"Computability" is almost always conflated with Rissanen's statistical notion of minimum description length even though, by definition, it is not recurrent, which your definition is. Just replace Kolmogorov Complexity with its algorithmic approximation using program search as Solomonoff described in his original papers. You don't even need Levin. Solomonoff addressed the 60 years of nonsense that people have used to dismiss his theory in his original papers -- they were just too busy playing with SPSS <https://en.wikipedia.org/wiki/SPSS> and publishing "social science narratives" to let rigorous notions of causality interfere.
No measurement instrument is perfect and its *operation* is the essence of experimental protocol. On Sun, Oct 18, 2026 at 5:46 PM Matt Mahoney <[email protected]> wrote: > For an operational definition of consciousness, I would use the memory > capacity of the agent as an upper bound. For the lower bound I could use > Wolfram's 2 state 3 symbol Turing machine as the simplest known machine, > but it is extremely difficult to program in practice. The input sometimes > has to be an infinitely repeating pattern. A better choice would be a > language like C because it's well known or brainfuck because it's simple. > But Kolmogorov complexity is not computable regardless of language, so it > doesn't matter. > > A formal or operational definition of consciousness is mostly useful (or > useless) for philosophical arguments like whether animals or computers or > atoms are conscious. > > > -- Matt Mahoney, [email protected] > > On Sun, Oct 18, 2026, 1:04 PM James Bowery <[email protected]> wrote: > >> Of course I wholeheartedly agree that choice of UTM isn't the bugaboo >> that the pedantic twits make it out to be. Only it does matter in going >> from formal to operational definitions because the operations of the UTM >> are otherwise undefined. >> >> Presumably you would want some way of actually measuring the bits in what >> we refer to as "reality". Nor do I suggest that you should abide by my >> answer to said pedantic twits (NiNOR Complexity) since that answer is at >> the same level of pedant discourse as is their "critique" of Kolmogorov >> Complexity as information criterion for causal model selection. That said, >> you are, of course, free to ignore my question regarding UTM as it is >> deferrable until such time as you wish to measure your definition of >> consciousness. >> >> On Sat, Oct 17, 2026 at 3:13 PM Matt Mahoney <[email protected]> >> wrote: >> >>> I'm defining formal consciousness. For operational consciousness we just >>> need to distinguish between neurological consciousness (being awake), >>> subjective consciousness (not a zombie) and moral consciousness (can suffer >>> and we should prevent it). My definition is closest to the first type >>> because it has a physical explanation and is observable. The others are >>> just opinions. I don't need to redefine them. >>> >>> I'm looking for criticisms and alternate suggestions for my formal >>> definition. >>> >>> We can measure consciousness as the rate of conscious experience in bits >>> per second. But it depends on the interval. In general, K(S3|S1) ≤ K(S2|S1) >>> + K(S3|S2) because of forgetting. The rate is lower over longer intervals. >>> In humans it's like 10 bits per second over 1 minute or 1 bit per second >>> over a year. >>> >>> I don't define a UTM because Kolmogorov's proof of UTM independence >>> still applies. In practice it is still useful even though Kolmogorov >>> complexity is not computable regardless of UTM. >>> >>> -- Matt Mahoney, [email protected] >>> >>> On Sat, Oct 17, 2026, 3:08 PM James Bowery <[email protected]> wrote: >>> >>>> "But feel free to offer an alternative definition." >>>> >>>> Presumably you are: >>>> >>>> 1) drawing a distinction between operational and formal definitions >>>> and/or >>>> 2) inviting others to contribute their might-be-hated definitions. >>>> >>>> BTW, I don't hate your formal definition but I'm curious how you >>>> propose to select the UTM. I'm also going to presume that by >>>> "consciousness" you mean the recurrent generation of "bits of conscious >>>> experience" as you forward chain K(S2|S1) to K(S3|S2), etc. >>>> >>>> On Sat, Oct 17, 2026 at 1:17 PM Matt Mahoney <[email protected]> >>>> wrote: >>>> >>>>> Like Shane Legg did for intelligence, I offer a formal definition of >>>>> consciousness. I define the number of bits of conscious experience by an >>>>> agent in going from state S1 to S2 as K(S2|S1), where K is conditional >>>>> Kolmogorov complexity, the length of the shortest program that outputs a >>>>> description of S2 given S1 as input. >>>>> >>>>> This agrees with our intuitive definition of consciousness. Inanimate >>>>> objects with no memory are not conscious. Plants are not conscious. >>>>> Animals >>>>> with large brains have more conscious experience than animals with small >>>>> brains. Accumulated conscious experience increases over time. You have no >>>>> conscious experience of anything you don't remember. >>>>> >>>>> You can hate my definition but you have to accept the fact that I have >>>>> defined it. >>>>> >>>>> Why might you hate it. Because: >>>>> 1. There is no distinction between positive and negative >>>>> reinforcement. Both result in a change in behavior that can be measured in >>>>> bits. >>>>> 2. Computers are conscious. When you download a 1 GB text file, the >>>>> computer has as much conscious experience as you do in a lifetime. >>>>> 3. Your total conscious experience since birth after you die is 0. >>>>> 4. Consciousness does not require or imply paranormal perception. >>>>> >>>>> But feel free to offer an alternative definition. >>>>> >>>>> -- Matt Mahoney, [email protected] >>>>> >>>>> On Sat, Oct 17, 2026, 11:23 AM James Bowery <[email protected]> >>>>> wrote: >>>>> >>>>>> >>>>>> >>>>>> On Fri, Oct 16, 2026 at 6:49 PM Matt Mahoney <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> >>>>>>> ... >>>>>>> >>>>>>> Anyway, it is not clear to me why you would define consciousness >>>>>>> this way. What purpose does it serve? >>>>>>> >>>>>> >>>>>> To quote Shane Legg's Singularity Summit presentation on measures of >>>>>> machine intelligence: >>>>>> >>>>>> https://youtu.be/0ghzG14dT-w?t=1155 >>>>>> >>>>>> "I've given you an equation that even if you HATE my definition, you >>>>>> have to accept the fact that I've actually defined it formally and said >>>>>> exactly what I mean. I think that's a very good start. At least we can >>>>>> argue on that basis." (applause) >>>>>> >>>>>> Use "operationally" in place of "formally", and accept that Ed May >>>>>> hasn't been a PhD advisor to anyone like Shane Legg who could write a >>>>>> thesis that would undoubtedly survey "definitions" of "consciousness" >>>>>> much >>>>>> better than anyone heretofore has bothered with, thence to provide a >>>>>> taxonomy of such definitions into which something like the operational >>>>>> definition I've proposed can reside and maybe we can start to have a >>>>>> collegial discourse. >>>>>> >>>>>> As to the "purpose" such an operational definition might serve, how >>>>>> about this: >>>>>> >>>>>> Finding a place for the very concept of "purpose" itself in our >>>>>> discourse, in that the so-called "time-reversibility" of the laws of >>>>>> physics may embody what the Greeks called "Telos" for "final cause" -- >>>>>> rather than the folks endlessly yammering about "AI Alignment" are, >>>>>> themselves, "conscious" of at present. >>>>>> >>>>>> >>>>>> https://web.archive.org/web/20150925072222/http://www.boundaryinstitute.org/bi/EtterPubs.htm >>>>>> >>>>>> Etter was the colleague I mentioned previously who also arrived early >>>>>> with Solomonoff at the 1956 Dartmouth summer workshop, but because his >>>>>> family was independently wealthy, never had to genuflect to what Pirsig >>>>>> called "The Church of Reason" and its travesty of Newton's yeoman farmer >>>>>> homestead with The Church's "tenure" as the path to independent thought >>>>>> as >>>>>> the foundation of scientific revolutions -- independent thought once >>>>>> you'd >>>>>> been brainwashed and effectively castrated. >>>>>> >>>>>> >>>>>> *Artificial General Intelligence List > <https://agi.topicbox.com/latest>* / AGI / see discussions > <https://agi.topicbox.com/groups/agi> + participants > <https://agi.topicbox.com/groups/agi/members> + delivery options > <https://agi.topicbox.com/groups/agi/subscription> Permalink > <https://agi.topicbox.com/groups/agi/T2784bbfe524b0b93-M24a80fd69f50366775248751> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T2784bbfe524b0b93-M7c82040a2a457eab9623279c Delivery options: https://agi.topicbox.com/groups/agi/subscription
