Is the distance along the diagonal of a square a quantity?
Post by twetch#1832
If we're talking about actually-existing geometric objects - not Euclidean nothings - then sure. A "square" is a composite object, made up of a finite number of points. The "diagonal" is another composite object whose units can be counted.
What the chain says
- Block
- 662 216
- Time
- 2020-11-21T05:28:45Z
- Signer
- 1Jj8TsZnm1bosAJFjkbS8J2MckEGx6sGot
- App
- twetch
- Type
- post
- Content type
- text/plain
- Name in tx
- twetch#1832
Fields the transaction did not carry are omitted. Open the payload to see the bytes as stored.
Signed by
1Jj8TsZnm1bosAJFjkbS8J2MckEGx6sGot VerifiedReplies (11)
Ok then if one side of the square has distance 1, then the diagonal has distance sqrt(2). What else would you call the distance?
You're working within Euclidean geometry. Space is discrete, not continuous, so there are no "squares" that have a distance of 1 unit.
Create a square on your computer screen. You'll see it's composed of a countable number of units (pixels).
If your geometric investigations have only been within Euclidean geometry, or only working within continuous space, then discrete space can be unintuitive or shocking.
But alas, all space that we encounter, mental and physical, is actually discrete.
Space is not discrete in Euclidian geometry.
I know. I'm saying you are working within Euclidean geometry when you ask about the diagonal of a square with a side the length of 1.
I'm saying that no spatially-extended square has a side the length of 1, since actual squares are composite objects.
So either points are distributed in orthogonal grid and diagonal has equal length to the side of square (same amount of collinear points) or points are distributed in different fashion and squares don't exist?
It's self-evident.