(~∃∞) = (Infinity doesn’t exist)
“Where did the Big Bang come from? Who made it? Answer me that, wise guy!”
It would be plenty Daoist enough to imagine that the Universe popped into existence from the void. There was nothing, and there was nothing, and there was nothing, and then there was everything.
What Einstein’s equation tells us is another leap beyond what our diminutive brains can grok. Space-time came into existence at the moment of the Bang. We might stretch our minds to imagine existence outside of space. Existence outside of time is something else again.
(The world does not exist in time, but time exists within the world.)
The domain of time is part of our Universe. Another part, part of what exists, is outside of time.
Contemplation of paradox is a path to expanded awareness. This is the logic of the illogical Zen koan. The mind that forms rational structures to house and to order its knowledge gives up, and a larger mind takes over, one that is capable of encompassing a reality beyond our senses, beyond comprehension, beyond logic.
Existence outside of time.
Time is just one domicile, one possible home for being. Something birthed space-time, something larger, something capable of encompassing space-time as part of itself.
Dao is beyond understanding. Words may be used to speak of it, but they cannot contain it.
Dao existed before words and names, before heaven and earth, before the myriad things.
Therefore, to see beyond all boundaries to the subtle heart of things, dispense with names, with concepts, with expectations and ambitions and differences.
Dao and its many manifestations arise from the same source: subtle wonder within mysterious darkness.
To dwell in the world as it is, we must first dispense with the ambition to understand.
— Dao De Jing (or Tao Te Ching), Brian Browne Walker translation (all except the last line which is my own rendering)
Les Deux Infinis
Infinity as a concept has been made rigorous by mathematicians. It is assigned a definite meaning so that the symbol ∞ can be manipulated sensibly without undermining the logic of the systems in which it participates. Mathematicians can talk about infinity because they have come to agreement in advance about precisely what it means.
1 / 0 = ∞
In science, infinity has another meaning, a different meaning that must not be confused with mathematical infinity. To a physicist, infinity simply means “large enough that we don’t have to worry about running out, or coming to its end.” Alternatively, infinity is a conceptual tool for approximate calculations. We say something is infinite to justify neglecting terms that are in comparison, that might be added to it or subtracted from it. We always remember that an infinity must be divided by a comparable infinity before it has a meaningful place in our computations or in our conceptions. Infinity always cancels out of the equations.
The greater part of quantum field theory consists in rules for how to add and subtract infinities so that we are left with a finite answer.
Physicists acknowledge that we come to practical limits of what we can measure, or of what affects us, so we never have to grapple with mathematical infinity. Mathematical infinities are not part of our world, not in any sense that has consequence for science.
Astronomers commonly raise the question, Is our Universe finite or infinite? And the related question, Will the Universe go on forever, or will time come to an end? They adduce evidence in the form of measurements of speeds and galaxy counts and densities, plug those numbers into Einstein’s equations, and purport to tell us one way or the other. These questions and their answers must be understood in the context of physical infinity, not mathematical infinity.
Physics offers us enough challenges to stretch our mental framework without having to worry about forever, so there’s one subject on which you can set your mind at ease.
Time, even time had a beginning, and will have an end.