Laying out the representation to be solved.

[Rade]

Calling it with a more appropriate name doesn't remove it from your interest, it only means that your interest concerns data rather than information.

I agree that "data" is much better to use than "information", and in the recent definition of "information" provided by DD, his word "whatever", to the extent that it serves as a source of "recurring patterns of energy", is best thought of as being "patterns of energy data". However, as I mentioned before, for DD, also a possibility for the "whatever" is nothingness--lack of data, and this type of "whatever" also needs to be explained.

 

I think you make a significant contribution to the presentation to point to the fact that, "whatever" will be used to form a circumstance to be explained, that "whatever" must be "data" and not "information". Thank you for adding this clarification to my understanding. I'm sure DD will let us know if he does not agree that patterns of "data" logically must be prior to patterns of "information".

[Rade]

In other words, the difference in mass does appear as a difference in the number of elements that make up some composite object. Which means you can't consider something that is capable of doing things that a guitar is capable of doing, to be a fundamental element of any explanation.

In reading over past posts, I see we still are not connecting on this critical issue.

 

Your conclusion is valid only for the circumstance being explained as relates to two single Gibson guitars, not for the set of all possible circumstances in which any Gibson guitar may require explanation. So, read again my circumstance of 100 Gibson guitars placed in box A, and 100 placed in box B, and you want to explain why one box has greater weight than the other. Of course there are many such explanations, that is not what is being discussed here.

 

The issue is that, for all possible explanation for this new circumstance, you must consider that whatever a guitar is capable of doing, it is capable of sitting in a box and taking up space, and for this circumstance you MUST view each individual guitar as a unit, as a "fundamental element" for whatever explanation will be put forward by anyone, to explain why box A and box B do not have identical weight. Thus, in the same way you just explained to me how "mass" for each part of a single Gibson guitar will be derived from the notation by viewing each part of the guitar as a fundamental defined element(I know already it will be along the tau dimension), this exact same reasoning must be used for the box circumstance. That is, the mass of each box will be derived along the tau dimension when each of the 100 Gibson guitars are viewed as a fundamental defined element taking up space in each box and each box is a composite "object". (using your term).

[Rade]

Also, using the word undefined information makes me think that there is more information in any point then it just being an arbitrary point. Actually this might be part of Rade’s problem. He is thinking that any amount of information can be supplied in a single point and doesn’t realize how simple a definition of a single point must be and how more complex structures must be constructed from basic points.

Hello. No, this is exactly what I have been trying to explain. :shrug: That the concept of "single point" has many different applications that are scale and context dependent on the circumstance under question. A "definition" of a concept called "single point" is NOT simple, it requires that one consider all that is known at the time the definition is put forward for the circumstance. It is definitions of the concept "single point" that can change over time as more undefined information becomes available, not the concept "single point"--the concept is static, the definition is dynamic.

 

Also, not all complex structures are constructed from basic points. Three lines can be used to construct a triangle, but none of the lines are constructed from combining points, they are constructed from combining smaller lines.

 

This complex structure ^of two lines, can be considered to be a single point if the circumstance in question deals with this set of such points rotated {^,>,<,^}. The undefined set of information represents the composite object composed of single points that make up the representation of what was undefined, and each point is then a defined element that could enter the notation of any explanation where they are used.

 

If you do not agree with the above, please let me know why.

Edited November 20, 2010 by Rade

[Rade]

Hello Doctordick...I am now reviewing the thread to make sure all is clear, and I came across this statement you made

 

Expectations are clearly' date=' “what you expect”. The problem there is that “what you expect” is usually taken to mean a statement of the actual results. It should be quite clear to you that a general exact representation of such a thing is quite impossible;

 

however, I hold that the collection of yes/no answers to all possible questions (using a probability distribution for cases where the yes/no answer is not necessarily known) can represent such a statement. Given a complete set of such answers to all possible questions, it should be obvious to you that a statement of “what you expect” could be created.[/quote']OK, let me try to understand. There are two types of expectations (1) what you expect will happen in the future (2) what you expect will not happen in the future.

 

Now, it is not at all clear to me that a general exact representation of actual results of what you expect will happen in the future is impossible.

 

Let me offer this example. Suppose a light switch, it can move up or down. Now, I observe that the overhead light turns on when the switch is up, and turns off when the switch is down. These observations represent actual results of multiple trials. Thus, I can form a reasonable expectation based on actual results (that is, what I expect will happen in the future) that when I turn the switch up, the light will turn on. And this is the explanation I give my two year when she asks why the light goes on and off when my hand moves to the wall to touch something (she does not know it is called a switch).

 

And, repeated trails over times shows that my reasonable expectations hold true. Sure enough, I push the switch up or down and I observe a light response. But, once in awhile, I observe that the light turns on or off when I do not touch the switch, thus this possibility becomes part of my future expectations, even though the reason is completely unknown to me (I have a guess as to reason but have not investigated in detail). Also there are times when I move the switch up and the light does not turn on as expected, and I suspect either the power to house is out and/or that bulb is burned out.

 

Thus, I do not see why these "actual results" (based on observation) do not provide the complete set of expectations for the circumstance.

 

Now, let us apply your approach of deriving "what you expect" by providing yes/no answers to all possible questions without any reference to observation of actual results:

 

Q. Does the light turn on when switch is pushed down ? A. no

Q. Does the light turn off when switch is pushed up ? A. no

Q. Does the light turn on when switch is pushed up ? A. yes (if bulb is not burned out and power to house is on)

Q. Does the light turn off when switch is pushed down ? A. yes

Q. Does the light turn off when switch is up and not touched ? A. [impossible to give yes or no reply]

Q. Does the light turn on when switch is down and not touched ? A. [impossible to give yes or no reply]

 

As you can see, there is a major problem using the approach of providing a list of yes/no answers to all possible questions to create a valid statement of what you expect. Without data from "actual results" you cannot logically provide a yes/no answer to the last two questions on your list, yet these questions must be included in any complete list of "all possible" questions. I mean, any reasonable person would have to say they cannot answer yes or no about what would happen in these situations, given that they have past knowledge that lights can go off and on even if a switch is not touched. Also, notice that a definitive yes or no answer also cannot be given to the third question for the reasons given.

 

Now, even if you would allow for data from actual results to be used, the reasonable person still cannot provide a yes or no answer to the last two questions. Their answer would have to be, yes AND no, in other words, maybe-I am not sure, I cannot answer yes or no for sure (in your terms, they would answer they could not provide any definitive probability between 0 and 1 for the expectation--they would say it is not a valid question to ask).

 

So, a major roadblock in understanding for me. Please explain how you deal with these imitations of your "20 question" approach to representation of expectations for circumstances of any explanation--that is, when it is impossible to provide either a {edit} definitive {or probability based} yes or no answer for a logically possible question ?

Edited November 21, 2010 by Rade

[Bombadil]

Suppose that I simply define “information” as, “whatever the explanation is to explain”: i.e., that would make it identical to the collection of “circumstances” each represented by the expression [math](x_1,x_2,\cdots,x_n,t)[/math]. Regarding Qfwfq's complaint that the category “information” is reserved to defined data, I suggest that such a definition of “information” would totally remove all information from our interest as the definition can only precede from presumption and we wish to make no presumptions: i.e., the requirement presumes an explanation and is thus a situation not universally applicable to all explanations of “whatever it is that is being explained”.

 

I really don’t care how you define things as long as you remain consistent however every time you have defined things it seems that you then use your new definition to derive something, and so I ask the only question about this definition that seems of importance at this time and a question that probably doesn’t belong in this thread it is, is this the definition of information that you think will be needed to derive information theory from your fundamental equation? That’s what the problem really is isn’t it? No one has derived information theory yet and so there is no way to say what role it plays in the derivation.

 

When you say "how much one set of elements looks like another set of elements when interpreted in a particular way", do you mean the resemblence between undefined elements and some specific definitions?

 

I relay don’t know for sure and at this point I am hesitant to make a guess in fear that it will just add to more confusion, but I was thinking of the existence of a function that can map the expectations of one set to the expectations for another set. For anything more then that I think the only way to know for sure is to find someone that can derive us information theory form the derivation. Unfortunately this is unlikely to happen any time soon as I don’t think that it has yet been derived and I doubt that anyone here is up to such a challenge right now.

 

Nope. It's the probability that universe is found to be at some specific state at some specific "t". Or that some defined entity is in particular location at particular time. It's not a probability of undefined elements (we can't attach any probabilities to themselves, that would be impossible without definitions). It's similar to the idea of probability wave in quantum mechanics (which is also referring to the probability of finding some defined entity at some particular location at some particular time).

 

But doesn’t even definitions like mass and energy have a probability function in quantum mechanics. That is it is really a transformation of the wave function (that tells us the probability of finding something at some location) into a new wave function that tells us the probability of finding it with a particular amount of momentum. So that in quantum mechanics if we considered the momentum and energy of a particle to define it there is still a probability wave associated with the definition?

 

In this case since such things are not yet defined we can only suppose that the definition of an element might be a function of its location and so this would make the definition of an element part of the explanation. This is one reason that I am thinking of the location of an element as part of its definition.

 

In a nutshell, the argument is that our expectations are a function of the context (i.e. how defined things are positioned in related to each others), but not a function of something we just made up in order to mark down that context.

 

But how can we know the context. Of course any expectations that we might have must be a function of the context but how can we know what it is. Won’t it have to be defined by the explanation. Can we just choose a random context and expect our definitions to tell us where to expect all of the elements to go. Isn’t there still going to have to be an initial condition that the explanation has to obey. If so what is it and how can we possibly know what it is?

 

The remainder of the OP seems to be just the technical details needed to use a function as a probability. There appears perhaps a small amount of ambiguity in it but I think it is only because it is wrote so that any possible probability function can be included as an explanation. As a result functions that behave considerably differently must be included. As a result I don’t really see anything that I think needs brought up at this time as the details of the definition will most likely have to be defined by the context that is chosen to place the function in. And I really don’t have a problem understanding what is being said any way.

[Doctordick]

 

Q. Does the light turn off when switch is up and not touched ? A. [impossible to give yes or no reply]

Q. Does the light turn on when switch is down and not touched ? A. [impossible to give yes or no reply]

 

So, a major roadblock in understanding for me. Please explain how you deal with these imitations of your "20 question" approach to representation of expectations for circumstances of any explanation--that is, when it is impossible to provide either a {edit} definitive {or probability based} yes or no answer for a logically possible question ?

How about the question, “was George Clooney combing his hair at 1:00 today?”

 

And the answer please! ... That circumstance is not being explained in the explanation being considered. In essence that is not a circumstance of interest it the case: i.e., it is not a circumstance with which you have asserted any experience; the circumstances standing behind your explanation do not include any circumstances expressing any information on that particular issue.

 

Or, if it is of interest, no information is given concerning the outcome; you still might have “expectations”: like "probably not" (some small range of probability)! If the function [math]\vec{\Psi}[/math] does not yield the same probability “for your expectations” that your explanation does, then it is not the function which represents your explanation! This sort of problem is of no concern to me at all. The question is, does a mathematical function exist which yields exactly the same probability for the answeres to these questions that your explanation does?

 

By the way, any question which no applicable circumstances standing behind it which may actually have application to your other expectations, must be included by summing over all possibilities weighted by the probability of those possibilities. If you have utterly no information of those possibilties you are left with the probability of all possibilities summed up being one by definition. It is certainly possible that such a fact has import to your explanation. You have to think these things out Rade; they are not trivial: i.e., how would you handle answering such questions.

 

-- Dick

[Doctordick]

I really don’t care how you define things as long as you remain consistent however every time you have defined things it seems that you then use your new definition to derive something, and so I ask the only question about this definition that seems of importance at this time and a question that probably doesn’t belong in this thread it is, is this the definition of information that you think will be needed to derive information theory from your fundamental equation? That’s what the problem really is isn’t it? No one has derived information theory yet and so there is no way to say what role it plays in the derivation.

All I am talking about here is “what word I prefer to use to refer to the undefined things standing behind the explanation being discussed: i.e., what word or phrase should I use to refer to whatever it is that the numerical indices “x” refer to. Qfwfq wants to make that issue an arguing point for some subtle reason which is beyond me.

 

Given that the Webster's New World Dictionary circa 1951 (my personal reference for American English) gives the following definitions,

 

data things known or assumed; facts or figures from which conclusions can be inferred.

 

information from the Latin informatio a representation, outlining, sketch 1. an informing or being informed; especially, a telling or being told of something. 2. something told; news; intelligence; word. 3. any knowledge acquired in any manner; facts; data; learning; lore.

 

My question is extremely simple: which of those two words would you use to refer to a fact that “something happened” where what it was that happened is absolutely unknown? It seems to me that it certainly is not a thing “known” and, if it is assumed, what has been assumed? As defined, “data” seems to imply something beyond “something happened”. My attitude is that “information” is a much more ambiguous general concept (that is why it has a longer definition): i.e., anything “told” would qualify, defined or not.

 

I relay don’t know for sure and at this point I am hesitant to make a guess in fear that it will just add to more confusion, but I was thinking of the existence of a function that can map the expectations of one set to the expectations for another set.

Why would we be interested in mapping expectations of one set to the expectations for another set?

 

For anything more then that I think the only way to know for sure is to find someone that can derive us information theory form the derivation. Unfortunately this is unlikely to happen any time soon as I don’t think that it has yet been derived and I doubt that anyone here is up to such a challenge right now.

 

You seem to miss a very important point here. My fundamental equation follows from the definition of an explanation and thus includes all conceivable explanations. Any explanation which can be derived from my fundamental equation is not actually an explanation at all; it is merely a subtle restating of the evidence standing behind that, so called, explanation as it is true by definition: i.e., it is merely a complex tautology.

 

But doesn’t even definitions like mass and energy have a probability function in quantum mechanics. That is it is really a transformation of the wave function (that tells us the probability of finding something at some location) into a new wave function that tells us the probability of finding it with a particular amount of momentum. So that in quantum mechanics if we considered the momentum and energy of a particle to define it there is still a probability wave associated with the definition?

All you are talking about here is the fact that, “there is more than one way to skin a cat”. The shift symmetry of the problem as stated requires the conservation of a characteristic analogous to momentum. Mathematically, it follows from that fact that “knowing” all the momentums is equivalent to knowing all the positions: i.e., there exists a simple mathematical symmetry between the representation in terms of “x” and representation in terms of the partial with respect to x. You really shouldn't worry about these issues here. There are some deep mathematical transformations involved here: see “Fourier transforms”.

 

In this case since such things are not yet defined we can only suppose that the definition of an element might be a function of its location and so this would make the definition of an element part of the explanation. This is one reason that I am thinking of the location of an element as part of its definition.

In my presentation, “location” is not yet a defined concept. If you think about it for a moment, you should realize that the concept “location” carries a number of subtle presumptions with it.

 

But how can we know the context. Of course any expectations that we might have must be a function of the context but how can we know what it is. Won’t it have to be defined by the explanation. Can we just choose a random context and expect our definitions to tell us where to expect all of the elements to go. Isn’t there still going to have to be an initial condition that the explanation has to obey. If so what is it and how can we possibly know what it is?

Here you are getting well ahead of the game. These are issues which come up in my "A Universal Representation of Rules" post which I am in the process of composing now.

 

As a result I don’t really see anything that I think needs brought up at this time as the details of the definition will most likely have to be defined by the context that is chosen to place the function in. And I really don’t have a problem understanding what is being said any way.

Thank you Bombadil. I would tend to agree with you. As far as I can see the issues, you pretty well seem to understand what I am talking about. Most of your confusions seems to be from trying to get ahead of the information (or should I say "data") :lol:

 

Welcome to the club : You, Anssi and I; the three musketeers fighting ignorance.

 

Have fun -- Dick

[Qfwfq]

(my personal reference for American English)

Oh, now I know, finally. I'm supposed to learn American English in order to communicate. :rolleyes:

 

Dick, data is the plural of the Latin datum which means given. Now, this can be taken to imply it being "as is" or raw, without further interpretation. That's why your dictionary says that conclusions may be inferred from it: the data is not the conclusions. One could replace conclusions with meaning or expectations and say the same. The word information is more on this side than data.

 

Mathematically, it follows from that fact that “knowing” all the momentums is equivalent to knowing all the positions: i.e., there exists a simple mathematical symmetry between the representation in terms of “x” and representation in terms of the partial with respect to x. You really shouldn't worry about these issues here. There are some deep mathematical transformations involved here: see “Fourier transforms”.

On which grounds do you draw this conclusion, in your presentation?

[Rade]

...no information is given concerning the outcome; you still might have “expectations”: like "probably not" (some small range of probability)!...any question which (with ?) no applicable circumstances standing behind it, which may actually have application to your other expectations, must be included by summing over all possibilities weighted by the probability of those possibilities.

OK, thank you. So, you are saying that one must guess what number of probability (say 0.001, or 0.02, etc.) you wish to assign to any "probably not" expectation for any applicable circumstance.

 

If the function [math]\vec{\Psi}[/math] does not yield the same probability “for your expectations” that your explanation does' date=' then it is not the function which represents your explanation! This sort of problem is of no concern to me at all.[/quote']OK, sure, but this sort of problem may be of interest to someone, that they may then want to explain it, and of course they could not use your "20 question" approach. That is all I am trying to explain, that their are times when using the "actual results" of expectations can lead to explanations that your "20 question" approach cannot address.

 

The question is' date=' does a mathematical function exist which yields exactly the same probability for the answers to these questions that your explanation does?[/quote']Sure, that is one question. But, again, my point was, that it is equally valid the question, does a mathematical function exist which yields exactly the same probability for the actual results that your explanation does ?

 

You have to think these things out Rade; they are not trivial: i.e.' date=' how would you handle answering such questions.[/quote']Yes, but I was thinking on a different level, I was thinking on the level that there exists a set of "such questions" that are outside the representation of your notation that also are not trivial, and the answer you have given to my thinking is clear, your notational approach does not apply--as you said above:

 

This sort of problem is of no concern to me at all.

Yes, this is exactly my point, that there is a set of problems, that require explanation, that are of no concern to you. But this is really a minor issue, because we cannot expect you to have concern for everything.

 

So, as far as I am concerned, you can move on to the next topic in your presentation. What you have so far seems clear enough, given the many constraints you have placed on your "definition of explanation" itself.

[Rade]

How about the question, “was George Clooney combing his hair at 1:00 today?” And the answer please! ... That circumstance is not being explained in the explanation being considered.

Sure. But, perhaps each time George combs his hair to the left, a light goes on in a room of your house, and George knows it from the camera he has hidden in your room to view only the light, even if you do not.

 

This raises a question about your 20 question approach. Suppose there are circumstances that you are not aware of that are of critical importance to a proper explanation of a circumstance being considered by you. Clearly, your list of 20 questions alone would be of limited value to provide a valid explanation, in fact, you could reach a conclusion that could be dangerous in situations dealing with life and death issues.

 

So, it seems we have different levels of explanation (1) your explanation of the circumstance (what you and what George alone know), (2) a collective explanation (in the above example, what you know + what George knows). Now, suppose that the sum of (1) and (2)is only known by a third person, say John, a level (3) type explanation.

 

Would it not be true that only John can make a claim of having a complete and flaw-free explanation of the circumstance ?

 

So, some questions:

 

1. Is it the "i" within your (xi) that takes into consideration all the various possible circumstances that enter an explanation from the multiple perspectives (you, George, John) that can provide explanation of a circumstance ?

 

2. How does your notation rank the predictive value of the various explanations for the exact same circumstance, which, in the above example would be: George explanation (low predictive value), your explanation (mid), John explanation (high predictive value) ?

[Rade]

Doctordick quote

 

All I am talking about here is “what word I prefer to use to refer to the undefined things standing behind the explanation being discussed: i.e.' date=' what word or phrase should I use to refer to whatever it is that the numerical indices “x” refer to. Qfwfq wants to make that issue an arguing point for some subtle reason which is beyond me.

 

Given that the Webster's New World Dictionary circa 1951 (my personal reference for American English) gives the following definitions,

 

data things known or assumed; facts or figures from which conclusions can be inferred.

 

information from the Latin informatio a representation, outlining, sketch 1. an informing or being informed; especially, a telling or being told of something. 2. something told; news; intelligence; word. 3. any knowledge acquired in any manner; facts; data; learning; lore.

 

My question is extremely simple: which of those two words would you use to refer to [b']a fact that “something happened”[/b] where what it was that happened is absolutely unknown? It seems to me that it certainly is not a thing “known” and, if it is assumed, what has been assumed? As defined, “data” seems to imply something beyond “something happened”. My attitude is that “information” is a much more ambiguous general concept (that is why it has a longer definition): i.e., anything “told” would qualify, defined or not.

 

Your question asks ... to refer to a fact that "something happened"...

 

So, clearly you claim there to be a fact present in your question, the fact that "something happened". Your use of the word "fact" is the key to the answer of your question.

 

Note that "data" is defined in your dictionary as "facts", thus a "datum" as a primary (singular) would be a "fact". Therefore, by definition data = facts, datum = fact.

 

Suppose bit code, 1 and 0. Each bit represents a singular datum (a fact). Combined in various ways 10, 11, 00, 01 they represent information, "a thing told". The information comes from the constraint on the possible variety in the possible repetitive pattern of datum (1 or 0). If all datum were 1, with no other possibility, there would be {edit} perfect information, for information requires constraint on variety, and here you have perfect constraint. Information is told by combining two singular datum facts (1 and 0) in various ways, thus datum is prior to information.

 

Notice from the definition of information you gave, that it is a "word" told, not each letter as datum "w","o","r","d" that is "told" as information. Thus, to say that information is told, there must always exist a possibility of constraint. {edit} removed

 

Therefore, data (a datum) as facts (a fact) are always prior to information. So, to answer your question, you would use data to refer to the "fact that something happened", you would use information to help explain some unknown repetitive pattern of data from the something that happened.

 

==

 

You asked about the difference between a thing "known" vs "assumed" as used for definition of data. Using your New World Webster dictionary, we see these definitions:

 

know...to have a clear perception or understanding of...to have a firm mental grasp of.

 

assume....to take or put on (the appearance, form, role etc. of)...to suppose (something) to be a fact.

 

It seems logical to me that it would be "data as assumed facts" that would describe your "something happened". This would meet your requirement that whatever the "something" is that did happen, is completely unknown (it is not clear)--that is--the data are assumed to be fact of the "something", not known to be fact of the "something". Thus, you are correct when you say that it is false to say "data as known facts" would describe your "something happened".

 

What is being assumed in your example is that the "something" of the "something happened" is thought to be supposed to be data (facts), not known to be data (facts). This is completely in line with your requirement that the "something" be completely "unknown", that your initial understanding of the "something" is as assumption, and not knowledge. The reason you cannot find a role for assumption to explain your question is because you hold information to be prior to data.

 

==

As a time sequence showing the priority of data over information I offer this example:

 

1. something happened...a datum fact... 1 (completely unknown, except as a thing that happened)

pause

2. something happened...a datum fact... 0 (you assume it differs in unknown way from the first thing)

pause

3. something happened...a datum fact... 1 (you assume it is similar to the first thing)

pause

4. something happened...a datum fact... 0 (you assume it is similar to the second thing)

 

If we stop the process here, we have the set of data {1010} which represents some unknown repetitive pattern of something as information that happened from time step 1 to 4.

Edited December 1, 2010 by Rade

[Bombadil]

My question is extremely simple: which of those two words would you use to refer to a fact that “something happened” where what it was that happened is absolutely unknown? It seems to me that it certainly is not a thing “known” and, if it is assumed, what has been assumed? As defined, “data” seems to imply something beyond “something happened”. My attitude is that “information” is a much more ambiguous general concept (that is why it has a longer definition): i.e., anything “told” would qualify, defined or not.

 

From that view point it seems clear that the word information will include what you are trying to represent. In fact the definition of information includes the definition of data. The only question that seems to be left is what word will lead to less confusion. Unfortunately from that prospective I think that the only thing to do is remain consistent and hope that people will start to follow along.

 

But just as an initial reaction of the words the word information makes me think of something like instructions. Information makes me think it is telling me about something.

The word data on the other hand would make me think perhaps more of what a computer might process which is the only thing that might make me lean more towards it since data makes me think of something that must be translated into an understandable form before it means anything to me. Of course this is kind of like saying that I like the word data because it has a simpler definition given. I would hope for a similar reaction form other people but perhaps that is slightly unlikely.

 

Why would we be interested in mapping expectations of one set to the expectations for another set?

 

Well kind of like how it can be said that a topologist can’t tell the difference between a coffee cup and a donut because at some mathematical level they are really the same object. I ask is there a level at which we can call two tautology’s equivalent in a similar way. That is at some level the tautology’s will be the same at least as far as certain properties are concerned or that we can say that they won’t have certain purports in common?

 

I know that all such tautologies must have a interpretation that will satisfy the fundamental equation but it seems that from there that further constraints might be added or definitions made and I just ask the question at what point are we no longer working with every possible tautology and how can we know that we are or aren’t?

 

Thank you Bombadil. I would tend to agree with you. As far as I can see the issues, you pretty well seem to understand what I am talking about. Most of your confusions seems to be from trying to get ahead of the information (or should I say "data") :lol:

 

Welcome to the club : You, Anssi and I; the three musketeers fighting ignorance.

 

Well in that case I’ll move on to the next thread and continue the discussion there.