The past isn’t your master (part 3 of 5ish)

The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.

Bertrand Russell, Selected Papers

Scientific determinism isn’t sufficient for causality, as we pointed out last time. That’s because the laws of nature we actually have allow us to derive the past states from a complete description of the present, every bit as much as they allow us to derive the future from the present. Consider some very simple possible universes called checkerboard worlds (modeled after Carroll [2010: 127]), shown in the following figures.  They have one dimension of time, which will be displayed along the vertical, and one of space, along the horizontal.  To establish conventions, say that time t increases from t=1 at the bottom to t=10 at the top row, and position increases from x=1 at left to x=10 at right.  Discrete spacetime regions can have either of two states, portrayed as white or gray.  Our job as scientists is to come up with a most elegant statement of the rules, or patterns, embodied in the universe.  We can further imagine that after hazarding a hypothesis, more of the universe (more time and/or space) will be revealed to test it. Our first checkerboard universe is C, below.

state(t,x) = state(t-1,x-1) (or state(t,x) = state(t+1,x+1)

The law of nature of C is simple, and shown in the caption. Note that it can be stated as a rule for deriving later-time descriptions from earlier ones, or as a rule for deriving earlier descriptions from later ones. Let’s call that kind of law of nature bidirectional in time. That doesn’t mean that the direction of time make no difference. If we flip universe C in time, around the middle of the diagram, we get C-prime:

state(t,x) = state(t-1,x+1) (or state(t,x) = state(t+1,x-1))

Note that the law is different, in that the state at position x matches the previous state at position x+1 in C’, not the position at x-1. In three spatial dimensions, if we flip all spatial directions at once, physicists call that parity reversal.  Universe C has Parity-and-Time (PT) reversible laws.  The best accounts of the laws of physics of our actual universe,  general relativity and the Schrödinger equation of quantum mechanics, are Charge-Parity-and-Time (CPT)-reversible.

It’s worth staring at picture C’ and asking:  does row 8 make row 9 have gray cells at positions 4 and 8?  Or does row 9 make row 8 have gray cells at 5 and 9?  Or does the whole metaphor of physical states bossing each other around lose its grip here?

Let’s look at a checkerboard universe that doesn’t have bidirectional laws. This one has four possible states for any spacetime location, which will be represented as white, light gray, dark gray, or black.

irreversible dynamics and information loss

A black pattern moves to the left (lower x) with time, but ends if it collides with a dark gray column. Similarly, a light gray pattern ends if it collides with a dark gray column. And a dark gray square can appear “out of nowhere” (that is, when no other dark gray square is within +/- 1 spatial location) – at least when the local neighborhood contains only white squares. It looks like universe M might contain at least one probabilistic law: something like “if x-1 through x+1 are white squares at t-1, then the probability of dark gray at t,x is 0.01”. If not for this last feature, universe M would have been unidirectionally deterministic. Information about the past would be lost, but the future could still be derived from the present. But with the addition of the probabilistic law, universe M loses information in both temporal directions.

M is for macroscopic. The world we can observe with our unaided senses, and which we are accustomed to acting on and caring about, is like M. In the human-scaled world the same effect can come about from multiple causes, and different results can issue from the same situation. On the latter point, to vary our earlier example, a cup of cool water could be caused by leaving a cup of cool water in place, and no heat exchange taking place. Or it could be caused by leaving a cup of hot water with some ice in it for a long time, instead.  So, tracing from the same state (same in macroscopic terms) and going backward in time, different possibilities appear, which all converge on the same present state. And likewise forward in time: the weather, and human decisions, are notoriously unpredictable. We can offer Alice the choice of lunch destinations, and sometimes she picks Mexican and other times Korean, without any observable difference (such as how long it’s been since her last visit to these places) to explain it. Her futures diverge from the same macroscopic present state.

It’s the convergence of macroscopic causality – the fact that the cause (ice water left in the room) guarantees the effect (cool water) but not vice versa – that leads to the idea that the cause is master, and the effect its slave. From our everyday experience, we infer that there is a power differential which is explained precisely by time-order: the past has power over the present, which has power over the future, in a one-way chain of relationships. And that’s a reasonable inference to a simple and elegant theory which neatly fits the macroscopic data – but it’s wrong, as our best theories of microphysical processes reveal. It’s lower entropy, not being in the past as such, which explains why different past states converge on the same macroscopic present state. (More on that next time.)

When someone tells us that the divergence from the present state into multiple future states is an illusion, but neglects to tell us (or notice) that the convergence from past to present states is also an illusion, they’re telling half truths. Half truths can be misleading. This one is.

The Future-Rewound Argument

“I can prove you don’t have free will,” says your strangest friend. “If you had free will, that would mean you’d be able to do something different, even keeping all facts about the future beyond that act fixed. So for example, you think it was up to you where you took your last winter vacation. But if we hold fixed the fact that you were in New York on December 31, and rewind the movie of the universe from there, we find that necessarily, you arranged to travel to New York earlier. So in fact, you had to arrange to travel to New York.”

That’s a crazy argument, which no one would make. The crazy is easy to spot, it’s the idea of keeping all facts about the future beyond that act fixed. You shouldn’t keep those facts fixed, because they are not independent of your decision. But in a universe of bidirectional-in-time fundamental laws, the complete (microscopically detailed) past state of the universe is also not independent of your decision.

But many future facts, like being in New York, are not only not independent of your decision, they are caused by your decision. Causation involves an additional condition: a one-way relationship from cause to effect. Maybe it’s only this one-way causation from your decision to the future that frees you from the need to “keep fixed” those future facts? No: a symmetric relationship will suffice. We can see this in the next two thought experiments.

Self-Referential Pie Chart

inspired by Randall Munroe, XKCD comic https://xkcd.com/688/ (hat tip: Ismael 2012)

The pie chart makes two statements, both of which are true, and it has two pie slices of different size. The size of the reddish slice doesn’t cause the corresponding statement to be true in an asymmetric way: the reddish slice being the size it is, is identical with the truth of the corresponding statement. Once we have a convention that the color of a slice stands for the portion of the chart which is that color, we don’t even have to leave room for a statement written in the same color-range.

Readers are invited to make their own self-referential charts. Be careful in sizing portions and choosing colors: you wouldn’t want to get it wrong! (In the original XKCD comic, Randall Munroe makes his pie chart only partially and indirectly self-referential. So he actually did need to be careful. I call self-nerdsniping.)

The same logic of self-reference that frees us, in this chart-making, from the need to match an independent reality, also applies to our relation to the past under time-symmetric determinism.

Betting on the Past

In my pocket (says Bob) I have a slip of paper on which is written a proposition P. You must choose between two bets. Bet 1 is a bet on P at 10:1 for a stake of one dollar. Bet 2 is a bet on P at 1:10 for a stake of ten dollars. […] Before you choose whether to take Bet 1 or Bet 2 I should tell you what P is. It is the proposition that the past state of the world was such as [to correspond, according to laws of nature, to your action to] take Bet 2.

Ahmed 2014, p. 120

If we take Bet 2, we pocket a dollar. Our usual ignorance about which present states relate to microscopic past details has been removed, thanks to the logic of self-reference. Instead of trying to control a specific macroscopic past event – which is how we usually think about “affecting the past” – here we refer to a present macroscopic event, our taking Bet 2, and work backwards to refer to a widely scattered set of past events, down to the microscopic details.

It’s vital that proposition P is about you. If Bob’s proposition is about what Alice will take when offered this bet, it no longer makes sense to take Bet 2 unless you are Alice. What is up to you depends on who/what you are, including where you stand in the universe. This shouldn’t be surprising.

You might wonder how Bob is supposed to know that the past state of the world was such as to lawfully correspond to your taking Bet 2. But that is easy, if we suppose that Bob is a scientific determinist. He will take our choice as sufficient evidence. Does this mean that we only care about the future, i.e. Bob’s reaction? No: we are honest bettors, who want to take Bob’s money, but only by genuinely satisfying the winning conditions of the bet.

Let’s go back to those counterfactuals. What would happen if we had taken Bet 1? We would have lost a dollar, that’s what. The experiment can be repeated as many times as you like: it would support the hypotheses that “if you had taken Bet 1, you’d lose money” and “if you had taken Bet 2, you’d win money”. Normally, experiments don’t have logically foreseeable results like this; we normally need to know what the specific laws of nature are, not just that they are deterministic. But apart from that, these experiments support “would” statements just as other experiments support more ordinary statements such as “if I dropped this cup, it would fall.” (Remember, even well grounded scientific laws and meta-statements (like determinism) about laws can be supported or undermined by experiments.)

If we can show in more detail that there’s no need to posit an objective Power Hierarchy of Time in which earlier times rule over later ones, then counterfactuals can reach into the past just as easily as into the future. This doesn’t mean that we can change the past, as if some particular past time could be one way – Kennedy was assassinated on Nov 22, 1963 – and then be another way – Kennedy retired after two full terms. Nor does it mean that we can affect the past, if “affect” is a causal verb. It just means that if we had taken Bet 1, we would have lost a dollar. The fact that the consequent follows from the antecedent plus the natural laws, seems like a sufficient reason to accept that counterfactual.

It’s worth noting that even under time-symmetric determinism, the proponent of the Consequence Argument has one last-ditch option to preserve premise

(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.

They can assert as an additional premise that there is only one action you could take: the one you did take. So in other words, they simply assume you have no options – they don’t need no stinking reason! This eliminates the Consequence Argument in favor of a Consequence Assertion. There is nothing to recommend such an assertion.

Next up: we show in more detail that there’s no need to posit an objective Power Hierarchy of Time in which earlier times rule over later ones. Hint: entropy explains the irreversible behavior of macroscopic processes. Second hint: the scientific and engineering approach to understanding systems explains how we understand causality.

Sources

Ahmed, Arif 2014. Causal Decision Theory and the Fixity of the Past, The British Journal for the Philosophy of Science 65/4: 665–85. https://doi.org/10.1093/bjps/axt021

Sean M Carroll, From Eternity to Here: the Quest for the Ultimate Theory of Time. New York: Penguin, 2010.

Ismael, Jenann. Decision and the Open Future, in The Future of the Philosophy of Time, ed. Adrian Bardon. New York: Routledge, 2012.

Munroe, Randall, xkcd: Self-Description. https://xkcd.com/688/

Pearl, Judea. Causality: Models, Reasoning, and Inference. New York: Cambridge University Press, 2000.

Free will, part 2 of (5-ish)

As we said last time “alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) happen / be true”. A key concept here is a would statement, which logicians call a “counterfactual conditional”. For example, if I had written that logicians call a would statement “the cat’s meow”, you would think I was joking. The term “counterfactual” is a bit misleading because there can be would-counterfactuals with factual antecedents. For example if I had written that the Consequence Argument was formulated by Peter van Inwagen, you would have read the name Peter van Inwagen. And I did; and you did. What the would statement adds, beyond the simple statement that I did so write and you did so read, is the idea that there’s a robust connection between those things. A counterfactual is a bigger claim than the “if” from propositional logic (which logicians often symbolize with “⊃” — so A ⊃ B simply means that it’s not the case both that A is true and B is false.) Note that counterfactual antecedents and consequents (the “if…” and “would…” parts, respectively) range over processes, events (including boring events like a particular state obtaining at a particular time), and actions.

The premises of the Consequence Argument that we’ll question are (and here let’s spell out the counterfactuals contained in the shorter versions):

(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.

(3) The laws of nature are such that, for every action A you could take, if you did A, those laws would still obtain.

And we won’t question premise (1) from the last post, nor the formulation of scientific determinism from which it follows, but we will take a good hard look at that formulation. It turns out not to say some of the things that we might on first glance think it says.

Laws of nature

As I mentioned last time, premise (3) is controversial among philosophers. There’s a dispute over what kind of thing the “laws of nature” are. On the view called the Best Systems Analysis, laws of nature are just a sort of summary of facts. This view is held by the most zealous fans of Occam’s Razor — or at least, that’s what I think they would claim — because it avoids treating laws of nature as a deeply separate category of facts. (Occam’s Razor says “Entities should not be multiplied without necessity.”) Terrance Tomkow has a good explanation of the Best Systems Analysis at: https://tomkow.typepad.com/tomkowcom/2013/09/the-computational-theory-of-natural-laws.html and https://tomkow.typepad.com/tomkowcom/2014/02/computation-laws-and-supervenience.html

The Best Systems Analysis has a model in Algorithmic Information Theory, for which a very crude model is a .zip file, such as you might create from a .txt document on a computer. The .zip file contains compression rules plus compressed data (and the program that reads and writes zip files, say 7zip, contains additional compression rules). The compression rules (including those in the zip-making program) are like the laws of nature, such as the mass and charge of an electron; the remaining data is like the remaining facts, such as the locations of electrons at particular times. Different programs, say 7zip vs the Windows file compressor, might make somewhat different decisions about how to divide up the totality of information in a text file into “compression rules” vs “raw data”. And of course, if you put a different text file into the zip program, you typically get output containing both different “rules” and different “raw data”. For example, if I have a text file where most lines consist of a lot of spaces, the compressor program might make a rule where one special character represents 9 consecutive spaces and another represents 3 consecutive spaces. Then a line consisting of 13 spaces can be abbreviated with 3 characters. But if the text file instead contains a lot of consecutive z’s and no consecutive spaces, the rules part of the compressed file will contain rules representing z’s instead.

It’s this last point that casts doubt on the immunity of laws of nature to human action. If human actions were distributed differently, the totality of physical facts of the universe would be different, so different “compression rules” might most-efficiently summarize the total physical information. If all that laws of nature are, are just efficient summary rules for physical information, then they depend on all that information: the human related bits included every bit as much as the rest. The individual ground-level facts, including what people are doing, are fundamental, on the Best Systems Analysis. The laws are consequences of those facts, not governors of them.

Now, it would be nice if I could say whether the Best Systems Analysis is correct. But all I can do is register my hazy suspicion that it’s not. (My thoughts on that aren’t even worth setting down.) So it seems we are stuck on this part. But wait! What’s that smell? Yes, it’s the sweet smell of unnecessary work! (Hat tip: Dilbert comic.) There’s a chance we don’t have to decide about Premise 3 of the Consequence Argument, and thus we don’t have to decide about the Best Systems Analysis of laws. We don’t need to evaluate Premise 3 if we can undermine Premise 2 of the Consequence Argument. And we can.

The Past

Let’s look again at Premise 1 of the Consequence Argument, or better yet, at our definition of scientific determinism (abbreviated SD), from which Premise 1 followed:

(SD) Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.

Stanford Encyclopedia of Philosophy entry on “causal determinism”

SD says that the laws plus a complete description can logically entail the state of the world, either symmetrically both into the past and future, or asymmetrically just into the future. But the actual laws of physics that science has given us to this point are time-symmetric in exactly this sense, at least when they are deterministic. Conservation of information in quantum mechanics is a case in point. (There are deterministic interpretations of quantum mechanics, such as the Everett Interpretation, which interpret quantum probabilities as statements of rational expectation in the face of partial ignorance.) Because of conservation of information, the final state of a quantum system plus the environment, after an interaction, must contain the information that the system had beforehand. In other words, from the later state plus the laws of quantum mechanics, the earlier state is logically implied. Scientific determinism is a two-way street.

But now notice: “causality” is supposed to be a one-way street. A cause is not supposed to be itself caused by the very thing it supposedly caused. Let’s make this part of the definition of “cause”: causation is asymmetric, so that “A causes B” and “B causes A” are contraries. It immediately follows that

(Determinism ≠ Causality) The existence of laws of nature that logically entail state B at one time given state A at another, does not suffice to show that A causes B.

Causation is not interdependence, but one-way dependence. For example, a room-temperature cup of water could be caused by leaving a cup of steaming hot water in the room until the temperature equilibrated with the room. Or it could be caused by leaving a cup of ice water in the room for a long time, instead. The effect is guaranteed by the cause, but no particular cause is guaranteed by the later state. Without this kind of asymmetry in the relationship, causality is lacking, as physicist Sean Carroll explains in this 3-minute video. “There’s just a pattern that particles follow,” he says. “Kind of like how the integer after 42 is 43, and the integer before it is 41, but 42 doesn’t cause 41 or 43, there’s just a pattern traced out by those numbers.”

So where does causality come from? I’ll give two answers reflecting different interpretations of “causality” – both of them useful in different ways. On one reasonable interpretation (used by Sean Carroll), causality comes from entropy. On another reasonable interpretation, given by Judea Pearl in his book Causality, causality comes from our division of the world into a system of interest vs exogenous variables.

Now let’s look again at the Consequence Argument’s premise

(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.

Is it true? If the “distant past state” is given macroscopically, describing such things as glasses of water and their temperature, then (2) is true, but not adequate for the argument, because (as we’ll see later) the present state of the universe doesn’t follow from the past macroscopic state. But if the “distant past state” is given in microscopic detail, then it is not independent of the present state including what we are doing now.

There is no reason to believe (2), where the states in question are described in microscopic detail. Or rather, there is a reason, but it evaporates once you realize that there’s another explanation for why we never observe the past depending on the present or future. We don’t need to posit a magical “flow of time”, or a universal master/slave relationship between past and future. The idea that the past has power over the future but not vice versa is an overgeneralization from our experience of the macroscopic world: our experience of states and processes large and complex enough for entropy to be well-defined and increasing in only one temporal direction.

All this has gone by way too fast, and there are many points that need further justification and explanation. Along the way, we’ll use modern science to deeply challenge our intuitive conceptions of time and causality, then show how those wrong intuitions about how our universe works have affected our views of the free will “problem”. Scientific determinism isn’t the problem – our misconceptions of it are. The traditional free will problem doesn’t hinge on the definition of “free will”, but of “determinism” and “causality”.

Free will: the argument against (part 1 of 5ish)

Let’s start with some popular versions of what I call “the main type of argument” against free will. Here’s Jerry Coyne, from the conference called Moving Naturalism Forward:

(stolen from Anthony Cashmore) Free will is defined as the belief that there is a component to biological behavior that is something more than the unavoidable consequences of the genetic and environmental history of the individual and the possible stochastic laws of nature.

Jerry Coyne, Free Will and Incompatibilism: Jerry Coyne et al – YouTube, at 2:00

There are two words there that are doing a lot of work: “unavoidable” and “consequences”. The “unavoidable” becomes both more and less clear, in different ways, when Jerry comments on the “stochastic laws of nature” part of the definition.

My definition used to be: If you put yourself in the same situation in the same universe with every molecule in the same place, free will would mean that if you come to a decision point you could make more than one decision. But then I realized that quantum indeterminacy if it acts on the neuronal level could make you make a [conscious and] different decision.

ibid., at 2:22

What gets less clear after this explanation is why the word “unavoidable” is appropriate. when it is hypothesized that human behavior might be different even putting yourself in these highly restricted conditions. And worse, the “same universe with every molecule in place” includes all of you. If something flows from you, that seems an especially poor reason to call it unavoidable. But what gets more clear, I think, is why a non-stochastic (deterministic) view is thought to make behavior “unavoidable”. Genetic and environmental history, after all, can be traced back before you were born. And the universe before your birth doesn’t include you. So let’s forget about stochastic laws of nature at least temporarily, and just get clear on the basic argument, assuming that the laws of nature are deterministic. We will use the scientific meaning (not, say, a theological meaning) of determinism:

Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.

Stanford Encyclopedia of Philosophy https://plato.stanford.edu/entries/determinism-causal/

So we’ll assume now that our universe is deterministic in this sense, and formalize the argument against free will. If we need to see if it generalizes to the case of stochastic laws (teaser: we won’t need to), we can check that later. We can interpret the phrase “consequence of genetic and environmental history” (from Cashmore and Coyne) as the logical entailment mentioned in the definition of determinism. And we can add two plausible premises: the state of the past before your birth is for you unavoidable, and the laws of nature are unavoidable. (To save words later, “the past before your birth” is abbreviated “the distant past”.)

Here’s how we’ll understand “unavoidable”: “Alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) be true”.

The argument we get is the Consequence Argument, a famous (infamous?) argument in modern philosophy. The original formulation was by Peter van Inwagen, but that relied on an inference rule which was invalid. A better version was later constructed by van Inwagen, David Widerker and Alexander Pruss. It goes like this:

(1) The distant past state of the universe, together with the laws of nature, together logically entail your action now.

(2) The distant past state of the universe is unavoidable (for you).

(3) The laws of nature are unavoidable.

(4) If a proposition X expresses a fact unavoidable for you, and X logically entails Y, then Y is also unavoidable for you.

(5) Therefore, your action now is unavoidable for you.

The argument so formulated actually makes premise (4) a tautology, and I want to continue assuming for the sake of argument that (1) is true. But premise (3) is controversial and (2) even more so. We’ll take them up in the next part.

Sources

Pruss, Alexander 2013. Incompatibilism Proved, Canadian Journal of Philosophy, 43/4: 430–437

Van Inwagen, Peter 1983. An Essay on Free Will. Oxford: Clarendon Press.

Widerker, David 1987. On an Argument for Incompatibilism. Analysis, 47/1: 37–41.

Free will part 0 of (five-ish)

There are two main sub-topics to the free will debates in philosophy, or three, if you count moral responsibility. But I don’t count it, because people who basically agree about when people have genuine choices and when they don’t, often still disagree about moral responsibility. So let’s call that a separate albeit closely related topic. That leaves two main free will topics, corresponding to two main argument types that advocate the conclusion that you don’t have free will.

You’re here, reading this

The first type diminishes “you” to the point where you don’t exist, or don’t have a will. The second admits (at least for the sake of argument) that you exist and have a will, but claims that you are systematically coerced and enslaved by forces alien to you, so you don’t have a free will. I think the second type is far more influential among the general public, so I will focus on that in subsequent posts. (I’m not discounting the possibility of third+ types, but they’re rare beasts if they exist.)

The “non-existent person/will” argument is plausible only to a few people, mainly those who are in the middle of abandoning a dualistic (“soul vs machine”) view of mind and body, but haven’t quite gotten there yet. To reforming dualists, it often seems like the body or brain can’t possibly have consciousness, will, and so on. But really, either the body does have these features, or else non-dualism has an enormous pile of evidence against it. (Hint: the body does have these features.) As human activity is traced to various brain regions, the fearful (ex-, but not utterly ex-)dualist carves off those parts from “me”. That’s a bad move. As Daniel Dennett says, “If you make yourself really small, you can externalize virtually anything.” Don’t make yourself really small.

A less common reason for the Disappearing Self Trick is a bizarre metaphysics recognizing only the properties of microscopic objects (and/or only micro-particles and not composites) as real. As if there could be no cherry pie unless there were cherry pions: fundamental microscopic particles with an inherently cherry property. Or as if there weren’t large objects composed of small parts. But such restrictive “principles” of what’s real are usually selectively applied, indicating that the real concern is mind-body dualism. Often this is accompanied by accusations that people like me, who find mindful states in the human body, are secret dualists: a feat of projection that would make Donald Trump envious.

And that’s all I have to say about the Disappearing Self Trick. If you need more, Eliezer Yudkowsky has several posts (that’s three separate links) that are pretty good. Up next: an intro to the most influential argument against free will, with highlights for closer scrutiny.

Fool’s gold

I had just returned home from my work in the AI lab.  I was feeling great.  Our new program had passed the Turing Test for a half hour – a new record.  Twenty human judges had been unable to tell, at better than chance level, between a human interlocutor or our program, as they chatted by text and audio.

My career was going great and my personal life was also ready for the next level.  It was time to propose marriage to my girlfriend Rebecca.  Browsing the internet for engagement rings, though, I was getting a severe case of sticker shock.  Gold prices were insane!  There had to be a better way.  Luckily Google Ads came up with a helpful suggestion for once.  There was an equally beautiful ring that wouldn’t break the bank.  It was a copper-silver alloy with pyrite nanoparticles in its surface.  It was every bit as yellow, shiny, durable, and non-tarnishing as gold.

“PYRITE?!?!” yelled Rebecca as she threw the ring in my face.  “You got me a fool’s gold ring and asked me to marry you?!!  I couldn’t be more insulted if you tried!  Get out of my face before I do something to you that I’ll regret!  And if you ever want to give me a ring, it had damn well better be real gold!”

I hadn’t meant to tell her about the materials that were used to make the ring – it’s not important, after all!  But when she held it in the palm of her hand, she asked why it didn’t seem to weigh as much as it should.  At that point, I had to tell.

After things calmed down a bit, I looked again at gold rings on the market.  I still couldn’t stomach the prices.  Desperate, I called my brother.  Kevin is a materials scientist at a cutting edge electronics manufacturer, and I know he’d worked on developing substitutes for gold in circuitry.  I explained my problem.  “You’ve got amazing luck,” he said.  “Our new substitute for gold had to be not only as electrically conductive and non-corroding, but also have the same heat capacity, and the only way we could manage that is to give it the same density.  Furthermore, the electron behavior at the surface of this metal also gives the same color.  There is absolutely no way to tell Gold Minus from any other gold without looking inside it, with X-rays for example.  We call it Gold Minus because it’s gold, minus the price tag – get it?  I have excess from our last test batch; I can just give you a little.”

I found an artisan who would forge the Gold Minus into a ring.  I didn’t tell them where this material came from and they never asked, since it was just as malleable as they expected.  Their price was steep, but still under the rip-off artists’ prices.  And anyway, as an AI researcher and huge fan of the Turing Test, I thought I was proving a point.  This stuff had all the useful properties of gold – therefore, it WAS gold.

And that’s why I’m single now.

The day after I gave her the ring, I found it shoved under my door with a note in Rebecca’s handwriting saying “X-ray crystallography!  IT’S OVER!”  I tried to explain that this metal has all the relevant properties, therefore it IS gold.  But she countered that the one key property of gold is the one that EXPLAINS why it’s yellow, shiny, malleable, non-tarnishing, heavy, and so on.  And the property that does that explaining is having atomic number 79.  And the X-ray crystallography proved that this stuff didn’t have it.  And that while it might take genius to find such a matching set of properties, a genius who doesn’t listen makes a lousy spouse, and a lousy boyfriend.

Ring for sale, size 7, Gold Minus.

An ancient Greek dialogue

I recently stumbled across the following fragment of ancient Greek dialogue. Or maybe I made it up.

Herodotos: The youth today have no respect for tradition. Why just today I visited the shrine to Eros, and mine was the only offering. Where is the gratitude for the boons the gods give us?

Eudokia: That’s because Eros isn’t real, and some people are beginning to notice! We need to cast aside myths like Erotic love and focus on real things, like friendship, or sex.

Alexander: Now hang on a minute. I don’t believe in Eros either, but that doesn’t mean erotic love isn’t a real phenomenon. A little casual observation will show you that some people have a special bond – whether a winged god shot them with an invisible arrow or not, that’s beside the point.

Herodotus and Eudokia, in unison: Verbal gymnastics! Semantic trickery!

Herodotus: Real Erotic love requires Eros! It’s in the name.

Eudokia: Surveys show that the vast majority of people believe in Eros. Therefore, the concept of a distinctive kind of love is inextricably tied to the myth, and must die without it.

Alexander: Doesn’t follow. As for Eros being in the name, that’s why when I write “erotic love” I start with a small e rather than capital E. And I predict that centuries from now, people will still do the same, though no one will believe in the winged god with the arrows. And everyone will know what they are talking about.

Herodotus (morosely): Nonsense! Without Eros, there is only sex.

Eudokia (triumphantly): Without Eros, there is only sex!

And there the fragment ends.

The cherry pion fallacy

“There can be no cherry pie without cherry pions.”

That’s the fallacy. A cherry pion, in case it isn’t obvious, would be an indivisible particle which had an irreducibly cherry quality to it. I wish I could find the internet comment that inspired me here, but I can’t find it. Let me just admit that I didn’t invent the metaphor all on my own (but I did coin the horribly punny title! so there!)

The alternative to the Cherry Pion fallacy is called Emergence. Yes, that’s a word with many uses, not all of them so innocent. But give “emergentists” an innocent-until-proven-guilty verdict, I plead. Many of them are just observing that some concepts aren’t applicable at the finest level of detail, but find targets at higher levels of organization.

Another inspiration for my coinage is Ronald Dworkin’s “morons” in Justice for Hedgehogs. Dworkin wrote:

If there are morons, and morons make moral claims true or false, then we might imagine that morons, like quarks, have colors. An act is forbidden only if there are red morons in the neighborhood, required only if there are green ones, and permitted only if there are yellow ones.

Dworkin’s “morons” are a caricature of a straw man, i.e. an intentionally ridiculous version of some philosophical arguments about ethics. Not that I endorse Dworkin’s solution to the no-“morons” “problem”, mind you. But the caricature of the argument was good for a laugh.

Arrow Dynamics of time

A deep look at science shows that time and causality don’t work the way most of us intuitively think they do.  For example, some models of cosmology such as the one advocated by Sean Carroll in From Eternity to Here, claim that at some time in our past the (ancestor of our) universe was at minimum entropy.  At still further times from ours, its entropy was larger than that, and in its daughter universes on that other side of the minimum, entropy may grow as one goes further into (what we consider) the past.  So far, no big deal.  However, as Sean Carroll also argues, it appears that everything we experience as making time “flow” in one direction can be explained by the gradient of entropy.  As far as we know, it is physically possible that at some time intelligent beings exist(ed) in those daughter universes and perceive time to flow in the opposite direction. And their viewpoint is just as valid as ours.

Which direction the arrow of time points, depends on where and when you sit.  Arrow dynamics.  I will go a long way for a pun.

This – and other strange and wonderful discoveries of science – obviously have serious potential to change some philosophical thinking.  The area of philosophy I am most interested in, in this connection, is “the problem of free will and determinism”.  Most of the classic statements of this problem assume things about causality that find no place in modern science.  So here I list some resources that shed light on these issues.

Carl Hoefer points out that well known scientific deterministic theories are bidirectional in time: that is, they allow us to infer from the present or future to the past, just as easily as from past to future.

Huw Price and Ken Wharton explain how “retrocausal” QM theory can account for known violations of Bell’s Theorem.

Yakir Aharonov and Lev Vaidman discuss the Two State Vector Formalism (TSVF), an empirically equivalent formulation of standard QM that wears its time symmetry on its sleeve; and Aharonov et al apply TSVF to explain weak measurement experiments.  Guido Bacciagaluppi uses an alternative formalism to argue that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival.

E. T. Jaynes partially explains the relationship between entropy and information.

Eric Lutz and Sergio Ciliberto discuss experiments on information storage and entropy changes.

Steven Savitt explores Being and Becoming in Modern Physics.

Larry Sklar says that “The great problem remains in trying to show that the entropic asymmetry is explanatorily adequate to account for all the other [time] asymmetries in the way that the gravitational asymmetry can account for the distinction of up and down.”

Craig Callender discusses the relationships between the thermodynamic (entropic) arrow of time, and other intuitively appealing arrows like epistemic (memory), mutability (our actions affect the future), and explanatory.

Mlodinow and Brun show that given plausible physical assumptions, recording and then reading a robust memory always proceeds in the direction of increasing entropy.  H. M. Doss places their work in a larger context.

In a tour de force, Jenann Ismael explains (0:55:00 – 1:38:00) why we see the past as fixed and the future as something we can bring about.  This one requires Microsoft Silverlight to view, which is a pain, but worth it.

 

The Moon Illusion

The moon looks larger when it’s near the horizon than it does when it is high in the sky.  Sometimes, for example at this NASA website, this is phrased so as to imply that the view on the horizon is the one that’s illusory.

I once had the privilege of seeing this “illusion” in full force.  I was walking down a tree lined city street, with the moon on the horizon surrounded in my visual field by trees and houses.  The moon looked positively enormous – far larger than anything I’ve ever seen up-close and personal.  Since I’ve walked around it a lot, let’s say the biggest thing I’ve seen up close is my city.

Guess what?  The moon is far larger than an entire city.  With proper cues available to clue the visual system in, this becomes more apparent.

It’s not always the grand view of an object that is illusory.  Sometimes it’s when we see something as small that we are misperceiving it.

Causation: what is it?

I just read a beautiful passage by Don Page, who in turn is commenting on a debate between physicist Sean Carroll and theologian William Lane Craig on the role of theistic explanations in cosmology.  There’s a lot to this passage, but don’t worry.  I’ll try to walk you through it.

I agree with you, Sean, that we learn our ideas of causation from the lawfulness of nature and from the directionality of the second law of thermodynamics that lead to the commonsense view that causes precede their effects (or occur at the same time, if Bill insists). But then we have learned that the laws of physics are CPT invariant (essentially the same in each direction of time), so in a fundamental sense the future determines the past just as much as the past determines the future. I agree that just from our experience of the one-way causation we observe within the universe, which is just a merely effective description and not fundamental, we cannot logically derive the conclusion that the entire universe has a cause, since the effective unidirectional causation we commonly experience is something just within the universe and need not be extrapolated to a putative cause for the universe as a whole.

Let’s start by breaking that first sentence into three parts.  Hey, I said I’d walk you through it, right?

Part 1 is The lawfulness of nature:  we have a bunch of mathematical formulae, like F=ma, and F_g=G*m1*m2/r^2, that enable us to make reliable predictions.  Part 2 is The directionality of the second law of thermodynamics:  the second law concerns entropy.  It says that entropy does not decrease over time, but can increase.  Part 3 of Don Page’s first sentence in the above quote, says that parts 1 and 2 lead to the commonsense view that causes precede effects.

OK, at this point, even if you are not a physicist, you can kind-of understand what Don Page said in that first sentence.  Kind-of, because you might not understand what “entropy” is other than “something that physicists study, and which seems to play an important role in physical theories,” but at this point that’s OK.  But understanding what the sentence says is far short of seeing why it is true.  I want you to see, at least at a very introductory level, why it is true.  Let’s learn some more about this entropy stuff.

As Sean Carroll says in the God and Cosmology debate, it’s an important fact that we observe that the early universe had low entropy.  Given that fact, any other time will be likely to have higher entropy.  There’s a complication here, however, and to ponder it, we’ll need to split our thinking about time into two tracks.  We’ll call them quantum mechanical time, or t(qm), and thermodynamic time, or t(th).  Remember those mathematical formulae we called “laws of nature”?  We have a time parameter, t(qm),  in a quantum-mechanical equations like Schrödinger’s Equation.  And we have a time parameter t(th) in the Second Law of Thermodynamics, dS/dt(th) >= 0.  But why are we splitting “time” into two concepts?  Because we have promising physics models which require it:

I [Don Page] myself have also favored a bounce model in which there is something like a quantum superposition of semiclassical spacetimes […], in most of which the universe contracts from past infinite time and then has a bounce to expand forever. In as much as these spacetimes are approximately classical throughout, there is a time in each that goes from minus infinity to plus infinity.

In this model, as in Sean’s, the coarse-grained entropy has a minimum at or near the time when the spatial volume is minimized (at the bounce), so that entropy increases in both directions away from the bounce. At times well away from the bounce, there is a strong arrow of time, so that in those regions if one defines the direction of time as the direction in which entropy increases, it is rather as if there are two expanding universes both coming out from the bounce. But it is erroneous to say that the bounce is a true beginning of time, since the structure of spacetime there (at least if there is an approximately classical spacetime there) has timelike curves going from a proper time of minus infinity through the bounce (say at proper time zero) and then to proper time of plus infinity.

In Don Page’s model, we can keep our Second Law of Thermodynamics as we previously understood it, provided that we use a new “time” parameter which points in one direction at quantum-times quantum-before the bounce, and in the other direction at quantum-times quantum-after the bounce.  In each case, thermodynamic-time points in the direction of higher entropy, i.e., higher-entropy parts of history are thermodynamically-future.

You may have noticed that I haven’t explained anything yet.  It’s only gotten very complicated!  What these two physicists, Sean Carroll and Don Page, know about entropy but haven’t mentioned, is that entropy always increases when a physical record of an event is made and “read”.  A physical record is an enduring result of an event, such as a dinosaur’s footprint fossilized in mud, or an expanding sphere of high intensity light from a supernova, or a tape recording made by Richard Nixon – the kind of thing that lets us know the event occurred.  Another type of physical record, of particular importance here, is the memories in your brain.  Like any other physical record, the process of recording and then recalling memories necessarily increases entropy.

So, given that at time t1 a physical record is made, and that at time t2 the record is read/recalled, we know that entropy is higher at t2 than at t1.  At time t1 a memory is laid down; at t2, the memory is recalled.  It follows that t2 is thermodynamically later than t1.  It follows that the psychological arrow of time lines up with the thermodynamic arrow of time, insofar as our experience of time is based on remembering the past, but not the future.  (Hat tip: Stephen Hawking, A Brief History of Time.)

But there is another aspect to the psychological arrow of time, which relates to our ability to act on systems and thereby control aspects of their future.  If I replace my worn spark-plug wires, I can improve the performance of my car’s engine tomorrow, but I can’t improve yesterday’s performance.  Why not?  Because the entropy of the universe yesterday was lower than the entropy today, and my interventions today cannot reliably affect lower-entropy states of the universe.  You cannot un-scramble an egg.  But you can scramble one.  By replacing the wires to the spark plugs, I will be increasing the entropy of my car engine in certain ways – making tiny scratches in the connectors, re-shaping various lumps of grease and dirt, and so on.  The new wires may be in a lower-entropy state than the old ones, but remember that the old ones have not been removed from the universe.  They’ve only been removed from my car.  The new wires also got slightly scratched and bent in the process.  So, after car maintenance, the new wires still exist but with slightly higher entropy, the old wires still exist at about the same entropy, and the rest of the engine has gained some entropy – not to mention the atmosphere that I breathed into and radiated some body heat into, etc., etc.

Every time we accomplish some objective, we increase the entropy of the universe.  That is why we cannot affect the past – or rather, cannot affect the parts of it we care about.  The parts of it we care about all involve thermodynamically irreversible processes, i.e., processes that increase entropy.   When my car was running yesterday, it burned gasoline in air and radiated heat like crazy; those operations cannot be undone, in order to achieve better yesterday-performance.  We cannot un-scramble the necessary eggs, which it would take to bring about a specific, lower-entropy, macroscopic event.

So, not only do we remember the past and not the future, we also control some macroscopic future events but no such events in the past.  These two aspects of the “psychological arrow of time” both line up, for deep physical reasons, with the thermodynamic arrow of time.

We are now in a position to understand:

we learn our ideas of causation from the lawfulness of nature and from the directionality of the second law of thermodynamics that lead to the commonsense view that causes precede their effects

Causes precede their effects in our experience, because when we deliberately cause things, those things are in the future, in thermodynamic time, and hence also in psychological time.

Yay hooray!  We understood one sentence!  Let’s go for two:

But then we have learned that the laws of physics are CPT invariant (essentially the same in each direction of time), so in a fundamental sense the future determines the past just as much as the past determines the future.

Wait, whaaaat?  Paul Torek just said that we only deliberately cause events that lie in our future, and now he quotes Don Page (with approval) saying the future determines the past just as much as the past determines the future??

Yes, but look closer.  That “deliberately” is important.  But first, we need a clearer concept of “causing”.  Let’s borrow from Judea Pearl’s book Causality.  We’ll just suppose that we can set the value of some variable, and see what happens to the probability of other variables.  For example if we want to know if smoking causes cancer, we set Do(smoking)=True, and see what happens to the probability of cancer.  If it goes up, the answer is yes.

So what happens if we set Do(change-sparkplug-wires)=True?  Does the probability of Better Engine Performance Tomorrow go up?  Yes, quite a lot.  Does the probability of Better Engine Performance Yesterday go up?  No, not at all.  Does the probability of a particular quark being here, rather than there, a minute after the Big Bang, change?  Maybe!  It depends on which particle we have in mind, and where “here” and “there” are, exactly; but if we spell out the exact motions that Do(change-wires) involves, and so on, we could in principle derive new probabilities for the early-universe conditions, which would in some cases be higher or lower than in the scenario where Do(change-wires)=False.  Because as Don Page points out, the laws of physics are CPT-invariant, which means that if we reverse Charge, Polarity, and Time, we get the same equations.

Actually, CPT invariance is more than we need, to make the relevant point.  Given that CPT invariance is true, it’s pretty easy to see that if we can use the equations of physics to derive future conditions from past ones, we can just as easily use them to derive past conditions from future ones.  Let’s call the italicized part of that sentence “bidirectionality”.  CPT invariance implies bidirectionality, but the reverse is not true.

So:  using a Pearl-esque definition of causality, we do indeed cause events in the past.  It’s just that none of the events we care about are among them!  So, sorry, we cannot make the Detroit Tigers win the 2006 World Series.  We cannot have you-yesterday make that witty comeback to your annoying colleague, that you just thought of today.  All of those things – things you care about, things you (by utter non-coincidence!) remember – lie on the wrong side of a thermodynamic/entropic gradient, and you can’t touch them.  Alas.

We now understand two of the sentences from that beautiful passage I quoted to start, and there’s only one more.  I have only a brief comment on the third sentence:

I agree that just from our experience of the one-way causation we observe within the universe, which is just a merely effective description and not fundamental, we cannot logically derive the conclusion that the entire universe has a cause

Our one-way causation is at the macroscopic level, where we do our living.  And indeed, we cannot derive the conclusion that the entire universe has a cause.  But then, we couldn’t derive that, even if the one-way-ness were fundamental.  From

for all X, Y; (X causes Y) -> (X precedes Y)

it would not follow that

for all Y, there exists X: X causes Y.

But to take a step back and look at the big picture, what Don Page seems to be getting at, is that people take their own experience, and project it onto the universe as a whole.  They reason something like the following.  I do stuff, making the future certain ways.  Maybe the whole universe is like that, and Someone made it happen!  I’ve never seen a time which didn’t have a time one second earlier than it – there couldn’t possibly be a beginning of time!  I use causal relations to exert control – therefore all causality is control!  I can control some future events I care about, but not the past – therefore causality and control run strictly from past to present to future!

All those inferences do seem to have something in common.

For anyone interested in the philosophy-of-physics issues that I’ve discussed here, if you have time to watch a video, I recommend Jenann Ismael’s talk at 0:54:00 – 1:39:00 or so in the conference recording.  You will need Microsoft Silverlight, a free download, which has an Apple OS compatible version.