# If a point is one-dimensional, if so, why not?

How small can a point be, as a point, a point can be multidimensional, if so, from where does a point take all these dimensions?

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• 6 months ago

Points in a three-dimensional world only exist in someone's imagination. A true "point" has three degrees of freedom for location but NO degrees of freedom for size - because it has no size.

Because a point exists only in the imagination it has as many dimensions (all of zero length) as you happened to be imagining at the time.

• Dick
Lv 7
6 months ago

A "point" is just that ... a point, or maybe as Steve Hawking might call it a "Singularity". It goes nowhere beyond itself. It's the concept that it exists as a miniscule place, so small that it can't actually be physically measured except in our mind. A point can be smaller than a bosen or fermion particle. A point can be infinitely small. Think about that for a moment ... infinitely small ... kind of mind boggling when you actually try to wrap your mind around it.

• John
Lv 7
6 months ago

There is no such thing as a point, a line, or a plane in the real world. They are only mathematical concepts. In today's world it is handy to have them in 3D graphics. Draw a plane and there will be a visual plane to see but it has no dimension in your manipulations.

• 6 months ago

In terms of the concept, a point has no dimension. Attempting to physically make a point, it is more likely to take on 3 dimensions as sphere, but mathematically is taken as zero dimensions.

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• 6 months ago

The number of dimensions depend on what it relates to.

With a (hypothetical) zero-size point, the dimensions are it's location in space or from whatever the zero reference is for your coordinates (along the axes you are using), not size.

eg. An endpoint of a line, or corner of a square or cube.

You can define that point by coordinates in two dimensions or three dimensions (depending if it's a flat drawing or 3D model) to show its location, but in themself those coordinates are nothing to do with size.

Or points on a graph; no size, just coordinates.

Or, "A point in time" - no duration, just a reference that can be used as an endpoint of a duration (like clicking a stopwatch to start or stop it).

Add other points in the same coordinate system and you can measure/define distance or duration between them.

• Petter
Lv 7
6 months ago

It's only in theory. Like when you say a picture is two dimensional, but when you add the ink or whatever, it will be 3D even if it's just ever so slightly. So it's more of a theoretical point, than an acutal, physical point, that in real life has to be 3D.

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