The Mysterious Connections Between Irrational Numbers - e, pi, and phi

[matt grime]

"Take each note as a "true" statement"

and now you contradict that...

 

[WWW]

Take each note as a "true" statement

I wrote "true" and not true, which means that there is no true XOR false in my system.

 

[matt grime]

which highlights the fact that you've not explained what the possible truth values are in your systems. it appears that your diagrams just correspond to some constructions involving and and xor in some logic system that you're refusing to explain/ nor have you explained why these (ill-defined - xor is not assiciative so you can't use it without bracketing) diagrams are remotely important or useful.

 

[WWW]

No exluded-middle point of view can understand Complementary Logic, and the reason is very simple:

In CL we have at least two simultaneous levels to a logical expression:

( Its differential side(= a XOR b) / its integral side(= a AND b) ), where a,b are opposites.

If you can't understand that truth tables are not used in Complementary Logic, then don't west your time.

 

[matt grime]

but now you're saying that you can't get boolean logic out of it since it has truth tables that govern it, and there must be some analogous result there. if you're not going to even offer some way of describing the truth value, be it in 0,1, or some fuzzy, or even trivalued F,T,U system then you can't do anything.

what on Earth do you mean by opposites? what is the opposiite of the function sin(x)? remember you've said in the past that anything is allowed to be some 'information form' to be explored.

 

[Hurkyl]

And all of your information forms seem to be "seperable" in some sense; while I still don't think I understand them, I haven't seen anything from you that I could imagine is capable of describing: "I know that key #1 plays either A or B, and key #2 playes either B or C, and that key #1 and key #2 play different notes."


(By the way, I think the term you're looking for is 'chord' not 'accord')

 

[matt grime]

Here's a test for your theory. In mathematics the proposition:

If f is a continuous function on a compact subset of R, then it is uniformly continuous.

Is true.


That is to say, if a:={f is a continuous function on a compact subset of R} and b;={f is uniformly continuous} then (not(a))OR(b) is true.

domonstrate the corresponding result and truth value of that proposition in which ever of the subsystems of complementary logic you wish. I'll even let you work it out in the alleged boolean subtype.

 

[WWW]

Here's a test for your theory. In mathematics the proposition:

If f is a continuous function on a compact subset of R, then it is uniformly continuous.

Is true.


That is to say, if a:={f is a continuous function on a compact subset of R} and b;={f is uniformly continuous} then (not(a))OR(b) is true.

domonstrate the corresponding result and truth value of that proposition in which ever of the subsystems of complementary logic you wish. I'll even let you work it out in the alleged boolean subtype.

MY continuous concept is not your concept, therefore there is no meaning to find maps between a and b as you do in an excluded-middle system.

All your results ignoring the inner complexity that existing between (a XOR b/a AND b) mutual relations, which are included-middle results, where all your excluded-middle reasoning including continuous function and compact subset of R, are all limited to true XOR false logical reasoning, which is this CL private case:

 f   t   
 |   |   
 |#__| 
 |

Shortly speaking, no part of CL information forms can be used to get general conclusions on other information form, because each information form has its own unique reasoning that cannot be reduced to structurless_non_complex magnitudes, as you do in excluded-middle reasoning.

By your above test you damonstate again your inability to understand what is an included-middle reasoning.

Shortly speaking, any excluded-middle test is closed under (f XOR t) and there it is stays, as some unique private case of infinitly many ordered and unique(by their internal structures) logical systems.

 

[matt grime]

"MY continuous concept is not your concept, therefore there is no meaning to find maps between a and b as you do in an excluded-middle system."

Sorry, but you can't pick and choose like that. Especially as you've said that this system allows you to explore all information forms such as my definition of continuity. And you've declared boolean logic to be a subsystem of it. It is then up to you to translate statements into your system.

You only appear more crank like if you say 'ah, but I didn't mean you can apply it in that situation' if you refuse to state which situations you are talking about.

 

[WWW]

And all of your information forms seem to be "seperable" in some sense; while I still don't think I understand them, I haven't seen anything from you that I could imagine is capable of describing: "I know that key #1 plays either A or B, and key #2 playes either B or C, and that key #1 and key #2 play different notes."

First thank you for "chord", In Hebrew we call it "accord".

If you have n keys, then in the first stage any n-chord is a one unknown result out of n^n possibilities and you have no way to know what will be the next n-chord.

To this state I call maximum redundancy_AND_uncertainty of n-system.

In the last stage we have a one and only one n-chord, which is constructed of unique well-known n notes (a unique note for each key as we can find in any "normal" piano).

Please read again #95 and #97

 

[WWW]

It is then up to you to translate statements into your system.

I do not have to translate anything because excluded-middle reasoning with all its branches, theorems and proofs of the last 2000 years is already included as a tiny logical sub-system of the infinite grand universe of included-middle reasoning, which includes infinitely many other unique logical systems, exactly as our planet is a sub-system of the solar-system and the solar system is a sub-system of the milky-way... and so on.

If you still don't get it then look at this example:

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

and try to understand that each form in it is a unique logical reasoning.

The excluded-middle reasoning is the (x=2,y=1) form.


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

Your response to the idea that what is called logic (f XOR t) is only a tiny part of a gigantic universe of infinitely many different logical forms, is a normal response to unfamiliar new ideas.

1) Hurkyl tried to reduce this gigantic universe of infinitely many different logical forms to (f XOR t) and failed .

2) I gave a lot of examples that based in this included-middle universe of infinitely many different logical forms, and I showed new interpretations to: Natural numbers, sets, logical forms, infinity, irrational numbers, functions, limit, proof, probablility and more things. They can be found in more then 40 short papers here:

http://www.geocities.com/complementarytheory/CATpage.html

and most of them is the result of what I think is the most important thing in any living language, which is a dialog, mostly between Hurkyl you and me.

Recently I discovered that included-middle point of view on Math language is not a one man show.

Shortly speaking, I am not alone and misunderstood as I was in the last 2 years.

Some of the communities that developing an included-middle point of view can be found here:

http://arxiv.org/PS_cache/quant-ph/pdf/0012/0012007.pdf

http://perso.club-internet.fr/nicol/ciret/

http://www.quantonics.com/How_to_Become_A_Student_of_Quantonics.html

http://www.quantonics.com/Acronyms_Used_In_Quantonics.html#SOM

Here is some example that I gave in the past, which clearly shows how two oppsites preventing/defining each other with no-contradiction:

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

 

[matt grime]

Care to list any from reputable mathmaticians whose credentials we can check? Care to actually prove any of those statements? You've written lots of things, claimed they are the correct intrepetation of the proper objects despite not actually behaving as the proper objects must do. You cannot multiply 2 by 3 and not get 6. If you do then you've altered the defintions of the objects and the operations. You're entitled to do that all you want but you're not allowed to say they ARE the proper objects because they clearly aren't. Your opinions on what are the important things to consider are very moot since you can't acutally do anything with you system, as you've admitted yourself. As it is you've not even defined what the connectives "and" and "xor" mean. And if your system contains ours as a trivial subsystem then you ought to able to meet all the challenges I've offered since they are part of that trivial subsystem.

Edit: can't believe you've taken this long to come across contructivism.

 

[WWW]

Matt,

You don't want to see the included-middle, because you simply don't have the guts to see things beyond your tiny excluded-middle part.

For more than a year you asked me to reduce a gigantic unexplored (yet) complex universe to your tiny trivial size, without doing even a little step to an included-middle point of view.

I learned a lot, you learned nothing because you can't accept the Idea that any result is system depended.

Any consistent theoretical system is incomplete by definition --> any theoretical system cannot be THE ONE AND ONLY ONE system because any theoretical system is always trivial when it is compared to reality itself, and in my opinion, this is the deep meaning of Godel's incompleteness theorem, that hard logic mind like you simply ignored.

The best we can do is to create theories that including our abilities to define them as part of the theoretical system.

Through this attitude we do not afraid to be opened to changes, because any deep change in our understanding give us more possibilities to be creative living creatures through non-destructive participation.

 

[WWW]

More for Matt,

By keeping Your ONE AND ONLY ONE (f XOR t) point of view you ignored:

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

http://www.geocities.com/complementarytheory/3n1proof.pdf

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

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

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

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

and more...

 

[WWW]

ANOTHER TYPICAL EXAMPLE OF YOUR CLOSED SYSTEM ATTITUDE:

Your opinions on what are the important things to consider are very moot since you can't acutally do anything with you system, as you've admitted yourself.

and you reapinitg to write this after I already answered:

https://www.physicsforums.com/showpost.php?p=192318&postcount=25

Shortly speaking, I feel that I am westing my time if you cannot change your trivial attitude to a point of view, which is not your point of view.

Edit: can't believe you've taken this long to come across contructivism.

I don't have to believe in anything to understand that you can only see the shadow of yourself.