The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos
I told this story once before. Relevant to this posting, here it goes again. When I was in college I took a class on Mathematical Philosophy. On the first day of class I sat next to a woman who was an undergrad major in Philosophy. As part of exchanging basic introductions I told her I was majoring in Physics and Mathematics. When she heard I was studying Physics she asked me this question: “Why do you think that the World lends itself to mathematical formulation?”
I have never forgotten this question for these reasons:
First, in my naive way of thinking at the time, I did not think someone could ask such a question. Mathematics simply works. Using Mathematics one can make predictions about how the World works and verify these predictions experimentally. Even in Quantum Mechanics, the Schrodinger Equation makes a prediction about the probabilities of outcomes which experimental evidence has proven to be correct over and over. Some, like Einstein, would hold out for the “hidden variables” theory that mathematical models would predict exactly what would happen if we had a better model and more information. In this context Einstein made the famous statement, “God does not play dice with the Universe.” Einstein could not accept that the way the world worked was based on probability.
Second, it taught me a lesson that I validated over and over again. The people that will make the most progress in any discipline are the people who can formulate the right questions. As sort of a corollary, I will always remember this: “Discovery consists of seeing what everybody has seen, and thinking what nobody has thought”. – Albert Szent-Gyorgi.
Some who write about the sad state of Physics education today point to the fact that academic institutions are turning out physicists who are more practitioners (technicians and engineers) than they are scientists that are adept at framing critical questions and seeing things in novel ways outside traditional paradigms of thought. Progress in Physics is often about shattering existing paradigms by framing the right (probing) questions and seeing things in novel ways. But we also need the people who can do the work to test the theories that Einstein, Hawking, and others push out using pencil, paper, and imagination.
If you are one of those who likes to ask hard questions about the nature of Reality from the perspective of modern physics you might want to check out this book by Brian Greene
I told the story above because Chapter 10 ( Universes, Computers, and Mathematical Reality) and Chapter 11 ( The Limits of Inquiry) in Greene’s book treats this issue of the role of mathematics in Physics. Not only that but these chapters also tie together several other interesting topics. For example: the ability of computers to simulate the physical laws of a Universe; the ability of computers to simulate sentient beings; and finally, whether the reality of the world is exactly the reality of mathematics. (Mathematical Realism)
It’s easy to tie in Ray Kurzweil’s The Singularity is Near which predicts a time when human beings, using technology, will transcend their biology by creating computers that can exceed the mental capacity of humans. As regards simulated Worlds, one only need to look at Second Life where an alternate reality is created by computers and humans animate avatars in this world. How far is the final step for Second Life? That final step being that sentient beings become part of the simulation and those sentient beings wonder about their world while “we” (their creators) look in on their world in sort of a God-like privileged position of creator of their Universe
Here is what Greene has to say about the Reality of Mathematics
For centuries, mathematicians and philosophers have wondered whether mathematics is discovered or invented. Are mathematical concepts and truths “out there,” waiting for an intrepid explorer to stumble upon them? …
At first sight, the uncanny way that a great many mathematical insights find application to physical phenomena provides compelling evidence that math is real.
Examples abound. From general relativity to quantum mechanics, physicists have found that various mathematical discoveries are tailor-made for physical applications. Paul Dirac’s prediction of the positron (the antiparticle of the electron) provides a simple but impressive case in point. In 1931, upon solving his quantum equations for the motion of electrons, Dirac found that the math provided an “extraneous” solution—apparently describing the motion of a particle just like the electron except that it carried a positive electric charge (whereas the electron’s charge is negative).
In 1932, that very particle was discovered by Carl Anderson through a close study of cosmic rays bombarding earth from space. What began as Dirac’s manipulation of mathematical symbols in his notebooks concluded in the laboratory with the experimental discovery of the first species of antimatter.
So, there is this idea that Mathematics is not an invention of mankind so much as it is a discovery of something “out there” that exists apart from human beings. Math is a sort of Reality, or the machine that runs the World. In a sense, our Universe could be thought of as a giant computing machine.
If time in not continuous but discrete and if space is not contiguous but discrete and if the Math of the Universe is of a certain kind, then the World is emergent and computable. That is, a computer of sufficient speed could compute the state of the Universe for every increment of time across the entire space for every particle using Mathematics In this scenario what is the Big Bang other than the set of initial conditions and the particular math (program) that runs the World simulation? And couldn’t this include simulating sentient beings in that Universe where those sentient beings are thinking about the world in which they live and how the World works and perhaps also discovering mathematics – the mathematics that runs their particular world? Are we at that point now?
If the Universe does not run by Math then what is this non-Math? Or, to the point of the question that I never forgot, “Why do you think that the World lends itself to mathematical formulation?” If this is a priori true – that the World does not run by Math – then is there ever a chance that there will ever be the Grand Unified Theory or The Theory of Everything?
Here is how Greene explains it, in part
Even if you accept the possibility of artificial sentience, you may be persuaded that the overwhelming complexity of simulating an entire civilization, or just a smaller community, renders such feats beyond computational reach.
On this point, it’s worth looking at some more numbers. Our distant descendants will likely fashion ever-larger quantities of matter into vast computing networks. So allow imagination free rein. Think big. Scientists have estimated that a present-day high-speed computer the size of the earth could perform anywhere from 10**33 [ 10 to the 33’rd power] to 10**42 operations per second. By comparison, if we assume that our earlier estimate of 10**17 operations per second for a human brain is on target, then an average brain performs about 10**24 total operations in a single hundred-year life span. Multiply that by the roughly 100 billion people who have ever walked the planet, and the total number of operations performed by every human brain since Lucy (my archaeology friends tell me I should say “Ardi”) is about 10**35. Using the conservative estimate of 10**33 operations per second, we see that the collective computational capacity of the human species could be achieved with a run of less than two minutes on an earth-sized computer.
And that’s with today’s technology. Quantum computing—harnessing all the distinct possibilities represented in a quantum probability wave so as to do many different calculations simultaneously—has the capacity to increase processing speeds by spectacular factors. Although we are still very far from mastering this application of quantum mechanics, researchers have estimated that a quantum computer no bigger than a laptop has the potential to perform the equivalent of all human thought since the dawn of our species in a tiny fraction of a second.
If you allow the above: that Mathematics is the true Reality underlying the way the World works; that the human brain can be simulated; and that computing power, over time, will grow without limit, then could it be that the world that we live in right now is a simulation undertaken by a far advanced alien race? If we are living in a simulated world (the ultimate version of Second Life) then what would be the “cracks” in the World by which this simulation would reveal itself? Would “scientists” in the simulated world invent (or discover) the Physics (Mathematics) by which their World Works? Would those sentient beings in the simulated world invent computers and create their own primitive simulations (Second Life)? Could there be an infinite regress, similar to two mirrors each reflecting the others images, that create an infinite number of level of simulations of all possible worlds? If some higher being were to put this simulation into motion what would be the relationship of this being to the world that s/he brought into existence? Would this being “play” with the simulated sentient beings placing them into all kinds of existential dilemmas to see how they react – perhaps just for fun or play? The questions are endless.
All of these topics and more are taken up in Greene’s book.
So, if you want to take a wild ride on the tail of modern Physics to explore the deep laws of the cosmos and theories of multiple universes then I would highly recommend you take a look at his book – The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos
Reconstructing the brain piece by piece and building a virtual brain in a supercomputer
Read about the Blue Brain Project – http://bluebrain.epfl.ch/
Read about The Singularity – http://singularity.com/