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Comment by drexlspivey | Hacker News Reader

Counting pixels in a block of text to determine information density doesn’t sound like a very robust method to me. You could get very different results depending on the font you use to render the text.

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It is worse than just sensitivity to different fonts, it ends up being sensitive to totally incidental details of the glyphs. In a Latin script, all the letters carry as much information. But this metric would treat a lowercase i as much more efficient than a capital W.

Isn't that intentional? Picking sprawling glyphs for common items, and simple ones for rare meanings would be "inefficient" in some interesting sense. Indeed 'i' is the most common letter in Latin.

You are right but then is interesting to compare languages using Latin script. I find interesting that the first runner is Lithuanian, between non-Latin script languages, and the second is Swedish, with English coming third with quite a difference.

Lithuanian has quite a heavy use of diacritic signs, but it seems to pack more information than the others. And other languages with similar diacritic signs are not close to it.

Although the sensitivity to different fonts and details is real, we can draw some interesting conclusions from this Sunday exercise.

English could be rendered in a 4x3 font (or even 3x3 font)..

In this test it'll comfortably beat out any other language.

See: https://fontstruct.com/fontstructions/show/325977/4x3_pixel

1x8 pixel font: https://dotsies.org/

thats cool, but looking at that font, I'm not sure I'd be able to tell an 'e' from a 'c' if there was no context. Eg: "figure e5" wouldn't be clear to me (but "colour" would be)

This might be a good use for fractal image dimensional analysis; a letter would have a dimension between 1 and 2, since it covers a portion of a plane. It might better measure the complexity of a glyph, rather than just the weight.

(https://en.wikipedia.org/wiki/Fractal_analysis)

Another approach might be to take some large, well translated text and measure compressed sizes of it in different languages. With a good enough compression algorithm that will take into account used character set size differences as well as common word lengths, etc.

This is a metric that is relatively simple to calculate but probably not a good approximation. If I were to do that though, I would choose the effective bit length of the symbol in the language, i.e. log_2(number of symbols in the writing system)

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