Meditations on “infinity” (with apologies for taking liberties in the Holiday spirit)
Infinity has at least two meanings. We sometimes forget that the word is used very differently in math and in science, and we conflate the two.
For the mathematician, infinity is an abstraction with a pure and definite meaning, with some but not all the properties of a number. There is the magic that says that the infinity of even integers is exactly the same as the infinity of all integers, even and odd. More amazing is that the count of all fractional numbers like 1.65 and 3¾ and 0.142857142857142857… is also this same infinity. Yet there are infinitely many different infinities, labeled אo, אl, etc. and in the same sense, each can be demonstrated to be not equal, but “larger” than the one that precedes it.
But in the world of science, this kind of infinity doesn’t concern us. No experiment that can be performed will ever yield the result, “infinity”. There is only “beyond our ability to measure at this time”, and the related concept, “large enough that we need not worry about its effect on such-and-such a calculation.” Infinity has a practical meaning, relative to any given measurement or calculation.
We are finite creatures. All our experimental apparati are finite. Empirically, there is no such thing as “infinity”, but only a human-scaled limit for our ability to measure or calculate.
Does space go on infinitely in all directions, or is it merely larger than anything that we can measure (or that we can calculate from the measurements we make)? Mathematically, this may be a question we wish to ask, but scientifically it is not a meaningful question because it is not a question to which we can assign any empirical meaning.
Similarly, there is a mathematical meaning, but no physical meaning to the concept eternity.
We may wish for eternal life, but we cannot conceive eternity. Homo sapiens has been on earth for a mere 200,000 years, and even that is so far beyond our experience as to be an abstraction to us.
We like to think of “getting death out of the picture”, so we need never worry about dying. Think of it as a lifetime so long that, in practice, you just don’t worry about its limits. But don’t think about eternity – the very idea is full of paradoxes.
Start with the fact that you have a finite brain with finite memory capacity. Eventually, it would all get used up. You wouldn’t have the capacity to remember most of the stuff that has happened to you. (The mathematician would say, “as the duration of life increases without bound, the fraction of total life experience that remains stored in memory becomes vanishingly small.”)
One of the weirdnesses of quantum mechanics is that physical states are not continuous, but discrete and countable. The number of physical ways in which any finite amount of matter can be arranged is an unimaginably large number, but not mathematically infinite. If you lived forever, you would eventually go through every possible experience, and then you would have every possible experience again, and again and again…and you would have, at that point, barely begun.
So if we lived forever, we’d run out of experiences. For a finite being, there can be no eternal life, but only infinitely many repetitions from a finite set of experiences. I’m reminded of Pär Lagerqvist’s character who, for a momentary indiscretion, draws a curse from the condemned man bearing his cross: “You shall never die!”
Perhaps our wish for eternal life is no more than a paraphrase of our fear of death. Perhaps this is better addressed with attention to dissolving fear than to banishing death.
Of aging and eternal life
The fountain of youth has been a staple of stories, dreams and frauds for the duration of human history, but in the latter half of the 20th century the human life span has actually been extended by technology for the first time. Just in our generation, it has become possible to contemplate a thorough prevention of aging through medical intervention.
The absence of aging is not the same as immortality. At its low point, actuarial risk of death (for 10-year-old girls) is about 1 in 1,000 per year. So if we were never to age at all, perhaps we would live an average of 1,000 years.
This would be an inconceivably wonderful thing, at least for us as individuals. The danger of disease would be slashed, and the weakening and loss of faculties that come with age would be eliminated as well. For our human community, the effects would be more complex, probably with mixed benefits and risks. Imagine the wealth of human experience that would be available in the memories of our elders. Imagine the adaptability to change (phenotypic plasticity is the biological word) that would be demanded of us over that long a span of time, assuming we choose to remain engaged, rather than, say, to work for 60 years then retire for 940. Think how difficult it is for people educated and trained before computers to adapt to today’s work environments. Consider that this represents only 30 years, and that the pace of change is quickening, some say at an exponential rate.
1,000 years? I could get used to that
I find it utterly bewildering to contemplate eternity. I lose all perspective, and context for what I am doing in the present moment which (as Buddhists are fond of saying) is all we have.
In contrast, when I think of a lifetime of 1,000 years, I breathe a sigh, my imagination opens in scope, I experience a broadening perspective, empowerment, a loosening of anxiety about the immediate future and a freedom to experiment.
The short-term arc of the news cycle can feel sickening, alienating, arbitrary, even surreal in its lack of meaning or direction. But the long arc of history bends toward justice. Imagine the freedom to participate in that long arc, to be part of a larger human endeavor that spans lifetimes.
Imagine opening the paper and reading commentary on current events from Thomas Jefferson or Oliver Wendell Holmes.
If you had the opportunity to meet Leonardo, what might you like to ask him?
Imagine the privilege of presenting Beethoven with an iPod containing his 9 symphonies, 32 sonatas and 16 string quartets (though perhaps we would be wise to offer him first a cochlear implant).
Imagine explaining the power of nonviolence or the importance of scientific integrity to your 7th-great grandchild.
The biggest hazard of the 1,000-year life span is the spectre of tyrants clinging to power. Political institutions need to be able to adapt, and scientific understandings even more so. If ‘science progresses funeral by funeral’ because well-established scientists become gatekeepers with a stake in old ideas, then how will scientific institutions have to adapt in order to promote progress when people are living through multiple scientific revolutions?
These were idle fantasies in the past, but they have become dreams sanctioned by science.
Without aging, our lives will not only be much longer, but also of less definite duration. When life spans are fixed by aging, to live 20% beyond the average is an upper limit. No one yet has lived twice the average life span. But without aging, all deaths would be “accidental” deaths, and 1,000 years would be only the mean of a broad, exponential distribution. One person in 7 would live more than 2,000 years and one in 20 would live more than 3,000 years. With billions of people on earth, there would be many who had lived 10,000 years, and someone, somewhere who could remember 15,000 years ago.
To live without fixed duration is a good thing, precisely because it frustrates our propensity to make fixed plans. The blueprints for our lives, with limited career goals, limited horizons and planned retirement dates, are constraining in global ways which we do not apprehend because we are fish swimming in water.
We realize easily that it would be a great burden to know in advance the day on which we will die; the more approximate sense in which we know our life expectancies is also hurtful to us. Life should be open-ended. We have all heard stories, in one form or another, of the person who has planned for a fixed length to his years, then reaches the end of his plan and finds himself with blood still in his veins. At first relieved, then increasingly confused, he asks, “why am I still alive?”
Opening into unknown destinies is the essence of our being. Though our bodies have a finite duration, our creative spirits can thrive best at the threshold of the infinite.
…not in the mathematical sense, of course.
For basic information about healthy living for a long life,
see the author’s permanent page at AgingAdvice.org.