In his book "Darwin's Dangerous Idea" the philosopher Daniel Dennett suggests that you should not be surprised if aliens use similar arithmetic truths to earthlings (1 + 1 = 2), but you should be surprised or even flabbergasted if they used similar numeric symbols. Consideration of alien science might suggest otherwise.
A good many aliens are as lazy and unimaginative as humans, and would be quite content to use as simple, easy symbols as humanly possible. For a start, simple symbols are easier to recognise and quicker to write (no matter how many hands - or brain cells - you have).
And especially for numbers, it doesn't take too much imagination to make a single stroke to mean one, and a double stroke to mean two. A variety of human number systems show these similarities - at least for the low numbers. The Romans used a simple I, II, III; while the Chinese use the horizontal equivalents. Even the so-called Arabic numeral system has a vertical 1, then a 2 and 3 made up of lazily joined-up versions of the horizontal II and III.
Now, we can consider any (human or alien) vocabulary of symbols as a subset of all possible symbols imaginable. The total number of possible symbols we imagine will depend on what rules we use to compose the symbols: if we may use both straight and curved lines, if we allow diagonals, and little dots, and squiggly bits that loop round across each other.
If we assume for simplicity only symbols with horizontal or vertical straight lines, and consider symbols in ascending order of number of strokes, then the first possible symbols we get are I (or 1) and -. We should consider these symbols likely in any alien's alphanumeric system, since they are so simple and obvious and practical.
Next, we can consider symbols with two strokes: these would include II, T, and L. We can also add in the Greek (r), and the Japanese ニ (ni) and 十 (juu). All of these are also quite likely to exist as symbols out in the alien universe. If we allow diagonals we would also get V, X and 7, and the Japanese イ (i) and ト (to). We can continue for more and more strokes, until we end up with very complicated symbols such as Kanji characters like 驚く (odoroku). [Web editor's note: Switch your encoding to SHIFT-JIS to view the Japanese characters.]
Now, the simpler symbols are likely to coincide across cultures not just for reasons of practicality, but those of probability. If we measure the complexity of symbols by the number of strokes per symbol, then there will be a relatively small number of simple symbols theoretically possible, whereas there will be a vast number of potential symbols made from permutations of larger numbers of strokes.
That is, the greater the number of strokes, the vastly greater the number of possible permutations from which to create symbols. Therefore, not only is a very complex geometric figure - say composed of 100 strokes - unlikely to ever be adopted as a symbol (due to practicality), but the chances of even inventive and industrious alien civilisations coming up with the same 100-stroke symbol would become infinitesimally small. In contrast, precisely because there are fewer simple symbols to choose from, we are bound to bump into the same ones from time to time.
So we can guess that symbols with lower number of strokes are more prevalent in the universe than complicated symbols, both for reasons of practicality and probability. This is very roughly the case for Kanji characters. That is, in general, the most complicated symbols tend to be more uncommon than the simplest ones, though this is not systematically the case, and there are exceptions.
In a sense, then, the symbols are obeying a kind of natural tendency which is not completely arbitrary (unlike, say, the names given to numerals: one, ein, ichi). So, by this logic, the symbol 7 should be more likely to be an alien symbol for something than @ or #.
So, if an ambassadorial alien spaceship arrived in Science City, not only should you not be surprised that in their arithmetic one plus one equals two, but you might not be too surprised to find that they used symbols like I, +, 1, = and II.
The author welcomes any refutation of the above arguments.
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