Alex,
The diagrams you are thinking about are limited to what can be translated to a formal linear notation. But I am talking about the general theory of diagrams by C. S. Peirce, which is immensely richer. Those diagrams can INCLUDE full multidimensional images as parts at any arbitrarily refined precision.
They can also include as parts any mathematical structures of any kind in any number of dimensions. They can subsume as parts anything and everything that can be included in any digital device or any analog device that can simulate continuity at any resolution.
Please read the attached Excerpt234.pdf from Sections 2, 3, and 4 of the article I'm writing.
To answer your questions, they can represent EVERYTHING you are asking for in your list below.
Please read those excerpts. Then we can begin to discuss the issues in terms of the rich foundation that Peirce was developing. He died before he completed all the work, but he outlined the methods. And I have added some features along the lines that he had suggested.
John
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
John,
Diagram is just one kind of math structure: mostly labeled or attributed graphs. To model reality we use much much more. One of the most powerful is an analytical function - we can keep a movement inside like l=gt2/2.
I did not find any questions in the MN email. Just a rejection to discuss my very tiny question.
Let me show [1] my short discussion with Claude 2 as an example of participating in.
Queries are mine, answers are from https://claude.ai
Next questions should be:
-What are math structures there?
-What kind of mind tasks may be solved using these structures? Do we have these algorithms?
It is of course possible that these algorithms will use some kind of graph structure to solve mind tasks.
As G.W.F. Hegel wrote ~"All categories are working in any mental act".
Alex
[1]
Q:How to represent in a computer a 3D picture of a real object with the same level of detail as we see it?
Here are a few ways to represent a 3D picture of a real object in a computer with a high level of detail:
- 3D Scanning - Use a 3D scanner to capture the shape and surface details of the real object. This creates a 3D mesh model that can be imported into 3D modeling software. The resolution of the scan determines the level of detail.
- Photogrammetry - Take multiple photos of the object from all angles and use photogrammetry software to generate a 3D model by analyzing the 2D photos. The more photos from more angles, the higher the detail.
- 3D Modeling - Manually model the object in 3D modeling software like Maya, 3ds Max, or Blender. This takes artistic skill but allows full control over the level of detail. High polygon counts capture more detail.
- Point Clouds - Some 3D scanners generate point clouds which are collections of points in 3D space that depict the surface of an object. These can be rendered to visualize the object in very high detail.
- Volumetric Capture - Use special cameras and software to capture a full 3D volumetric video of an object. This captures surface details and internal structures. It requires complex hardware and software.
The key is to capture geometric details like shape, surface patterns, textures as well as color/shade information at a high resolution. The more surface and color data captured from the real object, the more realistic and detailed the 3D representation can be when rendered on a computer.
Q:Where to read about these techologies?
Here are some good resources to read up more on the technologies for capturing detailed 3D models of real objects:
- 3D Scanning: The book "3D Scanning and Printing for Dummies" provides a good overview of 3D scanning methods and technologies. The Artec 3D website also has some helpful articles explaining scanning techniques.
- Photogrammetry: The book "Photogrammetric Computer Vision" goes deep into the math and algorithms. For a more general overview, the Wikipedia article on Photogrammetry is a good starting point. The AliceVision project also has resources on multi-view photogrammetry.
- 3D Modeling: Pixologic has a free ebook "The ZBrush 2020 Handbook" that covers high-detail organic 3D modeling for characters and objects. The book "3D Art Essentials" also covers 3D modeling principles using Maya.
- Point Clouds: The journal paper "A survey of point-cloud semantics in geometry processing" provides a technical survey of point cloud techniques. The Point Cloud Library (PCL) documentation also explains point cloud concepts.
- Volumetric Capture: Microsoft has research papers and videos explaining volumetric capture on their Mixed Reality Capture Studios page. The book "3D Video Technologies" also covers volumetric video concepts.
For a comprehensive overview, the Siggraph organization has many technical resources on 3D imaging and modeling, including courses and videos from their conferences.
Alex,
Mihai Nadin is asking very important questions. Perception and action are fundamental for every kind of thinking. When you perceive something, that sets the sage for anticipating action. The anticipation stimulates the thinking that leads to the action. I have emphasized the methods that Peirce developed in detail, but I recognize that anticipation is an important piece of the puzzle. LLMs, by themselves, don't contribute anything useful to those issues, but they can be important for communication. That's what they were designed for: machine translation among languages, natural or artificial.
Alex> my main topic is How to represent in a computer a 3D picture of a real object with the same level of detail as we see it.
Short answer: Impossible with LLMs, but methods of virtual reality are developing useful approximations.
Next question: How do humans and other animals process the continuous imagery they perceive, decide what to do, and do it. And maybe if there is some reason to communicate with other animals friendly or not, decide to activate their communication methods. On this latter point, LLMs promise to make important contributions.
Language follows the heavy-duty thinking. Its focus is on communication. But it's impossible to understand what and how language communicates without starting at the beginning and following the many steps before language gets involved in the process.
I emphasized diagrams as an important intermediate stage. The first step from imagery to diagrams to language begins by breaking up the continuum of perception and action into multiple significant image fragments and their interrelationships.
Those fragments, which Peirce called hypoicons, retain a great deal of the continuity, You now have a diagram that links continuous parts to one another in two different ways: (1) geometrical positions in the original larger image, and (2) symbolic relations that identify and relate those fragments.
This analysis continues step by step to replace continuous parts with symbols that name them or describe them with discrete detail. But many interactions and operations can take place at that early stage. When you touch something hot, you don't have to identify it before you jump away from it.
Some people say that they never think in images. That is because they don't have a clue of what goes on in their brains. A huge amount of the computation on perception and action takes place in the cerebellum, which contains over 4 times as many neurons as the cerebral cortex. In effect, the cerebellum is the Graphic Processing Unit (GPU) that does the heavy duty computation.
Nothing in the cerebellum is conscious, but all its computations are processing that continuum of raw sensations from the senses and the huge number of controls that go to the muscles. That is an immense amount of computation and INTELLIGENCE that takes place before language even begins to play a role in what people call conscious thought.
The final diagrams that have replaced all the raw imagery with discrete symbols on the nodes and links of a diagram are the last stage before language -- in fact language is nothing more than a linearized diagram designed for translation to linearized speech.
The overwhelming majority of our actions bypass language interpretation and communication. Thatt's why people get in trouble when they're walking of driving while talking on a cell phone. While their attention is focused on talking, the rest of their body is on autopilot.
All the heavy duty intelligence occurs long before language is involved. Language reports what we already thought. It is not the primary source of thought. However, language that we hear or read does interact with all the imagery (AKA virtual reality) in the brain. The best intelligence integrates all aspects of neural processing.
But language that does not involve the deeper mechanisms is superficial. That's why LLMs are often very superficial. The only deeper thought they produce is plagiarized from something that some human thought and wrote.
And by the way, I recommend the writings in https://www.nadin.ws/wp-content/uploads/2012/06/edit_prolegomena.pdf
They're compatible with what I wrote about Peirce, but I believe that Peirce's analyses of related issues went deeper into the complex interactions. Those issues about anticipatory systems are compatible and supplementary to Peirce's writings, which I believe are essential for relating the complexities of intelligence to the latest and greatest research in AI today.
John
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
Dear and respected Mihai Nadin,
I look at my description as a problem statement. Your email means that you will not take part in the discussion of this problem. I'm truly sorry.
Best wishes,
Alexander Shkotin
чт, 16 нояб. 2023 г. в 00:32, Nadin, Mihai <nadin(a)utdallas.edu>:
Dear and respected Alex Shkotin,
Dear and respected colleagues,
- YOU wrote:
my main topic is How to represent in a computer a 3D picture of a real object with the same level of detail as we see it.
Let us be clear: the semiotics of representation provides knowledge about the subject. The topic you describe (your words) is in this sense a false subject. May I invite your attention to https://www.nadin.ws/wp-content/uploads/2012/06/edit_prolegomena.pdf
Representations are by their nature incomplete. They are of the nature of induction.
Visual perception is informed by what we see, but also by what we think, by previous experiences.
- Mathematics: I brought to your attention (long ago) the impressive work of I.M. Gel’fand. Read his work—the limits of mathematical representations (and on operations of such representations) are discussed in some detail.
- Mathematics and logic—leave enough room for diagrammatic thinking as a form of logical activity. C.S. Peirce (which John Sowa relates to often) deserve also your time. Read his work on diagrams. Mathematical thinking is not reducible to logical thinking (in diagrams or not). The so-called natural language (of double articulation) is more powerful than the language of mathematics—it allows for inferences in the domain of ambiguity. It is less precise, but more expressive.
- After all ontology engineering is nothing else—HUGE SUBJECT—but the attempt to provide machines, working on a 2 letter alphabet under the guidance of Boolean logic, with operational representations of language descriptions of reality.
Best wishes.
Mihai Nadin
Alex,
Those three points of yours are important:
1> Let's take a particular entity or kind of process, and look at terminology used by people who work with and study this.
That is a very good starting point. Let's take music. That is an example of a non-linguistic subject that all of us have some experience with. And we can study and compare the language descriptions by the experts in each genre. As you will quickly see, you will find a huge amount of variation among the most talented musicians, even of the same genre. Furthermore, musical notation (diagrammatic) is sufficiently accurate that it's possible to specify the exact sequence and combination of notes in any composition.
But -- and this is a very big BUT!!! -- you cannot use that notation or the words that describe it to distinguish precisely a performance by (a) Jascha Heifetz, (b) a typical violin player in a college orchestra, or (c) the kid next door who is practicing the same piece. A music critic can say many things in praise of (a) and the faults of (b) and the huge faults of (c). But none of that criticism will tell any listener how to modify the sound of (b) or (c) to make it equivalent to (a).
Natural languages are very imprecise. And it's impossible for any language-based notation to be more precise. I will also add that it's impossible for any discrete representation -- including diagrams of any kind -- to be sufficiently precise to express those differences.
2> give me an example of a diagram which is not a picture and vice versa... But let me point here again: I am not about terminology, I am about the unique ability of mind to keep inside and process 3D pictures, not diagrams.
A talented violinist who hears (a), (b), and (c) can mimic the limitations of (b) and (c) on the violin. That same person can also mimic a good performance that begins to approximate (a) and explain in words and musical passages on the violin where his or her own performance does not quite match the master's.
3> But let me point here again: I am not talking about terminology, I am about the unique ability of mind to keep inside and process 3D pictures, not diagrams.
I gave the example of music because it has an excellent diagrammatic notation that captures much of the sound. But it also shows that the human mind of the performer can add a very important amount of musical talent above and beyond what is written. It also shows that the human minds of people who cannot play the violin, can recognize the differences in (a). (b). and (c).
Good musicians are better able to appreciate the difference, but even people who can't play the violin can appreciate the differences.
The same is true for an open-ended variety of performances by experts in any field. My talent for gymnastics or ballet or hockey or racing a horse is non-existent, but I can appreciate the abilities of experts in those fields. And people who have worked in those areas have a much deeper appreciation than I do. But they can't explain the methods in a way that would enable somebody like me do those things.
The same is true for every important thing we do: words alone aren't sufficient. You must have the experience.
Diagrams alone aren't sufficient. But for each one of those fields -- music, gymnastics, ballet, hockey, horse racing..., an expert talking to another expert can use diagrams (including gestures) to express the critical issues BETTER THAN using language by itself.
As I keep saying, there is much more to say -- partly because language alone is not able to express what language cannot say. I can only give examples where language breaks down.
John
----------------------------------------
From: "alex.shkotin" <alex.shkotin(a)gmail.com>
By the way I asked my friends from MIPT alumni How many photons are in such an atto-impuls. And after some terminolgy aligment I got an answer: ~100 000.вторник, 14 ноября 2023 г. в 11:43:16 UTC+3, alex.shkotin:
IN ADDITION: We can take as an example of coherent knowledge a physics of atto-seconds impulses (2023 Nobel on Physics) and research if they have "Diagrams, Pictures, glyphs, Icons and Patterns."
вторник, 14 ноября 2023 г. в 11:24:46 UTC+3, alex.shkotin:
Ravi,
My way is more simple: Let's take a particular entity or kind of process, and look at terminology used by people who work with and study this.
This is for me some real theoretical and practical knowledge. And if in some such a community we find out that they use in the same one theory (coherent knowledge) all the terms you mentioned, we can ask them (not me) your questions.
Plus, for example, a question of this kind: give me an example of a diagram which is not a picture and vice versa.
But let me point here again: I am not about terminology, I am about the unique ability of mind to keep inside and process 3D pictures, not diagrams.
Alex
The attached Excerpts.pdf are from the article on phaneroscopy I'm writing. They show that Peirce's writings, especially in the last decade of his life, have strong implications for the latest research in the cognitive sciences (philosophy, psychology, linguistics, artificial intelligence, neuroscience, and anthropology).
I believe that these issues show that Peirce's writings are central to 21st c developments in those fields. They are likely to be critical issues at the Peirce Bicentennial in 2039. That's only 16 years away.
I participated in the Sesquicentennial at Harvard in1989 and the Centennial in 2014. I might not make it to the Bicentennial, but it's time to start thinking about the issues that will be discussed.
Peirce wrote that his writings would be central to the developments for 400 years. We're getting close to the halfway point.
John
Alex,
Absolutely NOT!!!!!
Alex> we should keep diagrams separately
Diagrams are the intermediate step between continuous images and linear notations. The first step in analyzing any kind of continuous space or structure is to draw a diagram.
Just look at any book on geometry, starting with Euclid. (There were earlier manuscripts. But after Euclid, nobody bothered to recopy them.)
Just look at any map. The first step between a continuous landscape and any notation of any kind is a map that identifies cities, towns, mountains, rivers, streets, and many, many POINTS and LINES of interest,
And look at any plan for any kind of structure -- airplanes, buildings, cars, bridges, etc., etc. etc. Every continuous design begins with a map or blueprint or other kind of diagram.
A diagram is a geometrical structure made of discrete points and lines that map to significant points and lines on a continuous space. That is the fundamental reason for diagrams in knowledge representation.
The most ancient monuments like Stonehenge and other structures on all continents except Antarctica are diagrams that reflect the significant points (stars, planets, and the moon) in a continuous sky. The constellations that people imagine are based on diagrams with lines that connect those points.
That is why I keep repeating the importance of diagrams. People who are born deaf can communicate perfectly well with moving three-dimensional diagrams. Children who have normal hearing, but are born to deaf parents babble with the hands, not by sounds. Their first languages are sign languages -- and they are not handicapped in any way when they finally learn to talk.
There is strong evidence that human spoken languages evolved from the sign languages of the apes. In fact, hearing people who learn signed languages score higher on IQ tests that involve diagrams -- after they learn a sign language.
That is one of many reasons why I keep emphasizing: LLMa are NOT a step toward a human-level intelligence. They're a useful adjunct, but not a fundamental form of knowledge representation. Diagrams are fundamental, and linear notations are useful for (a) typing, and (b) saving space on a printed page..
John
PS: There were some very smart, but hopelessly misguided mathematicians called the Bourbaki. They tried to get rid of diagrams. They wrote some interesting books, but their goal of getting rid of diagrams was hopelessly misguided. And it failed miserably. Their books still contain some useful ideas, but nobody uses them tp teach students..
----------------------------------------
From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
Ravi,
Relationships between World of Words and World of Pictures (3D by the way) is a great topic. We will need a new thread to collect ideas.
But we should keep diagrams separately, IMHO :-)
Alex
вс, 12 нояб. 2023 г. в 12:06, Ravi Sharma <drravisharma(a)gmail.com>:
Alex
Thiswas a 1-2 page written exchange with the then living philosopher Professor Norwood Hensen ay Yale. He was also known as a flying Professor and unfortunately he died young while flying.
The summary of my assertion with him was that what we model in our mind and understand as the meaning is often based on a picture or visual construct and not always the text to understand. We can talk about this later, it is also studied in infants or children who inherently understand many things such as fall due to gravity, etc,
Now as we are working in ontology, we can relate these days with graphs, knowledge graphs and AI beyond LLM!
Thanks for showing interest in my old theory, I will try to see in my archives if I based on what he then published anywhere that I read and responded or how we corresponded with each other, After 3 years at Florida I went to Yale for postdoctoral research and also did teaching in the physics Department.
Thanks.Ravi
Logical Graphs • Interpretive Duality 1
• https://inquiryintoinquiry.com/2023/10/26/logical-graphs-interpretive-duali…
All,
The duality between Entitative and Existential interpretations
of logical graphs is a good example of a mathematical symmetry,
in this case a symmetry of order two. Symmetries of this and
higher orders give us conceptual handles on excess complexity
in the manifold of sensuous impressions, making it well worth
the effort to seek them out and grasp them where we find them.
Both Peirce and Spencer Brown understood the significance of
the mathematical unity underlying the dual interpretation of
logical graphs. Peirce began with the Entitative option and
later switched to the Existential choice while Spencer Brown
exercised the Entitative option in his Laws of Form.
In that vein, here's a Rosetta Stone to give us a grounding in
the relationship between boolean functions and our two readings
of logical graphs.
Boolean Functions on Two Variables
• https://inquiryintoinquiry.files.wordpress.com/2020/11/boolean-functions-on…
Regards,
Jon
cc: https://www.academia.edu/community/5k4z9V
Peirce's Law • 1
• https://inquiryintoinquiry.com/2023/10/19/peirces-law-1/
A Curious Truth of Classical Logic —
Peirce's law is a propositional calculus formula which
states a non‑obvious truth of classical logic and affords
a novel way of defining classical propositional calculus.
Introduction —
Peirce's law is commonly expressed in the following form.
• ((p ⇒ q) ⇒ p) ⇒ p
Peirce's law holds in classical propositional calculus but
not in intuitionistic propositional calculus. The precise
axiom system one chooses for classical propositional calculus
determines whether Peirce's law is taken as an axiom or proven
as a theorem.
History —
Here is Peirce's own statement and proof of the law:
❝A “fifth icon” is required for the principle of excluded middle
and other propositions connected with it. One of the simplest
formulae of this kind is:
• {(x ‒< y) ‒< x} ‒< x.
❝This is hardly axiomatical. That it is true appears as follows.
It can only be false by the final consequent x being false while
its antecedent (x ‒< y) ‒< x is true. If this is true, either its
consequent, x, is true, when the whole formula would be true, or its
antecedent x ‒< y is false. But in the last case the antecedent of
x ‒< y, that is x, must be true.❞ (Peirce, CP 3.384).
Peirce goes on to point out an immediate application of the law:
❝From the formula just given, we at once get:
• {(x ‒< y) ‒< α} ‒< x,
❝where the α is used in such a sense that (x ‒< y) ‒< α means that
from (x ‒< y) every proposition follows. With that understanding,
the formula states the principle of excluded middle, that from the
falsity of the denial of x follows the truth of x.❞ (Peirce, CP 3.384).
Note. Peirce uses the “sign of illation” “‒<” for implication.
In one place he explains “‒<” as a variant of the sign “≤” for
“less than or equal to”; in another place he suggests that
A ‒< B is an iconic way of representing a state of affairs
where A, in every way that it can be, is B.
References —
• Peirce, Charles Sanders (1885), “On the Algebra of Logic :
A Contribution to the Philosophy of Notation”, American Journal
of Mathematics 7 (1885), 180–202. Reprinted (CP 3.359–403),
(CE 5, 162–190).
• Peirce, Charles Sanders (1931–1935, 1958), Collected Papers
of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and
Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard
University Press, Cambridge, MA. Cited as (CP volume.paragraph).
• Peirce, Charles Sanders (1981–), Writings of Charles S. Peirce :
A Chronological Edition, Peirce Edition Project (eds.), Indiana
University Press, Bloomington and Indianapolis, IN. Cited as
(CE volume, page).
Resources —
Logic Syllabus
• https://oeis.org/wiki/Logic_Syllabus
Logical Graphs
• https://oeis.org/wiki/Logical_Graphs
Peirce's Law
• https://oeis.org/wiki/Peirce%27s_law
Metamath Proof Explorer
• https://us.metamath.org/
Peirce's Axiom
• https://us.metamath.org/mpeuni/peirce.html
Regards,
Jon
cc: https://www.academia.edu/community/V1grBl
The attached Section 5 of the article I'm writing includes new material about the linguist Michael Halliday. I was not sure whether to include a discussion of his work because the connection to Peirce was unclear. But after studying a diagram I include as Figure 12, I realized that it could be interpreted as a major contribution to phaneroscopy. In fact, I believe that it is an important step toward Peirce’’s goal of phaneroscopy as “a strong and beneficient science.”
Comments, suggestions, and criticisms are welcome.
John
