a. My Collection


I like to collect calculators, both electronic and mechanical.  (As a service to other collectors, I remodel battery packs for some old electronic calculators so they can be used with modern batteries instead of the original rechargeable NiCads.)

A principal subset of calculators is slide rules, which come in a variety of form factors.  I make my own replicas of some exotic rules.

Use the navigation pane at left to browse to folders of descriptions and pictures.  Click on pictures for larger versions.

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I don't know for sure, but I think it's a safe bet that among all Earth-born lifeforms, we alone calculate.  Smart as a dolphin may be, I don't think she counts miles.  Close to me as an ape might be, I don't think he could choose which of two big bunches had more bananas.  But I can and do, and it seems so natural to me that it's eerie.

How do we do this? And what exactly is it we do?  Where is the calculating part of our brain?  Could surgery of just the right structure excise the ability to calculate while preserving everything else about us that makes us, in our own estimation, "human"?

I think of calculating as being a strictly mental activity.  I might compute with pebbles, rules, scribbles or electrons but only as aids.  In principle, there is no computation that could not be thought through.  

But I grant that, given limits to brain power and memory capacity, it may be necessary to use calculation aids.  In that case, isn't it convenient that they can exist?  Isn't it, in fact, curiously marvelous that there is a way to faithfully (isomorphically) map the purely mental world of numbers and operations into physical form?  

Maybe this follows from the fact that our brains are physical so obviously there's an isomorphic correspondence between mental constructs and physical ones.  OK, but why is there more than one?  

I think it has to be that we (alone) evolved ways to perceive and represent certain characteristics of the real world that provide significant survival advantages.  The count and amount of things is just awesomely useful information to be able to sense and process:
  • Is there enough food to last a month or a week?  
  • How many days until the monsoon?  
  • Take 10 steps forward and 3 to the left to get in/out.
  • Are there more of us or them?  
  • I need a stick that's twice my height.
Indeed, I think that the advantages of being able to measure and calculate are so strong at such a simple level of existence that even a small brain bias (mutation) in that direction would convey its host a big payoff in survivability.  And, as greater ability would heighten the advantage, a strong vector would carry evolution toward refinement (improvement) of the initial bias if at all possible.

In this way, our abstract numerical and mathematical concepts are just how we represent qualities of reality, so it's no surprise that we can map them back into a variety of real forms.  That we can do so easily and reliably in many ways is a just a reflection of how well our brains perceive reality in the first place.

Of course, none of this speaks to exactly what form the calculation mutation/bias takes in our brains, or what genes cause this functional difference between ourselves and other "smart" animals.  Yet, I suspect the ability to calculate will one day allow us to figure that out.