Photo: Geoff Oliver Bugbee, www.geoffbugbee.com

John Barrow is speaking on infinity. The subject of his talk is perhaps the biggest idea, but he says with a proper English emphasis, rather *curiously* big. He describes the idea as a stand in for other subjects that would otherwise be inaccessible to most, like the mathematics behind much of his work. Infinity has popular appeal.

He's also using an overhead projector to throw up slides instead of a slide projector. Haven't seen one of those in a while.

Infinity, or unboundedness (I like that word) is an old, old concept. The idea of always having one more thing is oddly intuitive. Of *course*, we can always add something else.

Being infinitely *small* is a similar concept. Halving something could in theory go on forever, a kind of Zeno-graphy.

Aristotle divided the notion into two: potential and actual infinities. Potential infinities can exist, but actual infinities that might affect us, might be real, cannot. That notion informed thinking through the middle ages.

Taking infinity seriously as an idea cost the lives of some pioneers. It was dangerous because an infinite universe lacks a center. He also used a basketball to illustrate that walking its circumference, one will never encounter an edge; it's infinite in its way. If there is no center, there is no special place.

Infinity comes in three flavor: mathematical, physical, transcendental. He uses a grid to illustrate where famous thinkers fell in the spectrum of thinking about the idea. Bertrand Russell, for example, believed that math and physical infinities existed, but not absolute infinities.

Galileo in the 1630's created a paradox that's interesting. Take two columns of numbers listed in a one to one correspondence - 1,2,3,4,5 corresponds directly to 2,4,6,8,10 etc. Which list of numbers is bigger? Isn't the list with even numbers half as big? The answer is no.

Just to show how disruptive the idea is, he notes that Georg Cantor, the German polymath, encountered prejudice form the other mathematicians who resisted the idea of math infinities. Cantor was able to identify *countable* infinities and *uncountable* infinities. He created a recipe for creating numbers that can never duplicated in a list of numbers. In essence he developed a method to distinguish *between* infinities.

This was alarming to some mathematicians, who grew concerned that math was becoming something else. Other philosophers and theologians, however, ran with the idea.

Dr. Barrow rhetorically asks: is infinity a signal in physics that one must try harder? How should infinities be interpreted? One way would be to suggest that whenever we encounter an infinity, it's a signal that the theory is flawed or incomplete. The assumptions have broken down. Perhaps what's breaking down, instead, is the ability to make predictions at all.

He describes string theory was a physical theory that has only finite answers, which is part of its appeal to many: its cosmology is finite.

Applied to the universe, he describes several possible scenarios for size. Is it expanding, contracting, going on forever? Is it possible to see "big crunches" when describing a history of the universe?

For astronomers, do black holes always occur on collapse? Is there a localized infinite in black holes?

He introduces the idea of "cosmic censorship?" Why are black holes alway hidden behind black hole event horizons? "It's a live issue today." Another feature expression of infinity in cosmology is the infinite replication paradox - an infinite number of the same event is happening infinitely often elsewhere. There are an infinite number of meetings between Dr. Barrow and his audience happening elsewhere.

Dr. Barrow puts some numbers to the idea, which I find interesting. What we can encounter (the speed of light is the limiting factor) is potentially 10 to the power of 26 meters. How many other copies of you and me might be floating about? THAT number is stupendously big. He displays the relative distances to find you and me, to find another whole universe. The finiteness of the speed of light, again, prevents us from ever visiting our twins.

Can an infinite number of things occur in a finite amount of time? Could such an infinite machine be created? Is such a device fantastically unlikely, or forbidden entirely?

He discusses Thompson's Lamp (is a lamp with a simple on/off switch "on" or "off" after an infinite number of clicks? Going through several different methods for adducing this problem, he illustrates that idea that methods can determine outcomes. The answer, curiously, may be one-half, neither on nor off.

CERN will be experimenting particle acceleration to experiment with such "supertasks" (an infinite number of developments in a finite amount of time).

And living forever? What would we get done? How would accumulated knowledge by conveyed? He concludes that in such a case some religious sects might offer us the chance to escape to a *finite* future.

Dr. Barrow's office is next door to Stephen Hawking at Cambridge. Those must be unbelievable discussions.

That's that. Off to get my copy of The Infinite Book autographed.

Wayne

Wikipedia: Infinity

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