Deeper than primes

[doronshadmi]

oppsss..

 

[doronshadmi]

There's a hole in your reasoning here you can drive a truck through.

Order is not important - you keep repeating that - to be more precise: elements of a multiset have no order.

So the entropy of [a,a,b] is the same as that of [a,b,a], since they are the same multiset.

And the entropy of [a,b,c] is the same as that of [a,c,b], since they are the same multiset too.

Do you see the contradiction with what you wrote above?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

Thank you ddt,

It was a typo.

The right one is :

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,b,c} has the same entropy as {a,c,b} (order is nor important).

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).

As for Set and Multi-set please look at this ( http://mathworld.wolfram.com/Set.html ):

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset).

 

[ddt]

Thank you ddt,

It was a typo.

It's more than a typo. You've done this before - frequently. It signifies that either you don't think your posts through before you post, or your grasp of the matter is so low you very easily make such mistakes.

Or a combination of both.

The right one is :

{a,a,b} has the same entropy as {a,b,a} (order is not important).

{a,b,c} has the same entropy as {a,c,b} (order is not important).

That's belabouring the obvious. They're the same multiset!

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).

And you carefully avoid saying which one is higher.

Drop the "distinction" word. It does not mean what you think it means.

Care to really go into the proposed definitions in posts #75 and #82? If you can't come up with an insightful reaction within 24 hours, it only proves you're out of your league here.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

 

[ddt]

As for Set and Multi-set please look at this ( http://mathworld.wolfram.com/Set.html ):

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset).

You're "forgetting" again to indicate your edits?

And so what? It only proves my point that the word collection is too vague here to use. It could refer to either a set or a multiset. You've used both in this thread. Sooner or later, you are going to abuse that - you've done that before.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

 

[nathan]

Bump

The the size of difference [of the Entropy] between the elements is not important.

So, it's an ordering. Is it partial or total? Given two multisets A and B, what is the procedure for ordering them by Entropy?

Doron, you've had three proposals for an Entropy formula, which you've rejected. You've said the value of the entropy isn't important, and the magnitude of the difference in Entropy between two multisets is not important. That leaves only the sign of the difference, hence it is an ordering.

How about coming up with that ordering? I mean as an algorithm (or set of functions, if you prefer to think of it that way). Do you understand the difference between partial and total ordering?

Do not keep posting examples -- those don't allow one to infer your meaning in a larger set of multisets. Proof of that is trivial, I refer you to the three alternative Entropy formulas that are consistent with all your examples, but you reject.

 

[nathan]

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,b,c} has the same entropy as {a,c,b} (order is nor important).

That you keep reiterating that order is not important, even though multisets (and sets) are unordered, leads me to suspect you do not know what a multiset (or set) is. So, let's start with some basic questions:

Do you agree or disagree that [a,a,b] and [a,b,a] are the same multiset?

Do you agree or disagree that [a,a,b] and [a,b,a] are different representations of the same multiset?

 

[TMiguel]

Lets try this one.
Being “A(n,k)” a partition k of a number n
Being F(s) the accounting function for the distinct (none repeated) elements within a multi-set
If F(A(n,k))=1 then the group is said to be un-distinct (in your case max entropy)
Else If #A(n,k)-F(A(n,k)=0 is said to be fully-distinct (in your case no entropy)
Else it is said to be semi-distinct (in your case intermediate entropy)

I really shouldn’t be giving you this apple since you already failed to base your “mathematical construction” without it.

 

[doronshadmi]

And you carefully avoid saying which one is higher.

As I already said in my first post, {a,b,a} has more entropy than {a,b,c} since {a,b,a} is less distinct.


The order of each multi-set is not important.

Distiction as a first-order property, is important.

 

[doronshadmi]

Lets try this one.
Being “A(n,k)” a partition k of a number n
Being F(s) the accounting function for the distinct (none repeated) elements within a multi-set
If F(A(n,k))=1 then the group is said to be un-distinct (in your case max entropy)
Else If #A(n,k)-F(A(n,k)=0 is said to be fully-distinct (in your case no entropy)
Else it is said to be semi-distinct (in your case intermediate entropy)

I really shouldn’t be giving you this apple since you already failed to base your “mathematical construction” without it.

You still try to reduce Distinction to the particular case of distinct results.

For example:

a = 0

b = 1

a < c < b

and we get {a,b,c} that is some case with no entropy.

Again Distinction is a first-order property of multi-sets, and as a first-order property it must not be limited to any particular case of Distinction.

{a,b,c} is not the only possible result, if Distinction is a first-order property of what is called multi-set.

 

[doronshadmi]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

 

[TMiguel]

You still try to reduce Distinction to the particular case of distinct results.

For example:

a = 0

b = 1

a < c < b

and we get {a,b,c} that is some case with no entropy.

Again Distinction is a first-order property of multi-sets, and as a first-order property it must not be limited to any particular case of Distinction.

{a,b,c} is not the only possible result, if Distinction is a first-order property of what is called multi-set.

It is how you tell the difference between the things you are trying to discriminate YOU R#%$rd, if you can not tell the difference between what is what, then what is the point of all of this?

A Stupidity certificate coming out, make your test right here: http://nonoba.com/thegamehomepage/the-stupidity-test

 

[nathan]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

What is this 'Distinction' property? Can you provide a definition for it?

I see you're avoiding answering my, somewhat fundamental, pair of questions about multisets. Your answers might clarify what you mean.

 

[jsfisher]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

So, is this going to be another classic doron thread in which you misuse standard terminology without defining what you actually mean (e.g. entropy), invent new terms without defining what you actually mean (e.g. distinction), attempt to distract us with irrelevant diagrams, invert meaning (each multiset defines its entropy), belabor the trivial (order is unimportant), remain oblivious to contradiction and inconsistencies (entropy of [4] versus [] or [4,4]), ignore questions, and then blame everyone else for not "getting" your idea?

 

[Reality Check]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

So long as you cannot define Distinction as multi-set's first-order property, you do not have an idea.

Perhaps you can give us a list of a multi-set's first-order properties?

 

[Reality Check]

So, is this going to be another classic doron thread in which you misuse standard terminology without defining what you actually mean (e.g. entropy), invent new terms without defining what you actually mean (e.g. distinction), attempt to distract us with irrelevant diagrams, invert meaning (each multiset defines its entropy), belabor the trivial (order is unimportant), remain oblivious to contradiction and inconsistencies (entropy of [4] versus [] or [4,4]), ignore questions, and then blame everyone else for not "getting" your idea?

You missed out that he has yet to define what a "first-order property" of anything is. And that he will blame everyone else for not "getting" his undefined term "first-order property".

 

[drkitten]

Bump
Doron, you've had three proposals for an Entropy formula, which you've rejected. You've said the value of the entropy isn't important, and the magnitude of the difference in Entropy between two multisets is not important.

I don't think she said that.

I think she said that the magnitude of the difference between two elements is unimportant, as long as they differ. I.e. the quasi-entropy of [2,1,1]* is the same as the quasi-entropy of [5,1,1] or of [Coke, Pepsi, Pepsi] as long as we're dealing with a multiset with one singleton element and one pair.

Similarly, I don't remember her saying that the value of the quasi-entropy isn't important. She's merely demonstrated a complete inability (or more charitably unwillingness) to quantify her notion of quasi-entropy so that we can actually calculate that value.


(*) See, DDT, I'm using your multiset notation. Happy?

 

[doronshadmi]

It is how you tell the difference between the things you are trying to discriminate YOU R#%$rd, if you can not tell the difference between what is what, then what is the point of all of this?

A Stupidity certificate coming out, make your test right here: http://nonoba.com/thegamehomepage/the-stupidity-test

Distinction is the relation between the certain and the uncertain.

The certain and the uncertain complement each other.

It means that they are not defined in terms of the other.

For example, if the uncertain is darkness, you cannot use light (the certain) in order to research the darkness (the uncertain) because by using light you change the researched subject (darkness, in this case).

The idea is to define the common property that stands at the basis of both darkness and light, and then you are able to get their relations and each one of them without changing them by your research.

By using this knowledge we can develop new methods in order to improve the relations between complement states (any cardinal of complement states can be found, it does not matter) in addition to their property to contradict (prevent) each other.

Multi-set is the result of things that simultaneously complement AND prevent each other, and the best knowledge is based on the non-trivial relation between the certain and the uncertain.

Please look again at ONN5 represented by Penrose tiling:

ONN5 is a one thing that simultaneously defined as several states of Distinction.

Please let your mind to get the perception of this distinction.

You can look into each state and directly get how your perception spontaneously defines its distinction (it can clearly be seen if you compare between the first top-left case (that has maximum entropy) and the last bot-right case (that has minimum entropy)).

But please do not forget that this comparison is nothing but the particular case of clear distinction.

The current paradigm of the mathamatical science is limited to clear distinction as its first-order property.

By the the organic paradigm, Distinction is itsef a first-order property of the mathematical science, and it is not limited to any particular case of it.

 

[drkitten]

Distinction is the relation between the certain and the uncertain.

Well, that's another great doron non-definition.

Distinction (an undefined term) is the relation (a term with a definition, but probably inappropriate here) between the certain (another undefined term) and the uncertain (another undefined term).

Interpret this in light of the assertion that distinction (still undefined) is a first-order property (another undefined term) of a multiset.

 

[Reality Check]

jsfisher was right: Here are the pretty pictures (irrelevant diagrams), etc. right on schedule!

ETA: And he is back to his non-mathematical organic paradigm.
Plus he thinks mathematics is all about perception (how you see things) not actual mathematics.

It looks like this is another doronshadmi thread heading for the Religion and Philosophy area. One of these days he really should learn the difference between Philosophy and Mathematics.

 

[jsfisher]

Please look again at ONN5 represented by Penrose tiling:

As will come as no surprise to most, doron has now demonstrated another thing of which he has no understanding, Penrose tiling in this case.