"Some Thoughts on the Mathematical Unfolding of Absolute Self-Awareness"

Some Thoughts on the Mathematical Unfolding of Absolute Self-Awareness 

Peter Sas

In various posts on this blog I have sketched the rough outlines of a contemporary version of Absolute Idealism, which I like to call – for lack of a better term – “Absolute Idealism 2.0”. The philosophical tradition of Absolute Idealism, stretching from the Upanishads in the East and Plotinus in the West to the German and British Idealists, can be summarized by the claim that everything exists because it is thought and/or experienced by an Absolute Mind, which in turn exists because it thinks/experiences itself. Thus, the Absolute Mind makes itself exist by being aware of itself, and it should as such be defined as Absolute Self-Awareness (ASA). This self-causing capacity of ASA (developed especially by Plotinus and Fichte) is in my view one of the strong features of Absolute Idealism, as it provides a possible (and, perhaps, plausible) answer Leibniz’s famous question why something exists rather than nothing.

This answer, however, is only worth anything if the concept of ASA can also explain why reality is the way it is. For we do not just want to explain the existence of reality; we also want to explain its nature. Why did reality take the form of this universe we see around us, developing in space and time, governed by physical laws? This is where Absolute Idealism 2.0 comes in. Taking its cue from modern physics, which shows the thoroughly mathematical nature of physical reality, Absolute Idealism 2.0 stresses the intimate connection between mathematics and the structure of (absolute) self-awareness. In earlier posts I already developed some ideas about this connection (see here, here and here). This post takes these ideas to a (somewhat) higher level.

I will end with some speculations about a mathematical solution to the problem of evil (the theodicy problem): given the randomness of by far the most real numbers, is it possible that the Absolute simply ‘lost itself’ in what Leibniz called the “labyrinth of the continuum”? Does this explain why the universe is not perfect, despite being the mathematical image of ASA?

The Ogre, the Onion and the Atman

As the German Idealist Schelling (1775 - 1854) said, the unconditioned (“das Unbedingte”) cannot be a thing (“Ding”), because a thing is always conditioned (“be-dingt”). That is to say: a thing is always some-thing and thus determined, limited, finite, conditioned by its (causal or conceptual) relations to other things. Therefore, the source of my freedom – in being unconditioned – cannot be a thing: it must be no-thing, the indefinable void out of which all my free thoughts and actions emerge (and to which they return once they have run their course). But this unconditioned at the centre of my being, isn’t it the same as the unconditioned source of all that exists, of the entire universe?

After all, the unconditioned must be no-thing. But how can the nothing in me differ in any way from the nothing out of which the universe emerged? (And into which it will dissolve again once it has run its course.) Obviously, there cannot be multiple nothings, since they have no distinguishing characteristics – indeed, what is nothing has no characteristics at all! So, the nothing in me, the unconditioned source of my freedom, must be the same nothing that is the unconditioned source of reality-as-a-whole. I guess that’s what those ancient Indian philosophers meant when they said that “Atman is Brahman”, i.e. that the Self is the Ultimate Reality. This comes out beautifully in the famous dialogue between the sage Uddalaka and his son Svetaketu.

Having told his son to cut open one of the tiny seeds of the fruit of the banyan tree, Uddalaka asks: “What do you see there?” To which Svetaketu replies: “Nothing, sir.” Then Uddalaka says: “This finest essence here, son, that you can’t even see – look how on account of that finest essence this huge banyan tree stands here. Believe, my son: the finest essence here – that constitutes the Self of this whole world; that is the truth; that is the Self. And you are that, Svetaketu.” (Chandogya Upanishad 6.12)

Leibniz's Question, the Crisis of Physicalism, and the Return of Absolute Idealism

Peter Sas

A recurrent theme on this blog is the idea that we need some notion of self-causation in order to answer Leibniz’s famous question: “Why is there something rather than nothing?” If we define “reality” as the totality of what exists (including past and future existence), then by definition nothing exists outside of reality (not even ‘the nothing’). If we then presuppose the Principle of Sufficient Reason – that there is a sufficient reason for every fact, including the fact that reality exists – then it follows that the reason for reality’s existence must lie within reality itself, since there is nothing outside of it. And since we generally call the reason why something exists the cause of that something, we must conclude that reality has to be self-causing.

In this post I will investigate this mysterious notion – the self-causation of reality – in light of the current crisis of materialism or what is nowadays rather known as physicalism, i.e. the ontology that takes (completed) physics as the final description of reality. It is a well-known fact that physicalism is presently under increasing attack, mainly by philosophers who point out the irreducibility of consciousness to a physicalist framework. Since self-causation is generally deemed impossible on a physicalist framework, the present crisis of physicalism means that the notion of self-causation gets a second chance.

Moreover, since it is consciousness which is largely responsible for bringing on this crisis of physicalism, the question arises whether consciousness is perhaps the key to understanding the self-causation of reality. This takes us in the direction of Absolute Idealism, where the self-causing essence of reality is generally conceived of in terms of self-consciousness. Thus Absolute Idealism can be broadly summarized as the claim that reality exists because it is thought and/or experienced by an Absolute Mind, which in turn exists because It thinks/experiences itself. It is through its self-consciousness, therefore, that the Absolute Mind lifts itself into existence – at least according to such Absolute-Idealist thinkers such Plotinus, Shankara, Fichte, Schelling, Hegel and Royce.

Some Thoughts on the Mathematical Unfolding of Absolute Self-Awareness 

Peter Sas

"The universe, then, would simply be an extremely complicated pattern in the recursive unfolding of ASA’s self-awareness, namely, that pattern whose (shortest) algorithm simulates intelligent agency to the highest degree."

See? That's what I said!

Absolute Idealism 2.0 and Plotinus

Peter Sas

Metaphysics continuous with science

Obviously, this self-consciousness I appeal to in order to explain reality as a whole is not the individual, finite self-consciousness embodied in physical organisms. Rather, it is a universal, infinite, absolute self-consciousness that is ontologically prior to time and space. I consider this assumption of an absolute self-consciousness as a metaphysical hypothesis that is justified to the extent that it helps us to explain reality. It is, therefore, a form of metaphysics, but one that aims to be continuous with science. In my view, Absolute Idealism is justified only insofar as it accords with the scientific world view. This also explains the mathematical orientation of my approach to Absolute Idealism. Physics, after all, shows that mathematics is the deep structure of physical reality. Thus, the Absolute-Idealist explanation of reality as a whole in terms of absolute self-consciousness can only work if it also explains this ontologically fundamental role of mathematics.

Royce’s mathematical view of the Absolute

In my view, we find the required link between mathematics and absolute self-consciousness by focussing on the recursivity of the latter, i.e. on the fact that self-consciousness, in being its own object of awareness, is also aware of its self-awareness, and aware of that awareness of its self-awareness, and aware of the awareness of that awareness of its self-awareness, and so on ad infinitum. As the American Idealist Josiah Royce has pointed out, this infinite recursion of self-consciousness is isomorphic to the recursion that defines the natural number system ℕ (i.e. the recursive successor function S(n)=n+1, which starting with n=0 generates 1, 2, 3 …). In this way, we can see the absolute self-consciousness, through its inner recursivity, as aware of all natural numbers. From here, as I have argued in different posts, it is only a small step to seeing the absolute self-consciousness as a ‘cosmic computer’, given the fact that computation is standardly understood in terms of mappings from ℕ to ℕ.

The Absolute as ‘cosmic computer’

Since physics shows the basic computability of all physical processes, we can view the physical universe as a privileged subset of all the computations going on in the absolute self-consciousness. But why is this subset privileged? Why does the absolute self-consciousness ‘think’ the computations that constitute this universe rather than any other universe? Two facts suggest an answer: (1) the anthropic principle in physics, which points out that the universe seems ‘just right’ for the evolution of life, and (2) the tautological fact that the aim of absolute self-consciousness is to attain complete knowledge of itself. Thus, it stands to reason that insofar as the absolute self-consciousness computes at all, it pays special attention to those computations that “simulate” intelligent, self-aware organisms. For by focusing its attention on those computations – e.g. the computational structure of the human brain – it sees its own essence reflected in the medium of mathematics. This gives us the following hypothesis: the universe is that proper subset of computations in which the absolute self-consciousness sees its own essence best reflected. It is, to repeat, only a hypothesis, which becomes acceptable only insofar as it enables us to explain reality, in conformity with the scientific world view.

Self-Causation, Time, and Quantum Physics

Peter Sas

4.1 "How come the quantum?"
Wheeler looked in particular at quantum mechanics as allowing such a closed causal loop. In fact he explained the existence and nature of quantum reality ("How come the quantum?") by arguing that it is the universe's means for self-creation: "The strange necessity of the quantum as we see it everywhere in the scheme of physics comes from the requirement that – via observer-participancy – the Universe should have a way to come into being." (Wheeler 1983: 206) On Wheeler's account, then, the classical universe – i.e. the universe whose wave function has been collapsed – brings itself into existence by evolving the very observers whose acts of observation retro-actively collapse that wave function: "Beginning with the big bang, the universe expands and cools. After eons of dynamic development it gave rise to observership. Acts of observer-participancy ‒ via the mechanism of the delayed-choice experiment ‒ in turn gave tangible "reality" to the universe not only now but back to the beginning." (Wheeler 1983: 209) To illustrate this idea, Wheeler came up with the U diagram of the universe as "self-excited circuit": "Starting small (thin U at upper right), it grows (loop of U) and in time gives rise (upper left) to observer-participancy – which in turn imparts "tangible reality" [...] to even the earliest days of the universe." (Wheeler 1983: 209)

4.2 "It from Bit"
It should be stressed, however, that this appeal to quantum retrocausation on a cosmic scale forms only one half of Wheeler's hypothesis of the self-observing universe. As noted above, quantum retrocausation can only explain the classical universe, i.e. the universe whose wave function has been collapsed. This still leaves unexplained the universe at the quantum level, i.e. the universal wave function and the Schrödinger equation which describes its evolution. Where do they come from? If Wheeler's idea of the self-observing universe is to answer Leibniz's question, then Wheeler must also explain their existence. In order to do this, Wheeler left quantum theory behind and generalized his idea by making critical use of information theory. Wheeler argued – as one of the first – that physical reality ultimately consists of bits of information, a point of view encapsulated by his famous dictum "It from Bit". On this view, physical reality exists only for the observers who pose the yes-no questions to which the bits are the answers. As Wheeler puts it: "It from bit. Otherwise put, every it – every particle, every field of force, even the spacetime continuum itself – derives its function, its meaning, its very existence entirely – even if in some contexts indirectly – from the apparatus-elicited answers to yes or no questions, binary choices, bits." (Wheeler 1999: 310-11) Since the observers posing the yes-no questions are part of the very same information space that emerges through their questions, we should conclude that on Wheeler's account these observers ultimately bring themselves along with all of reality into existence.

This is how Wheeler explains the existence of the universal wave function and the Schrödinger equation which describes its evolution: they emerge as special substructures in the information space created by the posers of the yes-no questions. Once the universal wave function exists in information space, and the evolution of its myriad superposed states is dictated by the Schrödinger equation, we find in one of its superposed branches the biological evolution of intelligent observers. These observers then retroactively collapse the universal wave function, resulting in their possible universe becoming the universe – the tangible, classical universe we observe around us. In this way concrete reality bootstraps itself into existence out of the abstract information space created by the observers who pose the yes-no questions – observers who, remember, are themselves part of that concrete reality...