A thousand words...

If "a picture is worth a thousand words", we can actually determine it's resolution.

We know the average length of an English word lies in the vicinity of 5.1 letters.
Assuming 8-bit ASCII uncompressed text, and using RGB bitmap with 24bit colour for the image,

1000 words ~ 5100 letters + 999 spaces + n punctuation marks.

Average length of an English sentence approaches 14.3 words. Each sentence needs a concluding punctuation in form of a period. Non-concluding punctuation is observed slightly more regularly than in every other sentence. For the sake of simplicity, let's consider it converges at 1.6 punctuation marks per sentence.

So, number of sentences =  1000 / 14.3  =  69.93  ~  70
Therefore,  n  ~  70  *  1.6  =  112

So, 1000 words ~ (5100 + 999 + 112) = 6211 characters = 49688 bits.

Getting to the image side of affairs,

Each pixel in a RGB bitmap with 24-bit colour (I really hope you don't need more than 16 million colours for that picture we are talking about) is naturally of 24 bits.

So we can fit in a mere 49688/24 = 2070 pixels into such an image. That would be smaller than even an iPhone icon, which requires 3249 of those dots (Android icon sizes vary).

Given that text is usually in Unicode these days (UTF-32 needs 4B per character), and jpeg/tiff/png, etc compresses images in a major manner(15:1 compression is passe), more pixels could be fitted into the 1000 words in question. About 3-5 times the pixels, to be precise. Text compression using Huffman encoding (~2.9:1 for a 27 letter alphabet), quite commonplace, however results in even fewer pixels.

All these and other intricate considerations may possibly average each other out in the greater scheme of things.

This, however, does not change the fundamental truth that if your average photo is worth a thousand average words, you need a new photo.

Or to paraphrase what I read somewhere on twitter, A picture may be worth a thousand words, but it takes up ten thousand times the space.

Anybody interested in helping me write an app/program that calculates how many words your picture is worth? Mail me.

P.S. I have corroborated the word statistics from several sources, but had no way of testing their authenticity/data. So I'm not linking to any of them.