Okay, pretend I’ve given you the axioms sufficient for you to +-*/. Can simulate squirrels now? Of course not. You still have to go out and collect information about squirrels and add it to your description of the axioms of arithmetic (which suffice for all of N) to have a description of squirrels.
You claim that because you can simulate squirrels with (a part of) N, then N suffices to simulate squirrels. But this is like saying that, because you know the encoding method your friend uses to send you messages, you must know the content of all future messages.
That’s wrong, because those are different parts of the compressed data: one part tells you how to decompress, another tells you what you’re decompressing. Knowing how to decompress (i.e., the axioms of N) is different from knowing the string to be decompressed by that method (i.e. the arithmetic symbols encoding squirrels).
By the way, I really hope your remark about Splat’s comment being “enlightening” was just politeness, and that you didn’t actually mean it. Because if you did, that would mean you’re just now learning the distinction between N and T(N), the equivocation between which undermines your claims about arithmetic’s relation to the universe.
And much of his comment was a restatement of my point about the difference between the complex arithmetic you refer to, and the arithmetic the universe actually runs on. (I’m not holding my breath for a retraction or a mea culpa or anything, just letting people know what they’re up against here.)
Okay, pretend I’ve given you the axioms sufficient for you to +-*/. Can simulate squirrels now? Of course not. You still have to go out and collect information about squirrels and add it to your description of the axioms of arithmetic (which suffice for all of N) to have a description of squirrels.
You claim that because you can simulate squirrels with (a part of) N, then N suffices to simulate squirrels. But this is like saying that, because you know the encoding method your friend uses to send you messages, you must know the content of all future messages.
That’s wrong, because those are different parts of the compressed data: one part tells you how to decompress, another tells you what you’re decompressing. Knowing how to decompress (i.e., the axioms of N) is different from knowing the string to be decompressed by that method (i.e. the arithmetic symbols encoding squirrels).
By the way, I really hope your remark about Splat’s comment being “enlightening” was just politeness, and that you didn’t actually mean it. Because if you did, that would mean you’re just now learning the distinction between N and T(N), the equivocation between which undermines your claims about arithmetic’s relation to the universe.
And much of his comment was a restatement of my point about the difference between the complex arithmetic you refer to, and the arithmetic the universe actually runs on. (I’m not holding my breath for a retraction or a mea culpa or anything, just letting people know what they’re up against here.)
Because remember—nothing is more important to SilasBarta than politeness!
Touche :-P