Deeper than primes

[jsfisher]

Ok, your inequality operator doesn't match the inequality operator in Mathematics. I can express the definition for A ≠ B as follows:
(A ≠ B) = ~(A = B)
How do you define your inequality operator?

So, Doron, why did you silently change what I actually wrote? While the difference between equality and equivalence may seem minor to someone intellectually bankrupt with respect to Mathematics, there is a difference. So, why did you change my statement?

Exactly as you do, which is: "A value is different than B value".

And yet, that's not how you used it. Curious, no?

I ask: What enables to know it?

You do not ask this question. You just define (A ≠ B) = ~(A = B) without trying to under-stand it.

No, I didn't. I wrote: (A ≠ B) = ~(A = B). That expresses, formally, what I already understand. See how that works? First comes understanding, and from that formal expression can follow.

How come you can't express anything formally? Do you not understand anything?

 

[doronshadmi]

So, Doron, why did you silently change what I actually wrote?

I simply forgot to use the undescore under = (U editor's oprtion) so take it as =

 

[jsfisher]

I simply forgot to use the undescore under (U editor's oprtion) so take it as =

So use the

function. It is less forgetful.

 

[doronshadmi]

No, I didn't. I wrote: (A ≠ B) = ~(A = B). That expresses, formally, what I already understand.

What you already under-stand (before using some expression (formal or not))?

 

[doronshadmi]

Doron, it doesn’t matter much to me what you want to agree AND disagree with.

Again the personal local-only view, which is expressed by words like "you" or "himself"(http://www.internationalskeptics.com/forums/showpost.php?p=6106556&postcount=10518), are used.

 

[jsfisher]

The Man,

As you can well imagine, I am very excited by the recent developments with Half-Adder Logic. I think you will agree, the interplay between HAL and ethics is far richer than anything Doronetics can express with its self-limiting NXOR reasoning.

As demonstrated with the brief presentation of the AND/OR variant, HAL captures head-on the complexities of life, compassion, charity, and greed. This is well beyond anything the neither here nor there NXOR reasoning can fathom.

As should be equally obvious, the common HAL can be applied to such ethical concerns as the marriage penalty in the US Tax Codes (T HAL T). Again, this is inexpressible in Doronetics.

But there is more....

Remember I said HAL is the foundation for FA Logic. Well, under FAL it is possible to embody the temporal sequencing of reality while embracing the Mathematics/Ethics interplay. This is clearly and unequivocally conveyed in the following:

The choice of colors magnifies the impact.

 

[epix]

Originally Posted by The Man
Well that is because he is simultaneously in two states, agreeing with himself AND disagreeing with himself.

"agreeing with himself AND disagreeing with himself" is exactly the Local-only view of Non-locality\Locality Linkage.

How do we know that your statement is correct? Your definition of locality and non-locality has been indigenous to the truth tables that only refer to the exclusive disjunctions XOR and its negation NXOR. You never defined the locality and non-locality via the conjunction truth table with the logical connective AND.

If someone gets the chance to grasp the definition of locality and non-locality with respect to True and False, then there is again that expression "Local-only view of Non-locality\Linkage." Is there any truth table on which that quoted expression can be put?

If there is none, then I have to stick with the traditional definition of the term "local view."

 

[The Man]

The Man,

As you can well imagine, I am very excited by the recent developments with Half-Adder Logic. I think you will agree, the interplay between HAL and ethics is far richer than anything Doronetics can express with its self-limiting NXOR reasoning.

Absolutely, and I’d be saying that even if we were in a service pod where he couldn’t hear us.

As demonstrated with the brief presentation of the AND/OR variant, HAL captures head-on the complexities of life, compassion, charity, and greed. This is well beyond anything the neither here nor there NXOR reasoning can fathom.

Again I agree, but that neither here nor there either.

As should be equally obvious, the common HAL can be applied to such ethical concerns as the marriage penalty in the US Tax Codes (T HAL T). Again, this is inexpressible in Doronetics.

But there is more....

Remember I said HAL is the foundation for FA Logic. Well, under FAL it is possible to embody the temporal sequencing of reality while embracing the Mathematics/Ethics interplay. This is clearly and unequivocally conveyed in the following:

[qimg]http://www.internationalskeptics.com/forums/picture.php?albumid=522&pictureid=3301[/qimg]

The choice of colors magnifies the impact.

Well I think you should use some more patterns too, some plaids, maybe a cross hatch pattern or two, perhaps a tiled pattern or even some paisley. That would give it a more striking impact and every one knows that the more striking the impact of your graphical representation the more fundamental your notions become. Proof without words for those who apparently just can’t be bothered with proofs or finding the right words.

 

[jsfisher]

Paisley!!!

Great observation. Now we can extend FAL into popular trends and the world of fashion.

We should co-author a paper.

 

[The Man]

Paisley!!!

Great observation. Now we can extend FAL into popular trends and the world of fashion.

We should co-author a paper.

Excellent Idea but you'll have to walk it down the runway, paisley clashes with my freckles.

 

[The Man]

Again the personal local-only view, which is expressed by words like "you" or "himself"(http://www.internationalskeptics.com/forums/showpost.php?p=6106556&postcount=10518), are used.

Again the almost pathological unwillingness to even accept your notions as yours, I Can't blame you though. Given their utter uselessness, direct contradiction and demonstrably inconsistent nature, if I were you I wouldn’t want to accept that they were mine either.

 

[jsfisher]

Deeper Than Choice

This is a first draft, proof of concept discussion document.


[SIZE=+2]Deeper Than Choice[/SIZE]

A monkey, a dog, a horse, a giraffe
They’re all gonna die but don’t to the math
Doin’ the math is kind of a bummer
You best avoid crunch’ that number

--Loudon Wainwright III​

These brilliant words of the neo-classic philosopher, Loudon Wainwright III, provide a clear guidepost bridging the abyss between physical existence and abstract Mathematics. In this paper we develop a new archetype which will be like a continuously variable transmission, providing a smooth shift between consequence and calculation.

Definition 1: Complementation, symbolized by “~”, shall be a unary relation with respect to some implicit or explicit universe, U, as follows:

~A ≡ U\A​

Within the field of Logic, the implicit universe consists of true and false, often presented as simply T and F. Therefore, in Logic, ~T ≡ F and ~F ≡ T.

Definition 2: Inequality, symbolized by “≠”, shall be a binary relation as follows:

(A ≠ B) ≡ ~(A = B)​

Definition 3: Paisley shall be either (a) a town in the lowlands section of Scotland or (b) a droplet-shaped design of Indian or Persian origins. Since the very best Scotland has to offer comes from the western isles, most notable from Islay, and not the lowlands, the second meaning for paisley shall be assumed unless stated otherwise.

Definition 4: Half-adder logic, also called AND/XOR logic and abbreviated HAL, shall be a binary relation in Logic as follows:

[table=head]A || B ||

A HAL B​

|
F || F ||

F​

|
F || T ||

T​

|
T || F ||

T​

|
T || T || F, carry the T |[/table]​

Theorem A: The so-called marriage tax penalty in the United States is fundamentally unfair.

Proof: Let A be the proposition the husband is a wage earner, and let B be the proposition the wife is a wage earner. The truth table for A HAL B has four possible input combinations, but since we are only interested in the case where both husband and wife are wage earners, we can dismiss from consideration all entries in the truth table except T HAL T. T HAL T evaluates to F, carry the T.

Therefore, when both spouses are wage earners, the government takes everything through taxation (“carry the T”) leaving nothing for the couple (“F”).

Therefore, US Tax Code marriage penalty tax is fundamentally unfair. QED.

 

[Apathia]

This is a first draft, proof of concept discussion document.


[SIZE=+2]Deeper Than Choice[/SIZE]

A monkey, a dog, a horse, a giraffe
They’re all gonna die but don’t to the math
Doin’ the math is kind of a bummer
You best avoid crunch’ that number

--Loudon Wainwright III​

These brilliant words of the neo-classic philosopher, Loudon Wainwright III, provide a clear guidepost bridging the abyss between physical existence and abstract Mathematics. In this paper we develop a new archetype which will be like a continuously variable transmission, providing a smooth shift between consequence and calculation.

Definition 1: Complementation, symbolized by “~”, shall be a unary relation with respect to some implicit or explicit universe, U, as follows:

~A ≡ U\A​

Within the field of Logic, the implicit universe consists of true and false, often presented as simply T and F. Therefore, in Logic, ~T ≡ F and ~F ≡ T.

Definition 2: Inequality, symbolized by “≠”, shall be a binary relation as follows:

(A ≠ B) ≡ ~(A = B)​

Definition 3: Paisley shall be either (a) a town in the lowlands section of Scotland or (b) a droplet-shaped design of Indian or Persian origins. Since the very best Scotland has to offer comes from the western isles, most notable from Islay, and not the lowlands, the second meaning for paisley shall be assumed unless stated otherwise.

Definition 4: Half-adder logic, also called AND/XOR logic and abbreviated HAL, shall be a binary relation in Logic as follows:

[table=head]A || B ||

A HAL B​

|
F || F ||

F​

|
F || T ||

T​

|
T || F ||

T​

|
T || T || F, carry the T |[/table]​

Theorem A: The so-called marriage tax penalty in the United States is fundamentally unfair.

Proof: Let A be the proposition the husband is a wage earner, and let B be the proposition the wife is a wage earner. The truth table for A HAL B has four possible input combinations, but since we are only interested in the case where both husband and wife are wage earners, we can dismiss from consideration all entries in the truth table except T HAL T. T HAL T evaluates to F, carry the T.

Therefore, when both spouses are wage earners, the government takes everything through taxation (“carry the T”) leaving nothing for the couple (“F”).

Therefore, US Tax Code marriage penalty tax is fundamentally unfair. QED.

Now that's comedy!

 

[jsfisher]

Now that's comedy!

I'm sure I have no idea what you mean.

 

[doronshadmi]

jsfisher,

Please do not ignore http://www.internationalskeptics.com/forums/showpost.php?p=6106789&postcount=10524.

 

[doronshadmi]

As for Relation\Element Linkage, let us use ~ , = as an example:

In "~=" expression "~" is the Relation (mutual or non-local aspect), and "=" is the Element (independent or local aspect).

In "=~" expression "=" is the Relation (mutual or non-local aspect), and "~" is the Element (independent or local aspect).

The data is changed, but the Relation\Element form is invariant w.r.t the data variance.

(Relation\Element Linkage) = (Non-locality\Locality Linkage) = (Mutual-Independency), and there is no meaning to "=" or "~" alone.

Also = is the Relation aspect and (Relation\Element Linkage),(Non-locality\Locality Linkage),(Mutual-Independency) are the Element aspect of "(Relation\Element Linkage) = (Non-locality\Locality Linkage) = (Mutual-Independency)" expression.

 

[doronshadmi]

You never defined the locality and non-locality via the conjunction truth table with the logical connective AND.

Worng.

AND is simply one of the aspects (T T --> T) of NXOR, where the other aspect of NXOR is NOR (F F --> T).

 

[doronshadmi]

Now that's comedy!

A pathetic one.

 

[doronshadmi]

Again the almost pathological unwillingness to even accept your notions as yours,

Look at the mirror of your mind, the pathological unwillingness is reflected there.

Intelligent creatures recognize their own reflection in the mirror, do you?

 

[doronshadmi]