Chinese and Indo-European Roots and Analogues
Here's some nuttiness for you: Chinese and Indo-European Roots and Analogues (1861), by Pliny Earle Chase.
The Chinese has usually been regarded as essentially different from the Indo-European languages, not only in its grammatical construction, but also in its radical etymology. Resemblances have been occasionally pointed out [...] but it has generally been assumed that the resemblances were merely accidental, and no systematic attempt appears to have been made to render this venerable idiom tributary to the fascinating though bewildering investigation of linguistic germs.
Spoiler: Chase would like to suggest that the Roman alphabet (and its sister scripts) are derived from the Chinese writing system. For example:
阝 [...] fa'u, a mound, numerous. The name and the hieroglyphic or phonetic value of this character, are retained precisely, and the form very nearly, in the German 𝔙.
Or:
日 [...] ɟi, sun ; day. 旦 [...] ta'u, sunrise. This hieroglyph has the form of Greek theta, and the ideas of warmth and power are found in θάλπω, θέρω, Ζέυς, dies, deus. If there is a radical connection between these several words, the primitive root was probably di. The several changes of di into dɟi and ɟi, θε and Ζε, are easy and natural.
To be fair, Chase shows an earlier, round form of 日 that really did look remarkably like a theta.
Comparisons to cursive forms are also made. ("It is hardly credible that so many resemblances to our guttural script are all accidental.") But the most interesting moments are the so-close ones. Are Cyrillic Ш, Hebrew ש and Greek Σ all related? Yes (was this really not known in 1861?), but they do not descend from the Chinese character 山 (mountain).
Similarly, Chase correctly notes that Chinese 三 and Roman III are structurally equivalent, as are 十 and X, more or less, if the "tally marks" hypothesis is correct — it's just the idea of direct influence that's unsupportable.
Incidentally, Victor Mair's Sino-Platonic Papers have published a couple of rather less freewheeling monographs on related ideas, except with the lines of influence going from Near East to Far: Julie Lee Wei's Correspondences Between the Chinese Calendar Signs and the Phoenician Alphabet, and Brian R. Pellar's The Foundation of Myth, On the Origins of the Alphabet, and On the Origins of the Alphabet: New Evidence.
leoboiko:
Dehaene has this very interesting book on the neurology of reading: http://amzn.com/B002SR2Q2I
He shows that writing systems evolve to make efficient use of the built-in capacities of the brain, including the primitives of the visual system. Thus they prefer to make distinctions with one-dimensional lines, intersections, curves and other fundamentals of edge detection; but avoid relying on, say, distinctions of line thickness, color shades, or gradations of line length, angle etc.
That is, we're all trying to make up symbols that are easy for humans to identify, and as a result all writing systems end up employing the same general type of graphical notation. It's to be expected that a lot of symbols will look alike (especially when you have like a thousand primitives, as in the Chinese system).