I have heard the term “The Church of Reason” to refer to our modern disposition toward rationality and science. Some thinkers are upset by this analogy, claiming that rationality is fundamentally distinct from a religion. In some ways this is true: for instance, rationality does not entrust a single institution or treatise with control of its truth (though some sects — I mean branches — come very close to a blind trust of scientific consensus). However, I sometimes get the distinct impression of a further belief, however never explicitly stated, that logic and science are not just the latest way, but the way to discover truth.
A succinct criticism from within the logical discipline describes my thoughts well. I quote:
If I see a coin come up heads twenty times in a row, I’m going to use the power of induction to predict that the coin is biased towards heads. Induction tells me that, the more something has happened in the past, it’s more likely to continue to do so in the future. I trust induction because induction has worked for me before.
Somewhere out there in mind-space is someone who believes in anti-induction: each coin flip of heads convinces him that the coin is biased toward tails. Anti-induction tells him that, the more something has happened in the past, the less likely it is to do so in the future. If asked why he trusts anti-induction, he exclaims: “Because it’s never worked before!”
This delightful morsel is so much more than an idle curiosity to me. Please do not mistake me for taking the surface interpretation: I do not claim that induction and anti-induction are equally valuable. But the anti-induction hypothetical illuminates, in an entertaining way, that belief in induction is circular. Observe that our unwavering trust in logic rests upon induction.
In this modern age it is sometimes easy to forget that there was a time when most of humanity was deeply religious. Humans of every intellectual prowess saw “God did it” as a sound explanation (allow me to assume omnipotent monotheism for the sake of argument). Some theorized about how God thought, what he looked like (whether that was a legitimate question), what would appease him, what actions would cause him to create rain or not. Instead of conjuring thoughts of mockery, I would like the reader to put him or herself into one of those minds. You are not stupid; you are deeply immersed in a cultural belief system. It rains — you think back upon the actions of your town recently to try to determine why it must have done so; determining this is of the utmost importance. You may even engage in scientific practices, coming up with hypotheses and testing them: if I sing to one, but not both, of my children at night, the probability that God will be pleased is increased. But this science is based upon a faulty foundation: a whole host of different phenomena could be attributed to “God will be pleased”, and the method is not scientific by modern standards. It is still superstition. What I am putting forth is that the very process of modern science and reasoning may be considered superstition — or perhaps some yet-uninvented term to describe our primitive thinking — to the cultures of the future. Maybe, like the character above, what we are doing is analogous to the search for truth, but we’re missing the point.
But we can make predictions! I will grant that we can make better predictions than traditional religious belief systems used to. I am no scholar of religion, but I can at least imagine a tribe understanding that the fire spirit, who loves the taste of dry wood, will duplicate himself to any nearby dry wood. This makes a prediction as well (at the time of this understanding, it had not yet been observed that he would duplicate himself from Honto’s wood to Jumara’s wood). Nowadays we have only a more accurate idea of the spirits, and we call them by silly names like Boson and Gluon. (I would like to stress that we cannot yet predict anything perfectly. E. T. Jaynes argues that the stunningly accurate probabilistic results of quantum electrodynamics do not count as perfection; i.e. that interpreting the quantifiable uncertainty of its predictions as fundamental to nature rather than to the theory is a boneheaded arrogance.)
Speaking of quantum theory, in the last century we have come across physical laws with an unsettling interpretation problem. Quantum systems are defined in terms of measurement amplitudes, and measurement occurs when a quantum system interacts with a classical system. Of course, if quantum theory wishes to be foundational, the term “classical system” must refer to a mathematical interpretation of a system, not a specific, real system, for every system ought to be a quantum system. So now we are talking about the point of measurement being one interpretation interacting with another — we are speaking on the mathematical and the physical level at the same time. Philosophically, this is utter nonsense. A dominant viewpoint among physicists is that of instrumentalism, summarized by Feynman as “shut up and calculate”. In other words: our logical and intuitive explanations fail us, but the mathematics work out. We have stumbled upon a stunningly accurate mathematical theory with fuzzy, unintelligible edges; could this not indicate an impedance mismatch between our logic and reality? Electrons do not obey classical physics, though large ensembles of them converge on classical physics. Why should we assume nature obeys classical logic; perhaps only large ensembles of truths converge on classical logic? Indeed, the calculation structure of quantum amplitudes seems to be logic-esque, with rules at least for conjunction and disjunction. Maybe the barrier lies not in the transition to a classical system, but the transition to classical logic. Perhaps, if we could only think differently, there would be no barrier.
In order to be heard, I am arguing from a position that we just have the laws of logic slightly wrong, and that a successor would take the same form merely with different laws. I do not necessarily believe this — my inner mathematician wishes it, for it would be comfortable and familiar — but it is simply the most concrete way, the smallest step I can take, to cast doubt upon the logical absolute.
You and I are immersed in a culture of reason, just as many generations of humans before us were immersed in a culture of theism. I cannot simply show you an alternative way to see the world; I am as clouded by these conceptions as anyone of our time. I do not wish to replace your foundation, just erode it. I wish to illuminate the possibility that we may, still, be looking at clouds, and not at the stars.
I have been going through an intense period of self-discovery and reconstruction. I realized that the path in life I have been following for the past several years is not working for me; it is not resonating with me, and it is taking me somewhere I don’t want to be. This realization was revealing itself to me at the same time as a complicated and heartbreaking end to a (short) relationship unfolded, and everything I believed crashed down and came into question. I was a programmer with no desire for a computer, I was a calm communicator behaving violently, I was an atheist experiencing God.
I believe that I am now picking up my pieces and realigning with my dreams — dreams I had forgotten or dumbed down. I’ve believed this several times during the past weeks, only to find another layer collapsing beneath me, so I may be full of shit. But all I can do is to use the best information I have now. It’s a very interesting, emotional time for me.
One of the axioms that crashed during this experience was the idea that I have any control over what happens in the world. This began as a grounded life principle: my attempts to control life only led to more suffering, so I should surrender to the flow of the world. It percolated up to my intellect, combining with the studies of physics I was using to distract myself from my emotions, eventually leading me to the confusing world of philosophy that I love to entertain.
The idea that there is something physically more to a human being than a physical system is something I consider absurd. The conventional non-spiritual idea is that you put more and more molecules together and suddenly a light turns on called consciousness. Humans have consciousness, dogs probably do, lizards perhaps not as they are simple stimulus-response machines, bacteria have no brains so certainly not. Associated with consciousness is the ability to make decisions as an independent entity: free will. Cognitive scientists are madly in search of the magical light that turns on consciousness, a holy grail in our search to understand ourselves.
My developing position — I won’t call it a belief, but I’ll say I am considering it and its implications seriously — is to reject the above narcissism. I see what we define to be consciousness as a gradual increase in sophistication of these biological machines. There is not self-awareness and self-unawareness, merely a band of sophistication in which we communicate that there is a definite “I” and that it is aware of itself. We can communicate that to ourselves, by having a little simulated conversation in our brains in which we say such things to some abstract person.
My experience, particularly at the end of the aforementioned relationship, showed me that a great deal of my self-awareness — my free will — is a hoax. I listened, I reasoned, I concluded the best action. I watched as a ridiculous prediction took hold of my reasoning process. I watched as I carried out, in a state of mental contradiction, the opposite of what I had concluded. I watched myself crying, simultaneously astonished and unsurprised by the way things actually unfolded. I saw myself not as a single unified “I”, but as an ensemble of communicating (or not) decision-making machines, combined with a mechanism retroactively justifying my ridiculous actions.
That free will I was so convinced I had struck me as a process, always living a moment in the past, existing to analyze and retrain my unconscious decision making processes for the future. I was a sophisticated machine, but a machine. I am governed by the same laws as a rock tumbling down a landslide. When asking whether it is possible that I will not push publish in a few minutes and share my thoughts with the world, I’m expressing not a set of a decisions available to me, but a state of uncertainty about what my action will eventually be.
I was walking down the mall and had the strongest urge to pick up a brick and throw it through a window. Jail schmail, money schmoney, I just wanted to do something nuts to release the pressure. And I did not; I watched the urge pass, frustratingly, as I didn’t carry out the action I had pictured so strongly. I couldn’t; my consciousness is not a decider but a justifier, and the action was not there to justify. There was no immediate reason it could come up with for why I didn’t — I was even disappointed that I didn’t. One might view this post as the belated conclusion of my justifier of that situation — that it does not in fact have control of my actions.
I see the universe as a great continuous four-dimensional tapestry, that I have the capability to view only a little slice at a time. I cannot ground the idea that there is some “I” which can cause the tapestry to be altered meanwhile existing within it. What could “altered” even mean in this situation: altered from what? I have been seeing this as a physicist studying something external for quite some time, but to incorporate it, to understand it as something I am part of, is taking me to a whole new place.
I have been working my way through Volume III of Feynman’s lectures, the one on quantum mechanics. A few months ago I watched his Quantum Electrodynamics lectures for the lay public and I was fascinated by the beauty and simplicity of the presentation. Now I want to dig deeper.
The basic idea is summarized in the quote (can’t find its source, probably Feynman though :-): “Everything that can happen, does. Physics is then reduced to the problem of finding out what can happen.” This is not philosophical many-worlds garbage postulating the existence of infinitely many alternative universes (I will get to that), but instead the interpretation of the Lagrangian form: if you want to find the probability amplitude of some event, you just add up the amplitudes for all the different ways it could happen. The generality of the principle is astounding, and making only very weak additional assumptions it is possible to completely derive the workings of electrons and photons (except for the mass of the electron, which is still a mystery). The rule is not just for electrons and photons though; those are just the easiest kinds of particles to get at. The entire universe works this way: the amplitude of an event is the sum of all the ways (including classically absurd ones) it could happen.
In the beginning of my studies, I was constantly tripped up by my conception of time. In the double slit experiment, a photon interferes with a version of itself leaving the excited atom at a different time. It was very hard to picture this when I was still attached to my idea of time and causality. This is the logic of the universe, not the dynamics. That is, we aren’t really computing the amplitude of an event to happen so much as the amplitude that, given some assumptions are true, some other thing about the universe will be true. We phrase the double slit experiment like this: given that this atom is excited at t0, what is the amplitude that this other atom is exited at t1? There is no notion of happening or the flowing of time, it’s just a connection between statements about the universe. Realizing this was an important step in my understanding. Of course, the way that these two atoms are connected does involve time — that manifests itself in the different “ways it could happen” and thus affects the amplitude.
Ok, so we have this logic which connects facts about the universe together as amplitudes, which are complex numbers. How do we take these amplitudes and get some information we can use? The rule is: the probability of an event, er I mean, a fact, is proportional to the absolute square of the amplitude. Simple enough. So you set up an experiment and calculate the amplitudes for all the different ways it could come out (you have to calculate all the ways, because the probability is only proportional, so you need to normalize them so they sum to one — I find this unsatisfying). Then you do the experiment, and what actually happens at the end of the experiment is one of those ways, proportional to the absolute square of the amplitude for that way.
This is extremely unsatisfying to me. Almost all of the resources I have used for learning QM have described it this way and left it at that. I’m pretty sure it’s because nobody really knows the answer to the next question: when, exactly, do you take the absolute square? If you take it too soon, e.g. before “the experiment” is over, then you will lose the interference effects and do not get an accurate answer. But you can’t just delay taking it forever, because then you only ever have amplitudes, not probabilities. There is this arbitrary barrier between the “quantum” world and the “real” world, and that’s when you take the absolute square. This is intentionally ignoring the idea that your experiment apparatus, your measuring devices, etc. are all governed by the quantum logic above as well, because that is too hard to think about. This is the piece I am determined to understand; I am interested in QM philosophically, not practically, so it is not at all satisfying to me to say “it works in practice, get used to it.”
The theory of quantum decoherence provides half of the answer. It shows how this interpretation of the barrier is equivalent to the state of the experimental apparatus (including the state of you, the scientist performing the experiment) becoming entangled with what happened in the experiment. Eventually the whole universe gets entangled with the result of the experiment and that’s what “really happened”. God got a bunch of amplitudes for the way the universe could be; he took their absolute squares, rolled the dice, and picked one. Now the arbitrary boundary has been pushed out as far as it can go — to the edges of spacetime — instead of being between experiment and apparatus. Quantum decoherence shows a sort of compositionality of this quantum logic. This is getting more satisfying.
I love it because it is right on the edge of my ability to conceptualize. All the “decisions” in the entire universe could go this way or that, and if they both lead to the same thing and have opposite amplitudes, they could interfere with each other and make that thing impossible. It is because the universe is a chaotic system, that small changes give rise to large changes, that we can’t observe quantum interference on large scales. These little decisions are very unlikely to lead to the same state. Entropy gives rise to the classical world.
When I get really deep into philosophizing, I explode into the annoying considerations of consciousness. Perhaps God did not pick a universe at random, but our consciousness did. Our memory must conceive of time linearly, it would violate entanglement not to, and that’s why we think there is a single “chosen” universe instead of the explosion of all possibilities. But whether all possibilities exist or there is a single universe chosen at random is likely not an observable distinction, so it is merely fodder for pipe dreams.
If there were some device that could measure some things about the universe, without disturbance, set up in such a way as to negatively interfere with itself when its measurements were “undesirable”, it could potentially control the way the universe would go. Now you see where the title of this post comes from. I have not been able to sketch this device as a black box, nor fully understand why it should be impossible. I suspect it has something to do with the uncertainty principle, the derivation of which I have yet to completely understand.
Quantum Mechanics is fascinating to me, and I am trying to keep my mind open to the deep, philosophical, passionate curiosity it invokes without descending into the insanity of a quantum crackpot. It is a challenge.