Notes on time and causality

A collection of philosophical essays on the subject of causality, determinism and time in general

Appendix

Table of M and W

  M W
Kantian equivalent World as we perceive it World as it is
Characteristic Fragmented Unified
Mode of perception Dogmatic Empirical
Defined by Causality Entropy
Time structure Chain Graph

Note that M is unified in some sense, since M obeys common principles, while W does not obey any principles. But W is unified in a much deeper way - the more chaotic and unstructured a given arrangement is, the more everything is connected to everything else, while our Mental world is fragmented in the sense that you can easily view a given part of it by itself.

Rules of life

Don’t focus too much to particular interpretations of reality and to the aspect of reality which is ultimately known as based on them - practice empirical thinking.

Don’t mind mistakes - anything worth doing is worth doing poorly.

Don’t compare things in terms of quantity, instead, compare them in terms of quality - buying more stuff will not bring you closer to happiness, just like living longer years will not bring you closer to immortality.

Short history of causality, determinism and time

~-500 - Zeno of Elea points out the issues with the concept of continuity and the way it clashes with our everyday notion of time in his famous set of paradoxes.

In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. (as recounted by Aristotle, Physics VI:9, 239b15)

~-520 - Heraclitus points out the allusive nature of the causal chain and its connection with the idea of the self

We both step and do not step in the same rivers. We are and are not. Moreover, we step into and out of the river as different beings.(B49a)

~360 Zeno of Citium, the original founder of Stoicism, had a simple but powerful idea of the causal chain - every event has a cause, and that cause necessitates the event and that given exactly the same circumstances, exactly the same result will occur.

It is impossible that the cause be present yet that of which it is the cause not obtain.

~300 Euclid publishes his Elements - one of the first and most famous axiomatic (formal) systems, showing how a very complex deterministic system can be developed from a very small set of rules using inductive reasoning.

~ 210 - Sextus Empiricus nailed it with his critique on inductive reasoning, positing that a universal rule could not be established from an incomplete set of particular instances:

When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite.

1687 - Isaac Newton published his Principia Mathematica one of the most fundamental scientific papers ever where he:

“Principia…” laid down the idea that later became central for all of physics, except quantum physics (i.e. classical physics) - the idea that the world can be modelled using a set of formal walls, a-la Euclid’s postulates.

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space … Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another …

1739 - 40 - David Hume publishes A Treatise of Human Nature, most famous for his critique of induction (resembling that of Sextus Empiricus) and lays down the groundwork for the modern views on the topic of causality, insisting that (while completely valid) the connections we make using the concept of cause and effect are subjective and imaginary.

This deficiency in our ideas is not, indeed, perceived in common life, nor are we sensible, that in the most usual conjunctions of cause and effect we are as ignorant of the ultimate principle, which binds them together, as in the most unusual and extraordinary. But this proceeds merely from an illusion of the imagination; and the question is, how far we ought to yield to these illusions. This question is very difficult, and reduces us to a very dangerous dilemma, whichever way we answer it. For if we assent to every trivial suggestion of the fancy; beside that these suggestions are often contrary to each other; they lead us into such errors, absurdities, and obscurities, that we must at last become asham’d of our credulity.

On Newton:

While Newton seemed to draw off the veil from some of the mysteries of nature, he showed at the same time the imperfections of the mechanical philosophy, so agreeable to the natural vanity and curiosity of men; and thereby restored her ultimate secrets to that obscurity, in which they ever did and ever will remain.

1781 - Immanuel Kant reads Hume’s treatise and decides to refute it, an effort which results in probably the most serious work on the subject of causality, “The Critique of Pure Reason”. In it, Kant says that causality cannot be the result of experience, because it enables experience and plunges in a multidisciplinary investigation to discover what it actually is while refuting Newton’s notion of absolute time in the process.

Now let us proceed to our problem. That something happens, i.e., that something or a state comes to be that previously was not, cannot be empirically perceived except where an appearance precedes that does not contain this state in itself; for a reality that would follow on an empty time, thus an arising not preceded by any state of things, can be apprehended just as little as empty time itself. Every apprehension of an occurrence is therefore a perception that follows another one. Since this is the case in all synthesis of apprehension, however, as I have shown above in the case of the appearance of a house, the apprehension of an occurrence is not yet thereby distinguished from any other. Yet I also note that, if in the case of an appearance that contains a happening I call the preceding state of perception A and the following one B, then B can only follow A in apprehension, but the perception A cannot follow but only precede B. E.g., I see a ship driven downstream. My perception of its position downstream follows the perception of its position upstream, and it is impossible that in the apprehension of this appear­ ance the ship should first be perceived downstream and afterwards upstream. The order in the sequence of the perceptions in apprehension is therefore here determined, and the apprehension is bound to it. In the previous example of a house my perceptions could have begun at its rooftop and ended at the ground, but could also have begun below and ended above; likewise I could have apprehended the manifold of em- pirical intuition from the right or from the left. I n the series o f these perceptions there was therefore no determinate order that made it nec- essary when I had to begin i n the apprehension in order to combine the manifold empirically. But this rule is always to be found in the percep- tion of that which happens, and it makes the order of perceptions that follow one another (in the apprehension of this appearance) necessary.

(…)

If, therefore, we experience that something happens, then we always presuppose that something else precedes it, which it follows in accordance with a rule. For without this I would not say of the object” that it follows, since the mere sequence in my apprehension, if it is not, by means of a rule, determined in relation to something preceding, does not justify any sequence in the object.d Therefore I always make my subjective synthesis (ofapprehension) objective with respect to a rule in accordance with which the appearances in their sequence, i.e., as they occur, are determined through the preceding state, and only under this presupposition alone is the experience of something that happens even possible.

On Hume:

I freely admit that the remembrance of David Hume was the very thing that many years ago first interrupted my dogmatic slumber and gave a completely different direction to my researches in the field of speculative philosophy.

1814 - Pierre-Simon Laplace invented the modern concept of scientific determinism:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. A Philosophical Essay on Probabilities

1905 - Albert Einstein publishes the paper “The Thermodynamic of Moving Bodies” where he proposes the special theory of relativity which slowly killed off Newton’s concept of absolute time, confirming some of Kant’s views on space and time in the process (although Einstein himself famously opposed Kant’s formulation and specifically the idealistic aspect of it).

the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous in as much as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.

On Kant:

The very fact that the totality of our sense experiences is such that by means of thinking (operations with concepts, and the creation and use of definite functional relations between them, and the coordination of sense experiences to these concepts) it can be put in order, this fact is one which leaves us in awe, but which we shall never understand. One may say “the eternal mystery of the world is its comprehensivibility.” It is one of the great realizations of Immanuel Kant that the setting up of a real external world would be senseless without this comprehensibility. (Albert Einstein, Out of My Later Years)

1935 - Einstein (again) along with Podolsky and Rosen argues that the universe puts forward what is now known as the EPR paradox, and argues that the quantum-mechanical wave function must be an incomplete description of the physical world. But the real significance of the paper is that it takes as a given the assumption that the universe is deterministic.

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

Or in Einstein’s own words:

I, at any rate, am convinced that [God] does not throw dice

1964 - John Stewart Bell publishes a paper titled “On the Einstein Podolsky Rosen Paradox” where he makes the simplest and at the same time most ground-breaking discovery in this list by just realising that there exist some quantum phenomena which cannot be accounted for any deterministic model of the universe (that is unless you are willing to believe that two particles can “communicate” with each other so that they can synchronise their states, and they can do so faster than the speed of light). This article is largely an effort to examine the philosophical implications of Bell’s inequality are outlined in this article.

Einstein said that it is theory which decides what is ‘observable’. I think he was right - ‘observation’ is a complicated and theory-laden business. Then that notion should not appear in the formulation of fundamental theory. Information? Whose information? Information about what? On this list of bad words from good books, the worst of all is ‘measurement’. It must have a section to itself.

On Euclidian geometry

I agree with them about that: ORDINARY QUANTUM MECHANICS (as far as I know) IS JUST FINE FOR ALL PRACTICAL PURPOSES. Even when I begin by insisting on this myself, and in capital letters, it is likely to be insisted on repeatedly in the course of the discussion. So it is convenient to have an abbreviation for the last phrase: FOR ALL PRACTICAL PURPOSES = FAPP.

(…)

I expect that mathematicians have classified such fuzzy logics. Certainly they have been much used by physicists. But is there not something to be said for the approach of Euclid? Even now that we know that Euclidean geometry is (in some sense) not quite true? Is it not good to know what follows from what, even if it is not necessarily FAPP? Suppose for example that quantum mechanics were found to resist precise formulation. Suppose that when formulation beyond FAPP was attempted, we find an unmovable finger obstinately pointing outside the subject, to the mind of the observer, to the Hindu scriptures, to God, or even only Gravitation? Would that not be very, very interesting?

From “Against ‘measurement’”, Physics World (August 1990)