I greatly appreciate your citations from ancient times to today. They document the slow evolution of human understanding of our natural world. Rousseau simply chose to imagine this history, then build a utopian world based on his vision. AI does not yet encompass this full range which could easily send us down a wrong path. I also was drawn to the statement, "Because the world is better viewed as indeterministic, decision making remains a human task, linked with responsibility." None can know everything and decision making is always under uncertainty as Heisenberg convinced me long ago. Or to paraphrase the pragmatist, Charles S. Peirce, we make decisions based on, "What it is reasonable to believe". Then there are those devilish things called "responsibility" and "accountability". I wish more humans would think on these terms when making decisions.
Excellent generalization of the concept of the dual nature of the scientific laws of physics, either as deterministic or as stochastic, similar in a way to the classical conflict particle physics versus wave mechanics, leading to a rather obscured but now profound scientific conclusion, stated for first time, that every scientific law has a dual character, being either deterministic or stochastic in nature!
After all, Aristotle distinguishes SCIENCE as demonstrative knowledge in two branches:
- Deals with things that are “always the same” (ἀεί ὡσαύτως ἔχοντα = eternal beings) and
- things that occur “for the most part” (τα ὡς ἐπί το πολύ = statistically predominant);
According to Aristotle, concepts and ideas are deriving from the abstraction of sensible things, in contrast to Plato who defines them as reminiscence of the soul from the ideal world of ideas. Of course this definition of ideas, by Socrates and Plate, is justified by the fact the scientific laws can not be founded on the basis of imperfect and ever changing ideas, but only on eternal fixed ideas. This problem was solved by Aristoteles who defined ideas as abstractions of the sensible things. Other than that, both approaches are equivalent!
Therefore this dual nature is generically explained by the Aristotelian approach, as all scientific laws are based on mathematical abstractions, focusing on the most important parameters of a physical problem and ignoring the rest, the less influential ones, which under certain conditions, manifest themselves, as "uncertainties" to the deterministic formulation predictions and therefore leading to the need for the stochastic approach, in order to "explain" the behavior of the unaccounted infinite ignored parameters.
And here comes again Aristotle with his statement about the Four Causes (Metaphysics) of every thing: the Material cause (υλικό αίτιο), the Formal (μορφολογικό αίτιο) cause , the Efficient cause (ποιητικό αίτιο), and the Final cause (τελεολογικό αίτιο) of a thing.The Example: The one-dimensional focus on CO2 of the Climatic Change dogma as the sole efficient cause, ignores the complexity of other causes (e.g., clouds, Sun, water cycles). By ignoring the material and formal complexities of the Earth’s chaotic atmospheric systems—as highlighted by Nobel laureate John Clauser and others—we risk transforming science into Scientism.
The science of Thermodynamics exemplifies this dual nature of physical laws in most profound way. There are several and equivalent statements of the second law of thermodynamics like the :
- Clausius statement: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time
- Lord Kelvin statements: It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature
- Principle of Carathéodory: In every neighborhood of any thermodynamic state S of an adiabatically enclosed system there are states inaccessible from S
- Boltzmann's approach: It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same
- He also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution.
In other words, Boltzmann demonstrated the second law on purely statistical grounds, whereas Caratheodory proved, on purely deterministic grounds, that certain thermodynamic states, no matter the complexity of the thermodynamic system, are inaccessible with purely adiabatic processes. And here arises again the Aristotelian concepts of potentially accessible states or transitions (δυνάμει-ενδελέχεια-diligence) versus the actual ones (θέσει- actual position).
Thanks for the comment and the suggestion for Nair's book, Apostole!
I hope to be able to show in the next chapters that the celebrated laws of thermodynamics, highlighted in the book, are just consequences of the two principles highlighted in Chapter 1, the principle of least action and, primarily, the principle of maximum entropy--as also is the Maxwell–Boltzmann distribution.
You could add that Sir Isaac Newton realised that the mathematical account of the solar system he set out in his Principia entailed that the solar system was unstable, yet the system was, in his view, highly stable. He concluded that his Principia proved the existence of God, because, reasoned Sir Isaac, it was obviously necessary for God to keep adjusting all the orbits to keep the system stable. You can find Sir Isaac arguing this in the Principia's General Scholium. Sir Isaac states, amongst other things:
"This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. And if the fixed Stars are the centers of other like systems, these being form'd by the like wise counsel, must be all subject to the dominion of One; especially, since the light of the fixed Stars is of the same nature with the light of the Sun, and from every system light passes into all the other systems. And lest the systems of the fixed Stars should, by their gravity, fall on each other mutually, he hath placed those Systems at immense distances one from another.
This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God παντοκρáτωρ or Universal Ruler. For God is a relative word, and has a respect to servants; and Deity is the dominion of God, not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: These are titles which have no respect to servants."
However, there were flaws in Newton's Principia.
Pierre Simon LaPlace presented his his multi-volume treatise, Mécanique céleste (Celestial Mechanics) to his former pupil, Napoleon Bonaparte, around 1802. Napoleon remarked that he heard the book made no mention of the Creator. Laplace famously replied, "Sire, I had no need of that hypothesis".
However, there were flaws in LaPlace's Celestial Mechanics.
The clockwork idea, initiated by Descartes, was fatally flawed.
The French astronomer, Jacques Laskar, finally discovered the truth of the matter. See, amongst other things, his 1994 letter "Large-scale chaos in the solar system" to the journal Astronomy and Astrophysics - the randomness in the solar system is irreducible: solar system is unstable!
Thanks, Epitrochoid, for the neat comment. I will try to add something related to it in the next version of the chapter.
I guess your main point is not that there were flaws in Newton's Principia and in Laplace's Celestial Mechanics. This is the rule in science, and it is the reason that we have scientific progress, in an endless self-correcting process.
It seems to me that your main point is that Newton, who accepted divine action (by παντοκράτωρ), at the same time rejected determinism, while Laplace, who "had no need of that hypothesis", favoured determinism. Am I right? Do you think that determinism is a substitute of God for those having difficulties to believe in God (and also reject free will)?
Thanks Demetris. I made a big mistake in my note. Unpredictability, chaos in a deterministic system does not mean randomness as I stated. I recall you being clear about this somewhere in your many papers. But it is a matter making very clear. A deterministic system such as the deterministic equations for the solar system will generate unpredictability and chaos; but there is no randomness. I suppose my main point, having now disposed of my main error, is to note how the mind sets of even the greatest intellects (Sir Isaac and the Marquis La Place) compel them to an erroneous conclusion. I suggest predictability is probably not the best way to deal with the free will issue. The predictability of human behaviour is well known. It is a godsend to assassins and others! Sir Isaac, who was deeply religious was true to his science, realising that the System of the World in his magisterial Principia meant an unstable solar system. But he rejoiced in this because it proved to him that God exists. I am a practicing atheist, so like LaPlace, have no need for that hypothesis. I suggest the evidence for free will is overwhelming!!
I am changing the related paragraphs as follows; hopefully in a more understandable formulation:
---
It should be clarified that the concept of randomness is used here in a sense quite different from the most common one. According to the prevailing dichotomous view, natural processes consist of two distinct, usually additive, components: a deterministic part (signal) and a random part (noise). Over large time scales, the randomness averages out and does not produce net change. Thus, under this view, only an exceptional external forcing can produce sustained long-term change.
In contrast, the perspective adopted here (better explained in Koutsoyiannis, 2010, 2013, and Koutsoyiannis et al., 2016) regards randomness as none other than unpredictability. In macroscopic systems—even those governed by fully deterministic dynamics without any random excitation—unpredictability (i.e., randomness) emerges intrinsically. Depending on the time horizon and time scale of the prediction, there can be either predictability or unpredictability, i.e. randomness, which is not mere noise but the voice of nature itself (cf. rain falling or water flowing). With the exception of very simple systems—mostly idealized or imaginary—all natural systems, from dice to planets, behave in this way. The specific time length at which the transition from predictability to unpredictability occurs can vary widely: from about a tenth of a second for dice, to tens of millions of years for the solar system. At long time horizons (longer than this characteristic time length) all is random—and far from static.
Thanks again, Epitrochoid! As I have tried to show in my papers linked above, in the macroscopic world randomness is none other than unpredictability. A deterministic system is one governed by deterministic laws. These enable predictability on short time horizons, which however ceases on long horizons, rendering the system random, despite its deterministic laws. In one of the two papers I give an excel file with a simple system with fully deterministic dynamics and no random excitation at all, which behaves in a manner that we would characterize random, i.e. unpredictable. Excepting very simple, typically idealized, systems, all natural systems, from dice to planets, behave in this way. Their difference is quantitative, in the time limit of predictability.
"Belief" in determinism is not merely a denial of choice of action, it is a belief that all thought (including the belief in determinism) is meaningless cosmic noise predetermined at the big bang. Free will is axiomatic to thought. Determinism is an instant self contradiction.
Determinists exempt their own thoughts from their determinism. Instead, they think that if Free Will cannot be explained by their deterministic model of the universe, then it cannot exist. It's similar to denying the existence of life or consciousness because we don't understand how they could have emerged.
I received another comment by email saying that my formulation that "decision making remains a human task, linked with responsibility“ is rather arrogant and (all) decisions are not only human task, as artificial intelligence is already a whole ecosystem, and is developing, more and more, and faster and faster.
My reply is this:
Perhaps I am too traditional (hopefully not too arrogant). Can a bot go to prison or be executed if it violates legislation? Wouldn't there be a physical person responsible for a decision? Shouldn't a person put a signature? Or should we accept "auto-pen" signatures by bots?
I think responsibility is a high ethical value that belong to humans.
I have rephrased the relevant paragraph and added two footnotes as follows:
---
Apparently, the dilemma of determinism vs. indeterminism is not just an issue of philosophical belief. It affects our perception and orientation in scientific inquiry, as well as our decisions and actions. If the world were deterministic, decision making would be trivial and, by now, would be undertaken by computers and robots. Because the world is better viewed as indeterministic, decision making remains a human task, linked with responsibility.[1] This is vividly expressed by Julius Caesar's famous words when crossing the Rubicon in 49 BC, reportedly uttered in Greek:
Ἀνερρίφθω κύβος (Let the die have been cast).[2]
---
[1] Acknowledging the expanding role of artificial intelligence (AI) in decision support and automation, true accountability—e.g., for violations carrying imprisonment or equivalent moral weight—still requires a responsible human actor, as no bot can bear punishment or ethical culpability in the way persons do.
[2] This is known from Plutarch’s Life of Caesar, 32, and the exact quotation (from https://www.perseus.tufts.edu/hopper/text?doc=Plut.+Pomp.+60.2) is this: Ἑλληνιστὶ πρὸς τοὺς παρόντας ἐκβοήσας, «Ἀνερρίφθω κύβος», διεβίβαζε τὸν στρατόν. (Declaring in Greek to those present in a loud voice, 'Let the die have been cast,' he led the army across.). Later, the phrase rendered in Latin by Suetonius as Iacta alea est (The die has been cast). The phrase ἀνερρίφθω κύβος is traced back to the Greek playwright Menander (Μένανδρος, c. 342 – 290 BC) of the Athenian New Comedy. It appears is his play Ἀρρηφόρος (Arrhephoros, i.e. the bearer of ritual objects), or Αὐλητρίς (Auletris, i.e. the flute-girl), preserved only in fragments (http://www.poesialatina.it/_ns/greek/testi/Menander/Fragmenta.html) via Athenaeus (Deipnosophistae 13.559e). From the surviving excerpt:
Character A: Οὐ γαμεῖς ἐὰν νοῦν ἔχῃς, τοῦτον καταλιπὼν τὸν βίον. Γεγάμηκα γὰρ αὐτός, διὰ τοῦτό σοι παραινῶ μὴ γαμεῖν. (You never marry, if you're smart, for the rest of your life. I've married myself, so that's why I advise you not to.)
Character B: Δεδογμένον τὸ πρᾶγμ’, ἀνερρίφθω κύβος. (The matter has been decided; let the die have been cast.)
I am posting my reply to a comment I received by email, in order to be registered along with other comments, so as to facilitate revision of the chapter. The comment says that meteorologists predict the weather by numerical solutions of deterministic fluid dynamics non-linear partial differential equations, including measurements and uncertainties.
My reply is this:
Of course, I know about fluid dynamics equations being used also for weather predictions.
But these are not deterministic equations, as you say, except in laminar flow. When there is turbulence (i.e. in almost all cases except trivial) the equations are stochastic. For example, in the Reynolds-averaged Navier–Stokes equations <https://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equations>, we have the apparent stresses owing to the fluctuating velocity field (generally referred to as the Reynolds stresses). We should not forget that these are stochastic terms.
In addition, in weather prediction, the Navier-Stokes equations do not suffice, and need to be complemented by thermodynamic equations, which are by definition stochastic.
Following this comment, I have rephrased some text in the end of section 1.4., which now reads:
Stochastic descriptions of phenomena do not neglect deterministic laws. Rather they fully incorporate them into the stochastic dynamics, primarily as constraints. For instance, in entropy extremization the energy conservation is imposed as an equality constraint. And as discussed above, energy conservation itself can be derived from the principle of extremal action and symmetries of space-time. The principle of maximum entropy does not appear to be a generalization of the principle of extremal action. Rather these two powerful principles seem complementary to each other, enabling effective descriptions of both simple and complex systems:
• Simple systems are studied in deterministic terms, with the basic principle being the extremization of action.
• Complex systems are studied in stochastic terms with the basic principle being extremization of entropy. The principle of extremal action is nonetheless accounted for, primarily through its consequential conservation laws, thus providing the deterministic core of the entropy extremization.
Many believe that there are additional deterministic laws, simple or complex, which do not fit the above categories—for example the laws of thermodynamics or fluid dynamics (Navier-Stokes equations). However, this reflects a misconception of what constitutes a deterministic law. As we shall see in Chapter 6, the laws of thermodynamics are fundamentally stochastic, closely related to the principle of maximum entropy. The Navier-Stokes in their original formulation are deterministic, but are applicable as such only in laminar flow. When turbulence is present (i.e. in almost all real cases except trivial ones) the equations become stochastic. For example, in the Reynolds-averaged Navier–Stokes equations, apparent stresses arise from the fluctuating velocity field (generally known as the Reynolds stresses). These are inherently stochastic terms. Hence, the atmosphere, for instance—whether in its equilibrium state or in flowing motion—can only be effectively studied in stochastic terms.
Reply to a comment sent to me via a text message. The comment is this:
"The way dice fall is not random because the process depends on forces like the strength of the throw, distance to fall, size, shape, weight of dice etc. It only seems random because we don't know all the forces or their quantities."
My reply (backed by the respective papers) is the following and disagrees with the comment:
2. Predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components; ibid.
3. For time horizons of a tenth of a second, the dice motion is not random; see "Predictability in dice motion: how does it differ from hydrometeorological processes?", https://www.itia.ntua.gr/1538/
4. For longer time horizons, the dice motion becomes random (with respect to initial conditions). Hence, the dice fall is random; ibid.
You might want to take a look at David Wallace's "The Emergent Multiverse" which is a defense and exposition of the Many Worlds interpretation of quantum mechanics, and discusses probablities in that context. It is most certainly not an easy read, but he makes the case that Many Worlds is the most "natural" way to understand quantum probability calculations. A discussion of that could be an interesting digression from whatever direction youi are taking your book. I confess, however, that I did not finish it.
Thanks for the suggestion. My copy in one of the infinitely many universes would "probably" accept this theory, but in this universe I find it "natural" to use formal probability and stochastics, rather than save determinism.
I greatly appreciate your citations from ancient times to today. They document the slow evolution of human understanding of our natural world. Rousseau simply chose to imagine this history, then build a utopian world based on his vision. AI does not yet encompass this full range which could easily send us down a wrong path. I also was drawn to the statement, "Because the world is better viewed as indeterministic, decision making remains a human task, linked with responsibility." None can know everything and decision making is always under uncertainty as Heisenberg convinced me long ago. Or to paraphrase the pragmatist, Charles S. Peirce, we make decisions based on, "What it is reasonable to believe". Then there are those devilish things called "responsibility" and "accountability". I wish more humans would think on these terms when making decisions.
Excellent generalization of the concept of the dual nature of the scientific laws of physics, either as deterministic or as stochastic, similar in a way to the classical conflict particle physics versus wave mechanics, leading to a rather obscured but now profound scientific conclusion, stated for first time, that every scientific law has a dual character, being either deterministic or stochastic in nature!
After all, Aristotle distinguishes SCIENCE as demonstrative knowledge in two branches:
- Deals with things that are “always the same” (ἀεί ὡσαύτως ἔχοντα = eternal beings) and
- things that occur “for the most part” (τα ὡς ἐπί το πολύ = statistically predominant);
According to Aristotle, concepts and ideas are deriving from the abstraction of sensible things, in contrast to Plato who defines them as reminiscence of the soul from the ideal world of ideas. Of course this definition of ideas, by Socrates and Plate, is justified by the fact the scientific laws can not be founded on the basis of imperfect and ever changing ideas, but only on eternal fixed ideas. This problem was solved by Aristoteles who defined ideas as abstractions of the sensible things. Other than that, both approaches are equivalent!
Therefore this dual nature is generically explained by the Aristotelian approach, as all scientific laws are based on mathematical abstractions, focusing on the most important parameters of a physical problem and ignoring the rest, the less influential ones, which under certain conditions, manifest themselves, as "uncertainties" to the deterministic formulation predictions and therefore leading to the need for the stochastic approach, in order to "explain" the behavior of the unaccounted infinite ignored parameters.
And here comes again Aristotle with his statement about the Four Causes (Metaphysics) of every thing: the Material cause (υλικό αίτιο), the Formal (μορφολογικό αίτιο) cause , the Efficient cause (ποιητικό αίτιο), and the Final cause (τελεολογικό αίτιο) of a thing.The Example: The one-dimensional focus on CO2 of the Climatic Change dogma as the sole efficient cause, ignores the complexity of other causes (e.g., clouds, Sun, water cycles). By ignoring the material and formal complexities of the Earth’s chaotic atmospheric systems—as highlighted by Nobel laureate John Clauser and others—we risk transforming science into Scientism.
The science of Thermodynamics exemplifies this dual nature of physical laws in most profound way. There are several and equivalent statements of the second law of thermodynamics like the :
- Clausius statement: Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time
- Lord Kelvin statements: It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature
- Principle of Carathéodory: In every neighborhood of any thermodynamic state S of an adiabatically enclosed system there are states inaccessible from S
- Boltzmann's approach: It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same
- He also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution.
In other words, Boltzmann demonstrated the second law on purely statistical grounds, whereas Caratheodory proved, on purely deterministic grounds, that certain thermodynamic states, no matter the complexity of the thermodynamic system, are inaccessible with purely adiabatic processes. And here arises again the Aristotelian concepts of potentially accessible states or transitions (δυνάμει-ενδελέχεια-diligence) versus the actual ones (θέσει- actual position).
An excellent treatise of the second law proofs by Caratherodory and Boltzmann are presented in V. Parameswaran Nair open book, in chapter 9 and paragraph 7.2 respectively! https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=1052&context=cc_oers
Thanks for the comment and the suggestion for Nair's book, Apostole!
I hope to be able to show in the next chapters that the celebrated laws of thermodynamics, highlighted in the book, are just consequences of the two principles highlighted in Chapter 1, the principle of least action and, primarily, the principle of maximum entropy--as also is the Maxwell–Boltzmann distribution.
You could add that Sir Isaac Newton realised that the mathematical account of the solar system he set out in his Principia entailed that the solar system was unstable, yet the system was, in his view, highly stable. He concluded that his Principia proved the existence of God, because, reasoned Sir Isaac, it was obviously necessary for God to keep adjusting all the orbits to keep the system stable. You can find Sir Isaac arguing this in the Principia's General Scholium. Sir Isaac states, amongst other things:
"This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. And if the fixed Stars are the centers of other like systems, these being form'd by the like wise counsel, must be all subject to the dominion of One; especially, since the light of the fixed Stars is of the same nature with the light of the Sun, and from every system light passes into all the other systems. And lest the systems of the fixed Stars should, by their gravity, fall on each other mutually, he hath placed those Systems at immense distances one from another.
This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God παντοκρáτωρ or Universal Ruler. For God is a relative word, and has a respect to servants; and Deity is the dominion of God, not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: These are titles which have no respect to servants."
However, there were flaws in Newton's Principia.
Pierre Simon LaPlace presented his his multi-volume treatise, Mécanique céleste (Celestial Mechanics) to his former pupil, Napoleon Bonaparte, around 1802. Napoleon remarked that he heard the book made no mention of the Creator. Laplace famously replied, "Sire, I had no need of that hypothesis".
However, there were flaws in LaPlace's Celestial Mechanics.
The clockwork idea, initiated by Descartes, was fatally flawed.
The French astronomer, Jacques Laskar, finally discovered the truth of the matter. See, amongst other things, his 1994 letter "Large-scale chaos in the solar system" to the journal Astronomy and Astrophysics - the randomness in the solar system is irreducible: solar system is unstable!
Thanks, Epitrochoid, for the neat comment. I will try to add something related to it in the next version of the chapter.
I guess your main point is not that there were flaws in Newton's Principia and in Laplace's Celestial Mechanics. This is the rule in science, and it is the reason that we have scientific progress, in an endless self-correcting process.
It seems to me that your main point is that Newton, who accepted divine action (by παντοκράτωρ), at the same time rejected determinism, while Laplace, who "had no need of that hypothesis", favoured determinism. Am I right? Do you think that determinism is a substitute of God for those having difficulties to believe in God (and also reject free will)?
As per Laskar, yes, I am aware and have sited this in my paper "A random walk on water", https://www.itia.ntua.gr/en/docinfo/923/
I have also referred to this paper in another comment of this post, https://climath.substack.com/p/introducing-stochastics-as-physics/comment/216812191
Thanks Demetris. I made a big mistake in my note. Unpredictability, chaos in a deterministic system does not mean randomness as I stated. I recall you being clear about this somewhere in your many papers. But it is a matter making very clear. A deterministic system such as the deterministic equations for the solar system will generate unpredictability and chaos; but there is no randomness. I suppose my main point, having now disposed of my main error, is to note how the mind sets of even the greatest intellects (Sir Isaac and the Marquis La Place) compel them to an erroneous conclusion. I suggest predictability is probably not the best way to deal with the free will issue. The predictability of human behaviour is well known. It is a godsend to assassins and others! Sir Isaac, who was deeply religious was true to his science, realising that the System of the World in his magisterial Principia meant an unstable solar system. But he rejoiced in this because it proved to him that God exists. I am a practicing atheist, so like LaPlace, have no need for that hypothesis. I suggest the evidence for free will is overwhelming!!
I am changing the related paragraphs as follows; hopefully in a more understandable formulation:
---
It should be clarified that the concept of randomness is used here in a sense quite different from the most common one. According to the prevailing dichotomous view, natural processes consist of two distinct, usually additive, components: a deterministic part (signal) and a random part (noise). Over large time scales, the randomness averages out and does not produce net change. Thus, under this view, only an exceptional external forcing can produce sustained long-term change.
In contrast, the perspective adopted here (better explained in Koutsoyiannis, 2010, 2013, and Koutsoyiannis et al., 2016) regards randomness as none other than unpredictability. In macroscopic systems—even those governed by fully deterministic dynamics without any random excitation—unpredictability (i.e., randomness) emerges intrinsically. Depending on the time horizon and time scale of the prediction, there can be either predictability or unpredictability, i.e. randomness, which is not mere noise but the voice of nature itself (cf. rain falling or water flowing). With the exception of very simple systems—mostly idealized or imaginary—all natural systems, from dice to planets, behave in this way. The specific time length at which the transition from predictability to unpredictability occurs can vary widely: from about a tenth of a second for dice, to tens of millions of years for the solar system. At long time horizons (longer than this characteristic time length) all is random—and far from static.
Thanks again, Epitrochoid! As I have tried to show in my papers linked above, in the macroscopic world randomness is none other than unpredictability. A deterministic system is one governed by deterministic laws. These enable predictability on short time horizons, which however ceases on long horizons, rendering the system random, despite its deterministic laws. In one of the two papers I give an excel file with a simple system with fully deterministic dynamics and no random excitation at all, which behaves in a manner that we would characterize random, i.e. unpredictable. Excepting very simple, typically idealized, systems, all natural systems, from dice to planets, behave in this way. Their difference is quantitative, in the time limit of predictability.
"Belief" in determinism is not merely a denial of choice of action, it is a belief that all thought (including the belief in determinism) is meaningless cosmic noise predetermined at the big bang. Free will is axiomatic to thought. Determinism is an instant self contradiction.
Determinists exempt their own thoughts from their determinism. Instead, they think that if Free Will cannot be explained by their deterministic model of the universe, then it cannot exist. It's similar to denying the existence of life or consciousness because we don't understand how they could have emerged.
Καλή αρχή! Αισθάνομαι ότι θα είναι ένα σπουδαίο βιβλίο!
Ευχαριστώ πολύ, Νάση μου!
I received another comment by email saying that my formulation that "decision making remains a human task, linked with responsibility“ is rather arrogant and (all) decisions are not only human task, as artificial intelligence is already a whole ecosystem, and is developing, more and more, and faster and faster.
My reply is this:
Perhaps I am too traditional (hopefully not too arrogant). Can a bot go to prison or be executed if it violates legislation? Wouldn't there be a physical person responsible for a decision? Shouldn't a person put a signature? Or should we accept "auto-pen" signatures by bots?
I think responsibility is a high ethical value that belong to humans.
I have rephrased the relevant paragraph and added two footnotes as follows:
---
Apparently, the dilemma of determinism vs. indeterminism is not just an issue of philosophical belief. It affects our perception and orientation in scientific inquiry, as well as our decisions and actions. If the world were deterministic, decision making would be trivial and, by now, would be undertaken by computers and robots. Because the world is better viewed as indeterministic, decision making remains a human task, linked with responsibility.[1] This is vividly expressed by Julius Caesar's famous words when crossing the Rubicon in 49 BC, reportedly uttered in Greek:
Ἀνερρίφθω κύβος (Let the die have been cast).[2]
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[1] Acknowledging the expanding role of artificial intelligence (AI) in decision support and automation, true accountability—e.g., for violations carrying imprisonment or equivalent moral weight—still requires a responsible human actor, as no bot can bear punishment or ethical culpability in the way persons do.
[2] This is known from Plutarch’s Life of Caesar, 32, and the exact quotation (from https://www.perseus.tufts.edu/hopper/text?doc=Plut.+Pomp.+60.2) is this: Ἑλληνιστὶ πρὸς τοὺς παρόντας ἐκβοήσας, «Ἀνερρίφθω κύβος», διεβίβαζε τὸν στρατόν. (Declaring in Greek to those present in a loud voice, 'Let the die have been cast,' he led the army across.). Later, the phrase rendered in Latin by Suetonius as Iacta alea est (The die has been cast). The phrase ἀνερρίφθω κύβος is traced back to the Greek playwright Menander (Μένανδρος, c. 342 – 290 BC) of the Athenian New Comedy. It appears is his play Ἀρρηφόρος (Arrhephoros, i.e. the bearer of ritual objects), or Αὐλητρίς (Auletris, i.e. the flute-girl), preserved only in fragments (http://www.poesialatina.it/_ns/greek/testi/Menander/Fragmenta.html) via Athenaeus (Deipnosophistae 13.559e). From the surviving excerpt:
Character A: Οὐ γαμεῖς ἐὰν νοῦν ἔχῃς, τοῦτον καταλιπὼν τὸν βίον. Γεγάμηκα γὰρ αὐτός, διὰ τοῦτό σοι παραινῶ μὴ γαμεῖν. (You never marry, if you're smart, for the rest of your life. I've married myself, so that's why I advise you not to.)
Character B: Δεδογμένον τὸ πρᾶγμ’, ἀνερρίφθω κύβος. (The matter has been decided; let the die have been cast.)
I am posting my reply to a comment I received by email, in order to be registered along with other comments, so as to facilitate revision of the chapter. The comment says that meteorologists predict the weather by numerical solutions of deterministic fluid dynamics non-linear partial differential equations, including measurements and uncertainties.
My reply is this:
Of course, I know about fluid dynamics equations being used also for weather predictions.
But these are not deterministic equations, as you say, except in laminar flow. When there is turbulence (i.e. in almost all cases except trivial) the equations are stochastic. For example, in the Reynolds-averaged Navier–Stokes equations <https://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equations>, we have the apparent stresses owing to the fluctuating velocity field (generally referred to as the Reynolds stresses). We should not forget that these are stochastic terms.
In addition, in weather prediction, the Navier-Stokes equations do not suffice, and need to be complemented by thermodynamic equations, which are by definition stochastic.
Following this comment, I have rephrased some text in the end of section 1.4., which now reads:
Stochastic descriptions of phenomena do not neglect deterministic laws. Rather they fully incorporate them into the stochastic dynamics, primarily as constraints. For instance, in entropy extremization the energy conservation is imposed as an equality constraint. And as discussed above, energy conservation itself can be derived from the principle of extremal action and symmetries of space-time. The principle of maximum entropy does not appear to be a generalization of the principle of extremal action. Rather these two powerful principles seem complementary to each other, enabling effective descriptions of both simple and complex systems:
• Simple systems are studied in deterministic terms, with the basic principle being the extremization of action.
• Complex systems are studied in stochastic terms with the basic principle being extremization of entropy. The principle of extremal action is nonetheless accounted for, primarily through its consequential conservation laws, thus providing the deterministic core of the entropy extremization.
Many believe that there are additional deterministic laws, simple or complex, which do not fit the above categories—for example the laws of thermodynamics or fluid dynamics (Navier-Stokes equations). However, this reflects a misconception of what constitutes a deterministic law. As we shall see in Chapter 6, the laws of thermodynamics are fundamentally stochastic, closely related to the principle of maximum entropy. The Navier-Stokes in their original formulation are deterministic, but are applicable as such only in laminar flow. When turbulence is present (i.e. in almost all real cases except trivial ones) the equations become stochastic. For example, in the Reynolds-averaged Navier–Stokes equations, apparent stresses arise from the fluctuating velocity field (generally known as the Reynolds stresses). These are inherently stochastic terms. Hence, the atmosphere, for instance—whether in its equilibrium state or in flowing motion—can only be effectively studied in stochastic terms.
Reply to a comment sent to me via a text message. The comment is this:
"The way dice fall is not random because the process depends on forces like the strength of the throw, distance to fall, size, shape, weight of dice etc. It only seems random because we don't know all the forces or their quantities."
My reply (backed by the respective papers) is the following and disagrees with the comment:
1. Random means unpredictable; see "A random walk on water", https://www.itia.ntua.gr/923/
2. Predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components; ibid.
3. For time horizons of a tenth of a second, the dice motion is not random; see "Predictability in dice motion: how does it differ from hydrometeorological processes?", https://www.itia.ntua.gr/1538/
4. For longer time horizons, the dice motion becomes random (with respect to initial conditions). Hence, the dice fall is random; ibid.
You might want to take a look at David Wallace's "The Emergent Multiverse" which is a defense and exposition of the Many Worlds interpretation of quantum mechanics, and discusses probablities in that context. It is most certainly not an easy read, but he makes the case that Many Worlds is the most "natural" way to understand quantum probability calculations. A discussion of that could be an interesting digression from whatever direction youi are taking your book. I confess, however, that I did not finish it.
Thanks for the suggestion. My copy in one of the infinitely many universes would "probably" accept this theory, but in this universe I find it "natural" to use formal probability and stochastics, rather than save determinism.