Burington's Handbook

Today, an old book keeps informing me.  The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them. 

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     It’s 1947.  I’m in my first engineering class.  The textbook is Burington’s Handbook of Mathematical Tables and Formulas.  I used this odd old book over and over, for decades – a trove of old world knowledge.  Yet, just now, it’s shown me something new. 

Burington’s Handbook cover and title page

     But let’s first see what’s in it: It opens with short, compact, courses on algebra, geometry, trigonometry, analytical geometry, and calculus.  Courses? That sounds bizarre.  But what it offers are the learning outcomes of those courses.  (Most of which, I had yet to take.)  And that helped keep old learning alive. 

Turn more pages: Countless tables of logarithms, trig functions, and far more. Numbers we could only approximate with our old slide rules.  Today, the Internet simply spits all that out on command.  But the first one that caught my young eye tells a different story:

The Mortality Table (How I calculated 68 years, I cannot recall.)

Its: The “American Experience Tables of Mortality.”  Naturally, my young self immediately had to find out how long he would live.  He figured it was telling him that he’d likely die around the age of sixty-eight.  It would’ve denied me several more decades of technological evolution.  So, back to this in a moment.

But first: I finished my schooling and went on to do research. Now this old handbook helped me reconstruct parts of the calculus I’d forgotten – parts I now had to use. 

Typical page of Burington’s integrations

That table of integrals for example: So much experimental research means identifying a physical process – then learning how to predict its behavior. That means mathematics.  And a tricky calculus integration can be a big hurdle.  But here are four hundred and thirty four integrations already done.  A huge convenience that kept serving me, long after my teenage self first saw it. 

Now: back to that new thing which it hadn’t meant to tell me – a surprising window into the filigreed technological changes that so separate me from that young boy.  That so separates us all from the middle Twentieth Century.

It’s just shown me two ways in which an old technology gets left behind: Because it was replaced by improvement.  Or because it became obsolete. Those tables of logarithms, integrals, and such are still perfectly correct – just replaced by online convenience.  But that old mortality table ... It tells a different story.  Science had already made it obsolete, even back when I first read it. 

Now that tattered old book still lies within reach – while my old slide rule and drafting tools lie buried in drawers.  Sure, nostalgia’s part of it.  But – even today – it has just reminded me that some replacement is driven by improvement and some by obsolescence.   Technology keeps changing, right under our noses.  But it does so in two very different ways.

I’m John Lienhard, at the University of Houston, where we’re interested in the way inventive minds work.

(Theme music)

R. S. Burington: Handbook of Mathematical Tables and Formulas, Handbook Publishers, Inc. Sandusky, OH, 1940.

You may read Burington’s entire book online, here.  I should not be surprised if you come away with other insights about its relationship to our rapidly evolving world – insights that’ve eluded me. 

This Episode first aired June 30, 2026.