Letters and numbers are often mentally grouped together; they're both simple sets of symbols that are the building blocks for much more complex concepts, and mastering their relationships is a cornerstone of early education. But while illiteracy becomes a major social stigma almost immediately after a young person is introduced to letters, most people can proudly declare their innumeracy (aside from basics, like telling time or counting change) throughout their lives. This is doubly strange, as our ability to think about and compare sets of items of differing amounts precedes our verbal skills. Over at The Thoughtful Animal, Jason Goldman describes how, prior to making or manipulating the squiggles that we've come to know as numbers, we can suss out the relationships between amounts in surprisingly abstract ways. If you're a Martin Gardner devotee or recently picked up Alex Bellos' new book, Here's Looking at Euclid, you might recognize the inherent awesomeness of these relationships. And if that's the case, check out some recreational mathematics at Built on Facts: Matt Springer provides two thorny problems, one involving a tricky ten-digit number and another dealing with a classic word problem in terms of physics.
The Thoughtful AnimalAugust 17, 2010
"Surely, humans have something unique that allows us to do things like multivariate regression and construct geometric proofs, however, but let's start at the beginning. I will hopefully convince you that there is an evolutionarily-ancient non-verbal representational system that computes the number of individuals in a set. That knowledge system is available to human adults and infants (even in cultures that don't have a count list), as well as to monkeys, rats, pigeons, and so forth."
Built on FactsAugust 18, 2010
"'Find a ten-digit number with the following two properties (in base 10, of course): A. The number contains each digit (from 0 to 9) exactly once. B. For every N from 1 to 10, the first N digits of the number are divisible by N. Thus, for instance, 1234567890 doesn't work; while 1 is divisible by 1, 12 is divisible by 2, and 123 is divisible by 3, 1234 isn't divisible by 4.'"
Built on FactsAugust 16, 2010
"The new academic year is starting, and if there's one thing students love it's a good word problem. If Sue is four times as old as John will be when Sue is one year than John... So in that spirit I was amused to find basically this kind of problem in a college physics textbook I was perusing for post ideas as I get back into the swing of blogging."