you're going to post stuff which is not math in a math forum, you should expect to be told what math is. And since just about all of your posts are based on your incorrect interpretations of what math is, it's highly relevant.

9. Jan 22, 2004

### Organic

10. Jan 22, 2004

### matt grime

Firstly ET.

This is approaching a standard I might call legible. Indeed the langauge is far clearer than anything that has preceded it. One wonders how you can use 'hierarchic' and still, depsite me explaining it to you, misuse 'aspirate'.

In ET you start by looking at some partitions of numbers, and how one might combine them modulo some ambiguous handwaving about types. This sort of idea is already known and extensively studied - look at anything on A-infinity algebras.

You are doing well up until the diagrams of swirly circles, and all of a sudden you start using hand-wavy undefined terms such as

what is a fading transition in rigorous mathematical terms.
Incidentally you seem unsure about rigour. I mean, you call me unimaginative when I demand that you adopt rigorous attitudes, yet insist your pictures are rigorous. Pictures aren't. How do I know you've drawn it correctly? Example: prove that a regular icosohedron exists. Making one out of paper is not sufficient.

Other undefined terms:

structural-quantitative

information point

uncertainty

redundancy

So let's talk aspirating.

1. Given the several representations of a given number as partitions, how do I know which one to chose to multiply together? ASsuming that your multiplication operation is well defined?

2. What is {{},{__}}?

You still havent properly defined this.
And if you think you have, then it will be a s imple task to cut and paste the definition here won't it?

3. If it is the set of all 'numbers' int your system (that can't be the definition can it?) then how does this beat the 'definition' of number as we know it? I mean I can simply say a number is anything in the set N of natural numbers can't I?

4. Aspirating means something else in the English language. I know that is necessarily important, lots of words have dual meanings in mathematics and the rset of the world, but you meant it to impliy aspire. Oh, and you've not defined aspire properly: approaching but cannot become closer to? I don't think that does it:

4a define approach
4b define closeness

5. So, is 4 the set of all of these sub-partitions of 4 things? If so does, say, x*y give you all the sub-partitions of x*y in terms of x and y? Note that you are using the normal definition of 4 in your statements, so you are relying on ordinary mathematics which doesn't define 4 in your opinion to define 4. Thus it is still undefined.

11. Jan 22, 2004

### Organic

Matt,

'{' and '}' are only framework (a stage) to explore ideas, nothing more, nothing less.

By using {} the idea of emptiness examined.

By using {__} the idea of its oppsite examined.

Any form of {x} is only an x-model of some examined x-idea.

Therefore no x-model is x-itself.

These are my basic rules in this game.

{} and {__} CONTENTS cannot be used by any information system, therefore they are the unreachable limits of any information system.

The logic of the associations between these opposites can be found here, including rigorous models that clearly showing the difference between other logical systems (i added one more model at the and that clearly showing it):

http://www.geocities.com/complementarytheory/BFC.pdf

I construct the natural number by complementary associations between its integral side (its sum) and its differential side (some finite collection of 1’s).

By ZF set theory we know that {a,a,a,b,b,b,c,c,c} = {a,b,c}

It means that concepts like redundancy and uncertainy are not used as fundamental concepts.

The level of where we start using some concept is very very important.

When we allow these concepts to be inherent properties of set's concept, then we enrich our abilities to use set's concept, for example:
Code (Text):

<-Redundancy->
c   c   c  ^<----Uncertainty
b   b   b  |    b   b
a   a   a  |    a   a   c       a   b   c
.   .   .  v    .   .   .       .   .   .
|   |   |       |   |   |       |   |   |
|   |   |       |___|_  |       |___|   |
|   |   |       |       |       |       |
|___|___|_      |_______|       |_______|
|               |               |

Where:

c   c   c
b   b   b
a   a   a
.   .   .
|   |   |
|   |   |  = {a XOR b XOR c, a XOR b XOR c, a XOR b XOR c}
|   |   |
|___|___|_
|

b   b
a   a   c
.   .   .
|   |   |
|___|_  |  = {a XOR b, a XOR b, c}
|       |
|_______|
|

a   b   c
.   .   .
|   |   |
|___|   |  = {a, b, c}
|       |
|_______|
|

I think that any iprovment in set's concept has to include redundancy and uncertainty as inherent proprties of set's concept.

The above point of view leading me to what I call Complementary logic, which is a fading transition between Boolean logic (0 Xor 1) and non-boolean logic (0 And 1), for example:

Number 4 is fading transition between multiplication 1*4 and

These fading can be represented as:
Code (Text):

(1*4)              ={1,1,1,1} <------------- Maximum symmetry-degree,
((1*2)+1*2)        ={{1,1},1,1}              Minimum information's clarity-degree
(((+1)+1)+1*2)     ={{{1},1},1,1}            (no uniqueness)
((1*2)+(1*2))      ={{1,1},{1,1}}
(((+1)+1)+(1*2))   ={{{1},1},{1,1}}
(((+1)+1)+((+1)+1))={{{1},1},{{1},1}}
((1*3)+1)          ={{1,1,1},1}
(((1*2)+1)+1)      ={{{1,1},1},1}
((((+1)+1)+1)+1)   ={{{{1},1},1},1} <------ Minimum symmetry-degree,
Maximum information's clarity-degree
(uniqueness)
============>>>

Uncertainty
<-Redundancy->^
3  3  3  3  |          3  3             3  3
2  2  2  2  |          2  2             2  2
1  1  1  1  |    1  1  1  1             1  1       1  1  1  1
{0, 0, 0, 0} V   {0, 0, 0, 0}     {0, 1, 0, 0}     {0, 0, 0, 0}
.  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
|  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
|  |  |  |       |__|_ |  |       |__|  |  |       |__|_ |__|_
|  |  |  |       |     |  |       |     |  |       |     |
|  |  |  |       |     |  |       |     |  |       |     |
|  |  |  |       |     |  |       |     |  |       |     |
|__|__|__|_      |_____|__|_      |_____|__|_      |_____|____
|                |                |                |
(1*4)            ((1*2)+1*2)      (((+1)+1)+1*2)   ((1*2)+(1*2))

4 =                                  2  2  2
1  1                        1  1  1          1  1
{0, 1, 0, 0}     {0, 1, 0, 1}     {0, 0, 0, 3}     {0, 0, 2, 3}
.  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
|  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
|__|  |__|_      |__|  |__|       |  |  |  |       |__|_ |  |
|     |          |     |          |  |  |  |       |     |  |
|     |          |     |          |__|__|_ |       |_____|  |
|     |          |     |          |        |       |        |
|_____|____      |_____|____      |________|       |________|
|                |                |                |
(((+1)+1)+(1*2)) (((+1)+1)+((+1)+1))  ((1*3)+1)        (((1*2)+1)+1)

{0, 1, 2, 3}
.  .  .  .
|  |  |  |
|__|  |  |
|     |  |
|_____|  |
|        |
|________|
|
((((+1)+1)+1)+1)

Multiplication can be operated only among objects with structural identity .

Also multiplication is noncommutative, for example:

2*3 = ( (1,1),(1,1),(1,1) ) or ( ((1),1),((1),1),((1),1) )

3*2 = ( (1,1,1),(1,1,1) ) or ( ((1,1),1),((1,1),1) ) or ( (((1),1),1),(((1),1),1) )

Thank you.

Organic

Last edited: Jan 22, 2004
12. Jan 22, 2004

### matt grime

Your multiplication is not well defined then, because your 'numbers' are not well defined, that is there is no single element that represents it uniquely. For instance you give me several different answers for 2*3. To deduce anything from this you must acknowledge that '3' is not a number in your system and to call them numbers is misleading. And thus to liken it to ordinary multiplication is also pointless, as is expressing opinions about the so-called lack of distinction between addition and multiplication in ordinary mathematics.

As well as not answering any questions that were asked, you now introduce another undefined concept, 'opposite'. Something you've repeatedly failed to define in the past, relying on intuition. Well, I choose to define it with the empty meaning and conclude your system is vacuous, until such time as you offer a non-intuitive definition.

And, no *I* won't tell you anything about A-infinity algebras. I don't beleve that will accomplish anything as you've yet to understand the basics of common mathematics, and these are very advanced concepts.

13. Jan 22, 2004

### Organic

Matt,

If you wrote this:
Then I have to say that you are much more closed system then I thought, that has 0 ability to understand new fundamental ideas about what numbers are.

You are in your closed system cannot understand how multiplication and addition are complement operations that do not changing the quantity of the number, but only its internal scructure, by breaking and unbreaking its internal self symmetry.

Now, I see you jump and saying: "here comes more undefined terms".

All the rigoruos terms are infront of your eyes but for you terms is written text, not for me.

Also I looked at:

http://arxiv.org/PS_cache/math/pdf/9910/9910179.pdf [Broken]

http://arxiv.org/PS_cache/math/pdf/0108/0108027.pdf [Broken]

They do not based on my fundamental ideas, therefore cannot express my mathematical system.

Last edited by a moderator: May 1, 2017
14. Jan 22, 2004

### matt grime

Let me explain what I as a mathematician would like to see:

you use the labels 2,3 etc and call these numbers. Do we agree on that?

each of these labels corresponds to some set of partitions. Do we agree on that?

when you tell me what 2*3 is, you give me two different answers. So when you ask me to demonstrate the difference between addition and multiplication in boolean logic, I'm entitled to point out that you do not have a well defined multiplication on your 'numbers' because your number 'x' is some set of partitions. So you are asking me to compare chalk and cheese. I think you perhaps don't know what the term 'well defined' means.

this could be interesting combinatorics, but to call them numbers and imply something to do with counting is misleading.
You could demsonstate some interesting combinatorial facts about them.

1. Given two elements x and y of some 'number' and some other element z of a different number,
does x*z = y*z imply x=y?

2. If you take all x representing some number X and combine them with all y representing some number Y, to you get all elements of XY (odinary multiplication).

In fact, only if 2.is true can you claim to have a proper multiplication, I would suggest.

Your numbers aren't the numbers of mathematics, got it? By definition multiplication of ordinary numbers commutes, you are doing something else. If you stopped trying to call it by the names of ordinary maths you might not meet such hostility.

You are performing some operations on the sets of certain kinds of numbered trees.

you might wish to demonstrate closure, identity, inverse, associativity etc if they exist/are true. then perhaps when you've verified those we can find out what these ought to be called - it perhaps will be some monoid or semigroup.

I@m not closed off to new ideas, as i hope this reply demonstrates. I think you are using the wrong words and looking at the wrong things. if you stepped away from the philosophy then you might get some where when talking to mathematicians who naturally balk at phrases like 'approach but gets no closer to' when presented as you have.

15. Jan 22, 2004

### Organic

Matt,

You still don't understand what i am talking about.

1) There is no such objective thing called "Mathematics", it is only a rigorous agreement between some group of people in some period of time, no more no less.

2) Its most basic paradigms can be changed from today to tomorrow , when new fundamental ideas air their view.

3) Let us not forget Godel.

4) The new Natural numbers have the structure of a wavicle, therefore concepts like symmetry, redundancy, uncertainty , entropy and so on, are their inherent properties.

5) Boolean logic is an obsolete logical system for more then 70 years, and logical systems like Complementary Logic are going to take their place in the near future.

6) Theoretical mathematicians like Alain Connes (http://www.alainconnes.org/) say it, and a lot of great physics theoretical mathematicians developing an unordered tailor made pieces of non-Euclidean methods that helping them to solve their problems.

7) Only pure mathematicians are still dreaming in their “Cantor’s paradise” (which is by the way a very ironic name, gave by a community of people that sent Cantor to Mad House for the rest of his life because of their “rigorous” attitudes).

8) Realty and Philosophy were, are and will be the source of any meaningful Mathematical system.

Last edited: Jan 22, 2004
16. Jan 22, 2004

### matt grime

Numbers: an integer is either the result of adding 'one' repeatedly, or one can produce set descriptions to do with induction and cardinals. They are the units of counting. Demonstrate how to count sheep with your objects.

There maybe some theoretical and philosophical points to answer in the rest of your reply, but they don't seem very relevant to your constructions - everything you mentioned about other people and topics is rigourous and well defined.

Why do you introduce Alain Connes into the discussion? If you wish to talk about non-commutative geometry then I'm very happy to seeing as I've been following different aspects of it for the last 5 years - moduli spaces and C-star algebras at various points.

In fact very few mathematicians go along with Euclidean-geometry as the most useful (the most natural perhaps): as anyone can tell you Hyperbolic geometry is perhaps the most ubiquitous. Actually, that's a misleading statement - do you know the monodromy theorem for Riemann surfaces? There are few complex analytic structures that can be obtained from modding out be symmetries of the riemann sphere, and complex plane, but many more from the Poincare disc.

Of course the thing about that is that we can simply explain where the differences in geometry arise from: the parallel postualte. Your thinking is currently too badly explained. And when people try to point out what you need to do to clarify issues you either refuse, cite something unrelated or accuse them of not being able to understand.

And why do you trust Alain Connes, even though all his papers are not written using your philosophy, yet dismiss Bernhard Keller's very good papers on A-infinity algebras?

Last edited: Jan 22, 2004
17. Jan 23, 2004

### Organic

Hi Matt,

1) I am not talking about Non-Euclidean geometry but on Non-Euclidean mathematics, which is not based on Boolean Logic.

2) The fact that you as mathematician do not know what is a wavicle is another sad example of the state of Pure Mathematics of today that do not aware to the meaning of duality of Quantum objects, which are constructed from complementary link between wave(continuous) and particle(discrete). wave+particle=wavicle.

3) Complementary Logic basic principles is built on this kind of associations between opposite concepts, where one of its private cases (the last object of each complementary number) is the standard natural number (that can be used to count sheep).

4) You forgot to write about Godel's incompleteness proves (by the way I am vary close to prove the incompleteness of 3n+1 problem ( http://mathworld.wolfram.com/CollatzProblem.html ).

5) Hilbert in his 1900 lecture closed it by these words:
----------------------------------------------------------------------------
"The problems mentioned are merely samples of problems, yet they will suffice to show how rich, how manifold and how extensive the mathematical science of today is, and the question is urged upon us whether mathematics is doomed to the fate of those other sciences that have split up into separate branches, whose representatives scarcely understand one another and whose connection becomes ever more loose. I do not believe this nor wish it. Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.

For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

But, we ask, with the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which at the same time assist in understanding earlier theories and cast aside older more complicated developments. It is therefore possible for the individual investigator, when he makes these sharper tools and simpler methods his own, to find his way more easily in the various branches of mathematics than is possible in any other science.

The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfill this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!"

----------------------------------------------------------------------------

Mathematicians took his 23 problems but omitted the heart of its lecturer about the organic unity of Mathematics.

Complementary Logic is an example of an attitude to seek for the Organic Unity of Mathematics.

6) Professional Mathematicians like you does not have the ability to understand what I talking about because their word is based and closed by Boolean logic. If you go beyond Boolean point of view, then and only then you can understand my rigorous models.

7) "Cantor's paradise" is the transfinite universes.

8) Alain Connes in this lecturer http://www.math.ucla.edu/dls/2001/connes.html said that Boolean Logic is going to be replaced by systems that can deal with the complexity of the real world phenomena.

My friend was in this lecturer and hared him saying this.

9) Gauss ( http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Gauss.html ) was afraid to talk publicly on non-Euclidean geometry because he knew the influence of it on Euclidean standard mathematics word, and he wished to die peacefully without wars against closed-systems' mathematicians.

10) Hippasus of Metapontum (http://scienceworld.wolfram.com/biography/Hippasus.html ) is another sad example of what (maybe) can happened to people how think differently form their community. About Cantor, I already wrote about him.

I'll say it again clearly and loudly:

Any Information system that can be explored, is changeable because concepts like redundancy, uncertainty and entropy are inherent properties of it.

Last edited: Jan 23, 2004
18. Jan 23, 2004

### matt grime

The strange thing about all this is I've not actually defended Boolean logic at any point, merely pointed out where you've gone wrong (New Diagonal Argument) in misinterpreting infinity, and in your utter failure to define anything coherently.

I'm very aware of wave particle duality - I've never heard the word wavicle before, that's all.
This is looking like some kind of GRE test:

by 'complementarity'

wave is to particle as multiplication is to addition.

This is a fuzzy definition of complement that you could use to associate anything two things you wished. The physical one is that the particle nature of light cannot explain diffraction and that the wave nature of light cannot explain the dual slit experiment. Together these ideas explain its total nature, so in a sense the are complementary. Explain how the complement of addition is multiplication in this light. (No pun intended.)

I'd be interested to hear exactly what Connes said and in what context. But until such time as you define all the words you use, and admit that you made a mistake in New Diagonal argument I'll keep plugging away at it all. Connes is after all a mathematician and likes rigour. I guess your friend doesn't have a transcript of the talk, and in my experience people often hear what they want to hear.

The trees you have defined look like interesting objects, and I would like you to explore their properties (not the philosophy). If I may formalize this for you:

For each n in the Natural numbers, define [n] to be the set of trees you produce.

I don't recall the details, but there exists operations + and * on elements of these sets. Moreover, there exists a distinuished element in each [n] such that they are a model for the natural numbers with * and + mult and add as we understand them, that is there is a map from N to what we'll label [N] respecting the addition and mult of N

Does the composition of two allowable trees produce an allowable tree? Does the comp of all trees in [n] and [m] produce all allowable trees in [nm]or [n+m]? I recall that you don't allow all possible numbered trees, but I could be mistaken.

This seems like a good thing to examine, with genuinely interesting possibilities. It could be s subalgebra of an A-infinty alg, or similar, but you would need to insert some action of symmetric groups in there. Does the distributive property hold.

[n] is your complementary number. Now that you've put the word complementary in there you have removed one of the criticisms.

Is * or + associative?

what are the identities? are there inverses, what if you append formal inverses?

You need to improve your standard of exposition to remove ambiguity, and it would be beneficial for you to stop relying on emotive descriptions and alleged intuition and just say what something is.

19. Jan 23, 2004

### Organic

Matt,

There is a lot of work to be done on Complementary Logic.

Again, the main idea here is this:

Any Information system that can be explored, is changeable because concepts like redundancy, uncertainty and entropy are inherent properties of it.

Incompleteness is welcome by this point of view.

If you start asking questions, then use your professional skills and examine it by yourself.

20. Jan 23, 2004

### matt grime

I've got enough research of my own to be doing at the moment, I thought you might benefit from some suggestions. After all the statement that there is a multiplication implies that the object x*y*z is well defined as it implies associativity. I don't recall seeing a proof of that - which isn't to say that you haven't provided one, but that I don't remember seeing it. In particular you need to prove you assertion that the natural numbers are recoverable as the dsitinguished elements {{{{{{1},1}1}...}

or what ever it is, and that means demonstrating closure, associativity mult indentity, etc.

As for the other stuff, you'd need to state what you mean by entropy, uncertainty and redundancy before I could comment. I know what entropy is as a concept, and I know what it is a mathematical quantity in statistical physics etc, but I don't immediately see the relevance here.