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Quora Question #1, 07/26/2018:
In The Book of Why (page 199), by Judea Pearl, Can the coin-flipping example of Causal Paradox be applied to “acausal” Quantum Entanglement?

Elaboration on question :

THE BOOK OF WHY, Judea Pearl, 2018
In the chapter on Paradoxes Galore! (page 199), Pearl presents a thought experiment based on coin flipping. The result seems intuitively paradoxical, so he wrote : << Did the coins somehow communicate with each other at light speed? Of course not. In reality you conditioned on a collider by censoring all the tails-tails outcomes.>> That remark reminded me of an analogous statistical paradox in Quantum theory. Physically unconnected, but historically entangled, particles seem to exchange information at light speed via some mysterious "acausal" non-mechanism. I'm sure this absurdity is an embarrassment to quantum researchers, just as "spooky action at a distance" was for Newton and Einstein.

So, I'd like to see Pearl's casual diagrams applied to Quantum Entanglement, to discover if the observer, who set up the experiments, inadvertently <<conditioned on a collider>>. If so, then "acausal" entanglement may be an illusion due to some hidden <<confounder>> -- perhaps an artificial choice by the Observer to exclude (censor) some apparently irrelevant detail. <<Collider bias>> is a possible causal influence on outcomes, that may be negative or positive, but often produces a <<spurious association>> to intuition, yet can be detected by logical causal diagrams.

The Entanglement <<correlation>> may turn out to not be an illusion, but instead the result of unknowingly influencing the <<structure behind the data selection>>. This may not be a case of physical causation, but of mathematical causation, in the sense of changing the value of a link in the chain of causation (the mathematical structure), by an exchange of information instead of energy. Unfortunately, the notion of a mental cause may also be an embarrassment to materialist Physicists.

I'm merely an interested layman, and not qualified to apply Pearl's system to either Artificial Intelligence or to Quantum Physics. But, I'm hoping that some Quorans are up to the task.


Note: terms in <<quotes>> are defined in the book. Except he doesn't go into detail about the <<structure>> of the data, which I assume to be logical/ mathematical relationships, that are normally considered to be inert paths, not causal forces. But his related concept of <<counterfactuals>> refers to things that don't exist in reality, but only in mathematical possibility, or in human imagination. So, an experimenter could <<censor>> one possible causal branch (path) into the future, while permitting another to unfold in the experiment. I'm guessing that both the mathematical structure, and the structure-changing energy, are forms of causal Information (enformation).

Quora question #2, 07/31/2018 :
How can you demonstrate Freedom within Determinism mathematically?

Back in the 60s, at the Seattle World's Fair, I saw a large physical model of Galton's Quincunx. It dropped hundreds of randomly bouncing ping pong balls into several channels, and they always piled up in the shape of a Bell Curve. The standard curve was painted on the glass front to show that, without exception, the randomized balls conformed to the statistical principle of normal distribution. But one of the balls was painted red, and it ended up in a different slot every time. Thus illustrating that statistical determinism only applies to aggregates, not to individuals.

From that demonstration I learned that Freewill may not be not an illusion, but a degree of freedom built into the laws of Nature. Of course, humans seem to be the only species with the brain-power to discover and exploit those windows of opportunity, to take the path "less traveled by" the herd. The ping pong ball didn't choose its erratic route, but humans can imagine alternative paths, and take steps to follow one of them to a destination of their own choice. High School and College graduation speeches assume such freedom, but philosophers still debate its reality. Maybe no-nonsense mathematics will clarify the issue.

Request : I have searched the internet for a physical or animated model of the Quincunx. But all I found were intended to portray the rigid determinism of natural processes. I'd appreciate a link to a model with a red ball that refuses to bow to fickle Fate.

Quora Question : How can you demonstrate Freedom within Determinism mathematically?
JE reply 08/04/2018 :


I didn't intend to get into a debate on the freewill question on Quora. That could go on forever. And it doesn't matter to me if you think you are a zombie. I started this thread in hopes that someone familiar with the Bell Curve could help me find an animation of the quincunx, with a red ball defying the laws of probability, as-if it had freewill. I need it to illustrate a topic in my blog : Rationalism versus Fatalism.

I finally found a black & white still image of the Seattle World's Fair math exhibit, illustrating the principle of predictable normal distribution of large numbers of things. But it also, perhaps incidentally, demonstrated the principle of unpredictable abnormal behavior of individual things. If you could watch the animation over & over, you’d think the red ball had a mind of its own, stubbornly refusing to conform to the Law of Large Numbers.

By itself, this model doesn't prove that freewill is real. But it can serve as an analogy of how mathematical determinism is probabilistic in nature, as in quantum mechanics. Physical Mechanical systems seem to be driven by irresistible Destiny or Fate, until you look at single objects. A virtual particle is not even a real thing until an external probe, such as a scientist's observation (a choice), triggers a phase-change from continuous field to discontinuous particle. In the mathematical state (field) it has the freedom of fluidity, as demonstrated in the double-slit experiment.

Likewise, human behavior can be unpredictable, if we choose to think creatively. The act of creation causes a divergence from the chain of physical cause & effect, by introducing a meta-physical cause : a choice. By “metaphysics”, I don't mean spirituality, but simply mentality. Aristotle divided his encyclopedia into two volumes, the first dealing with the physical world, and the second with human ideas about the world. Physics is about concrete laws of Nature, while Metaphysics is about abstract principles such as Ethics. Our freedom seems to be limited to inserting a novel “cause” (choice) into the chain of causation. By contrast, absolute freedom would make us gods.

Note : The oval sign next to the display says : “When falling balls are observed one by one, the path of each is unpredictable, but taken many by many, they form an orderly predictable pattern.” So, if strict determinism causes a predictable step-by-step pattern, an element of freedom should allow pockets of unpredictable skip-step patterns.

Quora Question : How can you demonstrate Freedom within Determinism mathematically?
Sequential replies to Stannis Papanoalou, August 2 - 4, 2018 :

“It is a further question why you should equate freedom with randomness, “ The Quincunx is a mechanical system that produces predictable order from chaos. But human reason & will are metaphysical. So they allow us to predict hypothetical futures (counter-factuals), and to consciously choose one that leads toward a personal goal. The red ball is merely an illustration of an exception to the predictability of absolute determinism. Freewill allows us to choose our own exceptions.

By “metaphysical” I mean that human reason does not have the same cause & effect limitations of physical systems. Scientists often imagine “what-if” counter-factuals in order to discover possibilities unpredicted by current theories. Of course, any physical application of such alternatives will be restricted to the usual cause & effect paths. You can imprison the body, but not the mind.
Counterfactual Theories of Causation : https://plato.stanford.edu/entries/caus ... erfactual/

“ it must be either determined or random” That is the classical logic of causation. But quantum theory must explain entanglement effects that are neither fully determined, nor fully random. The current term is “acausal”, but that sounds like “spooky action at a distance”.

The arguments against human freewill are usually talking about physical cause & effect, like billiard balls. They ignore the role of immaterial Mind & Reason as feedback loops in the chain of causation. Metaphysical “mind” is the function of the physical brain. It’s what the brain does. Yet determinists negate the importance of the unique function that allows them to reach the conclusion that, for all practical purposes, the Mind doesn’t exist. Since they deny the causal efficacy of the mind, they should try to pick up a cup, without first imagining the cup on the table somehow moving to the mouth. The ability to imagine counter-factuals is the faculty of freewill.

Reply on Quora 08/06/2018 :

Freewill within Determinism
Here is a quote I found some time ago, maybe on Quora, that sums-up my concept of how humans are able to exercise a bit of self-determined choice within an evolutionary system that is overwhelmingly impersonally deterministic :
“Determinism is a long chain of cause & effect, with no missing links.
Freewill is when one of those links is smart enough to absorb a cause and modify it before passing it along. In other words, a self-conscious link is a causal agent---a transformer, not just a dumb transmitter. And each intentional causation changes the course of deterministic history to some small degree.”
___Yehya

Quora reply 8/7/2108 :
If humans have free will, why do they obey the laws of physics?

For the same reason you obey the traffic laws of your community. You are free to run that red light, but there will be consequences. You are free to jump off a tall building, but you may not enjoy the effects of gravity. The "consequences" in physics are "effects" of prior "causes". But your choice is an intermediate cause.

As you sit in your car, frustrated by the wait, you can freely imagine yourself zooming past the warning light. But you can also imagine other options : a collision or a traffic ticket. So, you choose the alternative that seems to lead to the most favorable consequences.

One of those three consequences gets you to your destination a bit sooner than the others. But you don't know in advance what the odds are, of getting away with flouting the public law for your own selfish purposes. Until you make your choice, those future hypotheticals are counter-factuals. But once you choose, "maybe" suddenly becomes reality.

Human freewill does not give you the ability to subvert the laws of nature. It merely allows you to take your chances of turning those laws to your own advantage. If you want to fly, you can make arrangements to use natural principles to propel and support your flight. Magical flight works well in imagination, but fails in the real world.

As a rational creature, you are free to insert your own purposes into the chain of cause & effect. A billiard ball is simple : input >> output. But a rational mind is more complex : input >> options >> output. As a causal agent, you are a middle-man, passing along the natural forces that impact you. You absorb a cause (energy) from nature, and with your knowledge of alternative effects, you modify the incoming vector toward a destination of your own choosing. You don't just "transmit", you "transform".

Nature has its own general traffic laws, but human nature can choose alternative ways to obey those laws.

Freewill within Determinism :
“Determinism is a long chain of cause & effect, with no missing links.
Freewill is when one of those links is smart enough to absorb a cause and modify it before passing it along. In other words, a self-conscious link is a causal agent---a transformer, not just a dumb transmitter. And each intentional causation changes the course of deterministic history to some small degree.”
___Yehya

Quora reply to Ruismaki, 08/10/2018 :
How can you demonstrate freedom within determinism mathematically?

“I think that this is what we can learn from the Quincunx machine: A large number of random chance events or free will decisions will lead to a bell curve type of probability distribution.”

Exactly! That’s what I call “freedom within determinism”. But it’s not “free-WILL”. To have “Freewill Within Determinism”, you must have a conscious mind able to choose between alternative futures. Just as a quantum measurement collapses the superposed waveform, a willed choice is a value measurement that “collapses” the manifold statistical probabilities (future paths) into a single present path for the chooser. At least, that’s my theory.

I’m not looking for an animated Quincunx for a statistical analysis, but for an intuitive analogy. Bouncing balls follow physical laws, while informed choices follow meta-physical laws (Logic). Unfortunately, most humans are poor prognosticators, with a weak grasp of statistical principles, and of logical implications. So, the majority of people possess the potential for Freewill (Reason), but in practice they act like predetermined pawns & ping-pong balls. Only the self-actualized few are like the red balls, taking the “path less traveled”.

Continuation of replies to Ruismaki on Quora :
How can you demonstrate freedom within determinism mathematically?


Footnote to “Freewill Within Determinism” : this is not the kind of freewill that most people imagine. As a pragmatic realistic concept, it’s actually compatible with skepticism toward some mystical, magical, religious, and New Age notions of miraculous mind-power.

In a recent interview, Yuval Noah Harari commented on the loss of privacy, even for your personal opinions & feelings. He describes how faith in freewill can open your mind to manipulation by nefarious outside causes. If so, it’s good to be aware of how fragile your freedom is :

“Even though neuroscience shows us that there is no such thing as free will, in practical terms it made sense because nobody could understand and manipulate your innermost feelings. But now the merger of biotech and infotech in neuroscience and the ability to gather enormous amounts of data on each individual and process them effectively means we are very close to the point where an external system can understand your feelings better than you.

We’ve already seen a glimpse of it in the last epidemic of fake news. There’s always been fake news but what’s different this time is that you can tailor the story to particular individuals, because you know the prejudice of this particular individual. The more people believe in free will, that their feelings represent some mystical spiritual capacity, the easier it is to manipulate them, because they won’t think that their feelings are being produced and manipulated by some external system.”

Yuval Noah Harari: ‘The idea of free information is extremely dangerous’


As a further footnote on a pragmatic notion of “Freewill Within Determinism”, here’s a link to a different thread on a related topic :
John Earwood's answer to If humans have free will, why do they obey the laws of physics?

Continuation of replies to Ruismaki on Quora 8/14/2018:
How can you demonstrate freedom within determinism mathematically?

“I would suggest using freedom only for living beings’ freedom of choice”

I appreciate your concern about using anthropic terms to describe mechanical operations. But I was just referring to the Quincunx as a physical analog to the metaphysical concepts that have always been called something like “freedom” and “determinism”. My concern was not statistical accuracy, but philosophical cogency.

Metaphors are often resorted to, in order to illustrate invisible & intangible notions. For example, Aesop’s fables were not really about talking animals, but human ideas & feelings, in religious, political and social relationships.

“ Cause & effect can never bring about any optional effects to choose from.”

I understand what you’re saying, but you missed the point of the FreeWill Within Determinism argument. It acknowledges that all effects since the First Cause can be traced back to that singular beginning. But in a vast & complex universe, POSSIBLE future effects are almost infinite. Thus, there is some indeterminism WITHIN determinism.
Indeterminism - Wikipedia

That’s why Quantum Mechanics is not mechanical at all, until some event (measurement, enformation, choice) “collapses the superposition” of a mathematical metaphysical waveform. A local Causal event instantly erases all OPTIONAL paths into the future, and transforms POSSIBLE properties into actual particles on a specific trajectory.

My theory of FreeWill WITHIN Determinism is similar to an impossible quantum leap that nevertheless happens a zillion times a second, as statistical waveforms (virtual particles) transform into actual subatomic particles. Since rational humans can imagine alternative futures, that are not yet real, they can make Choices that have a causal impact on the otherwise mechanical chain/web of Causation.

I’m aware that some people deny that the human mind has any causal effects in the real world. But they are ignoring how human Culture has transformed Nature in an eye-blink of cosmic time.

Such imaginary freedom does not negate the inevitability of mechanical destiny, or the normality of statistical distributions, it merely inserts a self-serving cause (choice) into the cosmic stream of causation. This does not abrogate any laws of nature; it merely takes advantage of a strange quirk of mathematics : statistical Probability, and a blind spot in physics : Uncertainty.

Since most people find Quantum Theory and Parametric Statistics incomprehensible, I resort to metaphors & analogies to get the idea across. Of course, metaphors don’t prove anything empirically, but they are effective at conveying abstract concepts in concrete forms. Then again, I could be just fooling myself when I act as-if can choose to swim against the tide of determinism.


Ruismani 8/15/2018 :
“You may perhaps be confusing determinism with causality. “

I was using mechanical causality as a metaphor for human destiny. Philosophical arguments about freewill use the term “determinism” to indicate that human choices are always caused by something external to conscious Will or Intention. Since machines have no intentions, they are not affected by “determinism”.

But the Quincunx model does illustrate a statistical law of nature that “predetermines” average effects of general causation upon large numbers of objects. Of course that kind of mathematical destiny is not subject to intention. So I was merely using that mechanical model to show that individual events are independent from the holistic effects of causation. You might call it “freedom within causation”, or simply “randomness”. The point being that individuals are free from the Law of Averages.

I refer to the graphic image of randomly bouncing balls, acting “as-if” they are free to choose their final destination, in the sense of “a picture is worth a thousand words”. I could, and do in other contexts, get down into the nitty-gritty of quantum randomness with zillions of particles swarming around unpredictably, even as their average behavior on the macro level seems to be predestined by a chain of causation linked back to the beginning of time.

However, quantum “indeterminacy” and mathematical “incompleteness” are way too abstruse for my present purposes. I have no training in such matters, and would make a fool of myself in dialog with those who are qualified to discuss them technically, instead of philosophically. My blog discussion of FreeWill is based on my personal notion of causation that I call EnFormAction. But that’s too broad a topic to discuss in the limited format of a question & answer forum.


Earwood reply : "Since machines have no intentions, they are not affected by “determinism”.

Book of Why, The New Science of Cause & Effect
by Judea Pearl, Artificial Intelligence theorist

In the last chapter of his book, Pearl discusses "Strong AI and Free Will". He describes the limitations of rule-based computers in communication with whimsical humans. The latest progress in AI has been "deep learning" in which "these networks do not follow the rules of probability". But current models still have a problem with understanding the unidirectional flow of Cause and Effect.

Pearl says, "strong AI should be a machine that can reflect on its actions and learn from past mistakes." He thinks it should have the ability "to conceive of one's own intent and then use it as a piece of evidence in causal reasoning.. . . . But how can a robot have free will if it just follows instructions stored in its program?"

"Our entire conception of 'self' presupposes that we have such a thing as choices."

"Granted that free will is (or may be) an illusion, why did evolution labor to endow us with this conception?"

"The illusion of free will gives us the ability to speak about our intents and to subject them to rational thinking, possibly using counterfactual logic." (counterfactual : imaginary, hypothetical)

"In order to communicate naturally with humans, strong AIs will certainly need to understand the vocabulary of options and intents."

"Can we make machines that are capable of distinguishing good from evil?" [read the book]

This reply is slightly off-topic, but still relevant. A dumb classical machine like Galton's Quincunx has no freedom. except on the quantum level of random in-determinism. But a strong AI might have a higher degree of intentional freedom, such as humans call "self-determinism". Being self-conscious, it can compare what-will-be with what-should-be, and take steps to realize that hypothetical future. [for example, if humans are about to destroy the world, AI might preempt that destiny, by destroying the infectious agents. ]

Quora Reply to Ruismaki 8/16/2018
How can you demonstrate freedom within determinism mathematically?


“This is wrong, you should not follow that lead. Determinism does not allow any choices to be made, there is no concept of choice in determinism.”

That misses the point of my concept of Freewill. Cause & effect determinism is not absolutely predestined. Human self-consciousness and reasoning give us the ability to insert a Choice (a causal event) into the stream of mechanical causation. Also, the inherent randomness of nature’s quantum foundation means that the future is always open to novelty.

“ You are assuming that there is a predestined chain of causation.”

No, I don’t think that world events are predestined, at least not in the details. In retrospect, history may seem to be foreordained. But at each moment, for self-conscious creatures — who can imagine the near future, there is room for a conscious choice of optional paths. Of course, our hypothetical futures tend to be less accurate as they extend into the expanding “light cone” (see Wiki) with more & more possibilities as the “probability space” expands.

“Back to the Quincunx balls: There is no causation determining the end channel of any single ball. “

Actually, causal relations are mental noumena, not physical forces (phenomena). David Hume noted that we infer (or induct) causation, but can’t justify it empirically. As usual, I’m using the notion of Causation and Determinism in their conventional meanings, instead of the technical & nit-picky sense. That’s partly because I’m an amateur philosopher with no training, and no credentials. I know just enough to be dangerous.

Hume on Causation :
http://www2.onu.edu/~m-dixon/100/Causation.html