Conservation Of Inherent Ignorance!

[Doctordick]

Again, I will insert a preamble in the hope that it assists the reader in understanding exactly what I am doing and why the issues I bring up are essential. If you have not digested my post “Laying out the representation to be solved” I would suggest your first make a good effort to understand the details of that post. At the moment, barring someone's demonstration of a fault in my representation, I think that, in that post, I have proved the following: for every specific conceivable flaw-free explanation of any information, there exists a mathematical function of the form [math]\vec{\Psi}(\vec{x},t)[/math] which can serve as an exact representation of that explanation. However, as I mentioned within that proof, the final result appears to be a somewhat useless representation as there are clearly an infinite set of such representations for each and every possible circumstances to be explained.

 

This post is an essentially a mathematical continuation of that proof designed to yield a somewhat more useful representation. Central to my approach is to make no assumptions not absolutely necessary to the definition of an explanation. In the interest of maintaining total generality, my attempt is to make no assumptions whatsoever; however, as it is always possible that I have inadvertently made an assumption I would appreciate any criticism relevant to that issue.

 

Mathematics is the central language of this presentation; however, this does not imply that the level of mathematics I use is of any real complexity. There is nothing in this presentation which can not be understood with introductory mathematical concepts. That being the case, there are some important characteristics of mathematics which need to be explicitly pointed out to anyone not familiar with the ins and outs of the subject.

 

The essential tautological nature of mathematics

 

It is very important that one recognize that no mathematical proof can produce any results not contained in the presumed axioms. In essence, mathematics is a very complex logical tautology which allows us to extend our thoughts far beyond that which can be comprehended by the human brain. Any mathematical proof of anything is actually no more than a re-expression of information contained within the underlying axioms. That fact and that fact alone should convince any rational person that the normal human brain falls far short of comprehending exactly what is required by those axioms. Any person who refuses to think in terms of mathematical relationships is simply not prepared to understand anything of any real complexity. Simple logic, sans mathematics, can only explain very simple things and our explanations of reality are far from simple things.

 

At the present, as I am presuming my earlier proof is understood, we are starting from the following assertion.

 

It is then clear, at this point, that the problem of finding [math]\vec{\Psi}[/math] is one of interpolation. We need to find a function which fits the known circumstances (known for some specific t indices) and use that function to express the hypothetical probabilities for all circumstances outside those known circumstances. The problem confronting us becomes quite obvious here: any mathematician knows that there exists an infinite set of solutions even for the simplest of such problems. Since every such solution is a flaw free explanation of the known circumstances, a blind search for the a solution from the given perspective is clearly a complete waste of time.

I do not deny that obvious fact; however, I do contend that there are some interesting further constraints which can be put on that blind search which can serve to close a considerable collection of blind alleys. This argument is based on a careful analysis of the issue of “symmetries”; an issue I like to refer to as “conservation of ignorance”.

 

A background on the issue of symmetries and conserved quantities

 

There is a very important relationship between symmetries and conserved quantities first laid out in detail via a theorem proved by Emmy Noether sometime around 1915. The essence of the proof can be found on John Baez's web site. This is a fundamental theorem accepted as valid by the entire physics community.

 

What I would like to point out is that any symmetry is essentially an expression of a specific ignorance: i.e., something very specific is not known. In Baez's case, he is essentially asserting that the “correct position” of q is not known information (i.e., that actual true position has no impact on the problem being solved). In the same manner, mirror symmetry means that there is no way to tell the difference between a given view of a problem and its mirror image: in effect you are in a state of enforced ignorance as to which view is being presented. If one makes a careful examination, every conceivable symmetry can be seen as a statement of some specific instance of enforced ignorance.

 

The fundamental issue behind the power of symmetry arguments is the fact that information which is not available can not be produced by any algebraic procedure. This is a direct consequence of the fact that no proof does anything more than verify that what is being proved is actually embedded in the axioms required by the proof: i.e., it can not be false; the essential definition of a tautology. That being the case, how in the world can someone state the solution to a problem in terms of a specific variable when changing that variable has no impact on the problem? For example, consider a common physics problem where the solution is given as some function x(t). If one moves the origin of their coordinate system, the value of x can be shifted to any value desired. (Such a circumstance is commonly referred to as “shift symmetry”.) Clearly, if the problem does not specify where the origin is, how in the world can the solution specify what x is?

 

The answer essentially lies in Noether's theorem. There must be another relationship which relates the range of possibilities for q (the transformations Baez refers to) to the various specific solutions: i.e., there exists a specific constraint which can carry any solution given in terms of that q into every possible specific solution. In shift symmetry, this required relationship turns out to be conservation of momentum; in rotational symmetry, the required relationship is conservation of angular momentum.

 

Symmetries arise in a problem because the structure of the representation of the problem (which is a creation of our minds) contains an element which cannot be known (like the position of the origin or the actual orientation of an ideal sphere): i.e., the information which the conceptual structure explicitly represents, exceeds the actual information available.

Since mathematics can not produce any results not included in the statement of the problem, it follows that, if the conceptual structure used to represent the problem exceeds the information available, the ignorance fundamentally amounts to a constraint on the solution of the problem. Thus it is that it behooves us to investigate the possible ways of expressing the actual constraints required by this ignorance in a mathematical form. In my opinion this is exactly what Noether's theorem is all about. Just as Noether's theorem turned out to be a very powerful tool in modern physics, a search for analogous relationships regarding my mathematical representation of explanations, should be expected to provide some important mathematical constraints on the acceptable mathematical representations of explanations via that functional representation, [math]\vec{\Psi}(\vec{x},t)[/math].

 

Creating an exact mathematical representation of the inherent ignorance embedded in shift symmetry

 

As I said in the original proof, every elemental event requires two numerical labels, one to represent the event as defined by the specific explanation being modeled (the "i" index) and one to represent the same event in all possible explanations (the unknown numerical label represented by x). When [math]\vec{\Psi}[/math] is seen as a function of a numerical argument (the representation I have alluded to above) it is important to recognize that the numerical argument must consist of the numerical label represented by the collection of unknowns "x" as, if one uses the numerical label represented by "i", one has essentially presumed all the constraints specified in the defined elements of the specific explanation are necessary: i.e., essentially a presumption that the specific explanation is correct. As argued in the proof of this mathematical representation of the explanation, if that were the case, no need for the unknown numerical labels exists.

 

Thus it is that the numerical labels "i" are defined by the specific explanation under analysis and the unknown "x" labels constitute the actual arguments of [math]\vec{\Psi}[/math].

Now, once we have discovered an explanation and thus know [math]\vec{\Psi}[/math] (that is, we know a method of estimating our expectations under that explanation) and we have established a set of numerical labels "x" to represent the associated elements being explained, the probability of a specific set [math](x_1,x_2,x_3,\cdots,x_i,\cdots)[/math] being the correct circumstance for time "t" is, by definition, given by

[math]

P(x_1,x_2,x_3,\cdots,x_i,\cdots,t)=\vec{\Psi}(x_1,x_2,x_3,\cdots,x_i,\cdots,t) \cdot\vec{\Psi}(x_1,x_2,x_3,\cdots,x_i,\cdots,t).

[/math]

 

However, the actual numerical labels, "x", used to represent those elements are entirely arbitrary as they are nothing more than numerical references to the specific elements being explained. That being the case, let us examine an interesting specific situation in detail.

 

Part 1: Setting up two identical solutions to a specific problem

 

Suppose we have two people who have solved a specific problem and come up with exactly the same explanation: i.e., they have both discovered exactly the same specific function [math]\vec{\Psi}(x_1,x_2,\cdots,x_n,t)[/math] which in fact yields exactly the expectations these two people assign to all of the known facts the explanation was designed to explain. (Of course, for the sake of argument, the known facts in this case are exactly the same.) Notice that I am assuming the number of “facts” is finite. We can worry about handling the “presumed facts” (which is the only way that number can become infinite) later.

 

Essentially, what they have is a function which is perfectly consistent with a finite number of specific observations, each observation being a specific circumstance, [math](x_1,x_2,\cdots,x_n,t)[/math], where we will presume the number of circumstances indexed by t is conceptually large but not infinite: i.e., there is considerable information backing up that explanation as, if there is not, the solution is quite trivial. I further require that this explanation be consistently correct throughout the entire accumulation of those circumstances: i.e., the same definition of that function yields the correct expectations for each circumstance as the index t increases. That is to say, up until the present (any present within their analysis), no new circumstance has ever violated the expectations yielded by that explanation. That assertion essentially defines a flaw-free explanation.

 

Now, the actual numerical labels represented by “x” are inherently arbitrary. As has been mentioned elsewhere, since they are totally unknown, if we want to talk about the referenced things themselves, we have no choice other than to use the terms defined in the specific explanation under examination.

 

The undefined underlying element (referred to by "x") needs a separate numerical label because it very definitely must be in alignment with every possible explanation. The problem is that there is no way that we can "know" every possible explanation so that, for convenience, if we wish to talk about what it is we are talking about, we only have one option: use the term referenced by the explanation currently being examined

: i.e., these would be the definitions referred to by the "i" index. In the case I am talking about here, we have two hypothetical people who have solved exactly the same problem so, since they will have exactly the same defined elements, we can certainly use the definitions indicated by the numerical labels “i” for the purpose of discussing the actual undefined elements represented by “x”. The only important issue here is that the two representations refer to exactly the same undefined elements. This has some profound consequences.

 

Suppose each of these two people create a list of undefined elements (determined by the specific defined elements referred to by the "i" index list I referred to in my Laying out ... post).

 

Also, since the explanation being represented must always define all these labels anyway, there is no real necessity to use any numerical labels beyond the normal counting set: [math]1,2,3,4,\cdots,i,\cdots[/math].

If both people use exactly the same procedure to list those undefined elements, they would most probably use exactly the same numerical labels for the “x” labels. In such a case, both representations would be exactly the same in every detail.

 

Part 2: Pointing out a specific ignorance embedded in this example

 

However, nowhere in our deduction did we ever require any specific numerical labels for the undefined elements; the only real requirement is that every member of these two sets of labels refer to exactly the element defined by the associated “i” label. So, let us examine the consequences of what is essentially shift symmetry. Suppose the two lists are absolutely identical except for the fact that each of the second persons list of numerical labels is exactly 3.55 greater than the corresponding numerical label used by the first person. This can have utterly no impact upon their calculations of the probability of any given circumstance: i.e., it must be true that

 

[math]

P(x_1,x_2,\cdots,x_n,t) = P(x_1+3.55,x_2+3.55,cdots,x_n+3.55,t)

[/math]

 

as these "x" numerical indices are no more than arbitrary labels.

 

Now the added factor being 3.55 is not the issue here as every x_i is no more than an identification label as to what x_i actually refers to; the added amount is totally immaterial so long as each and every specified "x_i" from the two cases are interpreted as labels referring to exactly the same underlying undefined elements. In fact we could add any arbitrary number [math]a[/math] to one set and [math]a+\Delta a[/math] to the other. In this case we would obtain the requirement that,

 

[math]

P(x_1+a,x_2+a,\cdots,x_n+a,t) = P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a +\Delta a,t)

[/math]

 

or

 

[math]

P(x_1+a+\Delta a,x_2+a+\Delta a,\cdots,x_n+a +\Delta a,t)-P(x_1+a,x_2+a,\cdots,x_n+a,t)=0.

[/math]

 

If at this point, we just define [math]z_i=x_i +a[/math], we can divide the above by [math]\Delta a[/math] and write exactly the same expression as,

 

[math]\frac{P(z_1+\Delta a,z_2+\Delta a,\cdots,z_n +\Delta a,t)-P(z_1,z_2,\cdots,z_n,t)}{\Delta a}=0.[/math]

 

Which cannot depend upon exactly what value we choose for [math]\Delta a[/math] and thus it becomes quite clear that, since the actual value of [math]\Delta a[/math] is of utterly no consequence, we can write:

 

[math]

\lim_{\Delta a \rightarrow 0}\frac{P(z_1+\Delta a,z_2+\Delta a,\cdots,z_n +\Delta a,t)-P(z_1,z_2,\cdots,z_n,t)}{\Delta a}=0

[/math]

 

which should be recognized by everyone to be the actual definition of the derivative of P with respect to [math]a[/math]: i.e.,

 

[math]

\frac{d}{da}P(z_1,z_2,\cdots ,z_n,t)=0

[/math].

 

must be an absolute requirement of all explanations put forward in the functional representation [math]\vec{\Psi}[/math].

 

Part 3: A major problem embedded in this conclusion

 

 

The deduced derivative can be multiplied by [math]da[/math] and integrated over [math]a[/math] yielding the result that P=k (where k is a constant). However, “[math]a[/math]” can be anything from minus to plus infinity, and it follows that the probability for a given specific “[math]a[/math]” summed over all possibilities must be exactly unity. Only one conclusion remains: the function “P” must equal zero. This shouldn't really bother anyone as the mathematics is treating the supposed arguments of P (and that would be the set [math]x_1, x_2 \cdots x_n[/math]) as constants. When we take into account the fact that P is actually a function of those n arguments, we get a somewhat different view of the situation.

 

Sure, P=0 for any and all possible values of those n arguments and the probability for any specific distribution is exactly zero but there is still a real constraint on the value of P as those arguments are changed. If one argument is changed, there are clearly constraints on how the others can be changed; however, that constraint certainly is not analyzable from this perspective: i.e., essentially we have failed to extract a mathematical representation of the required constraint.

 

The central problem here is that it isn't P we should be looking at anyway. We need to see how this constraint effects [math]\vec{\Psi}[/math], the actual mathematical representation of the explanation. That vector is in an abstract space and the probability density is to be given by the scalar product [math]\vec{\Psi}\cdot \vec{\Psi}[/math]. If we take the trouble to analyze this scalar product from the perspective that

 

[math]

\vec{\Psi}=\sum^{dim}_{k=1}\psi_k\hat{q}_k

[/math]

 

we have:

 

[math]

P=\sum^{dim}_{k=1}\psi^2_k=0.

[/math]

 

which, since the functions [math]\psi_k[/math] are to be real, also requires [math]\vec{\Psi}[/math] to vanish. Again, this is not really unreasonable as the same arguments used to defend the vanishing of P can justify the vanishing of [math]\vec{\Psi}[/math]; however, in this case there is a subtle mechanism for avoiding this shortcoming. That mechanism is embedded in the definition of the expression [math]\Psi^\dagger[/math].

 

The dagger is there to denote the conversion of each specific number in the “value” of [math]\vec{G}[/math] to a representation whose product with identical specific number in the output of the original function is a positive definite number. This extension in possibilities for the specific numbers in the “value” of [math]\vec{G}[/math] (for example those values can now be imaginary numbers and, in fact, many other more complex constructs) allows us the option of building into [math]\vec{G}(\vec{x})[/math] some important internal correlations which will be shown to be of extreme value later. For the moment it should be recognized that those same correlations can be expressed by multiple real numbers: i.e., I am not changing the definition of [math]\vec{G}(\vec{x})[/math], I am merely allowing some very interesting (and it turns out necessary) expressions of internal correlations.

When I introduced that dagger, I implied there were important internal correlations to be handled; this is the point where one of these important internal correlations arises.

 

Part 4: Extracting the required mathematical constraint

 

The central problem here is that the mathematical constraint we wish to extract from the representation is simply still totally embedded in that representation. There exists a rather simple route around that problem. P was expressed in terms that scalar product for the sole purpose of insuring the constraint that P was positive definite. However, since [math]\vec{\Psi}[/math] has been specified to be a representation of “any possible mathematical function”, doors have been subtly opened to other possibilities. There was no actual constraint that [math]\vec{\Psi}[/math] be limited to "real" values (other to impose a positive definite result for [math]\psi^2_k[/math]); in essence, it was only the product [math]\vec{\Psi}^\dagger \cdot \vec{\Psi}[/math] which was required to be positive definite.

 

The central question here is, for a given function [math]\vec{\Psi}[/math], does there exist a definable alteration of that function (the actual alteration to be represented by that [math]\dagger[/math] symbol) such that [math]\vec{\Psi}^\dagger \cdot \vec{\Psi}[/math] is guaranteed to be positive definite? If any such an alternation exists, the “dagger” symbol is to indicate that the required alteration has been performed. It should be clear that this opens up the possibilities by a wide margin. My interest is in generating a rational constraint on [math]\vec{\Psi}[/math] which essentially fulfills the original constraint on P without constraining the components of [math]\vec{\Psi}[/math] to be real. The solution of the difficulty is to show that any collection of real functions (the components [math]\psi_k[/math] mentioned above) can be represented as one half as many functions with complex values.

 

Mapping a collection of real numbers into half as many complex numbers

 

Consider a two dimensional abstract vector space. Multiplication can be defined which is totally analogous to what is ordinarily called multiplication of “complex numbers”. One axis can be taken to represent “real” numbers and the other can represent “imaginary” numbers. Any point in that two dimensional space can be seen as representing a complex number. If any two complex numbers are represented in polar coordinates, [math](r_1,\theta_1)[/math] and [math](r_2,\theta_2)[/math], their product can be represented by [math](r_1r_2,\theta_1+\theta_2)[/math]. The two representations (multiplication of two complex numbers and the above operation) uniformly give identical results. Thus it is that we can see [math]\psi_k[/math] as producing complex numbers in the form c+id (essentially collecting them by pairs). We can then define the dagger notation to change every c+id into c-id. In such a case, the product [math]\psi^\dagger_k \psi_k=(c-id)(c+id)=c^2+d^2[/math] which is once more positive definite.

Clearly, if the dimensionality of the abstract vector space is greater than two, that dimensionality may be reduced to half by collecting the components in pairs and converting all of the output to complex numbers. If the dimensionality happens to be odd, we can allow that stand alone component to be real. The usefulness of that odd term is exactly the same as the usefulness of that single real expression brought up earlier.

 

If someone can find a rational use for such term let them do so. I will simply ignore such a circumstance as not representing a useful explanation since I personally have not managed to define a mechanism for extracting the constraint necessary to conserve our ignorance: i.e., including such a term essentially implies we know something which we do not know.

 

Meanwhile, dealing with the complex output is relatively straight forward. Once again, we can use the arguments above to show that the derivative with respect to [math]a[/math] (that shift parameter introduced earlier) of every element of that scalar product must vanish: i.e., [math]\frac{d}{da}c^2=\frac{d}{da}d^2=0[/math] implies c and d must still be constants. However, now the lone terms have been combined as a complex number and the expression c+id can be represented by [math]Ae^{ika}[/math]: i.e., the correlations of interest I spoke of earlier have been extracted into the expression [math]e^{ika}[/math] (see common trigonometric relationships).

 

Of significance is the fact that [math]A=\sqrt{c^2+d^2}[/math] has absolutely no dependence on “[math]a[/math]” whatsoever as c and d are independent constants. What is important here is that the exponential term drops out in the multiplication (in the calculation of P). Thus it is that the fact that [math]\frac{d}{da}P=0[/math] (derived from the fact that P could not be a function of the parameter shift "a") no longer extends to [math]\vec{\Psi}[/math]. The entire consequence of any shift in "[math]a[/math]" resides in the the complex phase correlations expressed in the function [math]e^{ika}[/math].

 

The derivative of [math]\Psi[/math] with respect to “[math]a[/math]” turns out to somewhat different from what we had earlier. If the abstract space was originally two dimensional (in which case the abstract dimensionality of the complex [math]\vec{\Psi}[/math] is unity), we have now the expression

 

[math]\frac{d}{da}\Psi=ik \Psi[/math]

 

If the abstract dimensionality of this complex [math]\vec{\Psi}[/math] is greater than one, the partial with respect to the shift parameter yields an independent parameter k for each direction in that abstract dimensionality. The same analysis suggests that shift symmetry in the various dimensional components of [math]\vec{\Psi}[/math] can be handled as independent symmetries; however, the power and consequences of that possibility will be brought up later (under the coming post on "A Universal Representation of Rules") as it is a field all unto itself. For the moment, I will concern myself only with the actual form of the constraint required by shift symmetry in one dimension: i.e., [math]\Psi[/math] will be handled as a one dimensional complex function.

 

Part 5: The succinct expression of the constraint required by shift symmetry

 

There is but one quite simple step required to achieve the exact mathematical constraint required by shift symmetry. The required step is a well known relationship between derivatives and partial derivatives.

 

[math]

\frac{d}{dk}=\sum^n_{i=1}\frac{\partial x_i}{\partial k}\frac{\partial}{\partial x_i}

[/math]

 

In this case, we are particularly concerned with the shift parameter "[math]a[/math]" and the undefined numerical labels "[math]x_i[/math]" to which that shift is applied. The expression of interest is

 

[math]

\frac{d}{da}=\sum^n_{i=1}\frac{\partial z_i}{\partial a} \frac{\partial}{\partial z_i}

[/math]

 

where [math]z_i=x_i+a[/math] was introduced in the earlier proof that

 

[math]

\frac{d}{da}P(z_1,z_2,\cdots,z_n,t)=0.

[/math]

 

(Please note that the fact that I have called the arguments of P in one case "x" and in a second case "z" is of utterly no real significance.) Of supreme importance here is that the partial with respect to “[math]a[/math]” of "[math]z_i[/math]" is exactly unity: i.e., the impact of shift symmetry is exactly the same across all arguments. It is this unique combination which implies that we may write

 

[math]

\frac{d}{da}=\sum^n_{i=1} \frac{\partial}{\partial z_i}

[/math]

 

or

 

[math]

\frac{d}{da}\Psi(z_1,z_2,\cdots,z_n,t)=\sum^n_{i=1} \frac{\partial}{\partial z_i}\Psi(z_1,z_2,\cdots,z_n,t)=ik\Psi(z_1,z_2,\cdots,z_n,t)

[/math].

 

Returning to our original notation we can write

 

[math]

\sum^n_{i=1} \frac{\partial}{\partial x_i}\Psi(x_1,x_2,\cdots,x_n,t)=ik\Psi(x_1,x_2,\cdots,x_n,t)

[/math].

 

This is an exact expression of the dynamic constraint on the function [math]\Psi[/math] enforced by the requirement of shift symmetry in the "x" labels. Essentially, it is the basis of the underlying phenomena in dynamics commonly designated by the idea of conservation of momentum. If the mathematical operator [math]-i\frac{\partial}{\partial x_i}[/math] operating on the function [math]\Psi[/math] is defined to be “a momentum operator” (and please note that, except for the factor [math]\hbar[/math], this is exactly the “momentum operator” defined in classical quantum mechanics) then the constraint required by shift symmetry in any data collection is “conservation of momentum”.

 

Thus the concept of momentum is far broader than the dynamic concept defined in physics. This is a justification for the common use of the word momentum in the discussion of any change in any data. Economic changes can “have momentum” reaction to social changes can have momentum. The concept is seriously worth thinking about from an analytical perspective.

 

Likewise, the two people brought up above could use a different zero for the t index and they would still get exactly the same probabilities so long as the specific “t” index used by each of them referred to exactly the same circumstance the other was examining. This fact can be used to prove, in exactly the manner done above, that the following is also a required constraint on the functional representation of any valid flaw-free explanation.

 

There is a second constraint which may be immediately written down due to shift symmetry in the parameter t. Just as a shift in the labels [math]x_i[/math] can have no impact upon the expectations produced by [math]P(x_1,x_2,\cdots,x_n,t)[/math], "t" was also an abstract label of observed circumstances and thus cannot depend upon the actual label so long as the labels are for the same circumstances.

 

Thus it is that we know immediately that the correct [math]\Psi[/math] must also satisfy the constraint that

 

[math]

\frac{\partial}{\partial t}\Psi(x_1,x_2,\cdots,x_n,t)=iq\Psi(x_1,x_2,\cdots,x_n,t)

[/math].

 

I used "q" for the simple reason that any other letter seems to yield unwanted implications beyond the simple requirement of temporal shift symmetry.

 

Meanwhile, there is another issue I would like to bring up at this point. I know that almost everyone who reads this is going to jump to the conclusion that the collection of arguments represented by the specific circumstances [math](x_1,x_2,\cdots ,x_n)[/math] can be seen as a set of points on the x axis. That assumption is patently false as I will show in a following post which I will title "A Universal Representation of Rules".

 

 

In fact that set definitely cannot be seen as a set of points on the x axis. What I have shown has nothing to do with what these arguments represent. What I have actually shown here are some constraints on the function itself which are not constraints on the actual arguments.

 

Furthermore, the fact that the function which is to yield the probability for the expectation derived from a valid flaw-free explanation must be differentiable is a very important factor which has far reaching consequences.

 

Please give me any complaints you may have on this presentation.

 

Have fun -- Dick

[Qfwfq]

All men are equal. This means that we can't know which man is which.

 

Knowing that all men are equal means knowing that we can't know which man is which. Is this ignorance, or is it knowledge? :Guns:

[AnssiH]

Knowing that all men are equal

 

Recognizing a specific type of ignorance... (like symmetries to expectations)

 

means knowing that we can't know which man is which.

 

...and understanding the consequences, is exactly the basis of this analysis.

 

Is this ignorance, or is it knowledge? :Guns:

 

Maybe it can be called "understanding the consequences of ignorance". Or maybe people feel better with calling ignorance "symmetries". As long as people understand what is meant by this, it's all the same for me :doh:

 

Sorry I've been so quiet, I've been busy... I'll try to get around to contribute more next week...

 

-Anssi

[Rade]

post deleted

Edited December 3, 2010 by Rade

[Qfwfq]

Goodness, Anssi, what a relief! I was terrified I'd end up in jail for that! ;)

 

Recognizing a specific type of ignorance... (like symmetries to expectations)

Re-cognizing means re-knowing. In latinate languages the two verbs differ only by the prefix. I think there are some languages where the exact same verb is used in both acceptions. Therefore: Knowing a specific type of ignorance...

 

...and understanding the consequences, is exactly the basis of this analysis.

So, are these consequences of the knowledge of this ignorance?

 

Suppose we are not sure of being so ignorant. Can we draw the same conclusions? Can we be sure that these consequences hold? Suppose we are sure of the ignorance. Is this information, that Emmy translates into information?

 

Maybe it can be called "understanding the consequences of ignorance". Or maybe people feel better with calling ignorance "symmetries".

Some people feel better with calling the ignorance "independece".

[Rade]

post deleted

Edited December 3, 2010 by Rade

[AnssiH]

Goodness, Anssi, what a relief! I was terrified I'd end up in jail for that! :hihi:

 

Well, of course DD would much prefer getting into all those mathematical relationships as directly as possible, instead of endlessly getting stuck to unsolvable philosophical questions or word games... But it's hard to get there fast when you have to first make sure all the definitions are as unambiguous as possible... I am guessing the first thing he thought when reading your post was that it's not really relevant at all. All language is incredibly riddled with semantical issues like the one you pointed out. What would be relevant is trying to understand what DD is actually trying to communicate. I think I can help there because I already know what he is trying to say.

 

I skimmed through the OP, and I think I should read it through carefully too at some point to get completely up to speed with the exact terminology he has ended up with (there are so many ways to explain the same thing), but in the meantime, I think I can make meaningful comments anyway...

 

Knowing a specific type of ignorance...

...and understanding the consequences, is exactly the basis of this analysis.

 

So, are these consequences of the knowledge of this ignorance?

 

Is that "consequential knowledge" arising from that original "ignorance"?

 

Yes I would say so. Or alternatively I might say that that "consequential knowledge" is just another way to express that inherent "ignorance".

 

E.g. expecting a momentum conservation for some defined element is to say its expressed location does not affect its associated expectations (it is expected to obey momentum conservation everywhere in space), which is to say its "actual location" in space is not in any way part of whatever information underlies the definition of that element. Which is to say that whatever "locations" we (must) conceptually imagine to space, are just part of our comprehension of reality, while in actual fact identifying the locations of space itself is in no way measurable in any way.

 

That whole thing is to connect the conceptual idea of "space", conservation of momentum, and the problem of coming up with a world view & defined elements WITHOUT including ideas that are NOT explicitly given in the information that the world view is based on. (I.e. however you defined space is just another side of the coin of defining persistent elements)

 

Suppose we are not sure of being so ignorant. Can we draw the same conclusions?

 

It seems to me that the conclusions would be slightly different. Interesting, nevertheless. That being said, I can't see any way to suppose we "know" information that is not part of the problem to begin with, it's a bit like wondering whether we could figure out if two perfect spheres were in the same orientation after all... By definition, we don't "know" any information that is not given in the statement of the problem.

 

Can we be sure that these consequences hold?

 

If we are confident that the premise doesn't contain any hidden assumptions (which it may), then our confidence about the consequences would be exactly the same as our confidence towards the validity of the employed math.

 

I would also add that it would be very odd to have come up with modern physics via a logical error in the deductions... I mean, it would be a co-incident beyond belief all by itself...

 

On the other hand, I find the conclusions (related to modern physics) quite rational and in some ways expected even. There are some odd features to physics as long as we believe our defined elements are actually things carrying real ontological substance (with identity) from one place to another inside real ontological space (also with identities to its locations). There's no absolute reason to believe that a given persistent phenomena is made out of actually persistent things, is there? There's no way to actually verify that one entity at location "x" at t=1 is ontologically the same the entity in "y" at t=2, even if our world view is constructed like that. There may be some very good reasons behind it being constructed like that, having to do with predictability instead of ontological correctness...

 

If you can find the aspects of "ignorance" to logically lead to object definitions that obey modern physics (incl. relativity, quantum mechanics, electromagnetism etc), that means the apparently odd features of reality are also a side effect of our natural tendency to track the "recurring features" (or patterns) of reality via comprehending them in terms of such and such "apparently persistent entities". (Recurring behaviour gives you the opportunity of interpreting that phenomena as a persistent entity of some sort)

 

Suppose we are sure of the ignorance. Is this information, that Emmy translates into information?

 

I don't understand the question...

 

Rade, you are very much misunderstanding;

 

DD,

In your previous thread you placed a constraint on your definition of "explanation" to be limited to address "hypothetical circumstances". Thus, [math]\vec{\Psi}(\vec{x},t)[/math], by your definition, cannot address the infinite number of non-hypothetical circumstances that require "explanation".

 

Whatever you suppose "hypothetical" or "non-hypothetical" means is different from what DD meant to communicate.

 

Just take [math]\vec{\Psi}(\vec{x},t)[/math] as a probability function for some defined information. I.e. the required transformation from raw information to defined information is not specified. The differential constraints on [math]\vec{\Psi}(\vec{x},t)[/math] are placing some limits on that transformation, but there's no reason to directly trying to come up with what that transformation might be. The important bit is, that such transformation can exist; we all do it all the time.

 

I do not understand the concern raised here ? Why in the world would anyone ask for a mathematical solution to a physics problem and NOT specify where the origin MUST be ? Clearly, the value of x CANNOT be shifted to any value desired (that is, your shift symmetry argument does not apply) IF the origin IS specified. Sounds to me like you set up a strawman (your IF condition) then provide a solution to a problem that does not exist in reality. If I am incorrect, please someone provide a specific example from physics where the solution to a problem allows one to shift the position of the origin, exactly in the way discussed above by DoctorDick.

 

He doesn't mean the numerical values wouldn't change. He means the expectations, i.e. how defined things are expected to interact, do not change. As in, if you are plotting the orbit of a planet around a star, that orbit will be expected to look exactly the same shape no matter "where" in your idea of space you place those two bodies.

 

That is another way to say, that two star systems that look exactly the same, will be expected to behave in exactly the same way no matter where in space you find them.

 

Notice how the origin is not specified in the "original problem" (of having to come up with a working world view based on unknown information). And notice how convenient it is, if one manages to come up with a world view where the defined objects behave in such a predictable way? Don't you think there are some pretty good survival reasons for being able to build that sort of world view, even though there's no explicit knowledge about the real ontological identities of any (supposedly) persistent things around us. Apparent persistence means predictability, means survival. No?

 

So whatever definitions are built, they are better not based on any "information" that is actually an assumption, and thus cannot be known at all at any time... :I (Not that I'm suggesting world view is something we build consciously, for the most part we don't of course)

 

I hope this helps one way or another. And yes this feels much like idle philosophical talk compared to the actual logical analysis.

 

-Anssi

[Rade]

...Rade, you are very much misunderstanding...

Thank you AnssiH for the reply. Yes, I do have a problem with DD's limit that he placed on explanation--that explanation is limited to "hypothetical circumstances". Recall that he used the term, I only asked for an explanation why.

 

If I understand what you are saying, it is that [math]\vec{\Psi}(\vec{x},t)[/math] places constraints on hypothetical explanation of a "hypothetical" transformation of raw information---> defined information. OK, fair enough. But what I do not understand is why DD holds the worldview that "there is no reason to be trying to come up with what that transformation might be". ?

 

Why is there no reason, why must explanation be limited to the hypothetical circumstance of raw --->defined information ? Until DD can show exactly what the transformation is, his approach can not claim to have complete understanding of explanation. In my worldview, at least some understanding is required for transformation from raw ---> defined information for each circumstance under consideration to say one has valid understanding of the explanation. What am I missing here ?

 

He doesn't mean the numerical values wouldn't change. He means the expectations, i.e. how defined things are expected to interact, do not change. As in, if you are plotting the orbit of a planet around a star, that orbit will be expected to look exactly the same shape no matter "where" in your idea of space you place those two bodies.

And thanks for this reply. However, if true, then I would suggest that DD holds a false assumption if he claims that how "defined things" are expected to interact does not change from one place to another. So, using your example, the orbit would not be expected to look exactly the same shape no matter where in "space" you place the two bodies. The reason being that spacetime is curved and no two areas of curved spacetime would be the same given the presence of other bodies that would influence the curvature from one "place" to another. Also, would you expect an electron and proton to interact in exactly the same way no matter where you place the two in space, say one place where they are in contact with another such system, and another place where they are not ? Are not your expectations of how the defined things are expected to interact completely different for the two circumstances ?

[Rade]

So whatever definitions are built, they are better not based on any "information" that is actually an assumption, and thus cannot be known at all at any time... :I (Not that I'm suggesting world view is something we build consciously, for the most part we don't of course)

AnissH, I have no idea at all what you are claiming here. Are you saying the definitions that the human mind places on concepts cannot be "known at all at any time", or are you saying the raw information cannot be known, or are you saying something else ? And, how exactly do you suggest that any "worldview" is "built" from anything other than the conscious aspects of the mind ? The un-conscious does not go about "building" reality, it goes about "perceiving" reality, and it is the consciousness that "builds" a worldview by the transformation of raw information ---> to defined information via the process of concept formation. How can we be so far apart in thinking about something so basic as the relationship between perception and conception, assumption and knowledge ?

[Qfwfq]

All language is incredibly riddled with semantical issues like the one you pointed out.

Actually, I wasn't so much pointing out a semantic issue, the "word games" were only trying to illustrate the concept. It seems to me you did not catch my nexus.

 

Is that "consequential knowledge" arising from that original "ignorance"?

I would say no, it isn't.

 

You seem to be discussing the individual trees without seeing the forest I pointed to. What was that old Chinese proverb about the wise man pointing at the sky? ;) I've been saying that, in order to draw a conclusion (conservation law) as a consequence of a fact (ingorance, as Dick calls it) one must know the fact to be true. Otherwise one has the logical argument proving "If A then B." but can't apply modus ponens and assert that B is true. In essence, I was saying that the information "G is conserved." comes from the information "We don't know D." (or "This stuff doesn't depend on D." as some folks might put it).

 

If we aren't certain of the "ignorance" then How can Emmy tell us to be certain of the conservation law? As you can see, I wasn't making unwarranted assumptions; I was doing even somewhat the opposite. Apart from word games, I do think that "doesn't depend on" is more befitting than "ignorance".

 

There are some odd features to physics as long as we believe our defined elements are actually things carrying real ontological substance (with identity) from one place to another inside real ontological space (also with identities to its locations). There's no absolute reason to believe that a given persistent phenomena is made out of actually persistent things, is there? There's no way to actually verify that one entity at location "x" at t=1 is ontologically the same the entity in "y" at t=2, even if our world view is constructed like that. There may be some very good reasons behind it being constructed like that, having to do with predictability instead of ontological correctness...

 

If you can find the aspects of "ignorance" to logically lead to object definitions that obey modern physics (incl. relativity, quantum mechanics, electromagnetism etc), that means the apparently odd features of reality are also a side effect of our natural tendency to track the "recurring features" (or patterns) of reality via comprehending them in terms of such and such "apparently persistent entities". (Recurring behaviour gives you the opportunity of interpreting that phenomena as a persistent entity of some sort)

Actually, there is much in these considerations that I agree with and I find these things very interesting, although I might put some things in quite different terms. :) However, some of the odd features are not so easily reduced to assumptions of this kind. Actually, my studies of physics lead me to refrain from too many assumptions, including the corpuscular view ultimately being the ontological substance.

[Rade]

(Recurring behaviour gives you the opportunity of interpreting that phenomena as a persistent entity of some sort)

Well, no, you have it completely backward, imo. The correct statement would be (Recurring entity gives you the opportunity of interpreting that phenomena as a persistent behavior).

 

Consider the entity we define as the sun, and the daily crossing of the earth horizon by that "entity" for any given observer at a specific location on the earth. When, day after day you observe that the defined entity crosses the horizon in ~ same time interval (24 hrs), the continuous ontological becoming of the entity, completely independent of any human mind, gives you the opportunity of interpreting the phenomena as a persistent behavior that is a fundamental attribute of the persistent ontological entity.

 

The issue here is really very simple. Each human mind has to make an axiomatic choice when they decide to follow (accept as most valid) any philosophy. Either they grant as axiomatic the Primacy of Consciousness (entity from behavior), or the Primary of Existence (behavior from entity).

[AnssiH]

I've been saying that, in order to draw a conclusion (conservation law) as a consequence of a fact (ingorance, as Dick calls it) one must know the fact to be true.

 

Yes.

 

Otherwise one has the logical argument proving "If A then B." but can't apply modus ponens and assert that B is true.

 

Yes.

 

In essence, I was saying that the information "G is conserved." comes from the information "We don't know D." (or "This stuff doesn't depend on D." as some folks might put it).

 

Yup.

 

If we aren't certain of the "ignorance"...

 

But, we are certain that those specific ignorances exist; we are certain they exist in terms of the definitions that were given, as long as we are certain that we don't explicitly know the meaning of the information-to-be explained. I.e. at this junction, we are merely certain about our uncertainty towards the real meaning of the information.

 

I think you must be thinking something subtly different than I am right now, so let's see if we can find where we stray because I'm not at all sure...

 

First, it is certainly critical to the validity of this analysis that we are talking about aspects that are indeed universal to all valid explanations. If there are hidden assumptions there it would be meaningful to identify them properly. That, we probably agree about.

 

Consider, that the existence of "shift symmetry" in the universal notation (keep its definitions in mind), is not dependent on what the information-to-be-explained was. Because that symmetry, as its stated, arises as a feature of the universal notation itself. Consider, that the original meaning of the information is unknown at the get go, and after there is an explanation for it - i.e. after it has been transformed into a form of "a set of persistent objects" - and those defined objects have been mapped into a coordinate system following the definitions of the universal notation, then their associated expectations cannot be a function of their placement inside the coordinate system; it's a coordinate system that we just made up!

 

One way to look at it is that a coordinate system is necessary because it gives means to determine/represent the interaction between defined entities (their placement in terms of each others). But the exact placement of the entire system that is under consideration, is immaterial side-product of the representation form, and thus the expectations cannot depend on it.

 

It is certainly a critical point to consider, to really understand what exactly is meant by the ignorance, and why on earth it is something whose existence in an explanation is considered to be absolutely certain. You can look at it as a side-effect of making up a coordinate system for defined entities, while the fundamental structure of reality behind the ideas of those defined entities was not known.

 

I'd expect you to perhaps be wondering now, why would we consider shift symmetry then to be a universal aspect of all valid explanations when on the other hand I'm saying it's actually an aspect of the universal notation. If you think about it, it can certainly be seen as something that exists in any explanation that contains any defined persistent objects, i.e. if there is any way at all to state "such and such objects exist at this moment", there is a way to represent that statement as points in a coordinate system. I think it's safe to say that ALL explanations contain some element definitions (otherwise it's not an explanation), and thus we can say that one way or another, that shift symmetry and its impacts are to be found in there.

 

Let me know what your thoughts are at this point, I don't want to talk a lot and then realize our terminologies are not meeting yet at all :hihi:

 

I do think that "doesn't depend on" is more befitting than "ignorance".

 

That sounds okay to me.

 

Actually, there is much in these considerations that I agree with

 

I was expecting so, I think I do have at least some idea about what you think about these issues, and I would like to make some comments that I'd expect you to prettu much agree with, at least if I manage to explain what I have in mind... But one step at a time.

 

and I find these things very interesting, although I might put some things in quite different terms. However, some of the odd features are not so easily reduced to assumptions of this kind. Actually, my studies of physics lead me to refrain from too many assumptions, including the corpuscular view ultimately being the ontological substance.

 

Yes, I had that impression, and just in case you are wondering, DD's analysis doesn't imply a corpuscular view of any sort as the ontological substance either. Just that such view can always be formed to represent any unknown information. The fact that it can always be done means that it's not so much a representation of the meaning of the information, as it is a convenient way to represent the expectations that ultimately arose from becoming familiar with some recurring activities (instead of expectations arising from knowing/guessing the "real" meaning of the information in some sense). I would think you find that quite rational as well. (When he said quantum view is "more fundamental", he meant it is in his opinion more direct representation of the information we actually do know, i.e. contains less assumptions than a continuous representation)

 

I will have comments to make about the actual differences between "traditional" attempts to explain collapse of the wave function as something we just do in our mind (not really satisfactory IMO), and what DD is suggesting (somewhat different issue as it's not really a suggestion about what reality is like, but just an explanation about why the recurring patterns of something unknown can certainly be seen that way regardless of what that unknown really is)

 

-Anssi

Edited August 11, 2010 by AnssiH
Small clarification

[AnssiH]

Rade, I believe you are posting too quickly without thinking things enough; I'm pretty sure you could figure out many of the answers yourself. I think there are people reading this who could quickly point out some fairly obvious problems in your complaints; at least I'm sure Qfwfq could.

 

So, I'm just saying it doesn't make sense to me to spend the time in trying to write clear responses when I feel you could have thought it a bit more yourself first, sorry :I

 

That being said, IF I suddenly find a lot of free time in my hands at some point, I might try to come up with a clear response to your questions (at least to the more relevant ones), but until then, I just think my time is better spent walking through the algebra, and focusing onto responding to Qfwfq's concerns. I hope you understand.

 

And now it's almost bed time! Good night!

 

-Anssi

[Qfwfq]

But, we are certain that those specific ignorances exist; we are certain they exist in terms of the definitions that were given, as long as we are certain that we don't explicitly know the meaning of the information-to-be explained. I.e. at this junction, we are merely certain about our uncertainty towards the real meaning of the information.

Oh gosh, I'm needing a good puff on the bong here. :D

 

...then their associated expectations cannot be a function of their placement inside the coordinate system; it's a coordinate system that we just made up!

This is what is (especially in QM) called physical symmetry but isn't always dynamic symmetry. Oddly enough, Nöther's theorem concerns the latter, in which case the statement does constitute information. This is one of the misgivings I have about Dick's discussions.

 

Just that such view can always be formed to represent any unknown information.

The necessity of quantum formalism in physics is due to the fact that a purely corpuscular view doesn't wash, any more than a purely optical one.

 

The fact that it can always be done means that it's not so much a representation of the meaning of the information, as it is a convenient way to represent the expectations that ultimately arose from becoming familiar with some recurring activities (instead of expectations arising from knowing/guessing the "real" meaning of the information in some sense).

Induction vs. conjecturing/constructing a model. Research typically does the latter, but somewhat on the basis of the former.

 

(When he said quantum view is "more fundamental", he meant it is in his opinion more direct representation of the information we actually do know, i.e. contains less assumptions than a continuous representation)

:confused: I'm unable to connect this with something specific in his post and I would need to know in what sense he means it.

 

"traditional" attempts to explain collapse of the wave function as something we just do in our mind (not really satisfactory IMO

Surely you're not referring to the "concious observer" in this day and age? Yes, it is very "traditional", if this word is taken to mean old-fashioned. The buzzword of today is decoherence.

[AnssiH]

Still wanted to mention one more thing about the shift symmetry issue, that I think you should find quite rational.

 

Notice, that the existence of shift symmetry in terms of the [imath]x,y,z,\tau[/imath] notation does not mean that all valid explanations must contain a shift symmetrical space definition per se. Obviously it is entirely possible that a valid explanation defines its "space" in ways that shift symmetry does not apply in terms of its coordinate system.

 

But if it indeed is a valid explanation (see DD's definition of valid), and it has generated definitions referring to information that was previously entirely undefined, it means there exists a 1:1 translation from its definitions to DD's universal notation, and in that form, the explanation must be shift symmetrical. If it is not, it means there exists an undefendable assumption of some sort, connecting the expectations to entirely imagined aspect of a representation of reality*.

 

That is what DD means when he keeps saying that a translation between any valid view and his notation must exist, and I think his assertions about what "must be true" for all valid explanations can be confusing if the reader doesn't understand that the notation is inherent part of his communication.

 

That there exists a 1:1 mapping between any valid explanation and his notation means that the shift symmetry is embedded one way or another into the definitions of that valid explanation, and the logical consequences of that shift symmetry also can be seen as embedded somewhere in there, in one form or another.

 

But, we are certain that those specific ignorances exist; we are certain they exist in terms of the definitions that were given, as long as we are certain that we don't explicitly know the meaning of the information-to-be explained. I.e. at this junction, we are merely certain about our uncertainty towards the real meaning of the information.

Oh gosh, I'm needing a good puff on the bong here. :D

 

I know what you mean and I definitely wouldn't want to sound that cheeky, I just had to say it because the shift symmetry really does arise from NOT making certain extraneous assumptions about the meaning of the information. We can't really say that "being uncertain about everything" also means we must be uncertain about uncertainty... that's the word games I was referring to, and believe me, I've discussed with many people who really want to go there, and it's very tiring :P

 

I realize you did not mean it like that.

 

This is what is (especially in QM) called physical symmetry but isn't always dynamic symmetry. Oddly enough, Nöther's theorem concerns the latter, in which case the statement does constitute information. This is one of the misgivings I have about Dick's discussions.

 

I'm sorry but I don't understand this comment :(

 

The necessity of quantum formalism in physics is due to the fact that a purely corpuscular view doesn't wash, any more than a purely optical one.

 

Yes, it doesn't wash, as long as one is trying to explain what reality is made of in ontological sense, because that means you are trying to assign "real" identities to something, either to some substance or to some entities. The game is little bit different for a person who is not trying to answer that exact same question, but is instead interested of understanding why is it valid to take some information, and represent it in terms of the definitions given by physics. Something can of course be a valid representation, without actually determining the real ontological identities or structures of something.

 

In that sense, DD's work is not really satisfactory at all to anyone who wishes to really know what reality is ontologically like. I think those persons are in deep trouble already at the point they realize how many things they consider to be "facts" must always be expressed and understood in terms of definitions which contains arbitrary choices.

 

Induction vs. conjecturing/constructing a model. Research typically does the latter, but somewhat on the basis of the former.

 

Yeah, I think that's a fair assessment, that is indeed what is called research.

 

And as long as the information that a model is fundamentally based on, was something whose meaning was not explicitly known, it means all supposed facts must ultimately connect to inductive reasoning of some sort. Research is work conducted/understood in the terminology of definitions that arose from inductive reasoning.

 

:confused: I'm unable to connect this with something specific in his post and I would need to know in what sense he means it.

 

It was just something he said long time ago, that I thought you might have been referring to. Doesn't matter really, apart from pointing out that you should never assume he is making an assertion about anything being fundamental to reality, he is always talking about epistemological issues.

 

Surely you're not referring to the "concious observer" in this day and age? Yes, it is very "traditional", if this word is taken to mean old-fashioned. The buzzword of today is decoherence.

 

Heh, no, that's not what I was getting at, I was just saying I would like to discuss the differences between DD's analysis, and pretty much all the other previous attempts to take the collapse of the wave function (or whatever one wants to call that issue) as simply resulting from a cumulation of "more facts" about a situation. I was saying that because I remember you once commented, quite rightly so, something to the effect that it is quite problematic to explain away the quantum strangeness by taking it as a purely epistemological effect. It is problematic as long as one supposes there is ontological correctness to the identities of their defined entities. As long as you do that, your defined entities will keep doing funky things one way or another, no matter how you try to make the pieces fit... (At least, it appears so to me, of course I have not exhaustively investigated all the possible ways to define reality :D )

 

In short, a "traditional attempt" here refers to any attempt that tries to explain what sorts of entities/structures reality is REALLY made of, instead of focusing onto why information can be represented in such and such ways (and why such and such symmetries to that representation can lead to such and such apparently conflicting features to the definitions).

 

-Anssi

 

* I think it is entirely possible to argue at that point that perhaps some explanations can contain a very fortunate undefendable assumption, that just so happens to lead to correct predictions. I think it is somewhat besides the point though; it should interest people that those assumptions are NOT NEEDED to get to the validity of modern physics.

[Doctordick]

Hi Anssi, I thought a little positive feedback might be reasonable here. I am afraid Qfwfq is playing exactly the same game as is Rade. Both of them want to discuss everything in terms of their (presumed valid) world view. They simply cannot comprehend laying that solution aside as a presumption in itself. They can no more step outside their beliefs than a “religionist” of the dark ages could conceive of laying aside the presumed existence of God as a starting point of an argument. You would be an absolute master of everything I have put forth if only you had the training in physics and mathematics sufficient to comprehend all the mechanisms of the arguments; however, if you had that training, I suspect you would also possess their unwavering belief in the validity of their perspectives. It's part and parcel of the standard indoctrination perpetrated by the field. Read the OP of that sanctus thread I brought up.

It seems to me that all physics is only descriptive and in addition there is no explication which doesn't start from assumptions.

Qfwfq has already commented that, being trained as a physicist, he refrains from making too many presumptions. (To quote him exactly, he says, “Actually, my studies of physics lead me to refrain from too many assumptions”). That statement in itself is very telling. He is firmly convinced that he must make that minimum set of presumptions and won't let you take that away from him. He simply cannot conceive of simply viewing his world view as a possibly undefendable construct and he isn't about to do so. It's that bagage issue I complained about years ago.

You seem to be discussing the individual trees without seeing the forest I pointed to.

Qfwfq cannot, and never will be able to see that “forest” as a figment of his imagination. It's real and he knows it. He is as confident of that “fact” as Rade is that his view is built upon facts.

I've been saying that, in order to draw a conclusion (conservation law) as a consequence of a fact (ingorance, as Dick calls it) one must know the fact to be true.

Notice how he deftly slides away from quoting what I actually said, “information which is not available can not be produced by any algebraic procedure”. So what is he saying? He does not know that fact to be a basic axiom of mathematics? Or perhaps he dislikes my use of the word “ignorance” to portray the absence of the specific information. At any rate, he certainly is not going to presume any ignorances on his part. :lol: :lol:

 

It is a waste of time to argue with such fixed minds. As you are well aware, I make a very simple step which you alone seem to find quite understandable; a step which appears to be simply beyond their comprehension. You have alluded to it but I think it can be put somewhat more simply.

 

I assert that the goal of science is to find an explanation of something: a totally abstract issue where I go out of my way to never define what it is that is being explained. I then presume the problem has been solved: i.e., a solution has been found to this undefined cunundrum. (After all, science has seemingly discovered explanations of all kinds of things.) Once again I go out of my way to never define what the solution is. All I require is that the solution yields “expectations”. I simply define anything which provides expectations to be an explanation.

 

As I see things, that is a pretty universal perspective but they insist that their “explanations” are not included without ever pointing out why they “hold this truth to be self-evident”.

 

Finally, totally ignoring both the problem and the solution, I design an abstract mathematical representation of that solution holding firmly to the requirement that utterly no presumptions be made as to what the problem or the solution is. That is the crux of the entire argument. And all they want to know is, “what is the problem” and “what is the solution” and how do they apply it to some compartmentalized problem they have in mind. They want to see it from the perspective of their personal world view.

 

Essentially, what they are searching for are the boundaries of the compartment they think I am working in! They want to comprehend that "compartment" so they can constrain their thoughts to the proper "box" and discover my presumptions.

 

So long as they refuse to work with my definitions, the whole thing is a complete lost cause from the word go!

 

However, I will admit that your arguments with them are enlightening all on their own. From your responses I can can see the issues getting clearer and clearer in your mind.

But, we are certain that those specific ignorances exist; we are certain they exist in terms of the definitions that were given, as long as we are certain that we don't explicitly know the meaning of the information-to-be explained. I.e. at this junction, we are merely certain about our uncertainty towards the real meaning of the information.

Beautiful, we certainly don't know these things if we intentionally never define the problem. I find it rather astonishing that Qfwfq is driven to “puff on his bong” by such a simple statement. Perhaps he thinks that act is the only way to extricate his mind from his religious belief in the truth of his world view. :lol:

If there are hidden assumptions there it would be meaningful to identify them properly.

You certainly have that right. I would love for someone to point out “hidden assumptions” in my work. At one time, I had hoped that Qfwfq would provide such a feedback but he has throughly let me down. It was his complaints about my assertion that

[math]\sum^n_{i=1} \frac{\partial}{\partial x_i}\Psi(x_1,x_2,\cdots,x_n,t)=ik\Psi(x_1,x_2,\cdots,x_n,t)[/math].

 

which led to the form of my presentation in this OP. I personally think that was a great improvement in my argument and thus made his criticism well worth the trouble; however, I no longer believe he really understood why his complaint was valid in the first place.

Induction vs. conjecturing/constructing a model. Research typically does the latter, but somewhat on the basis of the former.

And once again we find Qfwfq worrying about how solutions are arrived at. Something totally beside the point of this whole discussion.

That is what DD means when he keeps saying that a translation between any valid view and his notation must exist, and I think his assertions about what "must be true" for all valid explanations can be confusing if the reader doesn't understand that the notation is inherent part of his communication.

I would rather say that “my definitions” are an inherent part of my communications and very few people have any interest in considering those definitions. They already know what their definitions mean and are fully confidant no unwarrented presumptions have been made. Thus they really don't care to worry about what I mean.

This is what is (especially in QM) called physical symmetry but isn't always dynamic symmetry. Oddly enough, Nöther's theorem concerns the latter, in which case the statement does constitute information. This is one of the misgivings I have about Dick's discussions.

I'm sorry but I don't understand this comment :(

I have a suspicion that this is little more than a reflection of Qfwfq's refusal to work with my definition of time. He's a trained physicist and he is throughly confident that his presumptions concerning that issue are absolutely essential! :lol:

 

Anssi, he simply has no comprehension of what we are talking about. He likes to think of himself as “thinking outside the box” but he certainly isn't going to let go of the box. It's where he lives.

I think it is somewhat besides the point though; it should interest people that those assumptions are NOT NEEDED to get to the validity of modern physics.

One would think so wouldn't one. I think the real problem is that human beings feel a strong need to know the answers to their questions. The need is so strong that having an answer actually becomes more important to them than the validity of the answer. They think I am the devil trying to bringing doubt and skepticism to the beliefs they hold sacred. ;)

 

Have fun -- Dick

[Rade]

I disagree that the goal of science is to find an explanation of something and that something does not have to be defined, that something can be anything and yet be a "thing" that is of interest to science. For me the goal of science is not to explain the set of all possible "somethings", to me the goal of science is to explain a very specific singular "something" called THE MATERIAL UNIVERSE. Logically, it must be possible for there to be a set of other "somethings" that are outside the material universe. In your philosophy DD, it is the goal of science to find explanation for this set of somethings outside the material universe--I do not agree.

 

I assert that the goal of science is to find an explanation of something

So, it is your goal for science to find explanation for God (clearly an undefined something) ? Edited August 15, 2010 by Rade