About me

It was why I was happy to go along with working at night.In fact, I was excited by the change.It felt as if, through Sheldon, we were being initiated into a way of doing research that came from one of the most creative ventures in the history of science.The two brilliant leaders, Robert Oppenheimer and Richard Feynman, surely knew something important about the dynamics of creativity.We filled them with equations and stood back and examined the whole movement of the mathematics.Sometimes we would argue over the ideas, but a lot of the time we stood in silence, thinking, staring at the equations.If we had an idea, we would try it out on the blackboard, to see where it went.If it turned out to be barren, we would erase it and sit down.We were exploring the equations that led to a surprising calculation made four years earlier by one of the world’s foremost mathematical cosmologists, Stephen Hawking.His paper was a milestone in the history of cosmology.As with the arrival of any radically new idea in science, it ignited a period of wild activity leading to a riot of mathematical speculations.We were intent on joining the fray.We now know that the universe has been expanding for billions of years.Would anything change if the initial expansion rate had been different? The vast pretension of the question gives a sense of why mathematicians develop an unshakeable certainty that equations deserve reverence.Here is Hawking, one human on a tiny planet spinning about one star out of hundreds of billions in the Milky Way galaxy, which is one galaxy out of a trillion.Whence such confidence?This was the Pythagorean breakthrough that asserted numbers were real and mathematics formed the fundamental structures of the universe.This axial assumption led to Western science’s conviction that with the magic of mathematics, humans can discover the laws governing the vastness in which we find ourselves.These equations work astonishingly well in predicting various empirical facts concerning the universe, such as the temperature of the ambient background, or the average density of the matter in the universe.But the equations fall apart at a certain point.To say that the equations fall apart is to say the equations soar off toward infinity at one point.They soar off at an exponential rate so that as we push time backward, it approaches a limit to how far back we can go.If we pressed the time parameter to this limit, the equations would predict that matter becomes infinitely dense at one particular point in time.It is nonsensical to say that matter becomes infinitely dense.We conclude that the equations simply fail at that point.The point at which they fail is the singularity of the equations.It is called the initial singularity because there is no singularity that occurs before this one.That is why Hawking and his primary teacher and collaborator, Roger Penrose, identified it as the initial singularity.Furthermore, as we travel conceptually toward this initial singularity, not only do the equations predict that the density of the universe soars beyond all limits, they also predict the space between any two particles moves toward zero.These astounding mathematical results come when we push the equations back to a unique point in time, 13.8 billion years ago.Cosmologists interpret this initial singularity as the beginning of the known universe, the big bang, when all the particles are squeezed together.It is either the beginning of the universe as a whole or the beginning of the special branch of the universe in which we find ourselves.However a person interprets this singularity, it has become a central research focus of some of the most creative scientists working within mathematical cosmology.The trajectory of any one point represented the evolution of that particular theoretical universe that began with its own expansion rate.If the marble is perturbed even slightly, it will fall off the crest of the hill and roll away.The slightness of the perturbation has to be emphasized.This was a stunning mathematical result.If a parallel universe has an expansion rate faster than our actual universe, the theoretical parallel universe would not be dense enough to build structures.On the other hand, if the expansion of one of these theoretical universes had a smaller value than our actual universe, its trajectory would end in a single point, a black hole.Particularly remarkable was the delicacy Hawking discovered.The size of a perturbation that would lead to these drastically different outcomes needs to be only one part in ten raised to the sixtieth.Before I describe these three approaches, I need to emphasize that all three approaches agree that the expansion of the early universe is extraordinarily elegant.The first group, the cosmologists of the multiverse school such as Stephen Hawking, explain the exactness of the expansion rate by assuming the theoretical universes in Hawking’s mathematics really do exist somewhere, even though we have no empirical evidence of any of these universes.This method of assuming mathematical equations point to the existence of something never experienced before has a long history.One of the most successful occurrences is Paul Dirac who saw in his equations what looked to be a new form of matter, antimatter, which was subsequently detected.If it turns out that the multiverse cosmologists are right, and there are an infinite number of parallel universes, our expansion rate has no explanation.With an infinite number of parallel universes, one of them will have the right rate.That we happen to be in the right one is just a matter of chance.These scientists have on their side Isaac Newton, who believed just that.There is no reason for the elegance.Thus, the elegant dynamics in the plasma at the beginning of time are regarded as something like a cosmic embryo.In this third perspective, the reason for the expansion rate of the universe is to be found not in the past alone but in the future form.