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The pointlessness of a pointless point

 A new definition of points and infinity
  (+1)
(+1) 		 

This idea is proposing (or at least posing) to be a logical equivalent of the physical claims for a plank-length like unit.

Where in "logical", I mean making it seem more plausible than not, when we imagine things. This was the way Euclid's sources and Euclid himself would describe logic.(if I understand correctly according to Proclus, Eucleidus only compiled the works of Eudoxus and Theaetetus)

"Logic" according to this definition is something which is "seen" correctly in the Mind's I.

I just want to point out that infinitely smaller points within a point, or a point with no area is pointless. It is the zero of geometry.

But the problem is that a line exists. If a line exists, with a distance between two points, there must be a small "unit" of distance that exists. It cannot be constructed from zeros.

Lets look at movement and speed. A movement means something is being displaced in timespace. At one time it was at a certain point and at the other it reached another point.

Since time measurement is relative there must be a smallest amount of space with zero distance between it and the next unit of distance. We can measure it with zero width and height and hence create a "theoretical" line, but this line would not have infinite points on it.

This number one unit, conceptually, cannot be divided into parts. And if it could, that would only be because a smaller finite unit exists.

It helps to think about an infinite infinity, but it pleases the mind to "know" that it is only a fiction of imagination, and "in the real world" you can break anything up to many small parts, but in the end you reach the fundamental unit.

I now realize that I am a fundamentalist. :-(

What is the "shape" of this "unit" in space. Is it a circle, or a square. An interesting possibility is that it has not one single shape but moves around, like an amoeba or similar to electrons in their "cloud".

Perhaps it could pulsate and change shape, spilling into the "square space" of the other "point's" plane as long as it keeps its overall area.

That would be an interesting point. What would the consequences be in physics?

—pashute, Mar 16 2026

https://en.wikipedia.org/wiki/The_Point! [normzone, Mar 20 2026]

Zeno's paradoxes https://en.wikipedi.../Zeno%27s_paradoxes
[pertinax, Mar 20 2026]

Unusual logic and infinitesimals - the current state of the art, as best I can find out. https://link.spring...036831.48866.12.pdf
Yes, I know, it's paywalled. This sucks ... [pertinax, Mar 20 2026]

A non-paywalled summary can be found here. https://plato.stanf...gic-paraconsistent/
Scroll down to the section called "Preservationism", if you're impatient. [pertinax, Mar 20 2026]

Bad infinity, no biscuit! https://hegel.net/en/v11123froeb.htm
Hegel's thinking here also implies to infinitesimals. Granted, it's kinda tangential. [pertinax, Mar 20 2026]

Hodons and chronons - indivisible units of distance and time. https://d1wqtxts1xz...GGSLRBV4ZA#page=354
I remember some theoretical physicists mentioning these back in the early 1990s, but it seems to be just philosophers now. [pertinax, Mar 20 2026]





       I think you might just have re- invented Zeno's paradoxes.   

       Also sp. Eucleides.
—pertinax, Mar 19 2026
   

       If the point is considered to have a shape, then the shape of the shape could be defined mathematically by Cartesian or polar co-ordinates defining vertices and edges of the shape (even approximately). The co-ordinates would specify points, but at a lower level of recursion than the point whose shape is being discussed. Each of these lower level points would presumably also have a shape, and so this shape of a point that is part of the shape of a point, could also be defined as points, and those points would themselves have shapes. I'm afraid it's points all the way down in a recursive nightmare of recursion. Unless of course the whole idea is bollox.
—pocmloc, Mar 19 2026
   

       First off, what is the "Mind's I"?...   

       ...if you mean "eye" then that's a whole other conversation involving the human Pineal, (strange misspelling), gland.   

       Secondly things travelling at close to light-speed don't perceive time as those of us at this speed do.   

       ...so just speed up.   

       //infinitely smaller points within a point, or a point with no area is // ... exactly how calculus works.   

       It so happens that the invention of calculus was the first example used by Brown and Priest in their 2004 exposition of the "chunk and permeate" model of paraconsistent logic, so it echoes back to your decision to define logic in a particular way. Regrettably, their paper is behind a paywall.
—pertinax, Mar 20 2026
   

       If the 'points,' for argument's sake, are virtual, and do not take up space but are only a vibration or rhythm, could a line drawn between two of them be a 'real' line and not a virtual theoretical object?   

       I think the real problem is what the hell is the medium in which any of this happens. Points, lines, or volumes, real or virtual, in order to manifest anything, the canvas has to be defined (or at least taken into account for the measuring part.)   

       In your next to last paragraph you seem to imply that 2 things can occupy the same 'space.' Please define 'space.'   

       [+] For the engaging pilpul.
—minoradjustments, Mar 20 2026
   
         


 

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