DC Nerd Nite
@jamesdabbs
If n is any integer, n² is greater than 0
If n is any integer, n² is greater than 0
If n is any integer, n² is greater than or equal to 0
If n is any integer, n² is greater than or equal to 0
This slide is false
This slide is false
The sky is blue
The sky is blue
Godfather III is the best Godfather
Godfather III is the best Godfather
There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no "we will not know".
– David Hilbert (1900)
(1930) In any* axiomatic system, there will be statements that are true but unprovable
(1931) No* axiomatic system can prove its own consistency
This statement cannot be proven from the axioms
If this statement is not provable is true
this statement is not provable has no proof
⇒ true statement with no proof
If this statement is not provable is false
this statement is not provable has a proof
⇒ false statement with a proof
This statement cannot be proven from the axioms
The sky is blue
Any* axiomatic system is either inconsistent or incomplete
If a set is bigger than the rationals, it's at least as big as the reals
Hilbert (1900): prove or disprove this
Zermelo–Fraenkel set theory with the Axiom of Choice
If you have a bunch of sets, you can pick one thing out of each of them
Cannot be proven or disproven (from ZF)
The more important fundamental laws and facts of physical science have all been discovered
– Morely (1903)
Time moves slower if you go real fast
– Einstein (1905)
It is impossible to know both how fast something is going and where it is
– Heisenberg (1927)
There is no algorithm to decide if a Turing machine will halt or if it will run forever
– Turing (1936)
This program runs forever if you feed it a program that halts
This program runs forever if you feed it a program that halts
X
Blue
There are fuzzy, unresolvable problems everywhere
Try to savor them
You're not going to have it all figured out
Don't try to figure it all out
Embrace your
DC Nerd Nite
@jamesdabbs
Define BB(n) to be the biggest number that a Turing Machine of size n can compute
Define BB(n) to be the biggest number that a Turing Machine of size n can compute
Define BB(n) to be the biggest number that a Turing Machine of size n can compute
Define BB(n) to be the biggest number that a Turing Machine of size n can compute
is undecidable