At first I thought I would post this in the philosophy section, but I figured you guys would have a lot more fun with it.

Sorry Guys

Let me see If I can remember the picture correctly. It was a chart contrasting Grok and Quine on opposite ends of a x-axis, and contrasting weak and strong positions on opposite ends of the y-axis. Kind of like what http://www.politicalcompass.org does...



Quine's position: that objective mathematical truths exist, and if there are aliens they would understand our math.

Grok's position: that objective mathematical truths don't exist, and if there are aliens they would have no clue how to make sense of our math.


So, where do you guys stand?

Math is on one level just the process of transforming axioms concerning classes of abstract objects into non-obvious facts about these objects derivable from the axioms using straightforward logic. As long as the axioms aren't too far out, the subject matter is going to be virtually universal. All that either party would make from knowing the other's math are those things one party discovers before the other. Such things as the esthetic ideals pertaining to mathematics are more apt to have one party doing things relatively incorrectly in some way, so that we (or they) might be left smacking our (or their) foreheads wondering why we (or they) have been doing things so idiotically for so long. I find this unlikely too, though. I don't think it's likely that we'd find ourselves to be dramatically offtrack. This is the simple answer. There are things going on in mathematics using inconsistent axiom sets. For the most part, all mathematics is connected in a diffuse kind of way with its applications, and this tree of connections is going to be mutually understandable (in the same universe with similar requirements for intelligence to advance). There is the issue of intelligences at different stages of development too, though. It is probably easier to bring a slower species up to speed than to dumb an advanced one down. Possibly it's a universal law of intelligent life that math just isn't at all interesting once computers get 1000 years more advanced than they are now for us. In this case, an advanced species' computers would understand our math, but the species itself wouldn't even care to look at its own past's much less our own. Let's hope this isn't the natural trajectory of intelligence. I think it would be a bit of a loss.