Can Everything be Reduced to Pure Physics?

[Daminc]

which is quite interesting. That is, if one is interested in thinking.

I'm sorry, but this highlights why I'm not interested in what you have to write. You imply that if I don't find it interesting then I don't think

I think all the time. Sometimes it becomes bad for my health because I cannot turn my mind of even though my body is crying out for sleep. You have to be one of the most self-centered, egocentric individuals I have come across on the Web.

If your intention was to be listened to then the smart thing to do would be not to alienate your target audience which is something you obviously haven't figured out yet.

I'll read your stuff when you learn a bit of modesty

 

[saviourmachine]

Labels

The real problem here is that the moment you begin to put meaningfull labels on these elements, you are proposing a solution (i.e., you know what you are talking about) and not examing the problem (trying to understand what you are talking about). Read my post to Les on the "Are Qualia Real" thread.

Yes, I understand. A message can be a composition/mixture of e.g. {3, red} or {2309.23 €, "bkkkpoi", banana-taste}. To label the elements '3' and 'red' is unwanted and unjustified 'labelism'.

The nature of a 'message'

I don't think you understand why I am talking about sets. Given any problem concievable, C constitutes the information available to you to solve the problem.

Does a message / obervation embed it's whole context {time, place, etcetera}? However, I think your representation is still that abstract that it can account for problem solving in general. I was confused because I'm thinking of neural nets, in which e.g. the order in which messages are received can be important. The elements of the message are unordered, but the messages itself are ordered, are they?

Question: 1 missing label

"suppose, for the fun of it, someone gave you the labels of all the elements but one from some B and asked you what element could be added to make that list a valid example of one of the sets you were given."
...
we are talking about answering questions about the C which is available to you.

That is very simple indeed. I was confused by your use of the word list. That denotes one message in this case.

Look for all B in C, compare every B_j with the B_asked and if there is only one that does match, than it's the one.

B_asked = {red}

B₀ = {5, 2}
B₁ = {red, 2}
B₂ = {apple, red}
B₃ = {apple, 5}
B₄ = {red, 2}

Here it is nr. 1, nr. 2 and nr. 4.

Simple procedure

There is a very simple proceedure which will create a set of lists from the lists you have prepared where this second list will answer the above question. 1. First, take each list you had to start with and, for any two lists which are identical. 2. Add a label which does not exist on any list (since we are using numerical labels and the number of elements already labeled is finite, there exist a plentyful quantity of unused labels). 3. Now, for each of these altered lists, make every list possible which is identical to that list except for the absense of one element. 4. Now repeat the first step above, eliminating any duplicate lists created in step two. 5. Finally, replace the labels which were removed in step two.

Odd way. It's amazing how you can obscure a very simple procedure. Can you write some programming code please? "5 ... removed in step two?"
It's just providing every entree in the table with an unique keyword / identifier isn't it?

Removing element

The result has a very curious property. That is the fact that no matter what list you choose of the finished collection, you can remove any element and there will be no list in the remainder of the lists which have the same set of numbers you are looking at. This property is achieved no matter what the original label assignment was.

Of course. Even removing the identifier does not lead to another entree (with - still - its own identifier).

The messages are coded

Given this new set of lists, if someone gives you the labels of all the elements but one, there is only one possible missing element so the question asked above may be answered.

Of course, if the messages are coded (and received) that way.

Valid lists

Mathematically this can be written:

$$x_n=f(x_1,x_2, \cdots, x_{n-1})$$​

If that is true, then it implies there exists a function F, defined by

$$F(x_1, x_2 , \cdots, x_n)=f(x_1,x_2, \cdots, x_{n-1})-x_n$$​

where the rule which tells you whether a particular list is valid is given by F=0, a very simple rule.

Okay, assigning x_i numeric value.

Universe

I can construct a very simple universe based on that simple rule F=0 which is quite interesting. That is, if one is interested in thinking.

I'm curious.

 

[Doctordick]

Hi "saviormachine", it's nice to hear from you.

Yes, I understand. A message can be a composition/mixture of e.g. {3, red} or {2309.23 €, "bkkkpoi", banana-taste}. To label the elements '3' and 'red' is unwanted and unjustified 'labelism'.

I am not entirely sure what you have in mind when you use the phrase "unjustified 'labelism'". I suspect you are commenting about my statement, "At the moment, in order to avoid making presumptions, I must assure that, whenever I make an assertion about C, that the assertion must be true no matter what labeling procedure was used." I don't know that I would use the word "unjustified"; what I want you to be aware of is the fact that the very act of labeling introduces a constraint on the interpretations which are possible. The act is essentially the creation of a language and the language itself implies constraints. Constraints are essentially the elimination of possibilities and I have no desire to do that. At the same time, in the final analysis, a real solution requires that we find a set of labels consistent with the information embedded in those "messages", "experiences", "tokens of change" or whatever one wants to call them. For the moment they are no more than the members of the sets B_j which make up C (that which we wish to understand).

However, I think your representation is still that abstract that it can account for problem solving in general.

That is exactly my contention. If you notice any reason at all that my presentation is not totally general, please point it out to me as, if such a difficulty exists, it constitutes a serious flaw in my work.

I was confused because I'm thinking of neural nets, in which e.g. the order in which messages are received can be important. The elements of the message are unordered, but the messages itself are ordered, are they?

Not really; and that is another serious issue with far reaching consequences. The sets B were created to make it possible to represent change in the set C and were created for that reason only. The concept of time is seriously embedded in our understanding of anything (particularly in our understanding of anything involving change). In my general representation the fact that B represents a change in C can not be taken to imply there is any order in that change. C constitutes all the information you have to work with. In a general problem you cannot assume you and another were given the information in the same order even if, at the moment you compare your solutions, you have exactly the same C available to you.

What I am getting at here is that the "j" label attached to that B_j is just another label attached by you. There are some subtle consequences of that fact that won't be evident for quite a while so let's lay the issue of order aside for the moment as any individual certainly has a specific order in mind: the order with which he became aware of the new information. That order is certainly important to him and can have a serious impact on his expectations.

Look for all B in C, compare every B_j with the B_asked and if there is only one that does match, than it's the one.

Exactly correct and your example is excellent except for two issues. First, I specified we were going to use numerical labels and you have decided to use "red" and "apple". That is not a serious issue at all as we are only talking about arbitrary labels but it might somewhat confuse the issue of "mathematical functions of those labels". I am presuming you are sufficiently intelligent as to understand that there is no real problem here. Some people might find the concept of something being a functions of words too abstract to comprehend.

The other issue is a little more serious. It has to do with determining the equality of sets B. In your example, you assume the asked set {red} is equal to the observed sets {red, 2}, {apple, red} and {red, 2} ( j = 1, 2, and 4). Under my definitions (as I intended them), you never received the set {red} (that would be "red" in the absence of any other elements). Also, as order is of no significance, your example might be better if you either included {2, red} or explicitly stated that order in your defined sets was not significant (a small issue but it might be confusing to some; the central issue is to avoid any misinterpretation of the instructions). Both these issues are quite trivial and I strongly suspect you have an excellent grasp of what I am talking about.

It's amazing how you can obscure a very simple procedure. :blush: Can you write some programming code please? "5 ... removed in step two?"

Sorry about that, in my head the steps you list as 1. and 2. were a single step. That makes your step 3. correspond to my step two (the step where elements were removed which created the possibility of duplicate lists). I apologize sincerely for not expressing the steps clearly. From your further comments I get the impression you understood what I was describing. Thank you for your indulgence.

It's just providing every entry in the table with an unique keyword / identifier isn't it?

That is exactly what it is. The only important issue is that these "invented" elements need to be seen as utterly no different from any other element in B when it comes to solving our problem. They essentially stand as "hypothetical" elements; if we find a usable solution, then we can certainly hold that these "invented" elements need to be there (at least with regard to that solution we found). That is the reason I described it the way I did: that is, I didn't want to use the words "keyword" or "identifier" as that implies a specific status to the entry. I want you to simply regard it as an imagined entry. (What I have called "unknowable data" elsewhere.) The fundamental issue is that there must be no way of differentiating between these imagined entries and the entries derived from "A". Once you include them, they are presumed elements of the B_j in any of your analysis. (Again, any assertion I make about C must be true for any possible "keyword", "identifier" or "unknowable" whatever you want to call this entry.)

I am very sorry that I obscured a very simple procedure. I could write some programming code but it would be pretty worthless as, although the number of elements to be included in any reasonable problem are finite, their number can be expected to be astronomical and there are other much more important issues to be discussed first. Actually, with the memory and speed of modern computers, I think it might be very valuable to write such a program. (Another project for another day.)

Of course. Even removing the identifier does not lead to another entry (with - still - its own identifier).

I think you understand. There is only one point I might make: when you are looking for the B_j (which corresponds to the B_asked with an element missing) you must look through the entire list of all B's you have created from the original B's with every possible omission. This expands the problem considerably (though it is still a finite problem).

What I want you to keep in mind is the fact that I have just proved that, so long as the number of elements in C are finite, it is always possible to add "unknowable data" (imaginary information) which will allow a rule F=0 to constrain the elements to exactly what was observed no matter what was observed (by "observed", I mean the specific elements in the B's which make up C).

To continue, we need a universal abstract way of expressing an explanation in order to describe the universe I am going to create. So, the first step is to define an abstract definition of an explanation. I tried to express this definition to Canute a while ago but I don't think he has much interest in exact science. I define "an explanation", from the abstract perspective, to be a method of obtaining expectations from given known information. It should be clear to you that the "known information" is the collection of B_js which go to make up C. If we use numerical labels for the elements of B, then every B can be seen as a collection of numbers. From these numbers (the numbers which define what B we are looking at) we are to supposed to express our expectations. What else are our expectations if they are not the probability that we expect to see that particular B just referred to? It follows that "our explanation" constitutes knowing that probability as a function of those arguments.

If follows that we can express our explanation with the notation:

$$P(x_1, x_2 , \cdots, x_n)$$​

If we can discover that function, we know our expectations and thus have an explanation of C. The first thing of interest to us is that our explanation should be consistent with all the $B_j (x_1, x_2, \cdots, x_n)$ that go to make up C (it doesn't explain C otherwise). Notice that we are actually talking about the collection of all those $B_j$ and the probability of seeing a particular one can not be a function of our labeling procedure as we were free to label things anyway we please (our labels are fundamentally meaningless). It should be obvious that, in most cases, any change in the labeling procedure will most likely confuse us as to which B's we were talking about before and after the relabeling (the form of that function is very dependent upon the labeling). None the less, there do exist relabeling procedures which will not confuse that identification. Any relabeling procedure which does not confuse the identification of $B_j$ must yield exactly the same expectations after the relabeling as it did before. If it doesn't, the explanation is inconsistent with C.

It is the expectations for the B's which interest us; not the arbitrary labels we happen to put to those B's. Those labels exist for the sole purpose of allowing us to refer to the elements of B. (That is exactly what language is all about.)

I will leave it there for the moment because I want to be sure you understand exactly what I have said. Meanwhile, when I was looking up that post to Canute above, I ran across a post by you which I had apparently missed.

<off-topic>
By the way, it's interesting to see the difference between the texts of DoctorDick and Philocrat. Both of you I find difficult to follow. DoctorDick, because your texts have such a small "definition density". With common words you tackle difficult concepts, without using many terms that are in use in contemporary science and philosophy. It's like you're writing assembly code. Philocrat, because your texts have such a big "definition density". You use many new definitions that nobody before, ever thought of creating words for. I guess you've immediately a word for the problem I've with understanding you both. It's like you're writing a high-level programming language that nobody knows.

I am very impressed with the fact that you picked up on that. I would say that my "definition density" is as close to minimal as one can get and your use of the metaphor "assembly code" is very apt. I would also comment that there are other similarities. The problem with the high-level language is that you can only express things which have already been prepared for in the design of the language while, in assembly code, you can express anything. However, expressing simple things in "assembly code" can easily get quite long compared to the same thing in a high-level language. I think I tend to exceed most peoples attention span very quickly. I hope you have the patience to follow my arguments through; the arguments themselves are actually quite simple.

Looking for your response -- Dick

 

[saviourmachine]

That is exactly my contention. If you notice any reason at all that my presentation is not totally general, please point it out to me as, if such a difficulty exists, it constitutes a serious flaw in my work.

As problem solving your presentation is general enough. However, like somebody pointed out in another thread, considering the problem of the origin of the apparatus that receives and distinguish as such the messages B_j, and that can contain memory (set C), I don't see how it can account for that. How evolution works is sending indirect messages by destroying the 'owners' of a set C less adapted to their environment. The idea of mutations in combination with natural selection doesn't fall into this scope. Or, if you have any idea how it does fall into this scope, I appreciate to hear that.

Coded messages

The other issue is a little more serious. It has to do with determining the equality of sets B. In your example, you assume the asked set {red} is equal to the observed sets {red, 2}, {apple, red} and {red, 2} ( j = 1, 2, and 4). Under my definitions (as I intended them), you never received the set {red} (that would be "red" in the absence of any other elements).

But how can you make sure that your messages are in the form you need? If you assign an arbitrary label, you can 'calculate' as if every message is coded like that, but 'at the end' it's possible to 'calculate' without this proposed construction, isn't it?

Order & numbers

Also, as order is of no significance, your example might be better if you either included {2, red}

Therefore I added B₂ = {apple, red}. I agree with using only numbers, so B₂ = {8088, 3945} is fine for me too.

Word 'identifier'

That is exactly what it is. The only important issue is that these "invented" elements need to be seen as utterly no different from any other element in B when it comes to solving our problem.

Yes, you're right. That went also through my mind when I wrote 'identifier', because the way your tabel is coded, every label [column] can be called 'identifier' (whatever element is deleted, the entry [row] is still unique). It's like adding an 'error bit' to make sure the amount of 'ones' in a binary message is even and subsequently not having to know which bit the error bit exactly is.

Hypothetical

They essentially stand as "hypothetical" elements; if we find a usable solution, then we can certainly hold that these "invented" elements need to be there (at least with regard to that solution we found). That is the reason I described it the way I did: that is, I didn't want to use the words "keyword" or "identifier" as that implies a specific status to the entry. I want you to simply regard it as an imagined entry. (What I have called "unknowable data" elsewhere.)

Yes, this is the clue, exactly the doubt I uttered in 'Coded messages'. I'm curious how handy these hypothetical elements will turn out to be. I agree that if there is 'unknowable data', that there is no point to dismiss beforehand the possibility that these hypothetical elements exist.

Expectation

If follows that we can express our explanation with the notation:

$$P(x_1, x_2 , \cdots, x_n)$$​

Agreed.

It should be obvious that, in most cases, any change in the labeling procedure will most likely confuse us as to which B's we were talking about before and after the relabeling (the form of that function is very dependent upon the labeling).

Aha! The message are received in code, or there is a 'relabeling' procedure. I thought the label was artificial, but inherently bounded to each message. So, there wouldn't be a 'behore' and 'after'.

It is the expectations for the B's which interest us; not the arbitrary labels we happen to put to those B's. Those labels exist for the sole purpose of allowing us to refer to the elements of B. (That is exactly what language is all about.)

Agreed.

Looking forward for more.

 

[Doctordick]

As problem solving your presentation is general enough. However, like somebody pointed out in another thread, considering the problem of the origin of the apparatus that receives and distinguish as such the messages B_j, and that can contain memory (set C), I don't see how it can account for that.

I don't account for that. I think you have a very slight misunderstanding of what I am doing. The issue is that we have come from nothing except the universe itself. Somehow, having begun with totally undefined information (what we have come to call the universe or reality) which was delivered to us via a totally undefined mechanism (what we have come to call our senses) we have constructed a very sophisticated mental model of reality which seems to be quite valid (our expectations are pretty much in line with what happens). I take that as evidence that the problem (creating a valid model of a collection of totally undefined information transformed by a totally undefined mechanism) is a solvable problem.

That is the problem I have attacked. I am not claiming that I know how "we" (human beings) did it, I am simply claiming it can be done. That is, it is a problem which can be solved. I analytically solved it over twenty years ago. And I find my solution both very reasonable and very interesting. In fact, my single greatest interest is in talking to someone about the implied consequences of that solution. You are one of the very few people who has had the patience to get this far and I am actually astounded by how well you have managed to comprehend what I am saying. Most everyone else fails to even comprehend there is a problem here. How can one explain a solution to a problem which they refuse to admit exists?

How evolution works is sending indirect messages by destroying the 'owners' of a set C less adapted to their environment. The idea of mutations in combination with natural selection doesn't fall into this scope. Or, if you have any idea how it does fall into this scope, I appreciate to hear that.

I wouldn't say evolution destroys 'owners' of a set C less adapted to their environment. The set C possessed by a rock is probably quite minimal if it exists at all and the rock isn't "destroyed"; it just lays there. What was C again anyway? All the information about the universe it has to work with wasn't it? Or at least that which "it" can "remember". I guess for a rock that would be the collection of interactions it has had with the rest of the universe and it's memory would be in the vibrations and/or make up of the chemicals which are part of it. Really, I think this aspect of the problem is better left to later, after you understand the solution I have discovered.

But how can you make sure that your messages are in the form you need?

I can't. Again this is a simple consequence of your slight misinterpretation of what I am doing. I am solving a very specific problem, not theorizing about how we do it. The problem is to start with totally undefined information and develop a model (or an explanation if you will) which will yield expectations in perfect alignment with the information you have. (I tried to interest the military in this problem about fifteen years ago but got the "quack" response. I actually have a letter from the pentagon signed by a "Captain Nasty" if you can believe that!) The problem is actually a very complex decoding problem.

If you assign an arbitrary label, you can 'calculate' as if every message is coded like that, but 'at the end' it's possible to 'calculate' without this proposed construction, isn't it?

At the end, everything that is possible will be possible; but, for the moment, being able to use mathematics is very valuable tool. As Feynman once said, "mathematics is the distilled essence of logic". My solution is analytic and not at all intuitive. Everything I say could be put into pure logic terms but you have already complained that following me is like following assembly code. I would like a little higher level language. Mathematics is actually little more than a language which has been constrained to internally consistent constructs which have achieved a high degree of acceptance. When I tell you to perform a procedure in mathematics I can be pretty confident you will understand exactly what that procedure is. Actually, in metaphor, it's a little like going from machine language to assembly language.

It's like adding an 'error bit' to make sure the amount of 'ones' in a binary message is even and subsequently not having to know which bit the error bit exactly is.

I think you understand the phenomena exactly. I only comment because I want you to know that I am again impressed with your ability to see the essence of these steps.

I'm curious how handy these hypothetical elements will turn out to be.

They are the essence of understanding itself. Think about the proof that any arbitrary collection can be made the only possibility by requiring F=0. The hypothetical elements were central in bring about that result. I think it will be a lot clearer later.

Aha! The message are received in code, or there is a 'relabeling' procedure. I thought the label was artificial, but inherently bounded to each message. So, there wouldn't be a 'behore' and 'after'.

I am not exactly sure I understand this comment. The labeling procedure is the first step to creating a language capable of expressing the relationships between the elements. I would also comment that "reductionism" is the process of reducing the number of "fundamental" things (labels) required: i.e., once you get to the minimum number of labels required, other important concepts can be explained in terms of those fundamental labels. But you shouldn't worry about that now; it is an issue which arises after the analytical solution is obtained. My process does not require reductionism as it implicitly sets up the minimum number of labels required and we will set up those labels as we proceed.

As I said in my previous post, "any relabeling procedure which does not confuse the identification of $B_j$ must yield exactly the same expectations after the relabeling as it did before". There are two very simple relabeling procedures with very significant consequences: since I am using numerical labels, I can either add some given number to every label in any given B or multiply every given label by an arbitrary number. If the label sets were unique before the labeling they will be unique afterwards. This means that I can write the following equations:

$$P(x_1, x_2, \cdots, x_n) = P(x_1+a, x_2+a,\cdots, x_n+a) = P(x_1+b, x_2+b,\cdots, x_n+b)$$​

$$P(x_1, x_2, \cdots, x_n) = P(a*x_1, a*x_2,\cdots, a*x_n) = P(b*x_1, b*x_2,\cdots, b*x_n)$$​

The consequences of the second will arise later in the presentation. The consequences of the first are important now. Look at what it says if I set $b=a+\Delta a$. Since the labels refer to exactly the same $B_j$ in all three expressions we know that the correct solution to the original problem (that function $P(x_1, x_2 , \cdots, x_n)$) must yield the same probability(we haven't changed the $B_j$, we have only changed the labeling). Thus we know,

$$\frac{d}{da} P(x_1+a, x_2+a, \cdots, x_n+a) =$$

$$\lim_{\Delta a \rightarrow 0} \frac {P(x_1+a+\Delta a, x_2+a+\Delta a,\cdots, x_n+a+\Delta a) - P(x_1+a, x_2+a,\cdots, x_n+a)}{\Delta a}=0.$$
​

Note that the equation is true even when $\Delta a$ is far from zero; the limit is only there to satisfy the definition of a differential. This is a pure consequence of the arbitrariness of the labeling and places utterly no constraint on the actual solution. It can be thought of as the consequence of the fact that the solution can be expressed in different languages; this is just a very specific and very subtle change in language (specific labels) not easily expressed in term of the ordinary concepts used in the translation between human languages I am aware of (other than secret codes that is).

At any rate, we can use that fact to create another very valuable expression. Since what we have above is a well defined mathematical expression, we can also see the addition of a as a simple change of variables $z_i = x_i + a$. Then we take the well known method of extracting a differential of a function with regard to a variable embedded in the arguments of that function. That is, replace $P(x_1+a, x_2+a , \cdots, x_n+a)$ with $P(z_1, z_2 , \cdots, z_n)$. We can then write

$$\frac{d}{da}P(z_1,z_2, \cdots, z_n)=\sum_i \frac {dz_i} {da}\frac{\partial}{\partial z_i}P(z_1,z_2,\cdots,z_n)$$​

But $$\frac{dz_i}{da} = 1$$ for all values of i. It follows as the night the day that

$$\sum_i \frac{\partial}{\partial z_i}P(z_1,z_2,\cdots,z_n)=0.$$​

We cannot change that fact by changing the variable from z to x (they are just numerical labels) so it follows that we may write

$$\sum_i \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n)=0.$$​

The only reason I changed the variable back to x was to be consistent with my earlier notation. What is above is nothing more than a consequence of the Noether theorem. That is why I brought up her theorem earlier and emphasized the ignorance aspect of symetry. The symetry here (or the ignorance) is the fact that we are free to label things any way we want and that fact has real consequences.

Please, think that all over a little and let me know if you have any problems with it.

Have fun -- Dick

 

[saviourmachine]

Derivation

There are two very simple relabeling procedures with very significant consequences: since I am using numerical labels, I can either add some given number to every label in any given B or multiply every given label by an arbitrary number.

Yes, how cool! Using numeric labels, adding as well as multiplying is possible.

Adding a number to every label in every B doesn't change the probability P. That's right. P(x₁+b, ..., x_n+b) should have the same outcome. Differentiating to b (or a) results in zero. I also agree with the ultimate equation [1]:

$$\sum_i \frac{\partial}{\partial x_i}P(x_1,x_2,\cdots,x_n)=0.$$​

Symmetry, Noether's theorem, equation [1]

The only reason I changed the variable back to x was to be consistent with my earlier notation. What is above is nothing more than a consequence of the Noether theorem. That is why I brought up her theorem earlier and emphasized the ignorance aspect of symetry. The symetry here (or the ignorance) is the fact that we are free to label things any way we want and that fact has real consequences.

Sorry, this is too fast for me. It's difficult for me to connect these two themes: this formula and Noether's theorem. Can you recapitulate shortly?

 

[Doctordick]

We might be getting somewhere here!

Yes, how cool!

My feelings exactly. I will never forget the first time I ever saw it. It is utterly astonishing that no one noticed that prior to the twentieth century. Think of all the math done prior to her discovery. It just goes to convince one that everything has not yet been done (even some mighty simple things).

Symmetry, Noether's theorem, equation [1]
Sorry, this is too fast for me. It's difficult for me to connect these two themes: this formula and Noether's theorem. Can you recapitulate shortly?

It shouldn't be. You seem to understand exactly what I did and that is the very essence of Noether's theorem. The central issue is the relationship between symmetry (which I see as a particular kind of ignorance) and conserved quantities. A "conserved" quantity is something which doesn't change. In mathematics, change is represented by differentials so, "a conserved quantity" means that there is a differential which does not change. If we can show that a symmetry leads to a differential of something which must be zero, then we have an example of Noether's theorem. John Baez (who I think is a member of this forum) has an excellent discussion of Noether's theorem on his website (from the purely conventional perspective).

I admit my view is a bit askew of the norm but it might be worth while for you to review my original post to you on this subject together with selfAdjoint's response and my response to him. I got no further complaint from him so I presume he had no further argument with what I said.

As I said in the post you are responding to:

It can be thought of as the consequence of the fact that the solution can be expressed in different languages; this is just a very specific and very subtle change in language (specific labels) not easily expressed in term of the ordinary concepts used in the translation between human languages I am aware of (other than secret codes that is).

I am pretty sure you have a decent idea of what is going on here because of your "Cool" comment above. It is very much the sign of that little light going on.

Exactly the same relationship can be used to generate a conserved quantity related to that "j" we attached to those B's which represent a change in C. The universe we are trying to explain (with that function which is going to yield our expectations) is derived from all the information embedded in the set C. Certainly no one will argue that the order with which we receive that information is an unimportant aspect of solutions we might propose; however, in the general case, that cannot be a fundamental issue. Remember, it is A we are trying to explain and the only thing we have to go on is C. Again, in the general case, we cannot presume that order is significant. Not unless the fact of that order is implicitly embedded in the data itself. We can assure that is the case by adding "unknowable" data which explicitly sets that order. Since we have already made sure (by adding imaginary entries in the B's we are working with – unknowable data) that all B's are different, we can simply add a numerical label which is to have a different value in every B and will indicate the order significant to the solution.

Now (having added that new label) our solution to the problem contains another (totally imaginary component) numerical label which I will call "time" and represent with the letter t. Again, multiplying that label by a constant or adding a constant to all t cannot alter the order and we once again have a fundamental symmetry in our representation. The fact that we can add any number to that t label yields another conserved quantity represented by the differential expression:

$$\frac{\partial}{\partial t}P(x_1,x_2,\cdots,x_n,t)=0.$$​

Once again, the critical issue is that the particular B being referred to does not change nor does the order of those sets. These facts are true, no matter what order the information was received in. Since this is an ordering parameter on received changes B, this leads me to some very simple definitions. A particular value of t will be called "the present". Any t less than that particular t will be called "the past" and any t greater than that particular value of t will be called the future. This is the simplest definition of time which can be made and, in the end, I will show that it is also sufficient to all usages known. Since B represents a change in the information we have to work with, the "past" constitutes what we have to work with and the "future" constitutes what is not yet known.

Note that $P(x_1,x_2,\cdots,x_n,t)$ is the probability of B being $(x_1,x_2,\cdots,x_n,t)$ when t was the present: i.e., if nothing was known about about any B's beyond the one referred to by that "t". Note that "time" as here presented is nothing but a parameter indicating the order in which you came to know things. Note also that "time travel" is pretty well a ridiculous concept under this picture as it amounts to going from knowing what we know to knowing less (the common idea of time travel is to "go into the past" and still know what you know).

If anything I have said confuses you, let me know. I will be happy to clarify anything.

Have fun -- Dick

 

[saviourmachine]

Introduction concept 'time'

In mathematics, change is represented by differentials so, "a conserved quantity" means that there is a differential which does not change. If we can show that a symmetry leads to a differential of something which must be zero, then we have an example of Noether's theorem.

Aha, it's that simple!

Not unless the fact of that order is implicitly embedded in the data itself. We can assure that is the case by adding "unknowable" data which explicitly sets that order.

Aha, that makes some things clear.

Now (having added that new label) our solution to the problem contains another (totally imaginary component) numerical label which I will call "time" and represent with the letter t. Again, multiplying that label by a constant or adding a constant to all t cannot alter the order and we once again have a fundamental symmetry in our representation. The fact that we can add any number to that t label yields another conserved quantity represented by the differential expression:

$$\frac{\partial}{\partial t}P(x_1,x_2,\cdots,x_n,t)=0.$$​

That's straightforward.

Note that "time" as here presented is nothing but a parameter indicating the order in which you came to know things. Note also that "time travel" is pretty well a ridiculous concept under this picture as it amounts to going from knowing what we know to knowing less (the common idea of time travel is to "go into the past" and still know what you know).

Yes, that makes sense. Providing the items in reversed order is still in order.

Looking forward,

Andy

 

[Doctordick]

Hi Andy, it's nice to hear from you. You seem to think about the things I say without getting your ego involved. You are a very rare bird indeed and I appreciate the opportunity to communicate with you. (Note, I have been having a very bad time with the latex interpreter; I think it has some bugs in it. I have been trying various work arounds.)

Aha, it's that simple!
Aha, that makes some things clear.
That's straightforward.
Yes, that makes sense. Providing the items in reversed order is still in order.
Looking forward,

I always tell people it's simple but they always want to complicate things. The math is not difficult at all. With regard to the issue of mathematics and simplicity, do you have any knowledge of matrix mechanics or matrix multiplication? I am wondering if I will have to teach you the subject as it comes up pretty quickly from where we are at the moment.

Meanwhile, there are three significant steps yet to be undertaken. Again, they are not really difficult but they are rather askew of the typical perspective. The first one has to do with the representation of probability. Probability, when viewed as the output of a mathematical function, constrains that function to have some very specific properties. These constraints come directly from the definition of probability. (Just as an aside, there is an individual out there who has some major difficulties with probability theory and is getting a reception roughly equivalent to the one I manage to generate with authorities. I have a strong suspicion his complaints are very rational.) But that is beside the point as I use none of the sophisticated aspects of probability theory he is referring to.

The first fundamental property of probability is that it cannot be negative and the second is that the sum (or integral if the number of possibilities become infinite) over all possibilities can not exceed unity. If you have been following the details of my approach you should have at least an inkling of the central motivation behind that approach. I have made every effort possible to insure that my representation imposes no constraints whatsoever on the possibilities which can be represented. I want my conclusions to be absolutely general without any presumptions as to where and how success (that explanation we are seeking) is to be found. Since we have established that our solution to any problem can be seen as finding the proper algorithm to apply to the set of numbers representing our knowledge, it is in our interest to remove constraints imposed by issues outside the information itself without making any constraint on the range of algorithms available to our analysis. The fact that probability must be a number between zero and one is just such a constraint. The need to satisfy this superfluous constraint may be removed from consideration via a very simple procedure.

A function can be seen as consisting of two components: the "argument" of the function (the input) and the "value" of the function (the output). Both of these components can be represented by a set of numbers (I think we have already discussed that issue). It follows directly that absolutely any function can be represented by the following shorthand notation.

$$\vec{G}(\vec{x},t) \equiv \left {{}G_1(x_1, x_2, \cdots, x_n,t), G_2(x_1, x_2, \cdots, x_n,t),\cdots, G_k(x_1, x_2, \cdots, x_n,t) \right{}}$$​

(Without this shorthand, the size of the equations which will soon appear will be far to complex to write out in full.) In the interest of obtaining a very specific representation, I will constrain the arguments, $x_i$, to be taken from the set of real numbers and the results of the algorithm, $G_j$, to be taken from the set of complex numbers. Note that the common meaning of such an expression, that G rotates like a vector in the space of x is specifically not to be the intended interpretation. Note further that there is no implied relationship between n and k: that is, the number of elements in the two sets is held to be a completely open issue.

Given this totally general representation of an arbitrary functional relationship, we can define (for any specific function) what is called its adjoint function and written $\vec{G}^\dagger (\vec{x},t)$. The adjoint is defined to be exactly the same as the original function except that each and every $G_i$ (the specific complex numbers defining the function) would be replaced with its complex conjugate ($G_i = (a+ib)$ goes directly to $G_i ^\dagger = (a-ib)$). The central issue is of course the fact that $G_i ^\dagger * G_i = a^2 + b^2$, a positive definite real number. (If b = 0 then the adjoint is identical to the original which of course means that "self-adjoint" means real; which I suspect everyone here knows.)

Now add to the above the standard definition of a "dot" product of vectors (seen as a definition of a procedure) and the notation $\vec{G}^\dagger \cdot \vec{G}$ results in a sum over a collection of positive real numbers which must be positive definite. Lastly, the sum over all possibilities (or the integral if the number of possibilities is infinite) must be greater than any sum (or integral) over any sub set of possibilities. It follows that

$$1 \geq \frac{ { \int \int \cdots \int \vector{G}^\dagger \cdot \vector{G} \, d^n x} }{ { { \int \int \cdots \int \vector{G}^\dagger \cdot \vector{G} \, d^n x} } } \geq 0$$​

so long as the denominator is summed (or integrated) over all possibilities. That also brings up another shorthand notation I would like to use.

$$\oint f(\vec{x}) dv \equiv \int \int \cdots \int f(\vec{x}) d^n x$$​

Ordinarily $\oint$ would denote a line integral but, since I have no need for line integrals in my work, there should be no confusion. If I knew how to do it, I might very well put a capital "V" in the circle to denote that I want a volume integral over the entire represented abstract volume. Meanwhile, I will just hope that anyone who reads this has the attention span to remember that identification.

If follows that, if one defines the function $\vec{\Psi}$ via

$$\vec{\Psi}(\vec{x},t) \equiv \frac{ \vec{G}(\vec{x},t) }{ { \sqrt{ \oint \vector{G}^\dagger \cdot \vector{G} dv} } }$$​

we can "define" the probability of the $B_j$ to be given by

$$P(\vec{x},t) = \vec{\Psi}^\dagger(\vec{x},t)\cdot\vec{\Psi}(\vec{x},t)dv$$​

where $dv \equiv d^n x$.

The really important issue here is that $\vec{\Psi}$ is an absolutely unconstrained functional relationship; absolutely any possible function can serve the roll of $\vec{\Psi}$ as it is identical to $\vec{G}$ except for the numerical factor $\sqrt{\oint \vector{G}^\dagger \cdot \vector{G}dv}$. There is to be no constraint on $\vec{\Psi}$ other than the fact that the probability generated by the definition given above be a correct representation of our expectations. If our expectations can be generated, $\vec{G}$, must be a member of the set of "all possible algorithms".

Two possible problems might exist. Both involve extreme values of that numerical factor $\sqrt{\oint \vec{G}^\dagger \cdot \vector{G}dv}$. The case where the factor is zero (and division would be undefined) is trivial. In that case, $\vec{G}$ will serve the purpose of $\vec{\Psi}$ and the division is unnecessary. The second case, where the factor is infinite is a little more problematical. In that case, the defined probability becomes zero. This case obviously occurs when the number of possibilities become infinite and the probability of any specific B becomes zero. This becomes a very real possibility as we will soon be dealing with the limit as n approaches infinity; however, in this case also, the division once again becomes immaterial. In this second case, our interest will be in comparing probabilities of various collections of B's and the ratios of those probabilities are the important factor (the denominator being the same in all cases, the division is immaterial).

The only factor of interest is that the output obtained from the definition can be interpreted as a probability.

The net effect of all this is that, in order to keep the representation totally open, we want to work with $\vec{\Psi}$ instead of working directly with the probabilities defined by $\vec{\Psi}$. If I can make it clear one more time, the set up I have arranged makes utterly no restrictions on the form or character of the method of arriving at expectations. The only constraint being put on the method is that it must yield satisfactory results; an issue not to be discussed until the notation is fully proscribed.

Finally, since we want to work with $\vec{\Psi}$, we need to re-express the relationships developed earlier in terms of the probability. The relationships already written may be rewritten as

$$\sum_{i=1}^n \frac{\partial}{\partial x_i}\vec{\Psi}\,=\, i \kappa \vec{\Psi}\,\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}\,=\, im\vec{\Psi}$$
​

This can be proved quite simply. The complex conjugates of the above expressions are,

$$\sum_{i=1}^n \frac{\partial}{\partial x_i}\vec{\Psi}^\dagger\,=\, -i \kappa \vec{\Psi}^\dagger \,\,\,and\,\,\frac{\partial}{\partial t}\vec{\Psi}^\dagger\,=\, -im\vec{\Psi}^\dagger .$$
​

This, together with the chain rule of calculus guarantees that any $\vec{\Psi}$ which satisfies the above relations also satisfies the relation on the probability stated earlier. In the interest of saving space, I will show the result explicitly for the time derivative (the derivatives with respect to the arguments $x_i$ go through exactly the same.

$$\frac{\partial}{\partial t}P(\vec{x},t)$$

$$=\,\, \left( \frac{\partial}{\partial t}\vec{\Psi}^\dagger \right) \cdot \vec{\Psi}+\vec{\Psi}^\dagger \cdot \left( {\frac{ \partial}{ \partial t}} \vec{\Psi} \right)$$

$$=\,\, -im \vec{\Psi}^\dagger \cdot \vec{\Psi}+im \vec{\Psi}^\dagger \cdot \vec{\Psi}\,\,=\,\,0.$$​

If you have any questions about anything I have put down, please let me know. If all this makes sense to you, I will establish the final two steps and then state the ultimate conclusion.

I hope I have not run you off – Dick

 

[selfAdjoint]

This seems OK to me, although I have a couple of questions.
1. Can you justify your basic assumption of functions: Rⁿ -> C^k?

2 Your definition of adjoint is pretty limited, in agreement with your generality concerns. As you undoubtedly know, the output variables could be a matrix algebra, in which case the adjoint would involve a transpose as well as conjugation, or it might be a general algebra of linear transformations over the complexes, in which case adjointness would have a definition involving the outer product (which in your general plan you have not required). In any case it would be prudent to call your operation conjugation rather than adjoint, to avoid misunderstanding.

 

[Doctordick]

This seems OK to me, although I have a couple of questions.
1.Can you justify your basic assumption of functions: Rⁿ -> C^k?

Maybe you could make your question a little clearer. I don't believe I have "made an assumption" here; I have made a statement about the representation I prefer. A "function" is a statement of a relationship. When one says there is a functional relationship between two things, it generally means that what is accepted as the "subject under discussion" depends on something else, what is usually termed the "the argument of the function". There is utterly no need for the "subject under discussion" and the "argument of the function" to be chosen from similar sets. ("My investment decisions are a function of what I read in the newspaper" is just as much a statement of a functional relationship as is $y=x^2$. ) People tend to omit "tabular" functions as valid representations. People our age used a lot of tabular functions when they were young; I suspect a lot of current students have never seen a log table much less thought about the concept of interpolation.

Certainly the collection of all possibilities for "the subject under discussion" can be mapped into a set of numbers. Likewise, the collection of all possibilities for "the argument of the function" can also be mapped into a set of numbers. Clearly, those statements are not made false by allowing one to be the set of real numbers and the other to be the set of complex numbers. This is nothing more than a choice of representation.

If you think there is more to it than that, please give me an example of something which cannot be represented in either set of labels. Note that, in my presentation, these numbers are merely used as a set of labels for arbitrary members of sets of interest.

2 Your definition of adjoint is pretty limited, in agreement with your generality concerns. As you undoubtedly know, the output variables could be a matrix algebra, in which case the adjoint would involve a transpose as well as conjugation, or it might be a general algebra of linear transformations over the complexes, in which case adjointness would have a definition involving the outer product (which in your general plan you have not required). In any case it would be prudent to call your operation conjugation rather than adjoint, to avoid misunderstanding.

Yes, that is true and your criticism is well founded; however, since I don't actually make any use of those additional properties of the "adjoint", the use of the word is not actually "wrong". One could just as well "conjugate" a real number (do nothing to it). Consider it little more than a personal preference. It actually serves no purpose beyond making my notation look like common quanta mechanics notation; an issue which only comes to bear further down the road.

I certainly appreciate hearing from you as I respect your judgment on issues like this. I also appreciate the latitude you are allowing me. Perhaps I have not chosen the best notation for my ideas but it is the notation I have chosen. The biggest problem I have is people trying to read between the lines. If the reader is so habituated to the standard expectations that they cannot remember my definitions then I don't think they really have the capability of following me anyway. I kind of see it as a way of getting those who don't want to think out of the picture. Notice that you, as opposed to others here, were driven to make some intelligent comments. At least I know you are following what I am saying.

Have fun -- Dick

 

[selfAdjoint]

My first question was addressed to the fact that you represent inputs by real numbers and outputs by complex numbers. Can you express group relations this way? Do you contemplate using different algebras (quaternions, matrix algebras, von Neumann algebras, etc.) for the values of your outputs? Does your general functional notation encapsulate such structure, or do you not need them?

 

[Doctordick]

My first question was addressed to the fact that you represent inputs by real numbers and outputs by complex numbers. Can you express group relations this way?

I don't quite understand what you mean by the question, "Can you express group relations this way? Absolutely anything can be expressed by a set of references to concepts. These under normal circumstances would be words whose definition is presumed understood; but, in actual fact, any symbolic label will suffice. I have merely chosen numerical labels because it is easy to express a certain kind of possible shift in meaning of those symbols which must exist in any possible set (just more difficult to express). I chose real numbers in one place and complex numbers in another for the simple reason that I like the form of the resulting expressions.

What I am presenting is not a theory; it is a very specific method of organizing information. It is no more a theory than is the Dewey Decimal system. The important point is that any set of significant concepts can be so labeled and so organized. There is only one constraint on my approach, that would be the fact that any possible information can be laid out for examination in such a manner. If you can show me a set of references to concepts which cannot be so laid out, then you have found a flaw in my organizational procedure. Or, if you can show me a flaw in the deductions based on such a layout, you have found a flaw in my deductions and my results are not supported. However, baring those two factors, I am free to lay out the information any way I wish. Think of it as a layout of coded data where no key to the decoding exists. All information available to us must be retrieved from that information itself a very strange problem indeed.

It is very important that I do not claim to be able to say anything about reality at all. All I am talking about is the consequence of laying data out in such a manner. Those consequences are very surprising in view of the fact that I am making utterly no constraint on the information being analyzed. In fact, it is the position of the scientific community that I could deduce absolutely nothing of significance. Either I have made a subtle error or what I do has very significant and far reaching consequences. If you can point out a significant error (see the above two factors), I would appreciate it very much.

Do you contemplate using different algebras (quaternions, matrix algebras, von Neumann algebras, etc.) for the values of your outputs? Does your general functional notation encapsulate such structure, or do you not need them?

Not for the outputs of my generalized functions $\vec{\Psi}(\vec{x},t)$. However, I will make direct use of matrix algebra quite soon. And down the road, some of the results I will obtain can quite likely be expressed through some of the other mathematical methods you refer to but I won't be using them directly. Actually everything I do is pretty simple and straight forward considering the consequences.

I hope my comments are clear to you -- Dick

 

[selfAdjoint]

Yes, thanks. So I think you contemplate possible math structure between your real variable inputs and your complex variable outputs. Now I have another dumb question. Since we do not observe complex valued quantities in our experience, do you plan to translate the complex variables back into reals some way? Of course you recall that this was a big deal in quantum mechanics where Born interpreted the square of the complex wave function, $$\psi\psi^*$$ as a real probability.

 

[Paul Martin]

Since we do not observe complex valued quantities in our experience, do you plan to translate the complex variables back into reals some way?

With all due respect, can you give me a single example of an observation of a real valued quantity in our experience where the real value is not also a rational value?

Paul

 

[zeithief]

hmm... after reading so many pages of this thread I've come to this conclusion : Our brain (or whatever that is causing us to think ) isn't 'powerful' enough to solve the many questions that we ask eg. How did the universe start? Now, i think even if there are creatures or aliens who is more intelligent then us (please do not tell me to define intelligence) who can answer this question 'How did the universe start?' there will be more questions like 'Why did it start?' 'What causes it'.
Btw, even IF we can decribe everything using mathematics, how can we know that our mathematics is accurate to decribe it? Therefore, we need something to prove our maths. BUT we need another 'thing' to prove the thing that proves our math. Therefore, we end up questioning and proving forever. I like (with no scientific evidences) to think that the world that we observe (however wrong our observation might be) can be explained by physics(mathematics) (however wrong our maths and physics might be) as long as our observations matches with our equations, we should be happy.
My 2cents worth

 

[Doctordick]

Yes, thanks. So I think you contemplate possible math structure between your real variable inputs and your complex variable outputs. Now I have another dumb question. Since we do not observe complex valued quantities in our experience, do you plan to translate the complex variables back into reals some way? Of course you recall that this was a big deal in quantum mechanics where Born interpreted the square of the complex wave function, $$\psi\psi^*$$ as a real probability.

Oh yes, I am going to show the existence of what one would call a "math structure" between the "real" arguments and those complex outputs. But that issue is still down the line a little way.

And I am well aware of Born's interpretation; however, I am sort of developing it from the opposite direction. (You should be pretty well aware of the fact that I tend to look at things from the other direction. ) By the way, with regard to the issue of "ignorance" vs "indifference" in the Noether theorem, suppose the universe contained a special point somewhere out there (call it God's survey point; which mankind might someday discover) and that the "correct" solution to the universe depended on where you were relative to that point. Certainly, until we discovered where that point was, any solution to any problem involving that fact would still be governed by Noether's theorem. Yet you really couldn't say we were "indifferent" to its existence.

In my definition of "an explanation", the explanation must yield one's expectations. One's expectations must be expressible as probabilities of possible outcomes. And, finally, the fact that any probability relationship can be represented via Born's "square of a complex wave function" completes the definition of a universal representation of our expectations. (Note that the word "wave" is not necessary to my presentation and you should keep in mind that tabular relationships are valid members of the collection of possible functions.) I take the issue of avoiding constraints on my "Dewey Decimal" type procedure very seriously.

The central issue of my attack is that there exists no problem which cannot be so represented. I do not believe this is exactly what Born had in mind at the time. I am pretty sure that his idea developed from the structure of the solution space for mechanical problems expressed in Hamilton-Jocobi mechanics. At least, that was the way I was introduced to the founding of quantum theory. The text we used when I was a graduate student was Classical Mechanics by Herbert Goldstein, sixth edition, 1959. I still have my copy and think it is one of the best discussions of classical mechanics extant. I used to know everything in there, but I have noticed over the last twenty years that my abilities to remember stuff has declined significantly (I am glad I kept the book).

I am enjoying talking to you.

Have fun -- Dick

 

[Doctordick]

hmm... after reading so many pages of this thread I've come to this conclusion : Our brain (or whatever that is causing us to think ) isn't 'powerful' enough to solve the many questions that we ask eg.

Well, perhaps not logically; but I think I would actually differ with you on that issue too! Meanwhile, I certainly think it is "powerful" enough (when one allows those illogical intuitive solutions I call squinking) to come up with a possible solution to almost anything.

How did the universe start? Now, i think even if there are creatures or aliens who is more intelligent then us (please do not tell me to define intelligence) who can answer this question 'How did the universe start?' there will be more questions like 'Why did it start?' 'What causes it'.

Well, a lot of people out there think (or should I say squink) that "God" just thought it up. Prove that answer is wrong if you can.

Btw, even IF we can decribe everything using mathematics, how can we know that our mathematics is accurate to decribe it? Therefore, we need something to prove our maths. BUT we need another 'thing' to prove the thing that proves our math. Therefore, we end up questioning and proving forever. I like (with no scientific evidences) to think that the world that we observe (however wrong our observation might be) can be explained by physics(mathematics) (however wrong our maths and physics might be) as long as our observations matches with our equations, we should be happy.
My 2cents worth

So, you apparently put a high value on internal consistency and logic. Are you willing to lay aside your intuition (when you do exact science) or not? We have to establish our priorities here!

Have fun -- Dick

 

[digiflux]

"Can Everything be Reduced to Pure Physics?"
_____________________

Everything, with the exception of the mystifying mass fluctuations of Oprah's butt.

 

[Philocrat]

"Can Everything be Reduced to Pure Physics?"
_____________________

Everything, with the exception of the mystifying mass fluctuations of Oprah's butt.

Oprah's butt is no exception to the rule. If we know about it, then it's explainable. Oprahs butt may fluctuate (infact as radically as it may seem) but at least it is still matter...and within the explanatory realm of physics. In fact, the standard assumption is that if it is matter, then physics should be able to explain it! As you can see the thread is getting more and more mathematical (thanks to Dr. Dick). May be you should ask him to subject the fluctauting part of Oprah's butt to pure mathematical examination or description. As you may well remember, I started this thread with a complete distrust of probabilistic explanations...eg. "OPRAH'S BUTT IS AN APPROXIMATION OF A BUTT!" or "I AM AN APPROXIMATION OF A MAN!" ... and so on. Of course, everything seems to fluctutate or have an aspect that fluctuates, hence creating an impression that there is some sort of deficit in the structure and function of it. In terms of Oprah's butt, it is not clear what deficit needs to be added to it to generate or give a 'Real' butt.

NOTE: The issue is not about what is out there, or what we are aware of or not aware of, but soley about whether we can explain everything humanly conceivable purely from the point of view of physics. But so far the debate seems to suggest that not everything that we are aware of is explainable by pure physics such as the human minds, angels, gods, souls,etc. There is another fundamental problem: we do not even know how many catigories of things are there in the universe, let alone the claim of explaining them in a single leap of fate! Well, on this one your guess is as good as mine!

 

[selfAdjoint]

But so far the debate seems to suggest that not everything that we are aware of is explainable by pure physics such as the human minds, angels, gods, souls,etc.

Minds I will accept, but those others you mention are not agreed to exist, nor have any good evidence for their existence been posted.

And of coourse whether minds can possibly, eventually, be explained by physics is the subject of a number of threads on these philosophy subforums.

 

[Philocrat]

Minds I will accept, but those others you mention are not agreed to exist, nor have any good evidence for their existence been posted.

And of coourse whether minds can possibly, eventually, be explained by physics is the subject of a number of threads on these philosophy subforums.

Would you be prepared to accept the Mind as a Fundamental Metaphysical Catigory, given that Matter is irreducible to nothing else but itself? I raised this issue of irreduciblility of matter to anything else but itself earlier on and no one seems to respond to it, perhaps everyone is agreeing with me about it. If so, good for them. But there is now an urgent need to state and agree on other existing metaphysical catigories, if any, namely (1) Nothing, (2) Mind, (3) Person etc.

Metaphysically, matter is self-standing and self-identifying as a fundamental metaphysical catigory, despite its spooky multi-status nature. That is, matter may multiply into many things or forms, yet it forever remains what it is - Matter! The pressing question now is: how does matter fundamentally relate to other metpahysical catigories, if such catigories really exist in the first place? This is a priceless question that demands an immediate answer. If for an argument's sake that you'er right about non-existence of other such catigories as angels, ghosts, gods etc, are you prepared to admit the mind that you most favour as a self-standing, self-dentifying metaphysical catigory? If so, how does it relate structurally and functionally to its counterpart metaphysical catigory - matter? You see, we are back to square one, almost!

 

[selfAdjoint]

Would you be prepared to accept the Mind as a Fundamental Metaphysical Catigory, given that Matter is irreducible to nothing else but itself?

Matter can be regarded as a derived concept, since its commonly accepted properties (localization, mass, etc.) are now seen as either special circumstances of quantum fields or the result of interactions between fields. So I think that the current scientific candidate for a basic physical category is the quantum field. In the formal metaphysics of academic philosophy, "mind" may be a separate category from anything physical, but I don't accept this as constraining my own beliefs. I think that consciousness including mystical experiences will yet be shown to be completely reducible to brain chemistry and physics, and the hard problem will turn out to be a "category error".

 

[vanesch]

I think that consciousness including mystical experiences will yet be shown to be completely reducible to brain chemistry and physics, and the hard problem will turn out to be a "category error".

I think that the *behavioural aspects* (and hence all that is experimentally measurable about it) will indeed be completely reducible to brain chemistry and physics ; but I don't see how this will solve any issue concerning the hard problem.
Let us imagine that we have superduper biophysical technology, and that you can now transpose "I-experiences" from one person to another, interchange them etc...
So you exchange them between two persons (or, for that matter, between a person and an elephant). After the experiment, the person who did the "mind travelling" tells you about all the weird observations, the strange sensation of being an elephant, he correctly tells you stuff only the elephant knew (namely how he remembers being badly treated when he was a young animal etc...).
Now, does that tell you much about his consciousness, or even WHETHER the person has a consciousness ? No, it just tells you things about the complicated relationship between the chemistry and physics in his brain, connected to the machine and the brain of the elephant, his nerves and muscles of his vocal chords which uttered the words he's been telling you. And if you know all of the necessary chemistry and physics, you could even predict this, voice intonations included (or at least explain it amongst different possibilities). So you are just observing a complicated physical construction which has some behavior you understand. And you STILL don't know if it is conscious or not. You assume it is, by analogy. And that's all you can do.
The only thing you can do is to connect YOURSELF to the machine, and live the weird experience of being an elephant yourself. And now YOU remember stuff of being an elephant, experiences which strongly resemble what the other person told you. And you say, that's normal because my consciousness being associated with the physical structure which is my brain, observes similar physical processes as what happened to the brain of the other person. As you now know how those brains function physically, it explains you your experiences. Because you know you are conscious yourself, you can thus relate the physics of your brain to your consciousness which observes your brain passively. But you can only know things about the physical brain of others, not about their consciousness (which might very well not exist). You can learn about how other brains relate to what their bodies tell you afterwards, and you can observe for yourself that you have similar experiences. But that still doesn't indicate whether those other persons have a consciousness. The hard problem remains intact.

Now, of course as long as we take on the working hypothesis that living persons are "just as conscious as I am" by analogy, we might have the illusion that we know what we are talking about.
The real issue will come up when we will start to make very complicated machines that have conscious-like behavior build into them. Are they, or aren't they conscious ? No way to know ! Ever. You (as many disciplines do!) can get out of the riddle by just redefining what you mean by "consciousness" of course - like behaviouralists do, and like neurologists do. But the "I think therefor I am" kind of consciousness can never behaviorally be determined in something else but yourself - it is a passive observer which doesn't influence any physical process. So how do you know whether a physical construction is being "passively observed by a consciousness" or not ?

EDIT: to push this into a carricatural example, I could claim that polycrystaline granite blocks of more than 2 kg, which are not too damaged, are also conscious. They feel pain each time that a crystal is broken (just as a neurologist could tell us that "the brain feels pain if these neurons in that corner fire"). How are you going to contradict this ?

 

[selfAdjoint]

I don't think your examples are very relevant. Suppose they had a machine they could hook up to you and make you conscious of whatever they set the machine to, and did many double blind experiements to verify that yes, their machine settings did agree with what you reported being conscious of, including whatever aspects of the "flavor" of the experience could be reported. Then that would convince me they understood consciouness, and I would regard demurs about "what it was like" to be just quibbles.

 

[vanesch]

I don't think your examples are very relevant. Suppose they had a machine they could hook up to you and make you conscious of whatever they set the machine to, and did many double blind experiements to verify that yes, their machine settings did agree with what you reported being conscious of, including whatever aspects of the "flavor" of the experience could be reported. Then that would convince me they understood consciouness, and I would regard demurs about "what it was like" to be just quibbles.

It wouldn't convince me. It would convince me that they perfectly know how human brains work, as physical devices. But what is the difference between setting up a machine that couples to a human brain and makes the human say things about what he experiences, and between programming a computer and make the computer say things about "what he experiences" ? This, to me, indicates only that the programmer knows well his computer. It doesn't indicate to me that the computer is conscious. Now, you can say, ok, they don't know anything about consciousness _in general_ but they now do know something about _human_ consciousness.
Ok, then, so "doing things to a human body" and "know what the human will experience" is a proof that you know about human consciousness ? Does that mean that when I tell you: "look at that movie on the screen" and you then say afterwards "gee, I saw a nice movie" that I "know about human consciousness" ??
You'll object that that is not sophisticated enough. Ok, I guess that all neural coupling to the senses is not good enough, because it is just neurology of the senses, and not yet of consciousness. So, if I could give you some stuff that makes you DRUNK, does that mean that I know about consciousness ?
No, you still mean more sophisticated. If I can make a contact to your brain so that I can read your memory, does that mean I know about consciousness ? No, I just know about the memory function of the brain. I could even CHANGE your memories (cfr "total recall" :-) and that just shows I know about the memory function of your brain.
If I could visualise on a screen what you are thinking, I still don't master your "consciousness" but your cortex processing ; I could even ALTER what you are thinking and I still do not have anything to do with your consciousness.
The only thing you learn from this is that I know very well how your brain physically works, and WHAT ASPECTS OF IT are experienced by your consciousness. But I can still not find out if a piece of granite is conscious or not, and whether it hurts when I break it.

To put it differently, can your machine also be used to couple to a computer's consciousness, to make it happy or sad ? And how do you know ? Or is the computer just running its program and by analysing the code, you "understand" how it works ?

 

[selfAdjoint]

They already have software that interprets a monkey's visual experiences sufficiently well that the monkey can learn to use it to direct his arm to a target. So I think in the future they will have the kind of capability I mentioned.

The machine I mentioned does not force the subject to say anything. Calibration would have to deal with all the variables of human interaction, including lying, fantasy, etc. Did you see where I said double blind? The experimenters would not know, nor would the subjects, what settings had been chosen. Only after the interaction would the subject's responses be compared to the settings.

 

[vanesch]

The machine I mentioned does not force the subject to say anything. Calibration would have to deal with all the variables of human interaction, including lying, fantasy, etc. Did you see where I said double blind? The experimenters would not know, nor would the subjects, what settings had been chosen. Only after the interaction would the subject's responses be compared to the settings.

Yes, fascinating stuff all this. But it is physics and chemistry of the brain. Nothing to do with consciousness. Imagine that we know EVERYTHING about all the neurons in a typical human brain, and that we have identified that when THIS neuron fires, the subject feels sad, when THAT neuron fires, he sees a red flash in the upper right corner of his left eye, when such a neuron fires, he thinks about "additivity", when that other neuron fires, he feels pain in his left foot...
With all this detailed knowledge, I can build your machine.
What do we know now about consciousness ?

 

[vanesch]

To give the discussion another twist, if you say that studying the brain enough so that we can "pilot" someone's conscious experience for instance, does that mean that what constitutes consciousness is a classical property of the brain ? I mean, do you think that consciousness (I'm not talking about intelligence, memory, sensory capacity etc...) as you think it can be described, is fully described by a classical theory of the brain, and that you do not fundamentally need to refer to its quantum state ? (meaning: concentrations of chemicals at different points, given by a finite but big number of reals etc...)
If so, I'd argue in the following way: is it the specific topology of the phase space of that classical brain that makes it "conscious" ? If so, are OTHER classical devices with a phase space with very similar (or identical) topology conscious ?

 

[loseyourname]

If so, are OTHER classical devices with a phase space with very similar (or identical) topology conscious ?

That seems to be what the popular writers around here think (Dennett and Chalmers most explicitly) and of course its the idea behind a lot of science fiction involving conscious machines.

 

[Philocrat]

Matter can be regarded as a derived concept, since its commonly accepted properties (localization, mass, etc.) are now seen as either special circumstances of quantum fields or the result of interactions between fields. So I think that the current scientific candidate for a basic physical category is the quantum field. In the formal metaphysics of academic philosophy, "mind" may be a separate category from anything physical, but I don't accept this as constraining my own beliefs. I think that consciousness including mystical experiences will yet be shown to be completely reducible to brain chemistry and physics, and the hard problem will turn out to be a "category error".

Yes, "category error" indeed it shall be! Worst stiil, it would be an absolute disgrace to suddenly dawn on all those involved that all there is to the notion of a "person" is matter playing very notorious tricks on the entire human perception. That all there is to a person is matter "multiply self-catogorising" into several of the same kind without in actuality manifesting into fundamental metaphisical catigories that may be construed as self-standing and self-identifying! Pure fiction, that is! There will be a voice from the crowed crying "So we were machines all along without knowing!"

NOTE: One thing self-categorising into several forms of the same kind is a possibility that cannot be easily rulled out. As spooky as this may outwardly seem, matter tends to possesses this spooky aspect. I guess the sooner we admit this, the earlier we would make a headstart and home in on the heart of the matter. Or is it?

 

[Philocrat]

I think that the *behavioural aspects* (and hence all that is experimentally measurable about it) will indeed be completely reducible to brain chemistry and physics ; but I don't see how this will solve any issue concerning the hard problem.
Let us imagine that we have superduper biophysical technology, and that you can now transpose "I-experiences" from one person to another, interchange them etc...
So you exchange them between two persons (or, for that matter, between a person and an elephant). After the experiment, the person who did the "mind travelling" tells you about all the weird observations, the strange sensation of being an elephant, he correctly tells you stuff only the elephant knew (namely how he remembers being badly treated when he was a young animal etc...).
Now, does that tell you much about his consciousness, or even WHETHER the person has a consciousness ? No, it just tells you things about the complicated relationship between the chemistry and physics in his brain, connected to the machine and the brain of the elephant, his nerves and muscles of his vocal chords which uttered the words he's been telling you. And if you know all of the necessary chemistry and physics, you could even predict this, voice intonations included (or at least explain it amongst different possibilities). So you are just observing a complicated physical construction which has some behavior you understand. And you STILL don't know if it is conscious or not. You assume it is, by analogy. And that's all you can do.
The only thing you can do is to connect YOURSELF to the machine, and live the weird experience of being an elephant yourself. And now YOU remember stuff of being an elephant, experiences which strongly resemble what the other person told you. And you say, that's normal because my consciousness being associated with the physical structure which is my brain, observes similar physical processes as what happened to the brain of the other person. As you now know how those brains function physically, it explains you your experiences. Because you know you are conscious yourself, you can thus relate the physics of your brain to your consciousness which observes your brain passively. But you can only know things about the physical brain of others, not about their consciousness (which might very well not exist). You can learn about how other brains relate to what their bodies tell you afterwards, and you can observe for yourself that you have similar experiences. But that still doesn't indicate whether those other persons have a consciousness. The hard problem remains intact.

Now, of course as long as we take on the working hypothesis that living persons are "just as conscious as I am" by analogy, we might have the illusion that we know what we are talking about.
The real issue will come up when we will start to make very complicated machines that have conscious-like behavior build into them. Are they, or aren't they conscious ? No way to know ! Ever. You (as many disciplines do!) can get out of the riddle by just redefining what you mean by "consciousness" of course - like behaviouralists do, and like neurologists do. But the "I think therefor I am" kind of consciousness can never behaviorally be determined in something else but yourself - it is a passive observer which doesn't influence any physical process. So how do you know whether a physical construction is being "passively observed by a consciousness" or not ?

EDIT: to push this into a carricatural example, I could claim that polycrystaline granite blocks of more than 2 kg, which are not too damaged, are also conscious. They feel pain each time that a crystal is broken (just as a neurologist could tell us that "the brain feels pain if these neurons in that corner fire"). How are you going to contradict this ?

Your analysis seems to decisively write off the mind as a fundamental metaphysical category, even while you are still generously hanging on to the "hard-problem" spectre. Equally, don't forget that far back in the history of philosophy there are some philosophers that have thought of the mind as a different form of matter, possibly governed by completely different set of laws of physics. If this were to be true, this could very well be the same matter self-catigorising again into an extremely decisive form... a very peculiar one, that is. In other words, mind is decisively matter! Or is it?

 

[outsider]

2 + 2 = 4. What does this mathematical equation tell us? It tells me that the author does not know mathematics. I am interpreting this using base 3. Aren't you? If not, how would we know? Mathematics must be interpreted. Such interpretation is not within the math, but is beyond the math. Mathematics is a tool, not an end in itself.

checkmate

 

[outsider]

can physics explain the posts on this thread? how do we quantify these thoughts and arguments?

Where do these thoughts lead to in the physical world? To all physical actions there must first be a mental aspect triggered from a previous influence (physical / mental).

There are far too many posts for me to read on this thread... but that's my POV.

 

[Philocrat]

can physics explain the posts on this thread? how do we quantify these thoughts and arguments?

Where do these thoughts lead to in the physical world? To all physical actions there must first be a mental aspect triggered from a previous influence (physical / mental).

There are far too many posts for me to read on this thread... but that's my POV.

There is a close resemblance between your thought and your name..."An outsider looking in". Or am I wrong?. Anyway, there is a substantial elements of truth in your thought. Quantifying the contents of this thread is one thing and loggically reconciling them in a coherent way is another. There are many mathemticians on this forum who can piece all the texts on this thread together, but the tricky bit is logically reconciling all the underlying and related thoughts to derive at a generally acceptable conclusion.

As you may well have noticed, all the thoughts so far generated on this thread are multi-disciplinary in scope and in substance, hence precisely why it is even more difficult to reconcile them, let alone come to a common conclusion. The underlying tasks in this discuss are undisputedly immense. The problem gets even worse when there is a huge divisionism between disciplines. Look at the result of th survey to at least get a glimpse of what I am getting at here. Until all the disciplines involved begin to accept the fact that there is no significant difference in what they are trying to explain at their specific scale or layer of reference, then we should all kiss goodbye to any form of progress in this project!

What I am trying to say here is that if there is any difference whatsoever between disciplines, it is only by layer or scale of reference. Therefore, whatever conclusions that they derive at in their overall explantions of this same subject matter must inevitably reconcile both quantitatively and logically. There ought to be neither a metaphysically vexing remainder nor a quantitativelly and logically irreconcilable deficit in a mutidisciplinarily derived explanation of this subject matter. That would be the day!