Question: Do you know of any resources for mathematical models of awareness, consciousness, and unconsciousness?

I am doing some work relating pure mathematics (among other things) to ideas of the conscious and unconscious. As of so far the only work that I am aware of other than my advisor is Matte Blanco's which is astronomically interesting! I am working out a model myself but am very weak in the psychological modeling concerning the conscious and unconscious. Blanco majorly advances some of Freuds ideas he attempts to embed his own ideas on a "logico-matematico" foundation and I am looking for other works trying to relate the subject matter.

I am also aware and incorporating ideas by Andrei Khrennikov but trying to advance more of a Categorical and Homological approach.

I apologize if this question is not an exact fit but the "consciousness" tag is for this room.

Thanks for any leads and/or thoughts.


  • You might consider investigating Lacan, who advocates a kind of topological model of desire/the unconscious (in particular the graphs of sexuation in Seminar XX seem possibly interesting here)
    – Joseph Weissman
    Jan 18, 2014 at 14:51
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    Terms like "psychological modeling" should immediately give one pause. Psychology is far from as exact as one would need to be for modeling to deliver much insight. The value of equations like E=mc^2 is that they are not just analogies but astoundingly precise descriptors of relations than can be observed. At the level of psychology it is a challenge to demonstrate that something is even a good analogy.
    – Rex Kerr
    Jan 19, 2014 at 19:49

1 Answer 1


I disagree with the comment made by Joseph Weismann. Lacan's topology is far away of mathematical topology and of having the formality required to be trated as a mathematical model, he did not develop a topological model of anything at all, but rather a new usage of mathematical concepts embodied with Lacan's own meaning and analogies to the related field that he did not quite understand.

A formal formal model for what you want will be unlikely to find, but a close one I know of would be a paper published six years ago by Miranker and Zuckerman entitled "Mathematical Foundations of consciousness".

You could also take a look to some of the papers of Koch that, even if they lack of formality -most of the time there is no mathematical formality at all-, he usually relates the topic of consciousness with mathematics; there is a TED talk entitled "The neurobiology and mathematics of consciousness" that you may want to give a look.

And the last I think you definitely read is the integrated information theory developed by Tononi since 1994. Here you may find a more formal approach, stating also a formula for consciousness given by

enter image description here

It should be understood basically, as a way to determine the integrated information an entity possesses, determining then the level of consciousness. That's how the previously mentioned Koch describes it on his paper "A theory for consciousness".

If you're interested in the latter approach a good introduction could be "Consciousness as integrated information" by Peressini.

Not entirely related to what you want, lately I've seen papers about the Gettier Problem coming really close to psychology and giving also formal models of concepts related that may come useful for your research (an example of this may be The Topology of Belief or The Topology of Common Belief).

  • It's fine to have a dissenting opinion, or not to like a thinker -- but do you have a specific claim about Lacan's graphs or models? (I.e., something particular he "misunderstands", based on a reading of his work or secondary sources?) It seems a somewhat vague and hand-waving dismissal as currently formulated -- which of course on SE we should try to be wary of...
    – Joseph Weissman
    Jan 18, 2014 at 18:30
  • @JosephWeissman - How about that it's gibberish, except possibly when you take every term as he defines it not as it would typically be used, which kind of defeats the point of using mathematical terminology? (And then you can't manipulate it symbolically or quantitatively, and the message is nonsense, biologically?)
    – Rex Kerr
    Jan 19, 2014 at 20:07
  • @Rex So I'm not sure it's entirely constructive to attempt to recapitulate an entire debate here, or on these terms; again however I'm tempted to ask whether there might be a specific point you feel was misunderstood? Again, I'm not trying to stake a claim here -- I'm only asking after specific citations or references that might indicate some minimal attempt to actually engage with the material (what doesn't seem suitable for SE to me is blanket dismissal based on a refusal to read...)
    – Joseph Weissman
    Jan 19, 2014 at 21:37
  • @JosephWeissman - Well, let's start with his most famous sexuation graph. exists(x: !ph(x)) forall(x: ph(x)). This is a contradiction. What is ph? A "phallic function", which has something to do with castration, which has something to do with being male, despite the fact that hysterectomy is perfectly possible. So right off the bat we've got wrongly used logical formalism, ill-explained linkages, and terminology that doesn't match up with biological reality. This might make for interesting conversation over coffee, but for a quantifiable logical framework? I think not.
    – Rex Kerr
    Jan 19, 2014 at 22:05
  • @RexKerr Alright, that's specific anyway :) Just in passing, note that Lacan re-contextualizes Freudian psychoanalysis in a somewhat non-biological context (so the frustration about placing hysterectomy patients in this context might potentially be somewhat misplaced.) --At any rate, all that I think I am trying to suggest here is that it doesn't strike me as appropriate to reject the models of an important psychoanalyst without grounding the rejection in some minimal way in the work itself...
    – Joseph Weissman
    Jan 19, 2014 at 22:10

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