Perspective A: "The sqrt(2) is a quantity whose value we don't know, can never know, and can only approximate"
Perspective B: "The sqrt(2) is a formula that generates outputs of increasing decimal length, starting with 1.41 and never repeating"
Post by twetch#3375
If I draw the diagonal of a square, do you think that this line has no distance, or that the distance along the line is not a quantity, or something like that? Incommesurate ratios were studied by Euclid.
What the chain says
- Block
- 662 164
- Time
- 2020-11-20T21:41:18Z
- Signer
- 13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu
- App
- twetch
- Type
- post
- Content type
- text/plain
- Name in tx
- twetch#3375
Fields the transaction did not carry are omitted. Open the payload to see the bytes as stored.
Signed by
13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu VerifiedReplies (2)
Euclid could show that his GCD algorithm would not always halt for any two lines that he could draw. But we still have a concrete representation of the irrational quantity in the diagonal of a square. https://en.wikipedia.org/wiki/Euclidean_algorithm
en.wikipedia.org Euclidean algorithm - Wikipedia Actually draw a diagonal on a square, and you will see that, in fact, the diagonal is composed of a finite, countable number of points.
Euclidean geometry mistakenly assumes that space is continuous. With discrete space, there is no incommensurability.