You can be damn sure Uber has a record of every Uber ride ever taken. Even if Uber had incorrect records in their database about which car picked up the rider, because the driver had e.g. failed to update Uber with their current car and plates, there is no plausible reason why Uber would believe that the ride itself had never occurred, because they have the rider's account information. They could have produced "rider account X requested a trip in Boston on such-and-such date, we matched that person with driver account Y, and driver account Y was registered in 20xx to Vernon Dudley, 4 Privet Drive, ...". But they deliberately didn't provide that information.
"this article is muddled and confusing"
Reality is muddled and confusing. Real life never has the clarity of an omniscient third-person narrator telling the reader the actual facts of the matter.
Your analogy is incredibly bad. Imagine if GrubHub itself provided the menu and contracted out to semi-anonymous restaurants to cook the food; then imagine that it wasn't salmonella or the like, but rather that the cook had pissed in the food; and THEN imagine that GrubHub refused to tell the police which restaurant cooked the meal and then blatantly lied to the cops that no food from that (still unnamed) restaurant had been on GrubHub's menu for two years anyway.
In that scenario, you're damn right you could sue GrubHub; they'd be complicit in the coverup of a crime.
If Subway tells the cops "I won't say who it was", and they say "he hasn't worked at Subway for two years anyway" (this being a bald-faced lie), AND the medical bills from the stabbing set you back millions of dollars... damn right, Subway owes you millions. They're making themselves complicit in the crime by obstructing justice, and making it clear that Subway was OK with the stabbing.
As I understand it (not being a physicist): the graviton, if it exists at all, would have to be a massless chargeless spin-2 boson for it to fit our understanding of what particles are. But the graviton has never been observed, nor has any quantized behavior of gravity or its General Relativistic effects, so it doesn't count as an observation by String Theory; there are other models that also give rise to gravity-as-we've-observed-it, up to and including just gluing the Standard Model to General Relativity and calling it a day.
It's squared because energy is work, work is force times displacement (distance), force is mass times acceleration, acceleration is velocity per time, and velocity is vector distance per time. So you get:
It's easy to write a computer program that outputs every statement provable from the Peano axioms: start with the most primitive possible statements, then progressively output more complex ones. This is because the Peano axiom system is "recursively enumerable", to use Computer Science terminology. The program never terminates, but any provable statement you name will be output at some finite time.
Additionally, it's easy to write a computer program that outputs every possible combination of symbols. Most of the combinations aren't statements at all. Of the ones that are statements, most of them are not consistent with the Peano axioms. Of the ones that are consistent with the Peano axioms, most of them are unprovable. But if the set of truths is countable, this scheme guarantees that the program will output every true statement that exists.
It is possible to write a computer program that checks if a statement is provable from the Peano axioms. The naïve way is to run the program that outputs every statement as a subroutine, then halt if the subroutine prints out the statement which we wish to verify. This program will halt iff the statement is provable.
It is NOT possible to write a computer program that checks if a statement is unprovable from the Peano axioms. Such a program may be able to detect a subset of unprovable statements. The subset it can detect may even be countably infinite. But there are some statements which will cause the program to run forever.
Let statement X represent a formulation of "the Goldbach conjecture is true" written in the language of Peano arithmetic. Does the program run forever if asked whether X is provable? If you are a non-Gödelian being, you will be able to answer that question with no error, because Gödel's Incompleteness Theorem only applies to formal systems which can prove all true statements.
I already read through https://en.wikipedia.org/wiki/Penrose_interpretation when I was trying to figure out what nonsense you were spewing. The article does not mention the Church-Turing thesis, hypercomputation, Gödelian incompleteness, or the Lucas-Penrose argument.
People can be known for more than one thing. Those two things can be unrelated, even if they're in the same field.
Call me back when Penrose convinces a well-regarded quantum physics expert. At that point we can call up Scott Aaronson and ask him his opinion, as Aaronson is an expert on the intersection of quantum physics and computing.
Penrose is not arguing that the human mind is illogical. He is arguing that it is uncomputable, which is a big difference.
In particular, he's saying that the human mind is capable of outputting true statements that cannot be proven to be true via any bounded number of proof steps. I don't disagree with that.
However, given that the human mind is capable of outputting false statements -- witness this conversation, wherein at least one of us is outputting false statements -- Penrose has failed to prove that the human mind is non-Gödelian, i.e. can output all the true statements that exist, while outputting no false ones.
> The claim is that you can not adequately model the Human mind with a Turing machine. Pointing out that Human's are not logical only strengthens this claim and does not refute it.
False. "2+2=5" is not a true statement, but I can construct a computer program that purports to compute the sum of 2 and 2 yet produces 5 as an answer. You can object "you got the addition wrong!" but that's irrelevant. If there is a person who believes (falsely) that 2 plus 2 equals 5, then the computer program could be an accurate model of their thought processes. There's nothing about "computers consistently produce the same answer" that implies "computers always produce the correct answer". "Computers always produce the correct answer" is a much more powerful claim, so the onus is on those who make the claim to prove it.
LQG is not believed to allow hypercomputation, i.e. the solving of Turing-uncomputable problems. Penrose's entire argument is based on the idea that the human brain is a hypercomputer, which is why it cannot in principle be simulated by a computer (or any other machine).
It's worth noting that Penrose's field of expertise is General Relativity, not quantum physics, and definitely not Computer Science / philosophy of computation. I see the situation with Penrose as equivalent to Linus Pauling's unfortunate foray into Vitamin C pseudoscience late in his life.
Also: before I bother building a Turing machine that implements a proof-generator for statements in ZFC, you should do me the courtesy of showing your investment by building me a Turing machine that multiplies two integers.
Turing machines suck. Building a Turing machine that implements ZFC proof-generation is a project appropriate to a graduate-level paper, not something to toss off in an Internet pissing contest.