Johannes Kleiner's Great Slide on Representing Phenomenology Mathematically

Published April 24, 2020, Page Last Modified May 22, 2023

A few weeks ago, I discovered Johannes Kleiner (a). He seems great! He organizes interesting scientific gatherings (a) like workshops and conferences about modeling consciousness as well as workshops on rethinking foundational physics.

While I haven’t fully dived into his research yet (though I plan on first checking out Mathematical Models of Consciousnsess (a) and Falsification and consciousness (a)), I did watch a presentation (a) of his recently and wow, what a wonderful powerpoint slide:

A photo of a man behind a podium in front of a presentation slide of text.

In case you can’t read what’s on the image, it says:

How to respresent [consciousness] mathematically?

Phenomenological facts:

  • Qualia can be recognized → Introduce set of labels
  • Qualia have collectable relations → Represent on set → Space of labels L

    Chalmers(1996): “Even if experiences are in some sense ‘ineffable,’ relations between experiences are not; we have no trouble discussing these relations, whether they be relations of similarity and difference, geometric relations, relations of intensity, and so on.”

    Nagel(1974): “Structural features of perception might be more accessible to objective description”

  • Examples: (Prentner 2019, Resende 2019)
    • Binary similarity relation → (Pre-)Topological structure on set of labels
    • Composition of qualia → Partial order on set of labels

I love this slide because people like Johannes (and those mentioned on his slide) are thinking really hard about turning subjective experience into objective mathematical objects we can talk about!

One way to do this (binary similarity relation) is to ask people:

‘is the experience of feeling warm similar or not similar to the experience of the scent of lemon?’.

You can ask a million of these questions!

‘Is the experience of blue similar or not similar to the experience of purple?’

And then you can build a giant graph that represents all of the relationships between all the labels people use to talk about their experience. From there, you can just throw away all the labels people use to talk about their experience and just study the structure of this graph using graph theory / topology. Is it similar from person to person? What is its overall shape?

A second way to add structure (partial order on set of labels) is if people connect different experiences that are hard to describe:

Suppose someone has two experiences that are ‘ineffable’. NO WORDS CAN DESCRIBE WHAT EACH EXPERIENCE WAS LIKE! What can we do?

Well we can still pull a similar move: “An experiencing subject may find that the ineffable aspect of an experience he/she is having at a particular time includes an ineffable aspect he/she has had at another time. In this case, we may say that the former quale includes the latter quale” (Kleiner, Models of Consciousness).

It’s like if someone was experiencing some new drug XYC and said “Wow, I literally cannot describe this feeling, but part of it is like the way I felt when taking drug ABC!” That’s still really valuable information.

These two examples of adding order to subjectivity are great.

Andrés Gómez Emilsson also came up with a method (a) to create a directed network that represents subjective preferences of conscious states—not only creating order out of consciousness, but also leaving a very important clue for any serious theory of ethics.

If you’d like to think more about these topics, Johannes Kleiner is organizing an online seminar series “exploring the role of mathematics in the scientific study of consciousness” called Mathematical Consciousness Science (a). I’ll be attending some of the talks. Maybe I’ll see you there ;)


Zuckerman, Andrew, "Johannes Kleiner's Great Slide on Representing Phenomenology Mathematically", April 24, 2020,


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