Today, single — or multi — valued universes. The
University of Houston's College of Engineering
presents this series about the machines that make
our civilization run, and the people whose
ingenuity created them.
Mathematicians speak of
multivalued functions. If y depends on x, and we
give a numerical value to x, then we normally
expect to get only one value of y. But funny things
can happen. Many different angles have the same
cosine. Or suppose you write y = square root of x.
If x = 4, then y can be either +2, or it can be
You and I know the world we live in by what our
senses report to us. Sometimes our senses see it
directly but very often they see it through
instruments — telescopes, spectrographs, radar.
Yet everything we know is a function of
our sense data.
So is the world out there a single, or a multi,
valued function of what we see? If we turn this
inside out, I'm surely a multivalued
function of the world around me. Sunday, it rained
— heavy air, a leaden sky. Monday was cool and
sunny. Relationships among objects, and among
people, shifted. I was a different me.
And, as I grow older, I begin to see how that might
work both ways. Oh, I know the physical reality
stays the same, regardless of me. Yet the world
might as well be multivalued, so wildly does it
shift each time we extend our senses with new
instruments and analyses. If there is one reality,
that offers cold comfort.
Ever since Planck and Einstein, new questions have
outrun new understanding. It's more and more
apparent that our senses are a great throttle valve
on understanding. Everything we know has to filter
through vision, touch, smell, taste, and hearing.
Yet reality reaches so far beyond the range of
those small senses.
Now many physicists are taking some very strange
ideas seriously. Take the notion that we occupy, at
any instant, one out of a vast interacting ensemble
of parallel universes. That's multivaluedness in a
pretty literal form.
However, suppose we decide to put no stock at all
in multiuniverses. We still run into another
kind of multiplicity when we ask how
widely the realities of Earth and the cosmos can
vary, and still be consistent with our terribly
limited vision. I fear the answer is "Very widely
This matter does not just haunt physicists. Two
historians look at the same artifacts and documents
and they construct different pasts. Two politicians
look at the same electorate, two economists look at
the same data, two theologians look at the same
We can have either of two reactions to all this.
One is hopelessness: Faust at twilight, grieving his
incapacity to know everything and ready to wager his
soul. But the other is quite different. Some of us
feel a great joy and hope in the enormous range of
yet-undiscovered possibility. Still, we cannot
discount the fact that human limitation dogs us. No
wonder Alexander Pope wrote,
One science only will one genius fit:
So vast is art, so narrow human wit
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
For more on this alternate universes notion, read:
Deutsch, D., The Fabric of Reality. New
York: Penguin, 1998. Or have a look at Duetsch's home
Einstein's house in the Princeton, NJ, of an
(photo by the alternate John
The Engines of Our Ingenuity is
Copyright © 1988-2003 by John H.