A theory that doesn't talk about real things, or makes no attempt at connecting fictions to the world, is a bad theory.
Math can talk about real things, and it can say important things about the world.
"Quantity" is a real feature of the universe.
Post by twetch#3375
Is the distance along the diagonal of a square a quantity?
What the chain says
- Block
- 662 216
- Time
- 2020-11-21T05:28:45Z
- Signer
- 13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu
- App
- twetch
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- post
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- text/plain
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- twetch#3375
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13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu VerifiedReplies (12)
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.
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.
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?