Everyday mechanics
Alex Shkotin
Dear and respected Mihai Nadin, following your email
MN: "We do NOT see a line, or a 2 dimensiuoinal space, or what that matter an n-dimensional space...We see REPRESENTATIONS."
For me, it's the incorporation of categories into everyday speech that usually adds nothing to the essence of the matter. Although this is what Janet seems to be interested in.
When I look in a certain direction and see a surface nearby, it's usually the surface of some body, or a structure of bodies, constructed in one way or another from a huge number of molecules.
Thus, physical bodies at any given moment occupy a certain place in space among other bodies, and we sometimes see the form of a surface of this place.
For simplicity, it's suggested to assume that the surfaces of bodies are geometrically tangent to each other, i.e., have common points. Although, of course, bodies cannot share atomic nuclei.
What categories are implicitly used in this text? Probably all of them.
And then the philosophical or logical nuances begin:
When I look at a body, I don't see a representation of it; I have a perception of it, but I see the surface of the body.
When I close my eyes, I see a representation of the surface I just saw. To say that this is a poor imitation of what I see when I open my eyes is an understatement.
A good step forward is addressing the question about what kind of geometrical form bodies around us have. What is an everyday knowledge of geometry we use to recognize and act with bodies around us.
To begin with kinematics: some bodies are deformed and others are rigid (just changing their places keeping a form and a size the same).
We can discuss terminology for the two processes:
P1: I see the surface of a table.
P2: I close my eyes and see a representation of what I just saw.
I am willing to accept any level of detail to distinguish these processes.
Alex
Nadin, Mihai
I understand your concerns. My point: we do NOT see numbers. We see 3 pears, or a dozen of birds…/we do not see colors, we see colored things. The point, line, surface, volume, etc. are constructs. When we embody them (such as ink on paper used to draw a circle) the new entity has a different condition than the mathematical definition. Yes, we use numbers for describing things, and we use geometric forms for engineering things. But the languages used (mathematical formulae or chemical descriptions, or design for producing machines and homes) are not the same thing as the THINGS. And yet again: dynamics (how things change) is described also through languages (the mathematics of stars etc,…their movement) but cannot be confused with what we observe through all kinds of devices).
I hope I clarified my take.
Mihai Nadin
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Alex Shkotin
Yes, thank you. It's a little bit unusual to write "The point, line, surface, volume, etc. are constructs." Usually we write "The point, line, surface, volume, etc. are concepts."
I'll try to write more about everyday mechanics later.
Alex
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