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In "A Brief History of Time" - Chapter 9, Stephen Hawking gives an explanation of how the arrow of time works, i.e. why time seems to move forward in one direction while space can go in different directions.

He first explains that there are 3 arrows of time:

  1. The psychological arrow of time: The fact that humans can only perceive time as moving in one direction and can only remember the past not the future.
  2. The thermodynamic arrow of time: The second law of thermodynamics, that systems move in the direction of increasing disorder (increasing entropy).
  3. The cosmological arrow of time: The direction of time moving with the expanding universe.

He then explains why we perceive all three to be the same, by first merging 1 and 2, and then merging 2 and 3.

My question pertains to how he merges 1 and 2, i.e. why the psychological arrow of time and the thermodynamic arrow of time move in the same direction. Here is his reasoning:

  • Every time a computer performs a calculation it consumes energy and increases the entropy of the universe (Although he doesn't mention it by name, here he is just spelling out Landauer's principle). Computation can thus only move in the direction of increasing entropy.
  • Since the mind works the same way a computer does (per Hawking), human thoughts can only move in the direction of increasing entropy.

So it is not that the psychological arrow and the thermodynamic arrow of time happen to move in the same direction. They are one and the same because humans can only process information (and therefore perceive things) in the direction of increasing entropy.

Here is now my question: Is Hawking here just refining Kant's idea that we perceive space and time the way we do because that's how the mind organizes our sensory input, not because that is how they really are? (i.e is my understanding of Kant correct?)

  • No. Kant makes a counterthesis for every common conception of time. Zeno and Kant are closer than Hawking and any great philosopher. – MikeHelland Apr 30 '15 at 5:26
  • What do you mean by channeling? – user234487 May 1 '15 at 2:32
  • i've always felt that causality was the fundamental reason for the arrow of time. i thought that pedagogically, the 2nd Law is a more secondary concept (albeit it true). – robert bristow-johnson May 1 '15 at 18:56
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    @robertbristow-johnson: for starters, 'causality' would explain (or is that presume?) the axis of time, but it leaves open the question. Essentially all physics is time-reversible: why does the arrow of time then point the direction it does rather than the opposite direction? – Niel de Beaudrap May 2 '15 at 4:59
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The Kantian approach to time is an approach that isn't mentioned by Hawking; and none of the approaches he mentions are akin to it - I think; I'm not sure whether Kant is directly concerned with the fact that time has a direction; it may be that he is - I'm not a close reader of Kant.

I'd say on the whole your understanding of Kant is on the right lines; space and time are the conditions for our experience; ie by organising 'sensory input' (so long as this taken in the Humean way as being unordered raw sensory 'input'; and not already ordered in time).

I find the first question about the psychological arrow of time difficult: what would it mean for us to remember the future? Does this we would no longer have any memory of the past? Or that we 'remember' both the past and future? Do seers 'remember' the future when they 'see' into the future? Would the far future look misty and dim as we are looking at a far horizon?

I wouldn't say that the mind operates like a computer, or even that the brain does either; but that the brain is physical; and thus we can apply physical notions; and this is what is behind the thermodynamic arrow; the the principle of converting information to energy is by way of Maxwell's demon; but there are aporias here; it's quite possible to have regions where entropy is decreasing so long as the overall entropy is increasing; for example a human being is an example of one; physically, he is an example of increasing order; thus should he perceive time backwards? Or is it that the arrow of time is orientated towards increasing order?

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If he channelling a philosopher, it is mostly Boltzmann, in his careful attempts to avoid Loschmidt's paradox.

Boltzmann felt that we needed to presume that time flowed forward only because our local part of the universe had somehow fallen into a state of quite low entropy, which he saw as a kind of 'well'. Phenomenological time then followed entropic time because the brain uses exothermic chemical reactions to store information. (As Hawking reiterates.)

In an attempt to placate or escape Loschmidt, he carefully presented his texts on thermodynamics in such a way as to allow for time to travel different directions in different parts of space.

Two of the strongest framings of the Big Bang indicate that the low entropy comes from either the initial emptiness of space, or the confinement of motion when space was quite small. So the idea of an 'entropy well' is no longer important to folks like Hawking.

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I don't think that Kant overtly elaborates on the arrow of psychological time as such, even though it resides implicitly in his descriptions of the series of events in time. On a rough characterization, Kant seems to hold the conditional relation between the events to be irreflexive and transitive. This relation would arguably determine the direction of the psychological arrow for Kant.

To answer your question, I do think that it can be said that Hawking is expounding upon Kant's view of time as a part of the Transcendental Aesthetic of Apperception, but on strenuous grounds. At least judging from your summary of Hawking's position, it doesn't seem like he is picking upon any particulars that would indicate that the theory of time he is elaborating on is Kantian. That is because there is so much more to Kant's theory of time than just its psychological aspect. The modern cognitive science holds multiple theories regarding the psychological perception of time, so, given the generality of his statements, Hawking could have just been 'refining' upon them.

To digress, I also don't think that Hawking succeeds in merging (1) and (2). For, suppose our brains perform the thinking (computation) and that in turn increases the entropy. Thus, the occurrence of thinking can be correlated with the increase in the entropy. However, that doesn't establish the fact that our thoughts present themselves to us as moving in the same direction as entropy. I'm not sure if this counter-argument works, so any comments would be appreciated.

  • Given computation and entropy flow in the same direction, and assuming consciousness is the result of a computation, we know that the computation computes some function of inputs residing solely in the past. Ergo one's conscious experience in the moment is of past and present events, and so the present experience of the present is time-directed. This of course doesn't prevent past experiences from getting chronologically mixed up (as they do). Thought itself is also correlated in this way since thoughts are exclusively a function of prior thoughts and present inputs. – Veedrac Dec 10 '15 at 23:00
  • I guess the weakness of this argument is that you can't argue that thought must be time-directed from first principles, since the perception of time is not an intrinsic necessity. You can only argue that given a uniform (local) perception of time, the only consistent direction is for it to be in agreement with entropy. – Veedrac Dec 10 '15 at 23:05

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