Using Math to defend scientific method?

[alterego]

@DSYoungEsq

Why is it that people here always get so unhappy when someone points out the simple fact that the “evidence” of evolution (a theory I happen to suspect is most likely to be an accurate explanation of our origins) is not proof of anything regarding the origin of the species, but rather is something we try to explain using the theory of evolution? You cannot prove one way or the other what the origin of the Earth, or of the species hereon was; we weren’t there when it happened, most likely, so all we can do is try to interpret what we have.

FAITH has no business in science, since FAITH is the acceptance as true of things that evidence seems to indicate aren’t true. Adopting as a tenet of faith the proposition that the Earth resulted from the myriad of physical interactions following a “Big Bang” is hardly taking a risk, given what we see around us. But those who try to explain what we see with theory should not in any way be bothered by an expression of faith in some alternate explanation, any more than those who have faith in the alternate explanation should be shaken by the evidence they see around them.

Which is why the whole debate over so called creationism is so stupid. Postulating a non-provable external supernatural causation as a “scientific theory” to support a belief based upon a religious tenet makes no sense; it’s an attempt to take faith into the realm of science, where it has no meaning. Similarly, for scientists to get all upset at expressions of faith that deny that currently most plausible theories accurately state the true past occurrences we cannot prove to have happened is stupid; the scientist should simply say, “if you choose to believe that, be my guest.”

Well said. But the one thing that really gets my panties in a bunch is the use of scientific concepts as a facade for inherently unscientific thinking. If I were chatting over coffee, I can see myself saying, “if you choose to believe that, be my guest.” But this is not IMHO, and I feel feel my statement was justified.

[Derleth]

Science does not deal in proof. Going into science to learn about TRUTH and CERTAINTY is like becoming a Catholic priest to meet girls. Science deals in probability and error bars and useful tools and models (including laws, which are equations, and theories, which are attempts to explain laws) that get discarded with passing generations if not sooner. Math in general is a tool used to think rationally about models and decide if the current predictive model is broken enough to throw away yet.

Mathematical axioms are the rules of a game mathematicians agree to play with each other to some end. That end might be “pure math”, in which case it has no obvious point to someone who does not love math, or it might be to solve some real-world problem, like trying to decide how to make the best use of a phone system.

Applying the consistency of mathematics to a model made of axioms that works like some aspect of the real world (a graph that looks like a phone system with axioms that model phone calls, a set of algebraic equations that model what we observe about gravity, etc.) allows us to think consistently about that aspect of the real world.

Barring pure math, that model is only useful as long as it represents the part of the real world we want to think about: Newton’s equations work extremely well for us here on Earth because we don’t accelerate to any appreciable fraction of light speed relative to the Earth and we don’t live near any monstrous gravity sources. However, once we accelerate particles to near light speed in cyclotrons and observe what happens to them, we cannot square what we see with Newton’s equations. The equations are perfectly valid in the axiomatic sense, but more-or-less useless in the describe-a-proton-in-a-cyclotron sense. Proving Newton’s equations up set theory and down predicate calculus does nothing to change that.