How much a thousand words are worth

According to popular opinion, a picture is worth a thousand words. But how much are a thousand words worth? And exactly what kind of picture is worth a thousand words? Important questions which will be given important answers.

What’s in a word?

For calculating the value of 1000 words, finding out the worth of 1 word is a good start. Let’s assume it’s an english word and let’s use Mark Twain’s The Adventures of Tom Sawyer as a sample of the English language. This book has 71343 words averaging 4.158 characters in length. When stored digitally (and uncompressed) an english character requires 1 byte. The average English word would then be worth 4.158 bytes.

If 1 word is worth 4.158 bytes, are 1000 words 4158 bytes? Not quite, because whenever there is more than one word there must be spaces separating them, 999 of them for 1000 words to be exact. The digital worth of 1000 words is therefore 5157 bytes, or just over 5 KiB (5×1024=5120).

5 KiB worth of pictures

So, what kind of picture is 5 KiB in size? Using uncompressed 24-bit RGB color, 5 KiB is only enough for 1706 pixels, roughly a 41×41-sized image. Doesn’t sound like much, but here’s what a wild strawberry looks like:

41×41 uncompressed

Not very impressive, I’d rather keep my 1000 words. To get the most out the 5 KiB, let’s compress the wild strawberry with an image codec suited for photographs, such as JPEG. With JPEG, 5 KiB can be made to last for an image 8 times the size while maintaining decent quality:

164×164 JPEG

To make the 5 KiB last for the whole picture, let’s compress it more:

648×486 JPEG

No, not quite the quality I had in mind. By downscaling the picture by a factor of 16 we get rid of the worst block artefacts at the expense of detail:

162×122 JPEG

Evidently, 1000 words worth of pictures isn’t much when it comes to photographs. Unless the people who claim that a picture is worth 1000 words are talking about artificial images (like diagrams) or vector images they are clearly mistaken.

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