What can we know of reality?

[arkain101]

Firstly, I want to appologize myself, for the fact that I don't very often provide a response that quotes sections throughout large posts such as the one you just did. The reason why is my sleep schedule is off the charts right now.. Somtimes I am just fuzzy tired like I am right now.. To be of no concern though. I am just currently not employed, and have all the free time to stay up late, or nap, or sleep in.. I've just kind of tossed routine out of the window, so I never really know when to expect that clear thinking time zone to pop up, where I can really get involved in a post.

Secondly,
Thanks for responding, and I follow quite clearly, but believe me, I will be reading it again, as I usually do read posts 2 or 3 times that are of interest to me.

Lastly, I wanted to share a bit of an interesting night last night that is related to this whole discussion. But just before I get to that, I thought I'd add a bit lead up background? I've been reading through the basic's here on these forums, checking my conclusions with what you people are presenting here. It was not even a month ago that I did not know the definition to epistemology and ontology. Nor have I really studied anything directed related to philosphy on purpose (ya know what I mean) (people calling me a philosopher before I even knew much about what that embodied, but none the less, one could just say it was my way of doing things before really being shown). Anyway, I came to many these conclusions, related to the epi and ontol concepts we are talking about here, just from my own observation and analysis and logical deduction. Thankfully however, these topics just recently opened me up to a language I could put these ideas into, and it really cleared up my ability to comprehend and see contrasts. Anyway, that is jut me blabbing a bit about myself and how I got to this stage. It has been a 3 or 4 year journey, just grasping it on my own time and methods..

Okay, so to the interesting night. As I have been browsing through, I was trying to start with the basics before moving into other things. So last night I decided it was about time to learn a bit bout, what exactly this "Schrödinger equation" was all about. So I got reading about it, and I know I've scanned through these things before on wiki, but I really dug in this time and tried to grasp it as much as possible.. but this time I really got a good hold on the material and I opened more link to learn a bit more about specific parts and terms, and I suddenly so much clicked in a way that it never had before.. all these things I've heard a thousand times, just as words describing something, but I had no sense of the essence of exactly all those words meant..

I thought about starting a topic sharing these topics that really interested me, but it mostly relates to here and what we are doing so I'll just post a brief summary of what material I was getting into.




Schrödinger equation - Wikipedia, the free encyclopedia
In physics, especially quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics.

In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger's equation describe not only atomic and subatomic systems, electrons and atoms, but also macroscopic systems, possibly even the whole universe. The equation is named after Erwin Schrödinger, who discovered it in 1926.[1]

Schrödinger's equation can be mathematically transformed into Heisenberg's matrix mechanics, and into Feynman's path integral formulation. The Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem which is not as severe in Heisenberg's formulation and completely absent in the path integral.

-----------------------

Main article: Theoretical and experimental justification for the Schrödinger equation

Einstein interpreted Planck's quanta as photons, particles of light, and proposed that the energy of a photon is proportional to its frequency, a mysterious wave-particle duality. Since energy and momentum are related in the same way as frequency and wavenumber in relativity, it followed that the momentum of a photon is proportional to its wavenumber.

DeBroglie hypothesized that this is true for all particles, for electrons as well as photons, that the energy and momentum of an electron are the frequency and wavenumber of a wave. Assuming that the waves travel roughly along classical paths, he showed that they form standing waves only for certain discrete frequencies, discrete energy levels which reproduced the old quantum condition.

Following up on these ideas, Schrödinger decided to find a proper wave equation for the electron. He was guided by Hamilton's analogy between mechanics and optics, encoded in the observation that the zero-wavelength limit of optics resembles a mechanical system--- the trajectories of light rays become sharp tracks which obey an analog of the principle of least action. Hamilton believed that mechanics was the zero-wavelength limit of wave propagation, but did not formulate an equation for those waves. This is what Schrödinger did, and a modern version of his reasoning is reproduced in the next section. The equation he found is (in natural units):



Using this equation, Schrödinger computed the spectral lines for hydrogen by treating a hydrogen atom's single negatively charged electron as a wave, \Psi(x,\,t)\;, moving in a potential well, V, created by the positively charged proton. This computation reproduced the energy levels of the Bohr model.

But this was not enough, since Sommerfeld had already seemingly correctly reproduced relativistic corrections. Schrödinger used the relativistic energy momentum relation to find what is now known as the Klein-Gordon equation in a Coulomb potential:



He found the standing-waves of this relativistic equation, but the relativistic corrections disagreed with Sommerfeld's formula. Discouraged, he put away his calculations and secluded himself in an isolated mountain cabin with a lover.[citation needed]

While there, Schrödinger decided that the earlier nonrelativistic calculations were novel enough to publish, and decided to leave off the problem of relativistic corrections for the future. He put together his wave equation and the spectral analysis of hydrogen in a paper in 1926.[2] The paper was enthusiastically endorsed by Einstein, who saw the matter-waves as the visualizable antidote to what he considered to be the overly formal matrix mechanics.

The Schrödinger equation tells you the behaviour of ψ, but does not say what ψ is. Schrödinger tried unsuccessfully, in his fourth paper, to interpret it as a charge density.[3] In 1926 Max Born, just a few days after Schrödinger's fourth and final paper was published, successfully interpreted ψ as a probability amplitude[4]. Schrödinger, though, always opposed a statistical or probabilistic approach, with its associated discontinuities; like Einstein, who believed that quantum mechanics was a statistical approximation to an underlying deterministic theory, Schrödinger was never reconciled to the Copenhagen interpretation.[5]





Wave function - Wikipedia, the free encyclopedia

A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe any physical system. It is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (i.e. the Schrödinger equation) describe how the wave function evolves over time. The values of the wave function are probability amplitudes — complex numbers — the squares of the absolute values of which give the probability distribution that the system will be in any of the possible states.

It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ(position,time) and where | ψ | 2 is equal to the chance of finding the subject at a certain time and position.[1] For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.




Potential well - Wikipedia, the free encyclopedia

A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy.

Energy may be released from a potential well if sufficient energy is added to the system such that the local minimum is surmounted. In quantum physics, potential energy may escape a potential well without added energy due to the probabilistic characteristics of quantum particles; in these cases a particle may be imagined to tunnel through the walls of a potential well.

The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (i.e., be a lake) without any water flowing away toward another, lower minimum (i.e. sea level).

In the case of gravity, the region around a mass is a gravitational potential well, unless the density of the mass is so low that tidal forces from other masses are greater than the gravity of the body itself.

A potential hill is the opposite of a potential well, and is the region surrounding a local maximum.

[arkain101]

It was when I really understood this statement here:

The Schrödinger equation tells you the behaviour of ψ, but does not say what ψ is. Schrödinger tried unsuccessfully, in his fourth paper, to interpret it as a charge density.[3] In 1926 Max Born, just a few days after Schrödinger's fourth and final paper was published, successfully interpreted ψ as a probability amplitude[4].

Most importantly, this part here: The Schrödinger equation tells you the behaviour of ψ, but does not say what ψ. is

And that because: "Solutions to Schrödinger's equation describe not only atomic and subatomic systems, electrons and atoms, but also macroscopic systems, possibly even the whole universe"

It was when I started understanding all of this that I really got a much better understanding the heavier math work being discussed here, and what exactly DD's math was trying to accomplish (accomplished w/e).

I really agree that a person has to get a strong understanding of these maths and physics, to even start to have a clue what DD's fundamental equation is expressing.

I look forward to picking those equations apart... and understanding further.. Now that these things have "clicked", I feel a lot more prepared to get into the heavier parts of discussion..

Great Stuff.

[AnssiH]

Originally Posted by modest

Clearly the difference (as Anssi has now pointed out) is that you have derived Schrödinger's equation in three-dimensional space with your equation while my banana-analogy has not been so derived. As such, the analogy is ill-made.

I think the fact that you originally missed this tells something about how confusing this thread has become, and was the reason for my previous post...

I think my trouble is the leap from 'a consistent (or internally consistent perhaps) explanation of unknown data' to what often seems characterized in this thread: 'a useful explanation for any given universe or any given reality'. If I accepted that DD's fundamental equation is indeed something that any consistent explanation of an unknown reality must follow then it would not immediately follow that any explanation derived from the fundamental equation would be a useful explanation for *any* realty. With the example I've been using:

If Newtonian mechanics in 2 dimensions is a useful and self-consistent explanation for some unknown data (or reality) then it should obey the fundamental equation. If Newtonian mechanics in 3 dimensions is a useful and self-consistent explanation for some unknown data (or reality) then it should obey the fundamental equation. It does not follow that deriving 2 dimensional Newtonian mechanics from the fundamental equation means that it will be a useful explanation for any given reality. It's a converse error.

Now, I may be right and I may be wrong about this.

Maybe so, I think if you dwell on that possibility, perhaps it is possible to point out that by an amazing guesswork, and if ontological reality was appropriate for it, one might come across definitions that yielded absolutely correct predictions for all our past. I think, if one wants to cover that possibility too, we should perhaps say something like "if any reality is expressed by first transforming it to "patterns", that are then transformed to a self-coherent model of persistent entities, then the probability of specific future for those self-defined persistent entities can be properly expressed via Schrödinger's equation"

Meaning, that's just one way to do it, and if instead of following the general symmetry requirements during making your world model, you rather made just the proper guesses about the ontological reality, and the ontological reality really was a set of persistent entities, and their behaviour was proper for absolute prediction (no unaccountable feedback from the rest of the universe etc), then perhaps you could land upon a more accurate model of reality.

There are a lot of difficult details involved with that idea, and I think it would be a good idea to look at the epistemological analysis first in terms of what it explains about our current physics models, before going into that issue. (Especially its implications to Bell Experiments are in my opinion quite striking)

But, regardless, I find it troubling that in bringing up the question I've yet to see it resolved by anybody addressing the issue or explaining the analysis. In fact, I've been away from this thread for a couple days (been too busy) and I return to find I've developed some interesting motives in my absence:

I can honestly say that I just tried to explain, as best I could, how that result would be within the realm of possibility. As I assumed you had picked up that it was the results of the analysis that implied it, so then it just sounded like you felt its results were non-sense. I.e. I felt like you were uninterested to even look at the proof.

Nevertheless, I must say;

If two people have absolutely equivalent worldviews (including the definition of a dimension) except that one worldview is 3D while the other is 4D then the worldviews are mutually exclusive and they cannot both be useful to the same reality.

Unless I'm misinterpreting you in some very strange way, that is unequivocally false. They can certainly both describe the same reality in a manner that yields proper predictions, much the same way as Minkowski Spacetime can be viewed as a description of 4 dimensional persistent objects (static, or perhaps following some multiverse scheme, dynamic?), or 3 dimensional persistent objects governed by very specific dynamics.

The problem in your example is simply that...

One person will deduce that 6 2D faces are required to bind an element while the other deduces that 24 are required. They can't both be right (if they share the same reality).

...you have restricted their worldviews more than necessary. They are not both forced to see those 2D faces as 2D faces in their conception of reality, and judging from your posts, I think you should easily understand why "they are not forced", yes? (their perception being their interpretation of the raw data and all that)

And if you follow the epistemological analysis all the way to Schrödinger's Equation, I think you can see more about that issue; that if the same raw data is available to both, what happens is simply that they'd come to conceive the same data in terms of very different looking persistent entities. In the form of defined entities, there just couldn't be things disappearing and re-appearing in manners that would break the self-coherence & symmetry requirements.

I'm sorry if you feel like I'm just repeating the same argument over and over. I don't want you to feel like I've just made things up or otherwise given a coloured picture to you just for keeping you motivated; I just really think this exact issue is resolved by the epistemological analysis. And thus, perhaps it is not necessary to dwell on this "conceptual explanation".

-Anssi

[arkain101]

I'm sorry if you feel like I'm just repeating the same argument over and over. I don't want you to feel like I've just made things up or otherwise given a coloured picture to you just for keeping you motivated; I just really think this exact issue is resolved by the epistemological analysis. And thus, perhaps it is not necessary to dwell on this "conceptual explanation".

Agreed. Anything our mind is going to be able to imagine or comprehend is going to be, at its max dimensional representation, 3 dimensional. Regardless of the geometry or math, and the scale an illustration is designed to represent. When we discuss anything visual and/or represent anything visual, when we put out imagination aside, what is left behind will be a product of our macroscopic 3D world.

Even something 2D is a concept. Like a square. You can't construct a square in the ontological sense, that is actually 2D in our epistemological world view. When we go to truly examine it, it will be 3D. Anything that is infact 2D, like the shapes and things on this computer screen are mental concepts of shapes, but what it really is, is a computer screen, and dots, and width, and length, and thickness. And furthermore, what those things really are, is unaquivacally unknown.

Its true to mention a person educated on the mathematics will understand that a multidimensional illustration may have some complex behaviors. A the same time, if a child came up and examined the illustration he might say something like, "Hey that looks like a Turkey", and in the end that is the extent of its expression realistically.

[Doctordick]

Originally Posted by arkain101

Agreed. Anything our mind is going to be able to imagine or comprehend is going to be, at its max dimensional representation, 3 dimensional. Regardless of the geometry or math, and the scale an illustration is designed to represent. When we discuss anything visual and/or represent anything visual, when we put out imagination aside, what is left behind will be a product of our macroscopic 3D world.

The issue is, "why is that so?" Does anyone besides me have an answer to that question?

If anyone has an alternate answer, I would love to hear it

Have fun -- Dick

"Knowledge is Power!" And all power can be abused!
The most popular abuse of the power of knowledge is to use it to hide stupidity!

Richard D. Stafford, Ph.D. Theoretical Physics,1971

[Kriminal99]

Originally Posted by Doctordick

Well sort of, yeah; but you make it sound like I am holding something over your head. I hope you don't think that I am forcing you into something.

I think we have a starting point. Maybe it would be best if we just used the word “noumenons” to indicate the nature of reality instead of my “valid ontological elements”. Or maybe we can call “valid ontological elements” to be ontological elements which can be directly related to these noumenons. I really don't see any real conflict there as, from my perspective, neither can be exactly “known”. What is important is that the purpose of our world view is to explain “what we know”: i.e., these noumenons or valid ontological elements, whatever we choose to call them. Unless you complain, I will use the the two terms as if they mean exactly the same thing and, when I use the term “know” I will be referring to exactly this same collection of noumenons totally sans understanding.

My first step in constructing that “map” of what we know is to assert that then number of these noumenons which reside behind our explanation has to be finite. I assert this because the word “infinite” means literally that no matter how many are explicitly taken into account as being behind your current world view, there are more that are not yet included. It follows that, if you have a current world view, the number behind that world must be finite otherwise, you are not including some.

Just as an aside, there are those who would say that it is possible to have something which is infinite behind that world view; I hold that such a view is unacceptable as that infinite entity is either one thing or it is divisible in which case it is not “elemental”. The issue is that you cannot take into account an infinite number of elemental entities as individual entities, not that an infinite number of elemental entities can not exist.

I invented and presented my definition of time as follows: “the past” is what we know (those noumenons on which the map is built); “the future” is what is not known (those noumenons which have yet to become relevant to that map). “The present” is the boundary of the past: i.e., noumenons added to those which are already part of our map.

The purpose of “time” was to allow our world view to accommodate changes in “what is known”: i.e., new noumenons. From the above it should be clear that “the past” can be seen as a collection of “presents”. We can see what we know as proceeding from “nothing” to what we now know as a collection of changes in “what we know”. Again, the number of “presents” we can actually know must be finite (same argument as above). If their number is finite, they can be indexed and I will call the index “time” and represent it with a number referred to as “t”.

Likewise, I defined another numerical index, which I called x, to identify a specific noumenon making up a specific “present”. At this point you should see that “the present” has been conceived as possibly consisting of more than one noumenon. If that is the case, I am going to further state that “order”, with respect to one another, cannot be a characteristic of these simultaneous (simultaneous meaning “occurring at the same time”) noumenons as “time” was introduced for that exact purpose.

So, at this point, the noumenons (or valid ontological elements available to construct that map) can be seen as a collection of discreet points in an (x,t) plane. The important point being that there exists no collection of noumenons which cannot be so displayed.

Now I earlier defined an explanation to be a method of generating expectations from known information. At this point, the “known information” in our map consists of a set of numbers. Now, down the road, when one has a viable explanation of reality, these noumenons (or valid ontological elements) will be identified by that explanation. The totality of the explanation includes explaining the meanings of the words used to identify those elements. The actual symbols used to identify these elements is of no real significance at all. It could be in English, it could be in French, it could be in Chinese or it could even be in Linear A (a currently undecipherable language) which someone would have to learn first. Actually, people seem to forget learning the other languages is also an important necessity prior to understanding an explanation in one of them. So the only real difference is that a specific explanation requires a specific set of indices which are internally consistent under that explanation: i.e., the idea that our references are numerical indices is no limitation on the explanation at all.

Earlier I stated that my only interest was in flaw free epistemological constructs (explanations lacking a flaw of any kind). Qfwfq was apparently confused by my justification for such a step so I don't know if he has just decided to vacate this discussion as irrational or was appeased by my attempt at clarification given in post #8 (this thread). At any rate, the next step is to begin the analysis of explanations in general given the basis outlined above (a collection of discreet points in an (x,t) plane).

As an aside, it should be clear that any flaw free explanation must explain each and every ontological element upon which it is based whether those ontological elements are valid or not. Any demonstrable error in that explanation will invalidate it. Thus we can be confident that a flaw free explanation must explain all valid ontological elements as they are a mere subset of the ontological elements it is required to explain. It follows that there is no real need to worry about whether or not the actual ontological elements required for that explanation are valid.

The absolute first step in that analysis is to recognize that, under my definition of an explanation, there exists only one explanation which requires no epistemological construct at all. That is what I call the ”what is”, is “what is” explanation. That explanation amounts to nothing more than a table of ontological elements available at a specific time. It is a table of the x indices associated with each t index which constitute the past (what is known). A flaw free ”what is”, is “what is” explanation is one which is consistent with the known past. (A valid ”what is”, is “what is” explanation would be one which was a table of valid ontological elements available at each specific t.)

One problem with the ”what is”, is “what is” explanation is that it gives us not a hint as to what to expect; but that does not mean that it yields no expectations. The expectations yielded by the ”what is”, is “what is” explanation are: exactly what was seen so long as the index t refers to the past and exactly equal probability for all possibilities when the index t refers to the future.

If one's expectations are to be seen as given by a mathematical function of those points defined by the indices in that (x,t) plane then the abrupt change in the nature of that function at the boundary of the past (i.e., the function changes abruptly in what has been defined as the present) is a very interesting phenomena. It is essentially equivalent to the phenomena often referred to as “the collapse of the wave function: our expectations go from zero everywhere (from a mathematical perspective, the (x,t) space is continuous so equal probability for every point is exactly zero) to one for every entry in our ”what is”, is “what is” table of indices and zero for every point not in that table.

Note that the above analysis is valid for all pasts within the referenced data. Prior to any specific present becoming part of “the past” the expectations are exactly as describe in the previous paragraph (there is no prediction) and immediately after that present becomes part of the past the entries in the table become fixed (and the actual indices in no way contradict the expectations as they could have been anything).

What makes that explanation “flaw free” is that it yields exactly the ontological elements upon which it is built (including the temporal relations). What makes it worthless is that it makes utterly no usable prediction. What makes it interesting is that it defines exactly what kind of conditions any “flaw free” explanation must fulfill: it must match the ”what is”, is “what is” table exactly. The only difference between a valuable explanation and our ”what is”, is “what is” explanation is that the “valuable” explanation yields non uniform expectations outside that defined ”what is”, is “what is” table: i.e., it establishes some kind expectations above and beyond “anything goes” and gives non zero expectations outside the established past (it is capable of making predictions).

If you have arguments with what I have said, I am ready and willing to defend them further. If you feel my deductions so far are rational and acceptable, I will proceed further.

Looking to hear from you -- Dick

You are basically taking what is a common philosophical argument and inflating it to gigantic proportions with unnecessary mathematics metaphors. And the funny thing is, these people buy it because they incorrectly attribute some privileged status to mathematics vs pure logic based arguments. All you are doing is rehashing lehrer's argument that we must work with what we have been given or we have nothing to do.

The only thing that you can perceive for certain at any one time is the present. Your past memories may have been slanted or perhaps even fabricated. At times I remember things from dreams as if they really happened. You seem to be attributing a perfect status to memories.

[Kriminal99]

Originally Posted by Doctordick

The issue is, "why is that so?" Does anyone besides me have an answer to that question?

If anyone has an alternate answer, I would love to hear it

Have fun -- Dick

"Knowledge is Power!" And all power can be abused!
The most popular abuse of the power of knowledge is to use it to hide stupidity!

Richard D. Stafford, Ph.D. Theoretical Physics,1971

Yeah. The answer is simply that humans are not fully creative beings. They can reorganize things they have seen into new things, but they cannot create something that is not a function of things they have experienced before.

[Doctordick]

Originally Posted by Kriminal99

The answer is simply that humans are not fully creative beings. They can reorganize things they have seen into new things, but they cannot create something that is not a function of things they have experienced before.

That is a patently false statement. If it were true, any newborn baby could handle any employment currently available in the job market. In growing up, they create (in their minds) understanding of many things they have never experienced before.

For the life of me I can not comprehend your overwhelming desire to put forth totally unthoughtout conclusions.

Have fun -- Dick

[Rade]

There is a big difference between creating new "understanding" of things within the mind, and creating new "things" within the mind, this is the point I believe being made by Kriminal99.

The human mind does not create new reality prior to the process of understanding, it takes reality as given by the senses and forms concepts that then lead to understanding. The human mind does not understand reality, it understands concepts it has created based on the reality given by its senses. If it were true that the human mind could understand reality, that would mean the human mind knows what is inside reality as subject outside itself as object--such is impossible. The human mind may take concepts and create new understanding of them, at times creating new concepts by combining prior concepts, as new facts of reality become known over time. All above is under the control of volition.

[AnssiH]

"Anything our mind is going to be able to imagine or comprehend is going to be, at its max dimensional representation, 3 dimensional. Regardless of the geometry or math, and the scale an illustration is designed to represent. When we discuss anything visual and/or represent anything visual, when we put out imagination aside, what is left behind will be a product of our macroscopic 3D world."

"And why is it so?"

"The answer is simply that humans are not fully creative beings. They can reorganize things they have seen into new things, but they cannot create something that is not a function of things they have experienced before."

Am I totally misreading you, or is your argument really "the reason we understand things in 3D form is because that is something we have experienced before"?

It is really mystifying to me, how can people cook up such a "just is" explanations without blinking an eye. We experience reality "just by looking at it", and "seeing happens"? Is that it? Also, I have no idea what Rade means when he says "reality given by the senses". Reality just hits the surface of our eye and that's when we see it?

But you guys probably also reckon that it is data patterns (instead of "picture") that enter our cortex? If so, I'm sure you also understand that there must occur some interpretation process there in some sense for the data patterns to be "understood" as anything, yes? And you should understand that "experience" is however we understood that data, i.e. there exists an an interpretation of the data but we don't see "the data itself" so to speak, yes?

The question was, how does reality become conceived in terms of a 3D representation. Notice, that before any idea of space is sensical, there must exist some idea of "objects". And there can be no explicit statements of "objects" in the sensory data (that you'd know about a priori), but instead the data must first become interpreted that way. So, how does the data become interpreted that way?

What DD was asking about has to do with that transformation process between "data patterns" and "spatial presentation of objects".

Before you jump into another "just is" reply, like "because it is correct" or "because we are so used to looking at reality" or whatever, please note that the "unnecessary mathematics metaphors" is actually a description of that exact transformation process between unknown data batterns and spatial representation. About how the spatial representation exists due to how the data is ordered for prediction reasons, but not due to what the data actually is. It is an explanation about why and how any data patterns (where there are no "objects" as such) can be translated into a useful "spatial representation of objects".

And don't worry, mathematics is not lifted to any priviledged status, apart from being a handy tool of tracing logical relationships. Just like "speed = distance / time" is a statement of a relationship between concepts that we defined, DD's work is a statement of not-so-obvious relationship between "necessary symmetries of a world model" and "modern physics definition of reality". It is not a statement of ontological reality itself.

-Anssi