The human (or primate, for that) way to think about numbers (as ascertained by cell-recordings, listening to what single neurons have to say about groups of objects presented) is logarithmic - one, two, three?, many, very many, heaps, woohoo!, etc. - and not very accurate. To help with this, i propose
an implant that relays a sensory impression of a number entered.

Current technology permits relaying of simple sounds, simple visual input etc. directly to the neural substrate, without using sensory cells. It is not currently possible to intercept the 'raw' input from, e.g. the eyes, count the objects via computer and then give back an accurate feeling. What i propose would be an external input (like a cellphone) that communicates with an implant that translates figures into something feelable, a sense of height or a sense of pressure for instance. This might help people to not fall for ' we have 10^6, but need 10^12 - so we're halfway there'.

Treatise on numbers & brainshttp://www.pnas.org.../93/4/1514.abstract this covers the intuitive grasp of numbers, of course, not the abstract one. [loonquawl, May 18 2009]

Right - the natural way to think about numbers is just like the Richter Scale - nothing much to apocalyptic in a few, scarcely distinguished steps. Of course, the implant-version would still be logarithmic (otherwise no chance of representing the national debt, etc), but finer graduated.

It still would not be fine enough for 'intuitive' computations (3.000.000 and 3.000.050 would feel the same), but computations are best left to abstract though anyways. The idea here is simply to have a better notion of huge numbers (how much more far away is the moon relative to satellites, how much are we spending on debt, rather than schools...)

You're trying to translate an infinite numeric scale onto a finite scale of perceptions. It's going to have to give out *somewhere*. Maybe you get 10^6 vs. 10^12 right, but 10^60 vs. 10^120 will be pushed towards the end of your perceptable spectrum, and if not that, how about 10^60000 vs. 10^120000?

[bungston]: saying out loud 'one thousand' and 'one million' does nothing to give you a feel for the magnitudes involved, but you are right, having a sound at different levels of loudness would be equivalent. My idea was to spare the rest of the world blaring or bright flashes when thinking about the national debt, but maybe that's added value in fact.

[jutta]: You are right in that there is just a limited dynamic range to perceptionis (say, 10^12), but this would still be [standing on the roof of a skyscraper] times better than the current malaise. Additionally, the scale would be logarithmic, so while both, 10^60 and 10^120 would feel incredibly big/high/soaring/[new category]/loud/fresh/whatever, the difference between those two would feel the same, which would be better than some abstract guesstimates people would make.

Thing is, number is more than just an expression of magnitude - more interestingly, there's a 'shape' to numbers that describes how they interact with one another, like complex chemical reactions - numeric synaesthesia (maybe an example of a naturally intuitive way to think about numbers) has been described by gifted mathematicians who describe abstract forms that twist and intertwine into one another in such a way that makes arithmetic operations a process of imaginative visualisation.

Never mind the dynamic range—what keeps the brain
from interpreting the signals from your device on the
same logarithmic scale it already uses for other inputs?