Diagrams - 2D or Fractal ?

Conventional speech has it that if you draw, say, a circle on a piece of paper then you have a 2D image.

However both paper and pencil marks are made of matter in three dimensions, and moreover both paper and graphite have fractal structures at the microscopic level.

So what dimension, really, does a paper diagram have ?

For the purpose of discussion it is a 2D image.

The 3-dimensionality of the image is slight enough that for most practical purposes, it can be safely treated as a 2-dimensional object, just as when we draw a line on a piece of paper, mathematically that line has no thickness, but practically it has a slight 2-dimensionality.

Define reality.

Not in THIS discussion bubba.

Moderator, please withdraw these boy’s cuttlefish for their irrelevant trilling and chirping

Moderator Note

MrQuertyasd, rudeness directed at people who are trying to answer your question isn’t appropriate in GQ. Let’s avoid further responses like this.

General Questions Moderator

Using the overly stringent definition given in your OP, there cannot exit a 2D diagram, since atoms, and even electrons, have depth and width. How powerful a microscope are we to use to determine whether a diagram is 2D or 3D?

You’ve already answered your own question. In a three dimensional world, the concept of 2D is always going to be an abstraction. Nothing is actually 2D, at least on a more than a subatomic scale. So the answer to the question depends on whether you consider the “diagram” to be the 3D objects that make it up, or the abstraction that it represents.

So it must be time to give up on the rather loose way we use the term 2D. We should demand that our intellectuals and pedagogues employ accurate language in their communications. :mad: Or we withdraw* their* cuttlefish too !

Not stringent, probing. I’m probing for insights.

When you say “accurately employ language” what do you mean? What particular relation between words and reality are you imagining?

Perhaps you should read Plato, who gave considerable attention to what is essentially this issue some two and a half thousand years ago, as nearly all the actual intellectuals who have lived since that time have been aware.

You can probe all you like, but nothing in the real world is actually 2D or 1D or even 3D since it has to exist in space time. Maybe they are all 10D but the extra dimensions are too small for us to see. But diagrams are conceptual things and, as such, are 2D (unless they are not, like space frames).

Moderator Note

Since the question has been answered, and your responses here are clearly not meant to be serious but are verging on trolling, I’m closing this. Let’s not ask questions in this forum that you already know the answer to.

General Questions Moderator