Editing Philosophical Research:MDem/5.2/1111 FreeWill (section)

== Does a perfectly-round dome have free will? ==

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<div class="bop-text">now that we have discussed digital video games, we are ready for the second thorny topic that always comes up in discussions of human consciousness and decision-making: _determinism_.

_determinism_, much like _phenomenology_, has two entirely different definitions depending on whether one is discussing it in the context of traditional philosophy or modern science. in traditional philosophy, determinism is often taken to be the same thing as _predetermination_; in science, determinism is taken to be approximately the same thing as _short-term predictability_. 

most people that you will run into tend not to have any clear understanding of what determinism actually refers to in physics. this even includes some number of scientists who make use of models based on determinism. not all scientists and science communicators are guilty of this, of course, or it would not make any sense to say that the majority of the group who had first defined the term were using the term _determinism_ wrong. but if physics really does have a unique scientific concept called determinism, it is important for us to have a good idea of what that is before we go opposing this concept to any particular logical concept of Free Will.

if we want to test whether scientists truly understand the basic principles of science, all we will need is a simple apparatus consisting of [https://sites.pitt.edu/~jdnorton/Goodies/Dome/ one maximally round ball and one maximally smooth dome]. assuming that the ball and the dome are as perfect as we can make them, and the ball is at rest on the top of the dome with nothing actively pushing it to accelerate, classical Newtonian mechanics suggest that the ball should remain still. but almost any time anybody actually tries to build one of these domes, the ball always at some point ends up rolling off the dome. why is this? is it merely because we have not been able to remove all the forces in the room and properly make the ball and the dome perfect in shape? or is there some kind of more fundamental problem going on?  [*p]

certainly, if we try to check the experimental setup for imperfections, there will always be some sort of tiny uncontrolled factor within the room to discover. in real-life conditions it is trivial for tiny imperfections in controlled environments to exist without there being any cause of them we actually know of due to the fact that gaining any information about any object requires physical processes and nearly every act of gaining information about a physical environment alters that environment. shine a lamp on a surface to observe it and you may warm it up. try to observe a photon with something the size of a photon and you may as well be shooting a cue ball at a pool ball to observe the position or velocity of a pool ball — by the time you hit the pool ball it's already moving with a given velocity from where you hit it, or knocked away from its existing directional movement. set up a seemingly perfect dome carefully calibrated with mathematics, and unless you know everything about the air, the atoms of the dome, and the ball sitting on top of the dome, you can almost /predict/ that an unseen "excessive pit" or "excessive air molecule" will interfere with your plans and tip the ball to one side of the dome allowing gravity to win. in the field of physics within fluids, there is a process called _Brownian motion_ in which all the molecules within a fluid tend to hit dissolved particles in a statistically random pattern, yet one which over time often tends to eventually cluster collisions in particular directions, and push particles to drift; if all the collisions are indeed random, then there is no filter preventing any molecule from hitting any particular side, and no reason a bunch of molecules hitting one particular side cannot happen. at a certain point, it almost begins to feel like unpredictable events have become totally predictable because it's so often that at least one of them will menace us eventually.

what kind of predictability are the ball and the dome showing, exactly? by a Newtonian model, the ball and the dome would not be predicted to be doing _anything_ unless, for instance, we assume the Brownian motion produced by air molecules is a major factor in the ball's movement and we somehow add this into the model. air molecules similar to helium atoms count as classical as long as nothing interesting is happening with protons, neutrons or electrons, so this is something we can get away with if we are willing to make our Newtonian mechanics much more complex. with that said, the minimal model of this system would look something like an unmoving ball on top of a dome which is to be struck from some unknown direction by some minimum number of air molecules at an unknown time, and proceed down the dome in a direction which is unknown at first but directly depends on the unknown direction from which it was pushed. the dome system feels like it has a similar kind of predictability to a Pokémon trainer walking into a patch of grass and eventually finding a Pokémon, with the exact Pokémon that appears and time or place it appears being apparently random yet with some sort of Pokémon showing up eventually. could an LCRNG be used to simulate the dome system? as funny as it may sound, an LCRNG algorithm is really just a kind of power series, so by one definition an LCRNG given a particular seed _is_ a kind of function; it does not have multiple y values for any x value, and always returns something. so, why not use a pseudorandom number generator to simulate one particular hypothetical trial of the experiment, and then give it different seeds to simulate others? to do so would create a kind of mathematical _superposition_ of different scenarios, slowly modeling every possible arrangement of air molecules and every possible path down the dome. as we overlay enough of these hypothetical trials on top of each other, we might begin to end up with a formula for the average time over all trials for the ball to initially start moving.

it is severely interesting that if we so much as simulate a system where many free-floating moving parts are expected to move in an apparently random pattern, we end up with something that looks for all the world like a quantum wave function. quantum-scale phenomena are infamous for being "in two places at once" (often two electron energy levels), for disrupting our ordinary understanding of time by snowballing fuzziness and imprecision up toward large scales to the point they can supposedly leave a cat both alive and dead at least specifically according to how much _information we have about it_ if we don't observe it. this is the key thing many people forget in respect to quantum mechanics: having no information about the cat does not by itself mean there is a possibility it is alive. if we are not able to observe the cat and collect information, we will have no information it is _not_ alive, but simply having no information it is _not_ does not immediately imply it _is_. here, as explained in the previous chapter, we can begin to see an obvious if vague connection between quantum mechanics and general relativity. in general relativity, the experience of time is defined within the process of isolated sections of space exchanging interactions with each other, and how closely suited or far removed these interactions are from being able to produce causal results which transfer an observational piece of information about the originating area of space; any light we observe or information we know is only something we have if it can physically reach us, regardless of what may or may not be happening behind the barrier of causality. relativity itself is easily capable of wrecking mathematical predictions — all that has to happen is some physical event taking place over a light-year away needs to be not quite what we expected. scientists can predict what should be happening a light-year away, it can be that whatever is happening over there is not aligned with predictions, and from that point on, the journey that signs of that particular event take from the place a light-year away to earth will transform itself into a mathematical superposition. one possibility for what could happen is the event will align with earth's predictions when light finally hits earth. another possibility is that it will turn out in some totally different way. in reality the event only happens one way by the time light has reached earth, but until that moment the whole _history_ of an event happening a light-year away and light moving across space to finally reach earth looks a whole lot like the ball-and-dome simulation, the ball seeming to go many different possible ways down the dome at once. at first we have no information. then we have a vast array of different possibilities. then an observation collides with us and information reaches us. then there is some particular single, non-superpositional account of history. it would appear that it is not just quantum phenomena that take on a particular state when they collide with an instrument of measurement, but in fact, we are constantly measuring history, and history is measuring us.

the basic nature of the Vegeta effect should be more than clear by now. its origin is the separation of physical spacetime itself into different coinciding histories. at small scales, light can become separated from space resulting in the suspension of all causality until photons or other such fundamental interactions actually hit something. at larger scales, free-floating objects such as pseudorandom power series algorithms, clocks, and human beings all proceed on their own differing paths sometimes resulting in problems when these paths intersect with each other. the physical definition of _history_ in the narrow sense of spacetime and the subjectively-experienced sense of _history_ that human beings participate in are only truly different and separate from each other in terms of what scale they occur at and the unique characteristics of that physical scale.

so, it would appear that the ball and the dome create _history_, in a particular material sense. inanimate objects such as dice and domes can more or less exert Vegeta effects before they have anything resembling consciousness or any kind of individual will. they appear unpredictable at first, but they operate according to what are actually a relatively-predictable series of mechanics, such that given as much as a pseudorandom number generator which can project _one_ hypothetical path the system will take, we can create a generalized overview of what the system will do and show that despite a bunch of unknown initial information, it _is_ ultimately more or less predictable.

within physics, _determinism_ is the concept that processes in reality can be predicted through the use of a fixed mathematical function. for some particular collection of objects in reality, such as a ball and a dome or a collection of helium atoms in a room, scientists will create an equation which is able to model the general shape of the behavior of that particular collection of objects under particular conditions: if the helium atoms within half of a room are warm and the other half is cold, a thermodynamics equation says the fast-moving atoms will drift to the other side and the room will eventually even out. this is determinism. determinism is almost the same thing as a particular process in the physical world having an understandable mathematical function which describes that process from beginning to end. the equation does not have to be perfect. there is almost always some tiny gap between a typical classical physics equation and its corresponding real-life system, and as much as scientists may later try to add adjustments to equations to make them more accurate, nobody necessarily expects physics equations to predict the results of a particular process exactly with zero margin of error. this is to say, there is always a certain very small difference between physical mathematics and physical reality. to say an equation is perfectly deterministic and predictable is not to assign that exact same level of certainty to physical reality itself.

aside from the distinction between mathematics and reality, there is another detail very important to the definition of scientific determinism that must not be glossed over: when we say that determinism applies to a category of _processes_, we mean events of a particular size and scale with a particular beginning and end. if a ball is tossed into the air horizontally and then lands, the arc of this ball can be considered a physical _process_ of the ball interacting with forces capable of accelerating it and the earth. a process is finite. a process typically consists of a particular collection of atoms and a particular collection of things capable of changing their current motion. by one definition, a _process_ involving particular things is near-synonymous with an open or closed _system_ of things; a _system_ is a bunch of objects interacting continually over time, and a _process_ is a bunch of objects interacting either for a long or short time. this has a critical implication for the relationship between processes and the overall universe: whenever we show that some particular localized process like a ball flying through the air is predictable, it does not necessarily by itself show that we can predict the formation or future trajectory of the entire universe. it could hypothetically be the case that this is true, that we can guess facts about the development of the whole universe in much the same way as we created a mathematical superposition about the development of the ball sitting on top of the dome and thought to be bombarded with air molecules. however, it could also hypothetically be the case that the universe is fundamentally a collection of many separate interacting objects which never properly reduce into a single process or system, because all of the separate objects, whether these separate objects might be best identified as fundamental particles or chunks of Planck-scale spacetime or anything else, always have the capacity to de-synchronize from each other's paths and create tiny relativistic rifts between each other's material-histories. this is only a hypothesis, and just because we do not have clear information that it is false, that is not to say we know it is true. nonetheless, the theories and findings associated with relativity that exist so far should make us question whether the universe as a whole is the same kind of thing as a simple system of a ball and a dome, or a ball and the earth. at each scale of reality, the mechanics associated with that scale tend to change, dropping some physical behaviors from the previous scale and acquiring new ones. could it actually be that the very assumption of localized processes being _deterministic_ in the sense of having a particular equation for their behavior is one that is _not physically possible_ with respect to the overall universe?

this is the problem with the common assumption that _determinism_ is easily interchangeable with _predetermination_. most philosophers, and even a few scientists, commonly make the logical error that just because a portion of the universe has particular characteristics of determinist predictability and appears to conform to the same overall set of physical laws that apply to other similar local portions of the universe that this must be the same kind of determinist predictability that applies to the overall universe. we've observed entropy everywhere we can see, we've observed energy conservation everywhere we can see, we've observed the cosmological constant all of these places, so does this mean all our overlapping observations of physical laws, constants, and also determinism apply directly to the overarching object we call the universe? in reality, what we seem to observe is that in various different parts of the universe the same small-scale physical laws emerge from the same small-scale physical things, and the same small-scale physical laws stack up to the same large-scale physical laws. there is a very important detail hiding between the lines of this observation: in some senses, the whole universe containing the same small-scale physical things is something of a favorable coincidence. looking at what quantum mechanics and relativity can each do to our ability to know anything, we should be surprised that there are not parts of the universe that have completely different small-scale structure and stack up to completely different large-scale behaviors that we simply didn't notice because those regions of space were too far away from us. to be clear, we have no evidence that this is realistically possible, so it _is_ more of an imagined philosophical problem than a real problem, but given the very limits of physical reality on us observing it without physical interaction, there definitely does exist a remaining philosophy-of-science problem as far as the limits of observation.

now that we have outlined the difference between narrow-sense _determinism_ and broad-sense _predetermination_, it should be clear that bringing up determinism does not ultimately do much to shed any light on either the existence or nonexistence of Free Will. assuming that there really was such a thing as Free Will, we would never be able to tell if Free Will did or did not exist if it happened the whole universe was subject to predetermination. people like to claim that the existence of predetermination would neatly rule out Free Will, but if anyone ever claims this, they have not really been thinking about it. in a universe which was seemingly physically-identical to our own but subject to predetermination, people would still roll dice, and all of those dice would still appear to be random. people would still not be able to predict the actions of other people, even if each person was pre-set to move on a certain path. in our world as we experience it, a pseudorandom number generator can go down a pre-set path of numbers, and yet present a series of events which is totally arbitrary to the point of appearing unpredictable and random. this would be true even if our universe was _not_ subject to predetermination and people somehow possessed Free Will — people would get fooled by the apparent randomness of pseudorandom number generators in either universe. if human beings cannot fundamentally tell the difference between artificial things that are intentionally predetermined and things that are not predetermined, how would an average person ever be able to tell a universe that was subject to predetermination from one which was not? things would appear to happen arbitrarily and unpredictably in either universe. and we know this is the case because as long as a universe has the same overall laws of physics as our universe, even a predetermined universe would still have spacetime, and it would still have relativity and Vegeta effects.

put more succinctly, if we are ever to tell whether Free Will exists or characterize its effect on people and relationships, the first thing we must understand is that predetermination has nearly no effect on everyday human experience compared to the local and immediate interactions between separate material objects with separate perspectives. the existence or nonexistence of Free Will and the characteristics of human decision-making all exist _within_ interactions and relationships.

so, to get back to our previous question. are the ball and the dome _deterministic_? well, that depends on how you personally feel about systems with finite possibilities for generating material-histories and mathematical superpositions. if superpositions don't scare you, and you don't think a dome is identical with the universe, then there is no real difference between determinism and the so-called "indeterministic" behavior of objects like the ball and dome. to paraphrase the words of a popular edited comic, there is zero difference between predictable and unpredictable things.
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