Thursday, March 15, 2018

Follow-Up On The Follow-Up On Fake Deter-Minism

Ok -  WHY do I think that Classical Thermodynamics alone without the help of quantum indeterminism is sufficient to destroy the unfounded belief in a deterministic universe?

You will need to know a little bit of Physics to become fully persuaded by this line of reasoning.  No - I lie.  You will need to know a LOT of Physics.

But I will endeavour to make it understandable to the lay person who wants to understand at least what this line of reasoning consists of.


Could the Universe go backwards?
Classical Newtonian interactions - nay even Relativistic Newtonian interactions - are time-reversible.  Newtonian Mechanics consists essentially of conservation of all momentums for either elastic or inelastic collisions, which includes the famous F=Ma law that expands momentum conservation to account for forces and fields.  Running the video backwards of any experiment in which particles interact using Newtonian Mechanics does not produce any violations of Newtonian physics, or specifically the three Laws of Motion that are the foundation of classical physics.

Interactions of individual particles in a thermodynamic body, whether solid, liquid, gas, or plasma, are individually Newtonian and hence time-reversible.  Individually, you can run each collision backwards without violating any physics.  From strictly a Newtonian point of view, all processes in the universe should be totally reversible.  This is the very reason, when you think about it, why many people are wedded to the idea of Determinism and feel that all future states of the universe are pre-determined by the initial state.

However, Entropy destroys information.  This makes Thermodynamic processes basically irreversible.  A large collection of particles, each interacting in strictly Newtonian fashion, can only proceed in the forward direction of time without violating basic Thermodynamic physics.  Why is this?

The reason for this is fundamentally statistical: higher-entropy states are vastly, ridiculously more probable than lower-entropy states simply because there are so vastly many more of them.  (Entropy is essentially a statistic which measures the degree to which energy in a system is evenly distributed throughout the system.) The probability is overwhelmingly that in any given transition from one state to another through the cumulative effect of countless Newtonian interactions of countless particles, that transition will be from a relatively rare lower entropy state to a relatively more abundant higher entropy state.  Note also that many higher-entropy states are physically indistinguishable from one another.  Going backwards even one step is just so ridiculously improbable such that it literally could never happen in the entire lifetime of a universe.

So, putting these two concepts of physics together, if we start from some initial state and roll time forward, each collision, each trajectory, each vibration of each particle perfectly obeying reversible Newtonian physics, following the laws of Thermodynamics we inevitably reach states of higher and higher entropy.  At some point let us decide to stop the video and run time backwards, supposing we were able to magically do this - say perhaps in a simulation.

From that higher entropy state, if we attempt to run the clock backwards and get back to the initial state of the system, we find that the information about that state has been lost - destroyed actually - by Entropy, and we will not be able to find that initial state again.  Even if artificially forcing the system into impossibly lower and lower entropy states, what we find is that although we manage to wrangle the system back into some minimum-entropy state, it is not the SAME minimum-entropy state that we started out in.  We do not get the initial conditions back again - the initial conditions that were supposedly deterministic of all future states of the system.

If you can get to the same or an indistinguishable higher entropy state from any number of initial states, and if the individual interactions are time-reversible, and by reversing time we do not get back to the one initial state because the information about that state has been erased by entropy, then that means that either initial states of thermodynamic systems are NOT deterministic of all future states, or that Thermodynamics is wrong.

And Thermodynamics is demonstrably not wrong.

To summarize the case against Determinism by Physics:

  • The N-Body System is ultimately chaotic and any given future state is in no way inevitable whether by initial-state ambiguity or by non-inevitable system perturbations. By what means?  Perhaps ultimately by the stochastic Gravitational Wave noise from the Big Bang itself that permeates the universe.  Any infinitesimal perturbation of a chaotic system is all it takes to tip it into a wildly divergent state trajectory over time. 
  • Thermodynamic systems are never Deterministic on a microscopic scale because initial-state information is erased by Entropy and is thereafter irrelevant and non-determining of subsequent states.
  • Finally, at the Quantum level Determinism doesn't stand a chance; even Causality has issues and must be regarded as at best an emergent property of more complex, large-scale physics.   The initial state of the universe at the Big Bang cannot be understood without Quantum Physics plus some other stuff we don't even know about yet, meaning that the initial state itself must have been ambiguous and undetermined, and subsequent states were random rather than causal consequences of that state.
In the end, Determinism from Physics is a purely speculative nonsense concept and is not a real feature of this universe.  Do Not base anything you think, including any conclusions about Free Will, on the nonexistent error known as Determinism.  Nothing is inevitable here except perhaps Entropy.


Wednesday, March 14, 2018

Follow-Up on Determinism: It's Still Fake News

The most well-reasoned objection to my demolition of Determinism was posited by none other than myself (who could be more qualified?) and is as follows:

Consider the example of the remarkable engineering masterpiece known as the Curta calculator, which was presented as having arithmetic competence as an emergent property possessed by none of its components individually.  Using the Curta to calculate the recursive formula X = R*X*(1-X) for R around 3.6 results in an essentially random (chaotic, technically) sequence of X's.  The evolution of values may not be apparently deterministic in the sense that values follow some consistent pattern; but if you started with the same seed value you would get the same sequence time after time; thus the sequence is determined and hence Deterministic.  

The Curta Type II Calculator
True enough, and fair enough.  Testing Determinism in this manner requires further exploration, since in practice as I pointed out to myself above, it does not seem to rule out Determinism.  However, when examined carefully, this procedure does not actually constitute a fair test of Determinism, because the calculator cannot handle infinity decimal places.

Chaos has the property that any infinitesimally insignificant variation in initial conditions or perturbation of subsequent states can produce an arbitrarily large divergence in outcomes at some future time less than infinity.  To contradict Determinism, we would have to show that with initial conditions specified with even infinity decimal places, the outcome is still not inevitable.    The Curta Type II (released in 1954) has 11 input digits, 8 counter digits, and 15 result digits. Alert Readers may notice that none of those numbers is infinity.  The effect of this is what we call quantization of the results, or in popular parlance, "round-off error."  This means that at every calculation, the result is forced artificially into one of a relatively few allowable values which are "rounded off" to the nearest decimal place retained by the mechanism.  Therefore the result does not accurately reflect the actual theoretical result of the algorithm.

The consequence of quantization is that at each step, the evolution of the process is reset to a fixed, known value.  There just isn't ever enough time for the true chaotic nature of the algorithm to evolve if it keeps getting reset to one of a relatively small number of possible values.  The only fair test of this form of non-determinism would be to see whether, with infinity decimal places, one result diverges from the result of previous experiments when the initial conditions are infinitely identical and infinite precision is retained at each step.

Why do I think that would be the case?  Purely mathematically it shouldn't happen in an idealized calculation.  But an infinity-digit version of the Curta calculator (the actual Universe, effectually) is a thermodynamic object, and those digits are represented by components which are thermodynamic bodies subject to entropy.  With infinity digits, the chances are good (100%, I'd say) that there will be random errors in the calculation eventually, making it impossible to obtain the same result twice in a physical process, thus making any given physical result not inevitable.  The evolution of the universe is essentially a physical (analog) calculation of the of states of the universe as time progresses.  While ultimately the states experience quantization similar to a 15-digit calculator's round-off error, this quantization is small enough to still allow plenty of uncertainty to creep in.  In addition, quantum uncertainty (à la Heisenberg) introduces its own bit-errors into the evolution of states.

Any limited calculator isn't a true representation of chaotic behaviour.  Only unlimited decimal places can accurately carry out a chaotic calculation, and when you have that many decimal places you will also have a meaningful probability of digit (or bit) errors.  These facts taken together essentially require that any two physical embodiments of a chaotic system must diverge from perfectly identical initial conditions and are thus in no way Deterministic.

An example of a non-deterministic calculation being carried out is human genetics.  The calculation is essentially, "let's combine two genomes and find out what happens, then combine that one with some other combination, and so on, generation after generation."  To do this calculation perfectly with the same result in any two hypothetical "runs" of this experiment starting from identical initial genomes requires that there be no computational errors.  Ever.  In reality, every human has something like 20 or 30 random errors (known as "mutations") in their genome.  Due to the thermodynamic nature of the mechanisms for encoding the genome and carrying out the replication, truly random, stochastic errors are inevitable and no result is ever "evitable" or assured, pre-determined, unavoidable, inescapable, or whatever the polar opposite of inevitable may be.

Notice that in a crowded cell where particles are constantly interacting with each other and with electromagnetic fields, quantum indeterminism does not really enter into it because quantum states are constantly being collapsed and re-formed at every interaction.  While others may, I do not think that randomness ultimately depends on quantum indeterminism, but that thermodynamic stochasticity is more than sufficient to provide for true in-principle and fundamental randomness in any physical system.

Therefore, it is inevitable that you are a Mutant; but what kind of mutant was in no way predetermined by physics.

Saturday, March 10, 2018

Free Will Versus Determinism

Certain scientists who seem to have only recently discovered philosophy on wikipedia have announced that finally, at long last, they and they alone have solved the question of Free Will for good and all.  Popular thing-sayers such as Sam Harris have informed us that because of a thing they read about called Determinism, there can be no free will.  Meanwhile professional philosophers such as Daniel Dennett who have spent just a wee bit more time on the subject say "Bollocks! Determinism is entirely compatible with Free Will; although Free Will might not be quite what you thought it was."
A simple mechanism which, when assembled, produces the emergent competence of performing arithmetic calculations even though no one of its parts has this ability!  Curiously, if used to compute x = r*x*(1-x) repeatedly with r chosen to be around 3.6, this simple mechanical device cannot even be said to be deterministic.

I would like to point out at this juncture that the title of this post is an unadulterated lie.  It is a lying, lying lie in every possible way.  It is lying about Free Will, it is lying about Determinism, and it is lying about the Versus part, too.  Hopefully the remainder of this post will make up for these despicable lies by acquainting you with some small part of the truth.

We start with Determinism.  This is the idea that the universe proceeds like a clockwork, obeying physical laws such that given the initial conditions, all future states of the universe can at least in principle be predicted in advance or calculated in retrospect.  The very idea came to prominence in response to Newton's physics in the late 17th C when philosophers, impressed by slightly improved (but by no means perfect) predictions of planetary orbits, began asking, "What if someday the planet's positions really COULD be predicted accurately forever?  And what if everything in the universe also worked just like that? Would that not mean that everything, every future state of the universe including human behaviour, would be predictable and thus predetermined by the initial state of the universe?"

Well, yes, it might mean that IF the universe worked that way.  People forget that key word, "if," and make the mistake of assuming that rigid-body Newtonian physics applied to a handful of structureless bodies is all the physics that the universe has or needs.  But "Deterministic" Newtonian physics could not even predict the planets' positions very accurately over a few hundred years; and in the case of Mercury, hardly at all.  Determinism as we shall see is a complete lie and a fiction.  It never existed, even in Newton's day, and doesn't exist now.

First of all, there are WAAAAAY more than seven bodies in the universe.  With more and more interacting parts, even perfectly classical Newtonian systems become chaotic over shorter and shorter periods of time.  Even with as few as N=3 single rigid bodies interacting in a system, you need to have infinitely precise information  - 12^N measurements out to infinity decimal places each - on the initial state of the system in order to make accurate predictions of the system's state out to large timescales, still more for an infinite timescale.  The Universe itself is not large enough to contain that infinite amount of information nor does it have enough matter in which to encode that infinity of information.

But whether or not the information of the initial conditions is encoded in anything other than the initial universe itself, the precision required for long-term determination of a chaotic system cannot itself even exist given the known limitations of matter, space, energy or, well, universes themselves.

Therefore I assert that the existence of sufficient information to make a chaotic system predictable and therefore determined at all time is not a thing that can exist in the universe; or in other words, it's not a real thing even in this simplest case of a universe with an unreasonably small and boring number of rigid bodies obeying Newton's boring version of physics.  Even in that simplified universe, there is no such thing as Determinism.

It gets worse though.  With any more reasonable number of bodies in the universe (say, a few million) Newtonian physics is no longer a suitable representation of physics.  Mind, it still can be used to describe individual short-term interactions between particles and energy; but the cumulative state of the universe is now a statistical, stochastic thing which any one of countless initial conditions could equally well produce.  That universe has an average kinetic energy represented by Temperature, an average potential energy represented by Pressure, and average quantities for particle sizes and masses represented by density and an equation of state.  Trajectories of individual particles and the momentary interactions between individual particles are meaningless, unknowable, and at best short-term phenomena with no long-term influence on the future states of the universe; only cumulatively do they have any influence.  In this realm of Thermodynamics, there is no Determinism.

But it gets even worse than that.  Bodies in the universe are not, as assumed up to this point, individual rigid particles.  They are thermodynamic globs of particles - solids, liquids, gasses, plasmas.  They have practically infinite numbers of possible internal states that can have at best only statistical representations such as pressure, temperature, and average density.  These thermodynamic systems are the bodies that interact in approximately Newtonian ways.  Each of these bodies contains not merely a few thousands or millions of identical particles, but unimaginable numbers of great varieties of particles.  Practically a universe within itself, a single grain of sand contains more individual particles than the number of grains of sand on the beach from which it is plucked.  Even the external parameters (e.g. the mass and shape of a grain of sand) have an unknowable infinity of possibilities, not to mention internal configurations.  The universe is a thermodynamic universe of innumerable thermodynamic universes, thus increasing the indeterminism of the universe exponentially.  It is Random raised to the power of Random.  Determinism disintegrates in a single grain of sand, and still more so on the greater beach of existence which is an ever-shifting system of forces, matter and energy obeying mainly Newtonian laws.

But we're not done destroying Determinism yet.  This absurd idea needs to be obliterated right down to the level of the fundamental nature of matter, energy, and existence itself.  You've probably heard of Quantum Mechanics; and some small part of what you've heard might even be correct.  While Quantum Mechanics predicts and requires that bodies consisting of more than a few thousand individual particles must always obey Newtonian Mechanics to an absurdly high degree of precision, those individual particles themselves have entirely different rules of engagement.  In fact, at that scale the notion of a particle as a tiny pellet of matter is something of a convenient fiction - merely an efficient way of maintaining an accounting of quantum numbers for charge, mass, energy, spin, and other quantities which must obey certain strict rules in order to interact and transform.

Let us take an atomic nucleus as an example.  A nucleus is a particle which itself is an arrangement of protons and neutrons that are all stuck together.  Let's pick as an instructive example one having 55 protons and 75 neutrons, which by convention we know as a Caesium 130 nucleus.  Protons have a unit of positive electric charge each, and are thus in a continual state of repelling each other with tremendous force owing to how close together they are.  This repulsive force would ordinarily overwhelm the inherent contact stickiness that these particles have for each other, causing them to fly off in opposite directions at high velocity; but the additional 75 neutrons surrounding and embracing those protons provide almost enough extra adhesion to keep this nucleus together.  Just three more neutrons are all that would be needed to render this nucleus perfectly stable forever.  But as it stands the poor hapless Cs130 nucleus is always just on the verge of breaking apart.

When will it do so?  At what time?  In what fragments and in what directions?  These questions have fundamentally no answers within the universe, even in principle.  Even the "when" question for an individual Cs130 nucleus can only be answered with the evasive, "any moment now, or possibly never."  A large assemblage of Cs130 nuclei can at best be treated statistically: on average, half of those nuclei will blow up within the next 29.21 minutes, and the remaining half anywhere from then until the end of time.  There is not even any underlying mechanism at work which could in principle be used to predict and determine the time of decay.  Physicists have searched for such an internal mechanism for a century and have found instead only the opposite: more indeterminism at every level.

By using the word "Determinism" in the title of this post, I was lying to you by allowing you to think Determinism was even a real thing in physics.  It is not in any sense a real thing, as we have seen.  At best, simple machines of only a few moving parts isolated from the messy, noisy universe can be treated as deterministic for specific periods of time.   But liquids, gases, complex systems of solid objects, very large objects, very small objects, thermodynamic systems, chemical systems, and, most importantly, biological systems cannot even theoretically be regarded as deterministic for any length of time, much less from the beginning of time throughout eternity.

While in a sense physics determines chemistry, and chemistry determines biology, and biology determines you, this line of reasoning uses a subtly different definition of the word and is not what is meant by Determinism with a capital D.  The kind of Determinism that could potentially have any impact on Free Will is the kind that states that all future states of the universe are able to be perfectly predicted by and are thus determined by the initial conditions of the universe.  In other words, the present state of the universe was absolutely inevitable and pre-determined, as are all futures that ever will be observed. And that, says physics, is Bollocks.

However, it may not even matter that Determinism from Physics is a silly fiction, because I was also lying about the "Versus" part.  Free Will and Determinism, as Prof. Dennett, pointed out, really have nothing to do with one another.  So what if your actions are Determined by something?  You'd better hope they are, actually.  Where would we be if all our actions were the result of random coin-flips, dice-rolls, card shuffles, or noise-based stochastic random number generators?  I mean, other than in the midst of a D&D game.  Hard-core believers in the fiction of Determinism may still complain that such processes are (as they believe) the determined results of make-believe physics and initial conditions in their make-believe universe.  But even allowing for that, would a coin-flip make you feel any better about your self-determination than having your actions locked in by something like reason, reflex, habit, or animal instinct?

The point is that whether your actions are determined by physics (no way), by chemistry (hmm...), by biology (quite possibly), by reason (sometimes), or are merely random noise, you are still accountable as a morally competent agent, even if (or particularly since) that agent is not some supernatural entity.  Even if a moral agent is really just a complex process and not an entity as such, that agent could well meet the requirements of  Moral Competence:

  1. The agent must have something of significance to gain or lose - livelihood, freedom, security, any of the fundamental needs or problems of a perishable organism.
  2. The agent must have the in-principle ability to select among any of several actions and privacy of mind for concealing its intentions until advantageous to reveal them.
  3. The agent must have at least the competence to make a judgement in its own best interest, regardless of whether or not it chooses to do so.  
Just as chaos emerges from complexity as a system acquires more and more moving parts, and just as temperature and pressure emerge as a system acquires more and more particles and becomes a thermodynamic gas, and just as Design emerges from a large number of natural selections with evolutionary pressure, and as Competence emerges from assemblages of large number of individually incompetent parts, and just as what we might call "intelligence" emerges from a large number of dumb little neurons in a brain, why then is it so difficult to accept that "Free Will" emerges from a sufficiently large number of stimuli, needs, impulses, influences, memories, desires, fears, information, rationale, instincts, and yes, even the occasional coin flip?

This leads to the final lie I need to correct: Free Will.  By referring to it, I have dishonestly mislead you into thinking that both you and I knew what Free Will even was.  Well, what is it?  This question remains unexamined by the people who rush to condemn it as impossible on the basis of something else that is even less possible (i.e. Determinism).  In struggling through the largely incoherent Sam Harris thesis, I find myself wondering whether he thinks Free Will is by definition a supernatural force of some kind.  A form of magic consisting of a disembodied Mind-Without-Brain, a sort of Ghost With A Plan that makes choices and steers its Meat Machine through life in order to fulfill the plan.  

At any rate, that is explicitly what theists think Free Will is.  And gods have the most of it, presumably.  As an aside, one notes with mild disinterest that the numerous gods promulgated by the various abrahamic mythologies cannot be regarded as having any Free Will when taken as presented. These gods have nothing to gain or lose because they are "perfect" and "eternal." They lack nothing and thus can neither be rewarded for their rare good acts nor punished for their frequent evil. The gods have no choice nor privacy of mind if we listen to their backers who insist they know exactly what the gods like, dislike, want, or ever will do. We are often told for example that the gods "cannot lie" or must unavoidably reward or punish us, etc, effectively limiting their possible actions and freedom. Failing the first two criteria for Moral Competence, gods cannot be regarded as morally competent and thus cannot be regarded even as free agents, or possibly even as agents at all. But that is no surprise to those who already realized that gods are nothing more than fictional characters in a bronze-age comic book.  

At any rate, the debate about Free Will has become a proxy battleground, in my personal experience, for the war between Naturalism and Supernaturalism.  I have been accused of defending Supernaturalism for little more than explaining that Determinism does not actually follow from Physics!

To be clear, by explaining how Determinism fails, I have not left open the door to Supernaturalism.  Instead, all I have pointed out is that Physics does not produce Determinism, not even in Newton's time.  Very little in the universe is inevitable, particularly on the scale of the short lives of Meat Machines From Planet Earth (which by the way would be an excellent name for a rock band).  It was not inevitable that smart monkeys evolved to look like we do.  Neither was it inevitable that the continents and coastlines of Earth appear the way they do, nor that the craters on the moon are precisely in those positions.  Perhaps only black holes and heat death are inevitable in this universe and are thus pre-determined.  But none of the details, particularly the humans, monkeys, dogs, spiders, and even bacteria, are necessary, unavoidable, inevitable consequences of this universe, even in principle.  Aside from even existing, each can and does make choices.  Simple organisms make simple choices: Left or right? Up or down?  Eat or avoid?  How they produce or arrive at that competence is not relevant to the fact that they do posses that competence.  Complex organisms make complex, abstract choices:  Rook or Knight? Red tie or blue?  Spend or save?  Mac or Windows?

In the case of the intractable problem of defining "intelligence" we get much further by instead talking about Competencies.  Similarly, Free Will is best defined as just one more layer of competence that organisms have to one degree or another.  Free Will is not some magic Ghost With a Plan.  Free Will is merely the competence to engage with and navigate a complex world.  

However, there is another thing that could be meant by Free Will that is neither the opposite of physical predetermination nor demonic possession.  It rests on the idea that the Self makes choices according to some set of values.  We know that this isn't actually how decisions are made most of the time: usually the brain makes a decision calculated to stave off emotional discomfort and satisfy some need; and then the rational human uses the cognitive parts of the brain to make up a clever post-hoc excuse for doing whatever that is.  Some people say that is not Free Will, but just the organism making "you" do stuff, (as though "you" and the organism are different actors), and if choices are in any way influenced by society or psychology, then it ain't no free will.  Well, no, I say that is still the organism's Free Will at work; just that actions are once again not mere random noise undetermined by anything at all.

But if you want a "higher" level of free will such that your actions are not predetermined by your brain's conditioning or your automatic emotional responses to stimuli, then that's another thing entirely.  In that sense, most of us filthy monkey-men never develop a free will and are entirely at the mercy of our condition and conditioning.  By engaging in intentional manipulation of the cognition of the brain by tactics involving impulse control, momentary suspension of cognition, intentional management of emotional states, or other forms of "mindful" reflection as some describe it, individuals can and do develop the ability to exert higher degrees of rational determination of their actions and thus can better control the trajectories of their lives.  If this is what is meant by free will - determination exclusively by rational reflection -  then again we see it has nothing to do with either Determinism from physics or choice-determination by external stimuli, nor is it in any way a supernatural phenomenon. 

That augmented form of free will is yet another emergent property or competence of the brain, which in the case of a self-reflective, mindful individual, has been turned in to a sort of GPU that runs the individual's selected apps in place of the evolutionary default operating processes that even monkeys use to navigate the world in the execution of their Free Will. It is still not evidence of ghosts with plans, and it is even further removed from Determinism from Physics, Chemistry, Biology, or Ecology.  This kind of free will advances even to the level of non-determination from human society, and even ultimately from psychology. 

"Wah! But Determinism!  A computer executing code is Determinism!  Wah!"

Nope!  Even if the hardware is entirely Deterministic within the timeframe of the experiment (one hopes that it is), a software program running on a hardware platform does not absolutely inherit the property of Determinism from the hardware.   Of course software algorithms are a long way from being complex enough to exhibit emergent properties of "higher" competencies.  There is also the problem that a mere algorithm abstracted from any particular hardware will struggle to qualify as Morally Competent because it will always lack the problems or needs of a perishable organism.  But the whole point is that as a system becomes more complex, new (higher level) properties emerge and old (lower level) ones dissolve.  

You may be able to pre-determine the behaviour of a watch that is wound up and running perfectly; but you will never be able to predict the exact way in which that watch corrodes and decomposes if left unattended in a riverbed for a few decades.  And as any system becomes more complex than that watch (a very simple mechanism, really), then less and less can be pre-determined about it.  If a system becomes sufficiently complex to exhibit emerging competencies of choice, then predicting its behaviour using physics becomes wholly impossible, and new more complex models are required.  These must include models of biology, sociology, and psychology, but will never have the accuracy or precision of physics or even chemistry.  

Therefore what ever the definition of Free Will, and whatever kinds of Determinism you want to talk about, there simply is no vital connection between the two ideas, and one certainly does not preclude the other.  Also, while certain meanings of Determinism demonstrably do not exist as realities, in no way can it be said that Free Will does not exist, for most of the definitions applied to it, with one exception: 

There are no Magic Ghosts with Plans; we Meat Machines are free to do as we please.