rob wrote:
Rick wrote:
Kurt Godel's Incompleteness Theorem in 1931 proved for all time that there's no Absolute Truth. All axiomatic systems of interest are incomplete, including DNA/RNA.
That's all long before you get to the Uncertainty of the Quantum Theory, it's the math the Quantum Theory uses.
But you can approach truth without limit.
Both we and viruses live in the macroscopic world where quantum effects are not significant. On the scale we live in, there is truth. The box with the cat in it got opened a while ago. The cat is dead.
A supermassive black hole isn't macroscopic? What is? Obliterating it isn't a "significant effect"? What is a significant effect?
And there is no absolute truth in the pure formal mathematics. As proved as anything in human existance, far more proved than anything in science. It's the math science uses.
Historical Introduction --- A Century of Controversy Over the Foundations of Mathematics G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The speaker was introduced by Manuel Blum. The lecture was videotaped; this is an edited transcript which appeared on pp. 12-21 of a special issue of Complexity magazine on ``Limits in Mathematics and Physics'' (Vol. 5, No. 5, May/June 2000).
...The real world we know is an absolute mess --- right? --- everything's complicated and messy. But the one place where things should be absolutely clear, black or white, is in pure mathematics.
So this is sort of what Hilbert is saying, and he proposed this as a goal, to have this formalization of all of mathematics and eliminate all the problems. Now this was a program, this was not supposed to be something you did over a weekend. Hilbert proposed this as a goal for putting mathematics on a very firm foundation. And he and a group of very bright collaborators, including John von Neumann, set to work on this, and for a while, for thirty years, it looked sort of encouraging. And then --- this is a quick summary of a century of work --- then as I'm sure all of you know there were a few little problems!
The problems are 1931, Kurt Gödel, and 1936, Alan Turing.
1931 Gödel
1936 Turing
They showed that it could not be done, that there were fundamental obstacles to formalizing all of mathematics and making mathematics absolutely black and white and absolutely crystal clear. Remember what Hilbert is proposing is that we should formalize all of mathematics so that everyone on planet earth can agree that a proof is either correct or incorrect. The rules of the game should be absolutely explicit, it should be an artificial language and then mathematics will give you
absolute truth. ``Absolute truth'' should be underlined in a very beautiful font and you should hear the angels singing when you say these words! This was the thought that we mathematicians have absolute truth. It's ours --- no one else has it, only us! That was the idea.
So it turns out this doesn't quite work.
http://www.cs.umaine.edu/~chaitin/cmu.html