I dwell on chaos theory. I don't think its significance has been properly absorbed by the public consciousness yet. There's something simultaneously liberating and unsettling about it.
For instance I'm often conscious that it's a mathematical near certainty that if I'd done anything different in my earlier years, absolutely anything at all, then my children would not exist, and therefore I cannot bring myself to regret anything I ever did. Conversely it's unnerving to consider how unlikely my own existence is in the first place.
Also, since appreciating chaos theory, I can no longer enjoy any movie involving time travel.
Correct me if I'm wrong, but chaotic systems are unpredictable because they are complex and infinitesimally small variations in starting conditions result in hugely different outcomes. They are not, however, non-deterministic. If the universe is merely chaotic and not actually stochastic, then the existence of you and your children are not only not unlikely, it was inevitable.
Exactly right. Unless you believe quantum mechanics throws a monkey wrench into determinism. Which it certainly does in the realm of the very small.
Chaos theory and QM are completely orthogonal (by which I mean they say different things about the universe, not that they are in conflict with one another). And they both screw up the idea of a predictable universe.
Quantum mechanics demonstrating non-determinism in the realm of the very small necessarily means that the macroscopic realm is also non-deterministic. A non-zero percentage of events occur in which that one particle appearing in one place rather than an is just enough to cause the macroscopic object to take a materially different path. In fact a simple thought experiment shows that a system could be engineered to demonstrate this. Add a sensor that reads which way a particle goes in a double slit experiment and based on the direction, flip a switch that makes a train go east or west based on the sensor read out.
Not sure what you mean. Quantum effects don't "disappear". They are physical laws. Which slit the particle enters after the wave decoheres is precisely a non-deterministic element of quantum mechanics.
It doesn't alter the outcome. It causes it to decohere into a particular outcome. There is no way to force a particular outcome, hence it being non-deterministic.
How do we know that what we perceive as randomness in quantum mechanics is "true" randomness, and not just something we say is "random" because we fail to model it?
(disclaimer: not a physicist, never looked into the maths, but I'm intrigued by QF)
There are deterministic interpretations that are very much on the table.
The Everett's Many Worlds[1] is fully deterministic (and depending on your view, the simplest one too): the universe is a quantum wave function evolving according to the Shrödinger's equation. That's it.
A lot (if not all) of the hidden variables theories are also deterministic. The apparent non-determinism stems from the aforementioned variables that we don't/can't see.
I keep hearing more and more about the Pilot wave theory[2] recently. And that's a hidden-variables deterministic interpretation.
I don't think that is the case, at least not as an absolute rule. There are stable and non-stable outcomes of what you do. If you choose one job over another definitely affects your life like you describe. But if you choose to have coffee over tea one morning you will still end up behind the same office desk later in the day.
Of course, if you met your wife by a random accident that would not happen if you were one minute late, there is something about it that the beverage choice could affect. But if you met her on your workplace, then less so.
right, now think how many children didn't come to existence because you did something. just enjoy the moment and what you have got:) and, chaos theory is one mind bender indeed.
My naive understanding of chaos theory was more about studying how minute changes could create measurable changes in chaotic systems. But it also often seemed that “all the noise” was very minimally affected by such changes. The smaller the change the smaller the affect. So I can’t help but think certain big things - like existence of children - are harder to perturb away.
If time exists then all that has happened and will happened has existence. Does this existence have energy when you factor out time? Do we need infinite energy to describe a model universe?
If there are bounds to this 'non-inertial entropy' then perhaps QM can be explained as quantization noise in 4D spacetime. In this model there are a lot fewer candidate universes.
The unpredictability of the consequences of our actions (in the context of free will and fate) has been in the consciousness of the Western public since Sophocles at least.
I remember reading about him in Chaos: Making a New Science where James Gleick portrayed him as a young man. That was in the late 1980s when I was a high school student. Time flies :(
I read the same book. I felt it was very useful. I remember a homework assignment to calculate bearing under various conditions. One of them wouldn't solve and I realized it was because the conditions produced chaotic behavior. So of course you couldn't produce a closed form solution.
I first read that book when I was 13 and I still go back for another read every few years. Not only did it make the subject accessible, it didn't over simplify. The stories of the people making the discoveries kept it personal and engaging throughout, and Feigenbaum's chapter(s) were my favorite. After finishing the book, you never see the world the same way again.
I was peripherally involved in chaos theory in the early 80s. I never met Mitch but I still think of him as a kid not much older than me. I had no idea he was 74. Age creeps up on one.
As a kid I remember playing with the logistic map (possibly pointed at it by Dawkins?) following Robert May and Verhulst explanations of population dynamics. Feigenbaum's constant(s) seemed to point a way through the chaos (this at a time when plotting the mandelbrot set - slowly - was all the rage).
One of Feigenbaum's best known contributions to the subject is a heuristic theory, based on renormalization group ideas borrowed from statistical mechanics, that explains the period doubling cascade and lets one calculate these constants. The first mathematically rigorous computer-assisted proof was due to Oscar Lanford. I think now there are proofs that are not computer assisted, though I'm not as familiar with these developments.
The Wikipedia article linked above links to some of this information. The following article has a slightly more technical summary together with references to many of the original papers (including Feigenbaum's):
For those of you with a bit more matheamtical background and access to technical books, I like the summary of Feigenbaum's renormalization picture in Guckenheimer & Holmes.
I spent some good times exploring deterministic chaos.
Mathematica had sound outputs for the logistic map. I remember one could distinctly hear the octaves progression, then noise, then a fifth. I remember making a video overlapping the sound and the cobweb plot to "see" what I was hearing.
Instead of studying calculus, I fell for the trap of trying neverending, eardrum busting, iteratibly non-converging functions.
For instance I'm often conscious that it's a mathematical near certainty that if I'd done anything different in my earlier years, absolutely anything at all, then my children would not exist, and therefore I cannot bring myself to regret anything I ever did. Conversely it's unnerving to consider how unlikely my own existence is in the first place.
Also, since appreciating chaos theory, I can no longer enjoy any movie involving time travel.