That's complete nonsense. There's nothing about Godel's theorem that says the physical rules of the universe can't be described. You're babbling religiously.
"A small number of scientists claim that Gödel's incompleteness theorem proves that any attempt to construct a TOE is bound to fail. Gödel's theorem states that any non-trivial mathematical theory that has a finite description is either inconsistent or incomplete."
That's from the Wiki, FWIW. I'm not big on using Wiki as a source.
"Babbling religiously" is right on the line in my opinion. It makes you sound like an arrogant jerk. If you have problems with the content of the comment, state your case in neutral terms.
Learn to live with other people's ambiguity and looseness in phrasing. Then perhaps they'll be more forgiving of yours. (Downmod)
You appear to misunderstand the meaning of the terms "inconsistent" and "incomplete" in the context of Gödel's theorem.
"Inconsistent": There is at least one statement within the system that can be proved both true and false.
"Incomplete": There is at least one statement within the system that is true, but cannot be proved to be true within the system.
Since Gödel's theorem applies to formal systems in mathematics, it does not say anything about the possibility or impossibility of constructing a "complete" (whatever that means) mathematical description of our reality.
What about it? All Godel's incompleteness theorem says is that there will be open questions about a universe describable by finitely many rules. The laws of physics don't need to provide answers to questions about whether computers in its universe will halt or whether planetary systems are stable.
What do you mean "the laws of physics don't need to provide answers to whether planetary systems are stable"? Since when are planetary systems outside of physics?
Your sentence "All Godel's incompleteness theorems says is that there will be open questions about a universe describable by finitely many rules" shows right there that there cannot be a theory of everything. How can you have a theory of everything yet still have open questions? That means that you have not answered everything.
It's my understanding that a theory of everything describes the rules by which the universe operates. It doesn't say anything about emergent properties of these rules.
For example, if everything in the universe obeyed Newtonian mechanics, I would say that Newtonian mechanics was a theory of everything. You would say that it isn't.
Technically, a "Theory of Everything" in physics is just a theory that relates the four known forces in the universe: gravity, electromagnatism, strong nuclear, and weak nuclear. The latter three (I believe) have already been unified. It's a "theory of everything" because it describes every force in the universe.
That of course does not imply that the theory of everything automatically gets you a complete description of the universe. Even in the context of a single force, it can be difficult/impossible to come up with a closed form solution for how many different objects interact subject to that force. For example, the behavior of gravity is really well understood but that doesn't mean that we can come up with straightforward, closed form solutions for the n-body problem of a bunch of stars interacting with each other's gravitational pulls in space.
Maybe it isn't comparing the list to itself, but to each item in the list to something it is a minimalist version of. Notepad is extremely minimalist when you compare it to Word.
But it does filter out people who don't have that tenacity. Those people who do have that kind of tenacity would already have learned about pointers and O notation.
You can perfectly easily write with-foobar functions of any kind, so macros aren't a win there, except maybe in Lisp where it saves you a parenthesis or two. You can replice define-memoized-function with
(define f (memoize (lambda args ...)))
so I don't see what macros gain you there. (Well, they save you from having to write lambda.) Especially if you're using a language with 'nicer' syntax, like Haskell:
withFile $ \h -> do
...
fib = memoize $ \n -> if n <= 1
then n
else fib (n - 1) + fib (n - 2)
Example (2) seems interesting though. And I'd like to see some examples of (3) that couldn't be so easily overcome. (Granted, my example is rather fake, since I don't know how you'd implement memoize for general types that only have a comparison function on them, without resorting to using some IO operation.)
Yes, with nicer closure syntax and/or lazy evaluation, lots of macro use cases can be eliminated. However, making single definition work as multiple definitions is a pattern that I haven't find ways other than macros.
For example, think of defenum macro that expands to a bunch of defconstants:
(defenum (ONE 1) TWO THREE FOUR (TEN 10))
=>
(progn (defconstant ONE 1)
(defconstant TWO 2)
(defconstant THREE 3)
(defconstant FOUR 4)
(defconstant TEN 10))
(Haskell programmers would use types for enum-kind of stuff, but suppose that you really need to associate numbers to those symbols.)
Or you can go further to name the enum itself, defining conversion functions between symbolic names and their values:
(defenum the-numbers ONE TWO THREE ...)
=>
(progn
(defun symbol->the-numbers (sym)
(case sym
((ONE) 1) ...)))
(defun the-numbers->symbol (num)
(case sym
((1) 'ONE) ...)))
(defconstant ONE 1) ...)
Without macros, you need to have some procedural interface to modify the global environment to realize these (which is, imho, worse than macros).
