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 -2.
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 indeed!"
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 God.
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 work.
For more on this alternate universes notion, read: Deutsch, D., The Fabric of Reality. New York: Penguin, 1998.
Also see the Wikipedia page about Deutsch.
Einstein's house in the Princeton, NJ, of an alternate universe
(photo by the alternate John Lienhard)