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Brains Hard-Wired for Math
mcgrew writes "New Scientist is reporting that "non-human primates really can understand the meaning of numerals." The small study of two rhesus monkeys reveals that cells in their brains respond selectively to specific number values — regardless of whether the amount is represented by dots on a screen or an Arabic numeral. For example, a given brain cell in the monkey will respond to the number three, but not the number one. The results suggest that individual cells in human brains might also have a fine-tuned preference for specific numerical values." The report itself is online at PLoS Biology, Semantic Associations between Signs and Numerical Categories in the Prefrontal Cortex."
No such thing as 'base 1.'
You're thinking of Peano arithmetic. (Defined by nought, 0, and the successor function, S, and a few other axioms. You define 1 as "0S" and 2 as "0SS", etc.)
You're thinking of Peano arithmetic. Unary is a common name for the number representation of Peano arithmetic. It also shows up in data compression, where it tells how many bits a gamma-coded number contains or the most significant bits of a Rice-coded number.
But 00 and 01 make up 10 values. Kind of like 0-9 being 10 values. The shirt makes perfect sense as is.
I see your informative link, and raise you a pithy comment.
A system of base N has available the digits 0 through N-1. So a unary system could only have the digit 1 - 1 = 0. So you couldn't have 111 in a a strict interpretation of the unary system, since the highest digit available would be 0. So you could only represent 0 with this system.