Towards an Artificial Consciousness

The steam-engine, made possible by advances in mechanics, became the enabling technology for the Industrial Revolution, and the computer, made possible by advances in electronics, became the enabling technology for the Information Revolution. It is tempting to wonder what revolution could be next, and whether we can even anticipate it.

One property that the computer shares with the steam-engine is its relationship with reversibility. Another is that a digital computer could, in principle, be constructed from steam-engine parts, either by implementing the standard electronics schematic using pneumatic/hydraulic logic gates, or else by implementing a Turing machine, for example using a steam locomotive "head" (still using pneumatic/hydraulic logic) and letting it affect/be-affected-by the state of inverted-pendulum flip-flops mounted on the traversal railway sleepers.

These pages explore the possibilities of building the next enabling technology from computer parts, used in such a way that they do not make the usual linear progress in program execution, just as the Turing machine steam locomotive no longer makes linear progress towards the next station.

Different types of reversibility

Quantum physics and relativity each stray beyond what our primate, heuristics-based brains have evolved to handle intuitively. Luckily, we have the tools of mathematical language to override this. Another possibility is to come up with a new set of heuristics, just as Faraday was able to reason intuitively about fields, even before Maxwell put it all back on a mathematical footing. Even popular science, non peer-reviewed sources (such as the New Scientist magazine, NS), and pure speculation can be justified, provided that it is followed up later by a more formal analysis. These pages unashamedly flit from one image to another (from balls on a snooker table, to clouds of helium, to a steam locomotive on a Turing tape), not unlike the author and the draft document having a free-ranging conversation on the various subjects, hoping to find pointers to such a new intuitive view.

Living in our far-from-equilibrium universe, we very rarely insist on perfect reversibility [Zurek] and will happily settle for a mere return to the original configuration of the system components. Carnot was interested in returning the relatively inert gas in the cylinder back to its initial state, akin to the way that moving averages are used as a way of cancelling out regular intermediate fluctuations. In this way, overall trends can be identified, not least figures for engine performance and fuel efficiency (as a tool to help steam-engine designers to minimize the number of tons of coal to do a given job, or microprocessor designers to minimize the problems of heat dissipation).

Two colliding balls on a snooker table exchange momentum and energy in such a way as to satisfy the simultaneous equations of energy and momentum conservation. However, when setting up the reverse collision, we not only neglect reversing each of the intermediate mini-collisions with the molecules of the air and the baize, but resign ourselves to incurring yet more of them during the experiment. Similarly, a steam locomotive repeatedly goes through Carnot cycles on its linear journey from one station to the next, and a microprocessor repeatedly goes through instruction cycles on its linear journey through a computer program, and reversing these would usually be assumed to incur further energy consumption. The reverse cycles of operation incur yet more burning of fuel, not a true reversal in which carbon dioxide is drawn out of the air to create lumps of coal (let alone identical lumps of coal to those originally consumed). Our lazy universe [Coopersmith] is one of convergent processes that dissipate information divergently.

Engineering: the pragmatic approach

Since Newtonian gravitational attraction never completely reaches zero with increasing distance, every problem is really a N-body problem, where N is the number of particles in the observable universe. Likewise, two-body entanglement is only an approximation of the experimental setup before the effects of N-body entanglement (decoherence) become significant again. Engineering involves the pragmatic use of broad brush-stroke approximation to make problems more tractable.

Even in the classical view, each mechanical collision, such as between the balls on the snooker table, comes as a complete surprise to both parties. To satisfy the constraints of causality, any description of the behaviour of the balls must have a piecewise flat-function behaviour at the moment of collision, with no valid Taylor expansion; similarly for the cam shaft that conveys the carry digit in a mechanical odometer, or the electrical wire that does the same in a binary counter. Even in the classical view, then, the constraint of causality still leads us to a type of measurement problem.

Abstraction and the modular black-box model

A balloon of helium gas travelling through space can be treated approximately as a single particle, with the constituent particles simply ascribed a mean position and velocity (relative to the external observer) with a standard deviation on each of these (related to the radius of the balloon, and the internal velocities of the individual helium atoms). The mean velocity describes the current (albeit more like a gust, in this case) and is used to calculate the energy that could be transferred by a collision with the face of a piston or inclined turbine blade. The internal velocities contribute to what we perceive as temperature (and are also capable of driving a Stirling engine or thermocouple if we find another balloon of gas at a different temperature). With quantum computing and particle physics, though, the gases are typically reduced to single particle interactions. Although there can be no standard deviation in a sample of one, we still find it convenient to aatribute one. The temperature of an alpha particle, for example, ought to represent the internal velocities of its constituent parts, or else to consider the velocity to be just a component of the temperature of a notional cloud of alpha particles being emitted by an alpha source. Instead, though, we take the internal velocity to be notionally the same as its external velocity, and to plug it in to the PV=nRT=E set of equations, with n set to 1/(6x1023). More sophisticated derivations include terms for the number of degrees of freedom [Born] but the qualitative result remains that the entropy of each individual particle stays constant, k in this case, and hence that all collisions are perfectly reversible, with no loss of information within the overall system.

After Shannon and Turing

The Shannon diagram describes what we do with our computer data over night (communication over time, in memory, or over space, conventional I/O) but it does not obviously describe what type of communication is involved when we are processing and editing during the day. Generalizing the noise input of the Shannon diagram to allow for intentional input, such as the G and H transform functions of simple processing [Moser], and also to be bi-directional, the Shannon diagram can be usefully adapted:

• Shannon information channel: InputSignal + Noise → OutputSignal
• Computing: DescriptionNumber + RewriteRules → ComputableNumber
• Kirchhoff's current law: ParticlesIn ± Leakage → ParticlesOut
• Carnot heat engine: InputEnergy → Work + WasteEnergy
• CNOT-gate computation: RawData → SortedData + DiscardedData

In the case of the third bullet, if the leakage passes to a capacitive component rather than to the normal resistive one, the leakage becomes temporary and reversible, as the leaked material goes into storage, to be retrieved later. When the material is composed of particles that are non-identifiable and interchangeable (such as electrons or water molecules) the capacitive device can be viewed as LIFO storage, and can be modeled like the side-pans of a canal lock (complete with all the implications of the speed of the water waves, or the speed of light in the capacitor dielectric).

A delay-line, such as a tube of mercury or a laser beam aimed at a reflector on the Moon, acts as a FIFO queue. The pipeline has a physical length, x, and must incur a time delay of at least x/c, but can be engineered to incur one that is greater than this, such as for the acoustic wave in the tube of mercury, or an electronic FIFO latched at a given clock rate, up to a limit that is set by the number of storage elements, N (where N:n is akin to the aspect ratio of the pallets of a high-speed moving-walkway). As soon as latency is introduced, so is memory, and Landauer's principle brings it all back to the second law of thermodynamics [Bennett].

Reverse-Sort

Writing computer programs involves Sort (as illustrated, for example, by a student in the 1970s sitting in a room of pre-prepared, commonly-used punched-cards). Similarly for program execution, information dissipation is the whole point of the program, sculpting away the superfluous information from the block of raw data, Michelangelo-like, to reveal the inner patterns. From the designer's perspective, a CNOT gate, unlike a NAND gate, does not dissipate information, but it does still sort information into that which is to remain visible to the user, and that which is considered discarded (the last bullet in the list, above). Indeed, none of the main organs of a computer (processing, memory, I/O) creates information, and processing is the most like the snooker balls dissipating information to the molecules of the air and baize.

Animals (at least from ants to humans) use the terrain as a common read/write area to leave information for each other. This is central in the AI blackboard architecture, the WWII ops-room table, document drafting, lean programming, and collaborative-working in today's networked office. Also seen in Lean programming in the 2000s, and project control at MSDS in 1976. Chance encounters between objects on a given blackboard/table lead to a whole that is equal to Σ(parts)+Δ. When Δ>0, the resonances within the new ensemble have led to new information that can be read from the new terrain (serendipity in the newly created context). Selectively bringing new combinations of things to the table, encouraging the opportunities for new experiences and conversations with new people, observing what others have not observed before (like Faraday, Lovell) or simply perceiving what others have not perceived before (like da Vinci) despite all have observed the same things. Meanwhile, when Δ<0, inconsistencies and clashes are present that need to be resolved.

The reverse of computer execution might, therefore, involve Reverse-Sort (albeit not reversing each step exactly, but merely returning to an equal level of unsortedness, having previously dissipated the information of the original). Reverse execution might explore arbitrary expansion of the execution tree, or the reverse of beta- or alpha-reduction [Curry] as tentative "what-if" fantasies [Hofstadter] that check if any have a Δ>0. Unlike evolutionary computing, though, the serendipity comes from the environment, with no internal random number generators.

Since computer execution and Sort are convergent processes, their reverse must be divergent, involving the breaking of symmetry, and thereby requiring extra bits of information to specify the extra initial conditions. Since information cannot be created, this information must be read from the terrain. A pencil balanced on its point, for example, acquires new boundary-condition information to specify in which direction it eventually (momentaneously, divergently) started to fall, before it locked in to that direction (convergently) and this information comes from the motion of the particles of the surrounding air, and vibrations in the table. So, the condensation of information (as a reverse of dissipation) leads to something like:

• InputStream + GleanedInformation → OutputStream

Unlike mountaineers, who do it "because it is there", human creative artists do it because they feel that the new structure ought to be there. This might even shed some light on what we mean, informally, by the word "will" (while noting, too, that "free will" is inevitably reading its information from the terrain of the current state of the subject's brain).

Need for a further law of thermodynamics

In its rush to transfer energy from the hotter parts to the cooler parts, the second law of thermodynamics leads to new structure being created. Convection currents, braid plains, deltas, and meanders are prime examples. We might even conclude that 'life' is on the same continuum as stable convection currents; DNA-based life in general, and gas-guzzling human culture in particular, are just the latest layers of convection current to have established themselves on one particular atmosphere-bearing rocky planet that is being heated on one side by its star.

Energy flows lead to a convergence on, and persistence of, those structures (NS, 18-Mar-2017, p11) as standing-waves in some abstract space. We are interested in how quickly each new equilibrium is established (NS, 29-Oct-2005, p51) noting, in particular, that evolution takes time (NS, 19-Dec-2020, p50; 18-Jun-2022, p43). For example, measures have been proposed for the amount of structure that is created for a given energy flow [Lloyd], or a measure of energy flow density, in ergs per gram per second (NS, 21-Jan-2012, p35).

Scientific method, the halting problem and 2nd law of thermodynamics

Bekenstein and Hawking showed the correspondence between entropy and the mass of a black-hole, each irreversibly increasing. Similarly, our confidence in a scientific theory monotonically increases towards 100% at each failed attempt to refute it (with this exponentially asymptotic parameter, in bulked cases, being characterized by a half-life of the assertion not having been refuted). As an illustration, an external observer, Bob, can never see astronaut Alice (or any other particle) crossing the event horizon of a black-hole, since the return signal becomes asymptotically red-shifted, and weak. He cannot rule out the possibility that she fired her ultra-powerful rockets at the very last moment, and can be settled in an instant (by noticing Alice re-emerging, perhaps decades or centuries later according to Bob's clock).

It was originally assumed that our brains analyze the incoming sensory signals, and attempt to build internal representations of ever-increasing complexity. However, it seems that it might be the other way round (NS, 08-Jun-2019, p38; NS, 09-Apr-2016, p42, and also p20) in which our brains build internal models to anticipate the sensory data, and refine those models using a feedback mechanism of 'prediction-error minimization' when they are wrong (NS, 04-Sep-2021, p44). What we call the scientific method might be what the human mind had been doing all along.

Similarly, the increasing feeling, with each passing minute, that a computer program has become caught in an endless loop, is resolved if the program does suddenly happen to halt. This suggests that the inverse theory, that a given program will always halt, cannot be a scientific theory, since it cannot be refuted. The Turing halting problem (THP) is, of course, what ultimately limits the syntactic pushing around of symbols and tokens (since there cannot be a set of rules that caters, in advance, for every possible future eventuality).

The distinction between necessary and sufficient is encountered in mathematical proofs, such as that of having a quadrilateral, and knowing that its two diagonals have the same length; and wondering if it can be concluded that it is a rectangle.

• Is this given property a necessary condition?
• Are there any rectangles that have diagonals whose lengths are not equal?
• Is this given property a sufficient condition?
• Are there any quadrilaterals whose diagonals are of equal length, but that are not classified as being rectangles? (This is the process of considering the thesis and its antithesis)

The questions in each of the white bullets carry a risk of being open-ended. Like the scientific method, the answer needs to be, "No," in every case that has been considered to date, but it only needs to be, "Yes," in just one case for the question to be refuted immediately.

The read-head that we call "Now"

With the Shannon diagram, the message (on the pages of a biographical or fictional book, or reel of celluloid film, or groove of a vinyl record) must pass under a read-head, just off to the right of the diagram. A similar current-position pointer manifests in a chain of reasoning, and in St. Augustin's distinction between the song and the sequence of notes, and in the parameterized equations for the orbit of Mars.

When a computation is not a simple linear process, such as the G and H transform or rewrite-rules suggested earlier, the steam locomotive read-head is placed on a message tape that can step in either direction (where the ± sign is because the term can appear on either side).

• TapeToTheLeft → TapeToTheRight ± ChangesToTheFSM

The THP then manifests because of the repeat and da capo annotation, as human shorthand for the loop unrolled version (or the human introduced difference, determined in advance, between call-by-reference and call-by-value). A feeling that the melody (or document) could have branched either way, and hence not knowing where it is going to veer next (allowed freely to create new structure).

Tools

Shannon's objective information carrier, and Turing's universal computable-numbers machine, move syntactic information from one place to another, with no regard for any underlying semantics [Hodges]. We can now contemplate some of the forms that a universal semantics machine might take.

But the semantics conveyed by a cam shaft, or a carry bit (mechanical or electronic) are very tightly constrained. Not just the wire carrying the carry bit, but each of the connectors of the transistors in a binary flip-flop. As noted earlier, there is no room for error or randmness in the settings of the bits on the Turing tape. The number of bits needed to express a given program is not just the size of the compiled code, but the specification of the instruction set, the central processor hardware, how the equipment of the silicon fab-line works, with the danger of an infinite regress into the entire contents of an encyclopedia. However, there is a diffference between the semantics of this tightly constrained engineering information, and the intentional, objective disregard for the semantics of the information that is being transported.

Table of contents:

1. What properties might the next machine-class have?
2. Building machines upon machines
3. Looking for workable definitions of some familiar terms
4. How might the next machine-class be built?
5. Principles of limitation
6. Taking stock

The above table of contents gives a top-down view. The problem with discussing the nature of consciousness, and also the various aspects of cosmology, relativity and quantum physics, is that we are trying to use natural language as a tool to tackle problems that it was never designed to tackle. As soon as we ask, for example, what it was like when there was nothing, we are automatically thinking of nothingness as a thing; but it is not; that is a logical error, and the cause of our misunderstanding; it is no-thing. Similarly, as soon as we ask what it was like before time, we are automatically thinking of events ticking away, to lead up to the start of time. Our brains, in general, and natural language, in particular, are not equipped for reasoning about these concepts intuitively. Given that humans have no choice but to use human brains as the tool, the only flexibility is not to use natural language. Mathematics is a far better tool in this respect, but by definition leaves us without intuition as a backup. Since quantum mechanics and relativity are both non-intuitive, either we need our intuitions be overridden by what the mathematics is telling us, or we need a new intuition, akin to those that Faraday introduced with his field lines, and to leave it to a later mathematician (Maxwell in his case) to firm up the foundations of that intuition later. So, from the bottom-up, there are several recurring themes based on generalisations of classically common-place principles:

• Comparative experiments, with Bob acting as the control for the experiment on Alice, or the consequences on Elinor and Marianne in "Sense and Sensibility". This leads into a generalised parallax effect, which is really just a comparison formed by the differences between the view from one place to that from another (dy/dx, as a measure of angle subtended at the observer), or from one moment in time to that a short duration later (dy/dt, as a measure of velocity, and as harnessed in something as simple as the Green Cross Code). The notion can be extended to include interpolation between long base-line observations: such as in the two so-called twins paradoxes of special and general relativity.
• Generalised Kirchhoff's voltage (symmetry) and current (conservation) laws: along with notions of latency and throughput of pipelines (and canal systems), and along with the notion of displacement current
• Generalised half-life: via the binomial and Poisson distrubutions, and even with de Morgan's theorem applied to probabilities.
• The selective (symmetry-breaking) properties of resonnance, filters, and generalised standing-waves.

Feynman remarked on the unreasonable effectiveness of mathematics to describe the behaviour of the universe, but here we find one subtle difference. Starting from the natural numbers, mathematics considers addition as a primary operation, and subtraction merely as its inferred inverse. The expansion of spacetime is not due to the expansion of space and time, since these are not physical objects, but the elongation of distance between previously nearby masses, and duration between events. Meanwhile, our physical equations are never concerned with absolute energy content, or absolute amount of entropy, but with the changes brought about to these quantities during an interaction. Distance and duration, and differential changes in other parameters, are what we think of as subtractive operations, and are primarhy; their inverses, the additive operations with respect to some notional absolute reference point, are merely inferred from these.

The first step in the scientific method is to collect observational data, and the second step is to seek invarient properties within those data. That is, to look for the inherent symmetries. A generalised parallax effect is obtained when an operation is found that breaks a symmetry, and allows the differences between the two view-points to be quantified.

Newton-Raphson's method illustrates how, though a bad initial guess is obviously worse than a good initial guess, it is still infinitely better than having made no guess at all, and breaks the initial symmetry. This appears in document writing, and the need to jot down ideas as they arise, regardless of how tenuous they are, and certainly with no immediate concerns for the details, such as grammar and spelling. This leads on to the notion of a self-writing thesis (or other document or story). The way that Faraday carried around a coil and a magnet in his pocket, hoping to trigger an intuitive view on how to connect them.

Submitting these pages to the world-wide web, where they are publically visible, encourages the author to maintain a certain level of presentability, whilst at the same time feeling safe that these pages probably only have a readership of one. At the lower level of themes running through these pages, images from past experiences also include:

• Rivers flowing down a sandy beach (such as the one in Porthcothan), and the way that it all ties in with Shannon and Carnot
• Viewing quantum field theory as hundreds of natural processes, called Alice, sending signals that are inadvertantly being picked up by other natural processes, called Bob, via hydrophone transducers across a large expanse of water (such as Southampton Water). Some of these are intercepted by a scientist, Eve, making observations and probings from her laboaratory (on a navigation buoy called Hythe Knock, or the bow of a ferry called Hotspur III). Notably, the interception by Eve's scientific apparatus is doing nothing different to what the interception by the natural process at Bob and Alice would have done. Likewise, an in-coming water wave can be observed by the sandy beach, even when there is no consciousness present.
• Taking the parallax effect even to the extreme of seeking Bragg-like analysis (Bragg-inspired) being applied to the natural numbers times-tables mapped out on a chess board.

Scratchpad blackboard area

Judging by the exponential rate of development of technology, the next revolutionary enabling technology might not be far off, and might already be nascent. There are many potential candidate projects to choose from, but most, despite the revolutionary claims by their backers, are really just cases of "more of the same". To our human-centric minds, the emergence of consciousness does seem particularly important, and might occur at some threshold of complexity [Hofstadter]. Latching on to this as the next revolutionary technology is just speculative, of course: just one possibility, based on a "thimble-full of base-cases" [Kurzell]; and there are many reasons why such an inductive process should not even be possible (NS, 01-Jul-2006, p50).

Since man is capable of conscious thought, despite being built on biochemical machinery so, too, ought other machines, if constructed in the right way.

Even pathological cases, such as phantom limbs, hallucinations and tinnitus are explained as by-products of what a correctly working brain does in the absence of sufficient sensory input (NS, 05-Nov-2016, p28). In this view, multiple internally-generated hypotheses compete with each other, with the most probable one becoming tagged as the one that will be considered to be our perception [Dennett], which lends support to the idea of the conscious mind being a self-writing story. Indeed, we note the way that text is repeatedly shuffled around a document during the drafting process. For example, I consider the paper to be having a conversation with me, its author, and that the reason that it is somewhat unfocussed in its lines of argument is that it is still thinking these through. When (if) it finally settles on a concrete conclusion, its astounding new results will be presentable at a conference, but the paper will then become static, and no longer conversing with its author.

The stochastic processes in evolutionary computing (such as genetic algorithms, simulated annealing, and artificial neural nets) do seem related to the way that stories acquire new, spontaneous, information each time they are imperfectly retold [Dawkins].

It might be tempting to wonder on a connection with Schopenhauer's "The World as Will and Representation" but this is not pursued further, here.

The reverse of beta- or alpha-reduction [Curry] might lead to the number of sides of a hexagon being "factorial(3)" or "the number of balls in a cricket over", or to even more spurious examples, can be explored. Here, then, is the selection gradient that follows up the mutations, crossings-over and sorting/reverse-sorting on the various tables/blackboards.

For evolutionary systems, the training data (or the fitness function) is applying the top-down influence, and the annealing temperature is providing the bottom-up manipulations. They also defend against other organisms that trespass on their extended phenotype [Dawkins].

Living through the events of the day, the assumption is that the loops (go to bed / get up, breath in / breath out) will iterate indefinitely, and it is only the wearing out of the external hardware that stands in the way of this happening.

From queuing theory, if all N resources are presently engaged by tasks, chopping each one into sub-tasks adds extra administrative overhead, as opposed to pursuing each task to its completion, thereby impacting the throughput, but at the cost of increasing the worst-case latency, and hence the range of latencies. The processing the tasks becomes grainy along the time line, in a similar way to VLB telescopes being grainy along the line of special resolution, and also along the time line if observations are taken once per month (say).

If n of the storage elements is presently engaged, and N is the maximum storage capacity, the occupancy, n/N, is an analogue to voltage (since Q=C.V would be analog to n=N.occupancy).

The N-body problem was mentioned earlier, too, as applying both to quantum physics and gravity, and is notorious for its chaotically unpredictable behaviour in the long-term (NS).

It cannot be random, though, just as the back-and-forth motion of the steam-engine Turing machine was extremely tightly specified, despite appearing haphazard to a casual onlooker, with even the slightest noise, or deviation from what was specified, leading to the whole computation failing. Noise leads to complete collapse of the pattern on Lovelace's Jacquard loom.

Perfect reversibility is not possible for a Carnot engine, and can only be approached in the limit of a machine that works infinitesimally slowly. The Carnot cycle involves energy transfer, and takes infinitely long to complete as the temperature differential approaches zero, and involves gain in entropy otherwise because bulk behavior, in fuel and exhaust gases, is involved, in which information is intentionally overlooked. Similarly, a perfectly isolated thermodynamic system is impossible, or at least, would go unnoticed by us if it ever did exist (as soon as we are interested in obtaining data from a closed system, it ceases to be a closed system). In computing, entropy must increase as the stuff that encodes that information is shifted from over here to over there (though perhaps spring-loaded, so that that energy can be recuperated in the reverse operation). Getting a project implemented must involve activity, as remarked by Hodges 1992, p422 as a point that Turing personally failed to take into account.

Acknowledgements

Acknowledgements.