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

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The discussion centers on the relationships between the irrational numbers e, pi, and phi, exploring whether they share any deep connections or symmetries across different mathematical systems. Participants debate the nature of irrational numbers, questioning how they can be accurately represented without relying on natural number notations. The conversation also touches on the concept of convergence in sequences and the implications of infinite series for defining irrational numbers. Some argue that irrational numbers can occupy fixed positions on the real number line, while others challenge the notion of accuracy in representing these numbers. Ultimately, the dialogue emphasizes the complexity and philosophical implications of understanding irrational numbers and their interconnections.
  • #61
Using the concept of "invariance/symmetry" :

T|F = F|T = T

The | represents a "choice" between T or F

Some might question the "equals sign".

Here is someone explaining a type of complementary logic also :eek:

http://users.erols.com/igoddard/gods-law.html
 
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  • #62
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  • #63
http://users.erols.com/igoddard/gods-law.html is very interesting and supports Complementary Logic main point of view.

But in Complementary Logic 100%A is some unique result that we can get out of x1 xor x2 xor x3 xor ...
 
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  • #64
WWW said:
http://users.erols.com/igoddard/gods-law.html is very interesting and supports Complementary Logic main point of view.

But in Complementary Logic 100%A is some unique result that we can get out of x1 xor x2 xor x3 xor ...

Of course! One asks oneself the question "What the heck does it mean for a wave function to collapse?"

According to Einstein, there is no instantaneous action at a distance!
 
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  • #65
What is 'distance' from your point of view?

For me 'distance' is the preventing side of some perevent/complement system for example: http://www.geocities.com/complementarytheory/4BPM.pdf

By Complementary Logic any existing element that can be chaneged, is the result of at least two opposites that simultaneously pereventing/defining each other.
 
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  • #66
Some times simple thinking can help us to understand simple examples.

Take your own advice. :smile:


I demonstrated how, using logic and a "1-dim system", we are able to fully "explore" a "2-dim system".

The lesson I'm trying to demonstrate is:

Even if one system is a special case of another system, the first system can still be just as powerful as the second system.


AND and XOR connectives are independed and can be changed according to the "logical environment" that using them.

Incorrect. The representations may be the same (e.g. they're both called AND and XOR), but your AND and XOR are certainly very different from the AND and XOR from boolean logic.


Please explain Why do you think they are not defined?

Because you have not defined them.
 
  • #67
I demonstrated how, using logic and a "1-dim system", we are able to fully "explore" a "2-dim system".
No you did not, because in 1-dim(=x-dim) universe no point can be found as a result of (x-dim,y-dim) system.

Your (c,d)(a0,b0) example is a (x-dim,y-dim) --> 2-dim system, and only then you can show a
"2-d Math picture" of mandelbrot set (which has a fractal-dim between 1-dim and 2-dim).

Shortly speaking, in a 1-dim universe any y-dim reduced to x-dim.

Therefore d reduced to c and b0 reduced to a0, and you have no 2-dim Math picture of some Julia set.
Even if one system is a special case of another system, the first system can still be just as powerful as the second system.
You did not show it yet.

WWW said:
AND and XOR connectives are independed and can be changed according to the "logical environment" that using them.

Hurkyl said:
Incorrect. The representations may be the same (e.g. they're both called AND and XOR), but your AND and XOR are certainly very different from the AND and XOR from boolean logic.

In Complementary Logic, probability is a first-order property that changing the results of AND and XOR connectives.


For example:

f=dead cat
t=alive cat
r=redundancy
u=uncertainty

When probability is a first-order property then AND connective is used whenever a no-unique result can be found:
Code: 
<--[B]r[/B]--> ^ 
 t   t  |
 #   #  [B]u[/B]
 f   f  |
 |   |  v
 |&__|_
 |
When probability is a first-order property then XOR connective is used whenever a unique result can be found:
Code: 
 f   t   
 |   |   
 |#__| 
 |

Simple as that.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

Code: 
              Uncertainty
  <-Redundancy->^
    d  d  d  d  |
    #  #  #  #  |
    c  c  c  c  |
    #  #  #  #  |
    b  b  b  b  |
    #  #  #  #  |
   {a, a, a, a} V
    .  .  .  .
    |  |  |  |
    |  |  |  |
    |  |  |  | <--(First 4-valued logical form)
    |  |  |  |
    |  |  |  |
    |&_|&_|&_|_
    |
    ={x,x,x,x}


   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  | <--(Last 4-valued logical form)
    |#____|  |      
    |        |
    |#_______|
    |
    ={{{{x},x},x},x}

[b]
============>>>

                Uncertainty
  <-Redundancy->^
    d  d  d  d  |          d  d             d  d
    #  #  #  #  |          #  #             #  #        
    c  c  c  c  |          c  c             c  c
    #  #  #  #  |          #  #             #  #   
    b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
    #  #  #  #  |    #  #  #  #             #  #       #  #  #  #   
   {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
    |                |                |                |
    {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}     
 
                                      c  c  c
                                      #  #  #      
          b  b                        b  b  b          b  b
          #  #                        #  #  #          #  #         
   {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |&_|&_|_ |       |#____|  |
    |     |          |     |          |        |       |        |
    |&____|____      |&____|____      |#_______|       |#_______|
    |                |                |                |
    {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x} 

   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  |  
    |#____|  |      
    |        |
    |#_______|
    |    
    {{{{x},x},x},x}
[/b]

A 2-valued logic is:

Code: 
    b   b 
    #   #    
    a   a     
    .   .   
    |   |   
    |&__|_   
    | 
 [b]   
    a   b     
    .   .   
    |   |  <--- (Standard Math logical system fundamental building-block) 
    |#__|   
    |
[/b]
 
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  • #68
WWW said:
I know it, but in 1-dim all you can get is the shadow of what you can find between 1-dim and 2-dim, isn't it?

Please explain Why do you think they are not defined?

in order the answers are:

that's at best wrong, at worst completely meaningless.

where in this thread have you offered a definition of uncertainty or redundancy? and i don't mean their plain english meanings.

it is a courtesy whenever you introduce non-standard terms to explain them.

you have i believe offered a vague idea of one of them in some other thread, but it didn't explain it fully.
 
  • #69
WWW said:
No you did not, because in 1-dim(=x-dim) universe no point can be found as a result of (x-dim,y-dim) system.

Your (c,d)(a0,b0) example is a (x-dim,y-dim) --> 2-dim system, and only then you can show a
"2-d Math picture" of mandelbrot set (which has a fractal-dim between 1-dim and 2-dim).

Shortly speaking, in a 1-dim universe any y-dim reduced to x-dim.

Therefore d reduced to c and b0 reduced to a0, and you have no 2-dim Math picture of some Julia set.

You did not show it yet.


sentence one ahs no content as far as i can tell.

the mandelbrot set is a subset of R^2, or C, so the second bit is silly too.

third part? nope, nothing there that makes sense either (reduces?)

and finally, show what?
 
  • #70
It is very simple matt,

Any b0 or d in Hurkyl's example is always 0 in a 1-dim universe, and if not then we are no longer in a 1-dim but in a 2-dim universe.

Therefore he gets (a0,0) or (c,0) 1-dim representation, which is definitely not a 2-dim representation of some Julia set.
 
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  • #71
Matt,

You ommited parts of it, so here is all of it:
Matt said:
mandelbrot's set doesn't have integer dimension...
WWW said:
I know it, but in 1-dim all you can get is the shadow of what you can find between 1-dim and 2-dim, isn't it?
Matt said:
still not defined uncertainty and redundancy, non-standard terms.
WWW said:
Please explain Why do you think they are not defined?

Your answer to the first part is:
Matt said:
that's at best wrong, at worst completely meaningless.
Please give more details why do you think so?

Your answer to the second part is:
Matt said:
where in this thread have you offered a definition of uncertainty or redundancy? and i don't mean their plain english meanings.
Please show us an example of how a definition of r and u when:
f=dead cat
t=alive cat
r=redundancy
u=uncertainty

When probability is a first-order property then AND connective is used whenever a no-unique result can be found:
Code: 
<--[B]r[/B]--> ^ 
 t   t  |
 #   #  [B]u[/B]
 f   f  |
 |   |  v
 |&__|_
 |
will look like?
 
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  • #72
you haven't said what you mean by "shadow between 1-d and 2-d". sorry but it makes no sense as a sentence, elaborate, explain and clarify. nor have you explained what you mean be representation of a julia set, and what that has to do with the ambient space. seeing as RxR and R are in bijective correspondence I can encode the points of a 2-dim space in a 1-dim one, and by induction, any n-dim space. And the same goes for fractals as it's just some subset of some space.

how can i tell you what a definition of u and r will look like. they're your objects to define.
 
  • #73
Matt,

seeing as RxR and R are in bijective correspondence I can encode the points of a 2-dim space in a 1-dim one,
You can ecode any {x} with any {x,y} so what.

By {x}_only 1-dim data you cannot represent {x,y} 2-dim data.
how can i tell you what a definition of u and r will look like. they're your objects to define.
Now it is clearly understood that you have nothing but a 'NO'_reflex in this r u case.

For example, your response to:
Code: 
<--[B]r[/B]--> ^ 
 t   t  |
 #   #  [B]u[/B]
 f   f  |
 |   |  v
 |&__|_
 |
was "what is v"? and from this question we can learn that your abstraction's ability totally depends on the standard way.

My abstraction's ability totally depends on my non-standard way.

So, the problem of translation is twice difficult in our case.

But I think that there is a deeper problem here, with is:

You simply do not understand my ideas, and therefore they are "non sense" for you.

So I think it is the time to say good bye to each other because I cannot help you and you cannot help me.
 
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  • #74
given you inability to explain clearly any of your objects i can't see how asking what the v is in the diagram is a bad thing in any sense.
 
  • #75
My logic is an included-middle yours is excluded-middle.

You say that included-middle can be defined by excluded-middle, I say it cannot, simply because probabilty is a first-order property in included-middle system, and in excluded-middle system it is not a first-order property.

If you can show how probabilty is a first-order property in excluded-middle logical system, then it will be the gate between our different worlds.

In Complementary Logic, probability is a first-order property that changing the results of AND and XOR connectives.


For example:

f=dead cat

t=alive cat

r=redundancy (more then one copy of the same value can be found)

u=uncertainty (more than one unique value can be found)


When probability is a first-order property then AND connective is used whenever a no-unique result can be found:
Code: 
<--[B]r[/B]--> ^ 
 t   t  |
 #   #  [B]u[/B]
 f   f  |
 |   |  v
 |&__|_
 |
When probability is a first-order property then XOR connective is used whenever a unique result can be found:
Code: 
 f   t   
 |   |   
 |#__| 
 |

Simple as that.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

Code: 
              Uncertainty
  <-Redundancy->^
    d  d  d  d  |
    #  #  #  #  |
    c  c  c  c  |
    #  #  #  #  |
    b  b  b  b  |
    #  #  #  #  |
   {a, a, a, a} V
    .  .  .  .
    |  |  |  |
    |  |  |  |
    |  |  |  | <--(First 4-valued logical form)
    |  |  |  |
    |  |  |  |
    |&_|&_|&_|_
    |
    ={x,x,x,x}


   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  | <--(Last 4-valued logical form)
    |#____|  |      
    |        |
    |#_______|
    |
    ={{{{x},x},x},x}

[b]
============>>>

                Uncertainty
  <-Redundancy->^
    d  d  d  d  |          d  d             d  d
    #  #  #  #  |          #  #             #  #        
    c  c  c  c  |          c  c             c  c
    #  #  #  #  |          #  #             #  #   
    b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
    #  #  #  #  |    #  #  #  #             #  #       #  #  #  #   
   {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
    |                |                |                |
    {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}     
 
                                      c  c  c
                                      #  #  #      
          b  b                        b  b  b          b  b
          #  #                        #  #  #          #  #         
   {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |&_|&_|_ |       |#____|  |
    |     |          |     |          |        |       |        |
    |&____|____      |&____|____      |#_______|       |#_______|
    |                |                |                |
    {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x} 

   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  |  
    |#____|  |      
    |        |
    |#_______|
    |    
    {{{{x},x},x},x}
[/b]

A 2-valued logic is:

Code: 
    b   b 
    #   #    
    a   a     
    .   .   
    |   |   
    |&__|_   
    | 
 [b]   
    a   b     
    .   .   
    |   |  <--- (Standard Math logical system fundamental building-block) 
    |#__|   
    |
[/b]

If this time your response is "non-sense" then good-bye.
 
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  • #76
WWW said:
What is 'distance' from your point of view?

For me 'distance' is the preventing side of some perevent/complement system for example: http://www.geocities.com/complementarytheory/4BPM.pdf

By Complementary Logic any existing element that can be changed, is the result of at least two opposites that simultaneously pereventing/defining each other.

Distance is a property between objects in space. Space is a structure, which is constructed of discrete units. The structure of space is a distributive lattice. A set of properties, being a "complementary logic?", expressing difference in wholeness.
 
  • #77
Distance is a property between objects in space...
So to define distance we need at least two states local(= a unique object) and global(=a space).

Therefore any existing thing is at least a product of the interactions between the local and the global.

When we research a QM product then this is exactly what we find: a product which is both particle(=strong locality) and wave(=strong non-locality).

Shortly speaking, Complementary logic is the logic of interaction between opposite properties, which means: any distance (logical or physical) is the preventing property, where any non-distance is the complementing property.

Form this point of view, the evolution of concessions is the story of the increasing ability of communication between the global and the local in a cybernetic way, for example:

http://www.geocities.com/complementarytheory/CK.pdf
 
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  • #78
WWW said:
My logic is an included-middle yours is excluded-middle.

You say that included-middle can be defined by excluded-middle, I say it cannot, simply because probabilty is a first-order property in included-middle system, and in excluded-middle system it is not a first-order property.

If you can show how probabilty is a first-order property in excluded-middle logical system, then it will be the gate between our different worlds..[/B]


i'd like to see you explain where i said any of that.

the rest is starting to be readable. see what happens when you actually explain the meanings of the terms you use?

now, the main thing you need to demonstrate is that there is any point to all this.

For instance, are the axioms of ZF(C) consistent in this "logical world"
 
  • #79
f=dead cat

t=alive cat

r=redundancy (more then one copy of the same value can be found)

u=uncertainty (more than one unique value can be found)


When probability is a first-order property then AND connective is used whenever a no-unique result can be found:
Code: 
<--[B]r[/B]--> ^ 
 t   t  |
 #   #  [B]u[/B]
 f   f  |
 |   |  v
 |&__|_
 |
When probability is a first-order property then XOR connective is used whenever a unique result can be found:
Code: 
 f   t   
 |   |   
 |#__| 
 |

Simple as that.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

Code: 
              Uncertainty
  <-Redundancy->^
    d  d  d  d  |
    #  #  #  #  |
    c  c  c  c  |
    #  #  #  #  |
    b  b  b  b  |
    #  #  #  #  |
   {a, a, a, a} V
    .  .  .  .
    |  |  |  |
    |  |  |  |
    |  |  |  | <--(First 4-valued logical form)
    |  |  |  |
    |  |  |  |
    |&_|&_|&_|_
    |
    ={x,x,x,x}


   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  | <--(Last 4-valued logical form)
    |#____|  |      
    |        |
    |#_______|
    |
    ={{{{x},x},x},x}

[b]
============>>>

                Uncertainty
  <-Redundancy->^
    d  d  d  d  |          d  d             d  d
    #  #  #  #  |          #  #             #  #        
    c  c  c  c  |          c  c             c  c
    #  #  #  #  |          #  #             #  #   
    b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
    #  #  #  #  |    #  #  #  #             #  #       #  #  #  #   
   {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
    |                |                |                |
    {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}     
 
                                      c  c  c
                                      #  #  #      
          b  b                        b  b  b          b  b
          #  #                        #  #  #          #  #         
   {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |&_|&_|_ |       |#____|  |
    |     |          |     |          |        |       |        |
    |&____|____      |&____|____      |#_______|       |#_______|
    |                |                |                |
    {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x} 

   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  |  
    |#____|  |      
    |        |
    |#_______|
    |    
    {{{{x},x},x},x}
[/b]

A 2-valued logic is:

Code: 
    b   b 
    #   #    
    a   a     
    .   .   
    |   |   
    |&__|_   
    | 
 [b]   
    a   b     
    .   .   
    |   |  <--- (Standard Math logical system fundamental building-block) 
    |#__|   
    |
[/b]
Can you show us a ZF(C) axiom whare probability included?

Matt said:
now, the main thing you need to demonstrate is that there is any point to all this.
Please give more details.
 
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  • #80
es, you keep reposting that but odn't actually demonstrate that it is useful at any point.

As you don't define what you mean by probability we cannot answer your last request. Seriously, mathematics is a formal construction; you cannot just informally use words and expect it to be meaningful. if we think of a proper quantum system (ie not the stupid cat experiment) then all of the things in it are modeled using properly defined mathematical objects. so why don't you demonstrate a way of producing pure states, say, within your system. hint, you'll have to construct the real numbers, the complex numbers, in fact everything if you want to do mathematics. if youy merely want to argue about philosophy then do so, but don't get angry and change your user name so that we might think you were pretending to do maths seriously.
 
  • #81
I did not choose to change my name. I actually had no choice because PF mentors shut me down twice in the last 2 years, and as you now, if you want to register again you have no choice but to do it under a new name.

QM element is naturally included-middle element, because it is based on two opposite properties that preventing from us to know exactly both of them simultaneously, as we can do in macro systems.

If we want to develop some formal language that deal with QM world, we have to do it by changing our logical reasoning from excluded-middle to an included-middle.

And here Complementary Logic entering to the picture, and using probability as first-order property.

Through CL (Complementary Logic) any n>1 has several variations of internal structures based on interactions between its integral side (root-like side) and its differential side (leaf-like side).

These internal structures can be ordered by their vagueness degrees, which vagueness is a combination between redundancy_AND_uncertainty properties that give us the "cloud of probability" of each ordered information form.

Redundancy exists if more then one copy of the same value can be found.

Uncertainty exists if more than one unique value can be found.

For example: http://www.geocities.com/complementarytheory/ComplexTree.pdf

Pay attention that I used the words "information forms" because these information forms, which are ordered by their vagueness degrees, can be used as general building-blocks that can help us to develop much more fine models that have to deal with included-middle problems.

From the pdf example we can learn that the standard base value expansion method is actually based on 0_redundancy_AND_0_uncertainty building blocks, which are a very small part of infinitely many different building blocks that can be used by us to construct and explode a very complex information models with variety of combinations of vagueness.

Another thing is that some experimental result is actually some single section which is cut out of 0_redundancy_AND_0_uncertainty building blocks that are ordered in several scales.

My system suggesting a much more complex information form as a result, as can be found in the last page of the pdf example.

Shortly speaking, because any information form in my system is at least structural/quantitative, it can be used straightly as it is, and we don't have to translate it to quantity before we can use it in our system.
 
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  • #82
why are all your information forms only numbers?
 
  • #83
Please see post #79 and also please read again my last post, thank you.

If I am more understood to you then please read:

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

Why are all your information forms only numbers?
I need help to develop it, it is only in its first stages, and it is definitely cannot be done by a one person.
 
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  • #84
Actually, you should be able to post here as Organic.


QM element is naturally included-middle element, because it is based on two opposite properties that preventing from us to know exactly both of them simultaneously, as we can do in macro systems.

This is a common misunderstanding about QM. Things aren't simultaneously (classical) particles and (classical) waves... they're neither; instead they're some new quantum mechanical thing that given the right circumstances, can approximate a (classical) particle or a (classical) wave.

Since quantum mechanical things aren't classical particles, it should be unsurprising that they cannot be represented exactly as classical particles.


If we want to develop some formal language that deal with QM world, we have to do it by changing our logical reasoning from excluded-middle to an included-middle.

As I've tried to point out with your Mandelbrot example, one can use weaker systems (e.g. a "1-dim system") to build new systems (e.g. a "2-dim system"). Even if you are right, it is not necessarily the case that the old logical reasoning is incapable of building the new logical reasoning.


And here Complementary Logic entering to the picture, and using probability as first-order property.

In particular, you seem to indicate now that probability is the key ingredient in your vision of the new way to do things. Well, the old way has known how to do probability for a long time, why do you think it is inadequate now?
 
  • #85
Good luck with convincing him that quantum objects such as photons are neither waves nor particles. I seem to remember posting a long sequence emphasizing the difference between "displaying wave like properties" and "being a a wave". I don't think it got through.
 
  • #86
Hurkyl,

Actually, you should be able to post here as Organic.
First, I really hope that it is not you who shut me down as Organic, because it is a west of time to speck with mentors which closing members because they have different point of view than them.
Hurkyl said:
...instead they're some new quantum mechanical thing that given the right circumstances,...
And this is exactly my point of view which is: wave/particle properties are under a probability state, and they are not physical realm until we change this probability according to our measurements tools, to some accurate particle-like XOR wave-like results.

Shortly speaking , I have Max Born's probability point of view ( http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/tourquan/born.htm ).
In particular, you seem to indicate now that probability is the key ingredient in your vision of the new way to do things. Well, the old way has known how to do probability for a long time, why do you think it is inadequate now?
The probability of convetional Math is not a first-order property, therefore a natural first-order system is much better in this case, even if the old way works.
As I've tried to point out with your Mandelbrot example, one can use weaker systems (e.g. a "1-dim system") to build new systems (e.g. a "2-dim system"). Even if you are right, it is not necessarily the case that the old logical reasoning is incapable of building the new logical reasoning.
The old logical reasoning is capable of building the new logical reasoning if probabilty is a first-order property of it.

If you don't think so then please show us how we can represnt Complementary Logic by an excluded-middle logical system.

To help you, please read this first:
http://www.geocities.com/complementarytheory/BFC.pdf
 
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  • #87
present here and now a rigorous explanation/definition of probability uaing only "first order" objects, whatever theyu may be. Or are you confusing the warm fuzzy idea of probability with its rigorous axiomatic abstraction?

can i suggest that the reasons you aren't allowed to post in the maths forum are your refusals to deal in mathematics and hijacking of threads to espouse your unmathematical views?
 
  • #88
wave/particle properties are under a probability state

The QM point of view is that wave / particle properties (when they appear) are approximate, not under a "probability state".
 
  • #89
can i suggest that the reasons you aren't allowed to post in the maths forum are your refusals to deal in mathematics and hijacking of threads to espouse your unmathematical views?
I was shut down after I put https://www.physicsforums.com/showthread.php?t=18972 in General Math.

Math , in my opinion, is not an unchagable monolitic objective state, but a living form of language.
present here and now a rigorous explanation/definition of probability uaing only "first order" objects, whatever theyu may be. Or are you confusing the warm fuzzy idea of probability with its rigorous axiomatic abstraction?
please give more details, because I do not really understand what do you looking for.
 
  • #90
The QM point of view is that wave / particle properties (when they appear) are approximate, not under a "probability state".
By saying "under a probability state" (sorry about my poor English) I speak about wave / particle properties before they appear through our experiment tools.
 

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