Punk Mathematics
kickstarter.com
kickstarter.com
I think the idea of a Punk Math book is pretty interesting, but honestly, I think he should do a lecture series (I think his personality would really come across better in that medium). He seems like a sort of Bill Nye for mathematics.
edit: I just realized neither of us posted the link to the podcast. It's at: http://www.mathforprimates.com
This could be a great candidate for a multimedia textbook... 10-minute videos + notes + interactive proofs?
Virtually nobody knows what "math" actually is before college. Even in college I suspect the number is still low. If nothing else his project has the potential to fix that.
Ten years seemed sufficient enough for me to place enough value on math that I was able to overcome whatever my original deficiency was. I'm all for finding a way to teach math that helps others in the same way.
I've never heard a better concise (one-sentence) description of what mathematics is.
Personally, I'm quite influenced by Pi's "Mathematics is the language of nature", though the sentiment dates at least to Galileo. For those of us who believe that alien intelligence must BY DEFINITION have recognizable mathematics (because we have no other way to recognize intelligence), this points to that universal quality, and also hints at the improbable success of mathematics in describing and predicting the physical universe.
Agreed. They stay on top of different assumptions: Prayer supposes that there is "god" that can overrule everything, mathematics stands on top of axioms.
Mathematics, even though can be amazingly beautiful in certain cases, is nothing more than a collection of maps (theorems, problems) from assumptions (axioms,definitions) to statements(solutions, proofs).
One of the awesome things about it is that the axioms and definitions are extremely portable to many different domains (in nature). The notion of "number" can be applied to almost everything around us, euclidean geometry laws fit pretty well (yet not perfect) the surrounding physics reality.
Yet, aliens may have completely different mathematics, built on completely different set of axioms, applicable to their needs and easy to process for their "brains". IMHO, it is a little arrogant of us humans to assume that alien intelligence would have the same type of mathematics as us.
He has a nice article here: http://arxiv.org/abs/math.HO/9404236
Consider for example the theory of differential geometry. Would we care about objects such as curves, surfaces, and manifolds if they (well, their low dimensional special cases) weren't ubiquitous in our world?
Would we care about permutations and symmetry if some people hadn't played around with arranging sets of objects?
Would we care about waves (sonic, fluid, E&M) if we didn't observe water flowing?
Even problems that seem to be mere puzzles with no basis in the ``real world'' are inextricably linked to the conscious perceptions that we learned to form by living in the world.
There was a great push to axiomatize all of mathematics beginning in the early 20th century and now it can be said that a lot of mathematics really is a collection of maps from assumptions to statements.
It could be that alien mathematicians have reached a collection of maps isomorphic to the one we have, but they ascribe completely different meanings to them.
Another possible scenario is that within the universe of all mathematics, our conscious perceptions and cognitive biases have carved out some subset, and alien mathematicians have carved out another. These two subsets could be so vastly different that they are mutually unintelligible, and very difficult (maybe impossible) to translate between the two mathematical languages. Even if we could translate the alien mathematics to a symbolic language familiar to us, and check that their theorems are correct, because of the vast difference in meanings ascribed to these two sets of mathematics, we just might not be able to understand what the alien mathematics means!
What I love about it—his main point—is his conjecture that it's not a far step from the "challenge everything" mentality of the original punk movement to "challenge everything" mentality that the brightest kids engage math with. Just apply some rigorous thinking.
It's a different way to approach math, directed to an audience that typically doesn't do a whole lot of it.
Math is pretty DIY since you don't need many resources.
'course by the folks from that era are scattered to the wind, as is normal for such scenes...