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@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.