The Perfect Theory by Pedro G. Ferreira Page B

reconnaissance unit on the northern front and later on in Lvov. For a short while, it almost seemed that the Russians would prevail against the enemy. On regular night flights over southern Austria, he would join his colleagues in bringing towns that were blockaded by the Russian army into submission. Town by town, the occupying Russians were taking control.
    Friedmann was different from the other pilots. While his colleagues dropped their bombs by eye, making rough guesses of where they would land, Friedmann was more careful. He had come up with a formula that would take into account his speed, the bomb’s velocity, and its weight and would predict where he had to drop it to hit the desired target. As a result, Friedmann’s bombs always hit their marks. He was awarded the Cross of St. George for his bravery in combat.
    Having specialized in pure and applied mathematics before 1914, Friedmann had a great talent for calculation. He often threw himself into problems that were too difficult to solve exactly in the era before computers. Friedmann was fearless and would strip his equations down to their bare essentials, simplifying the messiness wherever he could and getting rid of any extra baggage. If he still couldn’t solve them, he would draw graphs and pictures that would gently approximate the right results, giving him the answers he wanted. With a voracious appetite for solving problems, Friedmann tackled everything, from weather forecasting to the behavior of cyclones and the flow of fluids to the trajectories of his bombs. He was undaunted by difficulty.
    At the beginning of the twentieth century, Russia was changing. The Tsarist regime lurched from crisis to crisis, ill equipped to deal with the growing discontent among a hugely impoverished population and facing the increasing turmoil in an ever more unstable Europe. Friedmann was enthusiastic about playing a part in the social changes around him. As a high school student, he fought alongside his fellow students during the first Russian Revolution of 1905, leading some of the school protests that shook the country. As an undergraduate at Saint Petersburg University he stood out for his brilliance, and during the war he led from the front, flying, bombing, teaching aeronautics, and running an industrial plant for producing navigational instruments.
    After the war, Alexander Friedmann settled as a professor in Petrograd (later to become known as Leningrad). The “relativity circus,” as Einstein called it, had arrived in Russia. Intrigued by the weird and wonderful mathematics, Friedmann decided to deploy his formidable mathematical skills in attempting to solve Einstein’s equations. Just as Einstein had done before him, Friedmann untangled the complicated knot of equations by assuming that the universe was simple on the largest scales, that matter was distributed evenly, and that the geometry of space could be described solely in terms of one number, its overall curvature. Einstein had argued that this number was fixed once and for all as a result of the delicate balance between his cosmic term, the cosmological constant, and the density of matter, in the form of stars and planets sprinkled through space.
    Friedmann ignored Einstein’s results and started from scratch. By studying how matter and the cosmological constant affected the geometry of the universe, he came up with a startling fact: that one number, the overall curvature of space, evolved with time. The ordinary stuff in the universe, the stars and galaxies sprinkled all over the place, would cause space to contract and fall in on itself. If the cosmological constant was a positive number, it would push space apart, making it expand. Einstein had balanced these two effects against each other, the pulling and the pushing, so that space stayed still. But Friedmann found that this static solution was only a particular special case. The general solution was that the universe
had