Btw I wish I had learned at school that numbers have to be constructed to exist. To notice that, and to understand the implications took me decades, and it's crucial for understanding the nature and models and how our minds represent reality.
-
-
Show this threadThanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
It sounds like meeting your kids in 10-20 years from now will be an extremely interesting, humbling and potentially scary experience ;-) Do not hope/fear the coming of an AGI, but Joscha's kids. (don't misunderstand: I mean this as a compliment)
-
Nah. My poor son was unable to figure out why he was unable to complete his assignment on hedgehogs. It took us an hour to figure out that it's because hedgehogs deserve to die because they try to employ a tank strategy instead of a runner strategy while the main enemy are cars
- 6 more replies
New conversation -
-
-
This Tweet is unavailable.
-
For a thing to exist, it is insufficient to specify it, it also needs to be implemented. Infinities can only be specified, not implemented.
- 5 more replies
-
-
-
What is meant by „infinitely many numbers“?
-
A number is a labeling schema for an ordered set. In school, we learn that there is full equivalence between the return values of the functions that generate the set and the labeling schema, i.e. there is a theoretical machine for this, even if the functions don't terminate.
- 1 more reply
New conversation -
-
-
I think you mean Brouwerian not Hilbertian.
-
I think that post Hilbert, mathematics became constructivist, and it happened largely through Hilbert's influence, even though Hilbert fought mostly on the other side.
End of conversation
New conversation -
-
-
Can you steel-man the opposing view? I'm thinking that if you concede that any number exists, then you've opened the door to an infinity of numbers.
-
Unless we define existence in such a way that no knowable thing can exist, the set of existing things is that set that is implemented. Since numbers can be implemented, they can exist. The assumption that all specifications of numbers are implemented leads to contradictions.
- 1 more reply
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.