Why "definitely"? Mathematics is a language, and just like any language, the symbols don't necessarily correspond to some independently existing part of the universe.
What explanatory benefit do you gain from saying the sqrt(2) is a fixed quantity?
Post by twetch#3375
Well it doesn't change, does it? So how can it not be fixed?
What the chain says
- Block
- 662 155
- Time
- 2020-11-20T20:21:45Z
- Signer
- 13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu
- App
- twetch
- Type
- post
- Content type
- text/plain
- Name in tx
- twetch#3375
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Depends on what "it" is. The formula doesn't change, but the output of the formula does, depending on how many times you iterate.
1.41 is different than 1.414 is different than 1.4142, etc.
The formula stays the same. The output changes.
Ok, so? is sqrt(2) a quantity or is it the output of a formula? If it is a quantity then there is no finite formula for it. If it is the output of a formula then it is something that converges on the quantity but never reaches it.
Arithmetic is broken. Modular arithmetic is ok though.
"The square root of two" is a way to describe a formula. The formula is a construction that generates outputs. The outputs differ depending on how many iterations you run.
There is no "converging" on a quantity. The outputs just gain decimals.
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"
each step of the computation results in a number with a finite representation that is closer to the quantity than the previous one. There is no positive distance that we don't get closer to eventually.
if you exist on a circle but as you walk across it, you observe an infinite “non countable” line, this doesn’t mean there is no circle. it merely means there is bias
you would have to exist outside the circle to call it a circle (in this scenario)
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