Conjecture #1: Infinity (Part 3)

I Conjecture:  The Concept of Infinity Could not Exist in a Finite Universe.

Part Three: Human Imagination

“Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.”
Albert Einstein

It is certainly understandable how somebody as brilliant as Einstein could perceive the rest of us to be infinitely stupid.  Jokes about lawyers and politicians aside, I’m not sure about either.  I remain an agnostic on untestable scientific conjectures,  as well as on religion.  But my gut continues to tell me that my conjecture of infinity has merit, so I’ll proffer one final discussion before moving on to the next one.

Nothing is inherently more self-contradictory than infinity.  We can imagine it mathematically, but can’t measure it.  We can imagine–sort of–infinite time and space.  But physicists and philosophers tell us there are a finite number of possible combinations of matter and energy, at least in our observable universe with our laws of physics.  But we can imagine things beyond those laws (fantasies like Harry Potter, various science fiction scenarios,  and possibly real alternate universes with different laws of physics, to name just a few).  So our imagination does not seem to be limited by what is possible or observable in nature.  By that it would be reasonable to assume that human creativity and human stupidity are both potentially infinite.**

One of my favorite quotes about the universe is the famous J.B.S. Haldane proposition, “I suppose the universe is not only queerer (sic) then we imagine, it is queerer than we can imagine.”  This would seem to be a contradiction of the notion that human imagination is infinite.  David Deutsch says as much in The Beginning of Infinity, and he says so specifically in regard to this quote.  His point is that human imagination and creativity are potentially infinite and that Haldane is, therefore, wrong.  But where infinity is concerned, even Deutsch contradicts himself.  For as he points out elsewhere in the book,  there are mutually exclusive infinities and there are also larger and smaller infinities.  Consider the set of all even integers and the set of all odd integers.  They are mutually exclusive yet both infinite.  Now consider the set of all even integers and the set of all integers.  They are both infinite, yet the latter is twice as large as the former.  The point is: there might be both an infinity of things we can imagine, and an infinity of things we can’t imagine.   Deutsch himself indirectly alludes to this in his earlier book, The Fabric of Reality.

There is no question that the Haldane quote was true at least in the early part of the 20th century when he first espoused it.   The universe certainly turned out to be stranger than anyone could imagine at that time.  But the universe continues to surprise us, no matter what we imagine.  And if our imagination is only potentially infinite we cannot imagine, at any one time, everything that exists or the larger infinity that might exist.   To me, this is what makes the combination of human imagination with empirical knowledge so exciting.  No matter what we can test or what we can imagine, there are still surprises out there to delight and confound us.  But in my final analysis–the one that needs explanations and not just measurement–Einstein was absolutely right in another of his famous quotes:

“Imagination is more important than knowledge.”

Up next (after a few digressions and ridiculous timeouts): The conjecture of inevitability

**By potentially unlimited here, I mean no theoretical limit.  To be actually infinite, humanity would have to exist forever.


Conjecture #1: Infinity (Part Two)

I conjecture:  The concept of infinity could not exist in a finite universe.

Part Two:  The Possibility of Infinite Space

“The universe is a big place, perhaps the biggest.”– Kurt Vonnegut

Douglas Adams called the universe “mind-bogglingly big.”  But “mind-bogglingly big” pales next to infinitely big.  And while the question of space being infinite may be somewhat easier to get around than time, it is certainly no bargain.

The first problem is that Vonnegut is dead-on right.  Our universe is only possibly the biggest place.  It used to be that “universe” meant everything.  But then the concept of “multi-verse,” with countless alternate or parallel universes, began to creep into astrophysics and cosmology.  To make matters worse, there is not just one potential level of parallel universe proposed, but four.*  So far.  Physicist and author Paul Davies argues that the concepts, while fascinating to contemplate, amount to philosophy–or even religious faith–if you can’t test them.   David Deutsch, among others, disagrees and deduces that the many worlds interpretation of quantum mechanics is the only one that makes sense, in terms of scientific explanation.  I’ll have more background on the various arguments surrounding interpretations of quantum mechanics–particularly The Copenhagen Interpretation vs. all others–in future posts.

Getting back to the question of infinity of our universe and/or the multiverse, there is indeed some scientific investigation aimed at determining the potential infinity of our own visible universe.  It involves the topology of its three-dimensional space and whether it is flat or curved.   I can’t go into details, as it involves rather advanced calculations from observations of the Cosmic Background Radiation–the earliest remnants of the Big Bang we are able to detect with current technology.  But the weight of the existing evidence seems to be pointing towards a flat topology that could be infinite.  Add that to the possibility of countless alternate universes of various kinds,   and I will assume for our purposes that space is at least potentially infinite.  [For a discussion of actual vs. potential infinity, see the Wikipedia article].   In the final installment on this conjecture, I will address one dimension of existence that I feel without doubt is potentially infinite: human imagination.    For an extended, if somewhat dramatic discussion of the possibility of an infinite universe, watch the video linked at the bottom of this article.

7-year universe image of background microwave radiation from NASA’s WMAP probe. (2010)

*As classified by MIT cosmologist, Max Tegmark

Text of this post ©2012 Mark Sackler.


Conjecture #1: Infinity (Part One)

 I conjecture:  The concept of infinity could not exist in a finite universe.

“I am incapable of conceiving infinity, and yet I do not accept finity.”

 Simone de Beauvoir


Pure philosophy?  It might be.  It’s probably not provable in any scientific manner; but it’s certainly conjecturable.  So let’s discuss the implications, as many of the Millennium Conjectures to come herein presume the universe—or multiverse, if you please—to be infinite in some shape or form.  As most religions require a belief in god as a given, my worldview based on science needs to take a stand on infinity.

As best as can be determined, the ancient Greeks seem to have invented the mathematical concept of infinity.  (Okay—with the possible exceptions of baseball, hot dogs, apple pie and Chevrolet—what didn’t the ancient Greeks think of first?)  So the question begs, did we humans discover infinity or did we invent it?  It’s certainly conceivable that we could have invented it, at least in the mathematical sense.  Let’s look briefly at two other possible dimensions of infinity—time and space.  Of course, Einstein asserted that time and space are a single four-dimensional continuum, but let’s separate the two for the purposes of this metaphysical discussion.

The Possibility of Infinite Time

In 1949, using Einstein’s equations of general relativity, Kurt Gödel provided a proof  that a certain type of rotating universe would be static and spatially finite, but temporally infinite in a rather unnerving form: it would contain closed time loops that would permit time-travel into the past. While evident that it did not exactly describe our universe, which is indeed expanding, Einstein himself admitted it raised disturbing questions about the nature of time in our universe.  Gödel later expressed a philosophical argument that this  proof suggests that time in our own universe does not exist, either as Einstein described it or as we intuitively experience it.1

Kurt Gödel

More recently, philosopher-scientist Julian Barbour has taken complete issue with Einstein suggesting that time is an illusion created by change–that it in fact does not exist at all.  He asserts that time does not flow, but is a series of distinct, static and timeless instants that we experience as “flowing” time.2      David Deutsch, took this once step further in his book The Fabric of Reality, when he asserted that time not only does not flow, but each  instant we experience represents an alternate universe, each deterministic.  He essentially argues that our consciousness moves  from alternate universe to alternate universe and that it is this which is the source of perceived in-determinism and free will.  [For now, don’t worry about the “many worlds” interpretation of quantum mechanics if you don’t understand it.  I’ll provide some simple primers on these concepts in “asides” between the main posts.]

So let’s leave it at this: nobody really knows for sure exactly what time is, or if it even exists in anything like the form in which we experience it.  So let’s move on.  Next up is a discussion of space as a possible “infinite” dimension of reality.  And don’t worry–there will be some intervening silliness if only for comic relief.


  1.  Gödel universe, The Encyclopedia of Science (online)
  2. Barbour, Julian, The End of Time: The Next Revolution in Physics (1999) Oxford University Press p.9
  3. Deutsch, David, The Fabric of Reality (1997) Penguin Books,  Chapter 11, Time: the First Quantum Concept, pp. 259-288.

Introducing The Millenium Conjectures

“ reality, scientific theories are not ‘derived’ from anything.  They are guesses—bold conjectures.”

David Deutsch, The Beginning of Infinity


David Deutsch

In his provocative and stimulating tome The Beginning of Infinity, the British astrophysicist David Deutsch describes the role of science as one not so much as describing reality as explaining it.  It does this, he asserts, through conjectures which then may be tested by experiment.   But this leaves substantial problems in today’s complex and technical world, as there are many conjectures about reality which we cannot test, or at least, cannot test yet.  The existence of exo-planets—planetary systems around stars other than our sun—was only a conjecture until the technology existed to actually detect such bodies. Many mathematical conjectures were not provable for centuries until the advent of sufficient computing power to do so.  Many other scientific ideas—from simple speculations to profound interpretations—cannot be tested with today’s technologies; in some cases, we cannot even imagine how ever to test them.  The “many worlds” interpretation of quantum mechanics is one of these.   This is a subject I will deal with specifically in a later post.  But the point is: my concern here is with ideas we cannot yet, or maybe never can prove.

Why bother?  One of the most interesting books I have ever read is the 2005 volume What We Believe but Cannot Prove. Published by,one reviewer expressed its content quite succinctly:

John Brockman, writer, publisher and events manager for the science elite, has asked a hundred researchers the question, What do you believe is true even though you cannot prove it? The answers are posted at his e-magazine Edge (, and they exert an unquestionable morbid fascination—those are the very ideas that scientists cannot confess in their technical papers.  –JAVIER SAMPEDRO, Madrid,  EL PAIS, February 20, 2005

We all need a worldview.  And while some scientists and philosophers may simply say, “that’s just the way it is, no explanation is needed,” I cannot live with that.  My worldview is based on science, but it needs explanations.

I do not pretend to have any answers.  I don’t even have the viewpoint of a trained scientist.   My viewpoint is the journalistic approach of a layman generalist with a passion for science.  These are, in effect, my own interpretations of what I have read and learned about the present state of human knowledge of physical reality.  In some cases, I may be simply re-stating in my own terms, with my own views of the implications, ideas that may have been put forth or at least hinted at by others. Most of these subjects will involve issues we can’t really test now—maybe never.  I for one need a way of viewing reality that is based on science, but goes beyond what we can absolutely test.  I require explanations, but untestable explanations must seem at least scientifically feasible.  I cannot brook the mystical or supernatural—and yes, in some respects, the religious.  I am a non-theistic existentialist, and this is how I build my world view based on science.

So these are my conjectures.  They are indeed bold guesses.  They are not intended to be absolute assertions of reality—anything but.  They are my suggestions of things that might be true, that I imagine could be true, but that in many cases may not even be provable one way or the other.  What I am doing is asking: what are the implications of this viewpoint?  These are—essentially—what ifs.

UP NEXT:   #1 The Conjecture of Infinity

Text in this post ©2012 Mark Sackler

Suggested reading:

%d bloggers like this: