I don't really understand your question. I'm sure part of the confusion is over the word "information" which I'm only using very loosely.. and the term 'information' is already a horribly ambiguous term to begin with, as you may be aware. So my apologies for entering with that vocabulary. (Hey it's just a rough draft!)
Indeed; I'm fine with using words loosely, especially hard to define ones, and like to define them on a purely as-needed basis. This might be a point where the need arises. I'll discuss "information" more in response to the end of your post but for the main thing I'll try and understand your ideas independently of the use of the word "information".
Good that you bring this issue up. I don't think any subdivision would necessarily lose any potentiality for design. e.g. There's nothing stopping you from refining the donut back into a cube, is there? I can't think of any reason to impose that limitation. The point is that once you have designed the donut, it makes little sense to design completely backwards back to the cube - (it would refute your intention of changing the cube in the first place). Now that you have a donut-template, you can copy and refine from that, and so forth. In this way, a nested hierarchy of shapes branch out from the original grouping.
Your confusion probably comes in trying to weigh changing quantities and constraints of things, but there really isn't anything more than the constraint of one's application of intention. Very similar to a 3D modeler with the model of a cube. I can potentially model and sculpt that cube into the shape of a human with a trillion+ facets... and from that human shape, conform it back into a simple cube again. If you remove the human constraint of time, (and the hardware constraint of graphics rendering) the only thing I am constrained by is my own decision-making. (actually for my 2nd draft I should use this for a better visual example)
On the subject of quantities, I think when I refer to a "totality" in the image, that refers to the totality of potential design decisions. Think of an artist with a blank canvas. The canvas is both empty and completely full of potential for design. As soon as you begin making design decisions (adding marks to the canvas) you are removing the total amount of potential for what the final product may be. Which is kind of an interesting way of looking at it.
The purpose of this 'creation hypothesis' is to show that deriving a series of branching templates from an original would create a large variety of types whose characteristics would then fall into a nested hierarchy. They would have to because you'd literally be creating a nested hierarchy by your actions.
And, importantly, this type of design would not be some contrived series of events made to "look like evolution", but a very simple and elegant design process that I've actually used myself many times without even thinking of it.
So what I get from this is that when you talk about "potential information" you mean something like "accessibility" in the space of possible configurations; so, the original block might be the totality of all possible configurations there could be, and when it's "refined" this involves choosing a place/area in this configuration-space or changing/narrowing that area (donut-based configurations are different from "any configuration" or cube-based configurations, meaning if every configuration is a point in configuration-space, focusing on donut-like things means you're in a different "area" of configuration-space than if you were focusing on cube-like things), and the "potential information" you talk about being conserved is really the ability to go from one point of configuration space to any other point in that space. In that context, because that ability is completely conserved, then the choice to continue within a same template at every step is indeed a choice
, not something that's constrained by factors outside one's control.
Is this an accurate description? Considering this I will go back to two questions I was curious about originally.
First, I wanted to know what the difference was between differentiation after creation, which involved loss of information, and differentiation during creation. If I take "information" here to be about the ability to go from one design to another, would it be correct to say the difference is in the reversibility of the changes? So the varieties generated from mutation and environmental pressures cannot "go back" to the original forms or completely different ones in a way that the first created forms can?
Alternatively, your example of the artist limiting their freedom once they add marks to the canvas suggests that maybe the reversibility ends, or is greatly limited in a way it never was before, once creation has happened - that the design plan
for a lion can be re-oriented into being that of a tiger, or an ant, or a tree, at any point in the design process, but once a lion is actually created
then the reversibility ends, and the now-flesh-and-blood lion cannot be turned into a tiger/ant/tree?
My other question was about why this process would be used for life but not other things, and your answer at the time suggested you think it has
been used for other things. Your description of the process now seems to confirm this, because in your description it seems to be very general and many things you say make it clear you see this as a very generic creation process, that could be used by any designer to design many different things.
It also seems clear from your description that the nested hierarchy isn't the result of constraints forced by the process, but of the designer's choices within that process.
So if I am describing the process by which life was created and I want the person I'm talking to to conclude that life falls into a nested hierarchy, wouldn't I need to specify that the designer chose
at every refining/templating step to stay within the parent template? This wouldn't be necessary if the choice were obvious, and things you've said suggest you think that it is (you ask why one would bother going back from the donut to the cube after going from the cube to the donut in the first place), but templating is only one design principle. Another is modularity, where you integrate many different elements from different templates into a whole. It is also sometimes the case that a designer needs to solve a given problem, and the best solution isn't a subset of the current template one is in; this would be a case where one could justify the choice of changing or combining templates. In other words, would it be accurate to say that the design process you've described allows
a nested hierarchy, but doesn't necessarily predict
Almost all the examples you gave to illustrate the process involved the design of things that don't
easily fall in nested hierarchies, so clearly it is possible and common to use that process and not end up with a nested hierarchy.
I'm not sure I understand you're thinking here. If I have two copies of a book, and the chapters are reversed on the 2nd book.. are you suggesting the 2nd book now contains more information than the first? That seems very strange to me but maybe you have a deeper understanding than I. I'm still not sure of the relevance here but I'm happy to keep musing on the subject for now.
There is less relevance now that I think I better understand your process independently of the word "information" (well, at least there is if my "better understanding" is actually accurate
) but I'm happy to keep musing too.
To answer your question, I wasn't comparing the information in the first file with information in the second file; I was comparing the total information of all the files, in the case where a copy is rearranged vs where it isn't. It is clear that "I have two copies of a book" takes less data to describe than "I have two copies of a book and the chapter orders are inverted in one of them
"; I needed to add the italicised portion to correctly describe the system. This might seem a bit strange with books, where order both matters and it doesn't: it matters because we can tell a "normal" book from a garbled one, but because the normal book has meaning that the garbled one doesn't it's easy to ignore the garbled one, or assume it's so trivial to go from one to the other that we forget there's an actual step involved, or that you need to specify that it's garbled. But consider cases where order matters for different reasons, like a recipe. If you rearrange the order of the steps in a recipe you're likely to not just get a garbled version of the original recipe; you get a different
recipe. And it's easier to see that "one recipe + a reordered version of that recipe (which could be two recipes)" contains more information than "two copies of one recipe (which is basically one recipe)".
So to get back to the files, it's not that a rearranged file contains, on its own, more
information than the original file; but it does contain different
information than what is in the original file, namely the information that's related to the ordering of its content, meaning both together contain more information than the original file on its own did (or a set of perfect copies of the original file do). (again, that's only if order matters; if order doesn't matter then the rearranged copy can be considered identical to the original file. Just like two bags of identical scrabble tiles can be considered interchangeable)
But this doesn't seem to be the concept of "information" you were using at all, so it's only relevant insofar as you want to use the word "information" and want to understand why people might be confused.