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Counting on my fingers
SHM
rho
Insomnia can do strange things to a person.

There I was, lying in bed, failing utterly to fall asleep, when for some reason my mind starts to wander and I end up forming my fingers into the Vulcan "live long and prosper" symbol. From there, it's just a short stroll through the fields of finger-contortion to counting in binary on one's fingers.

At this point, I had my stunning revelation. Counting on one's fingers is in no way limited to the boring 0-1023 I had previously assumed it was limited to. Oh no! Obviously, if you're allowing each finger to be limited to either an "up" or "down" position you're still stuck with only 1024 possible numbers you can represent, but you can change which numbers you can represent by using a floating point approach. What's more, by differentiating between "palm turned inwards" and "palm turned outwards" on each hand, you can add an extra 2 bits of data.

This would then work as follows: the orientation of the left hand represents the sign (plus or minus) of the number as a whole, the 5 fingers of the left hand and the first two of the right hand representing the bit-before-the-exponent-whose-name-I-don't-know, the final three fingers of the right hand representing the value of the mantissa, and the orientation of the right hand representing the sign of the mantissa. This gives an overall ability to represent the numbers ±0–127 * 2^±0–7. Which is to say that you can still count all natural numbers from 0 to 127, but you can also give approximate numbers up to over 15,000, fractions down to less than 1/100, and negative numbers. Definitely an improvement.

Of course, you lose out by having +0 and -0 represented by different states, but I think that the trade-off is worth it for the increased readability by humans.

I find all of this to be supremely exciting. I am well aware that I am probably the only person who does, and that most of you probably think I've gone mad. I am putting this down to insomnia, and entirely distancing myself from any suggestion that it's actually because I'm a huge dork.

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If you use a two's complement representation instead of a sign bit, you turn the -0 into an extra useful integer and make the maths easier...

I never liked two's compliment. Possibly just due to lack of exposure to it, but I've always found it annoyingly non-intuitive.

What's not to like? You just have to think in terms of "this little piggy has a value of -128" (where the adjacent piggy has a value of 64, and so on), and you don't have to worry (algorithmically) about sign bits. Except for catching overflow, but you're going to have to do that anyway.

Obviously brains are fairly proficient at handling sign bits, compared to most other implementations, so YMMV. :)

Unfortunately, my brain didn't come pre-installed with the necessary module for intuitive calculations along those lines. I suppose it's my own fault for buying the physicist edition of BrainOS rather than the compsci edition.

[Penrose-esque rant about non-algorithmic nature of consciousness goes here]

(Not that I'm particularly sure I believe that, but it backs me up here so I can pretend I do.)

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See? Lack of sleep. It does strange things to a person. I'm sure I would know the difference between a mantissa and an exponent were I properly awake. Or at least, I'd be smart enough to look the damn things up.

How did you manage to count in ternary? I don't think I could reliably and independently manipulate my fingers into three different states.

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Psst... your geek cred is showing. ;)

Dear Rho,

I don't know you very well but I think I might love you.

--Muse.

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