“Conscious realism”: a new way to think about reality (or the lack thereof?)


Interesting interview in the Atlantic with cognitive scientist Donald D. Hoffman:

The Case Against Reality

“I call it conscious realism: Objective reality is just conscious agents, just points of view. Interestingly, I can take two conscious agents and have them interact, and the mathematical structure of that interaction also satisfies the definition of a conscious agent. This mathematics is telling me something. I can take two minds, and they can generate a new, unified single mind. Here’s a concrete example. We have two hemispheres in our brain. But when you do a split-brain operation, a complete transection of the corpus callosum, you get clear evidence of two separate consciousnesses. Before that slicing happened, it seemed there was a single unified consciousness. So it’s not implausible that there is a single conscious agent. And yet it’s also the case that there are two conscious agents there, and you can see that when they’re split. I didn’t expect that, the mathematics forced me to recognize this. It suggests that I can take separate observers, put them together and create new observers, and keep doing this ad infinitum. It’s conscious agents all the way down.”


Here’s the striking thing about that. I can pull the W out of the model and stick a conscious agent in its place and get a circuit of conscious agents. In fact, you can have whole networks of arbitrary complexity. And that’s the world.


“As a conscious realist, I am postulating conscious experiences as ontological primitives, the most basic ingredients of the world. I’m claiming that experiences are the real coin of the realm. The experiences of everyday life—my real feeling of a headache, my real taste of chocolate—that really is the ultimate nature of reality.”

I don’t agree with everything in the article (especially the quantum stuff) but I think many people interested in consciousness and metaphysics will find plenty of food for thought here:

The Case Against Reality

Also, the “conscious agents all the way down” is the exact position I was criticizing in a recent 3QD essay:

3quarksdaily: Persons all the way down: On viewing the scientific conception of the self from the inside out

The diagram above is from a science fiction story I was working on, back when I was a callow youth. It closely related to the idea of a network of conscious agents. Here’s another ‘version’ of it.


Not sure why I made it look so morbid. 🙂

Perception is a creative act: On the connection between creativity and pattern recognition

An answer I wrote to the Quora question Does the human brain work solely by pattern recognition?:

Great question! Broadly speaking, the brain does two things: it processes ‘inputs’ from the world and from the body, and generates ‘outputs’ to the muscles and internal organs.

Pattern recognition shows up most clearly during the processing of inputs. Recognition allows us to navigate the world, seeking beneficial/pleasurable experiences and avoiding harmful/negative experiences.* So pattern recognition must also be supplemented by associative learning: humans and animals must learn how patterns relate to each other, and to their positive and negative consequences.

And patterns must not simply be recognized: they must also be categorized. We are bombarded by patterns all the time. The only way to make sense of them is to categorize them into classes that can all be treated similarly. We have one big category for ‘snake’, even though the sensory patterns produced by specific snakes can be quite different. Pattern recognition and classification are closely intertwined, so in what follows I’m really talking about both.

Creativity does have a connection with pattern recognition. One of the most complex and fascinating manifestations of pattern recognition is the process of analogy and metaphor. People often draw analogies between seemingly disparate topics: this requires creative use of the faculty of pattern recognition. Flexible intelligence depends on the ability to recognize patterns of similarity between phenomena. This is a particularly useful skill for scientists, teachers, artists, writers, poets and public thinkers, but it shows up all over the place. Many internet memes, for example, involve drawing analogies: seeing the structural connections between unrelated things.

One of my favourites is a meme on twitter called #sameguy. It started as a game of uploading pictures of two celebrities that resemble each other, followed by the hashtag #sameguy. But it evolved to include abstract ideas and phenomena that are the “same” in some respect. Making cultural metaphors like this requires creativity, as does understanding them. One has to free one’s mind of literal-mindedness in order to temporarily ignore the ever-present differences between things and focus on the similarities.

Here’s a blog that collects #sameguy submissions: Same Guy

On twitter you sometimes come across more imaginative, analogical #sameguy posts: #sameguy – Twitter Search

The topic of metaphor and analogy is one of the most fascinating aspects of intelligence, in my opinion. I think it’s far more important that coming up with theories about ‘consciousness’. 🙂 Check out this answer:

Why are metaphors and allusions used while writing?
(This Quora answer is a cross-post of a blog post I wrote: Metaphor: the Alchemy of Thought)

In one sense metaphor and analogy are central to scientific research. I’ve written about this here:

What are some of the most important problems in computational neuroscience?

Science: the Quest for Symmetry

This essay is tangentially related to the topic of creativity and patterns:

From Cell Membranes to Computational Aesthetics: On the Importance of Boundaries in Life and Art

* The brain’s outputs — commands to muscles and glands — are closely  linked with pattern recognition too. What you choose to do depends on  what you can do given your intentions, circumstances, and bodily  configuration. The state that you and the universe happen to be in  constrains what you can do, and so it is useful for the brain to  recognize and categorize the state in order to mediate decision-making,  or even non-conscious behavior.When you’re walking on a busy street, you rapidly process pathways that are available to you. even if you stumble, you can quickly and unconsciously act to minimize damage to yourself and others. Abilities of this sort suggest that pattern recognition is not purely a way to create am ‘image’ of the world, but also a central part of our ability to navigate it.

Does the human brain work solely by pattern recognition?

The holy grail of computational neuroscience: Invariance

There are quite a few problems that computational neuroscientists need to solve in order to achieve a true theoretical understanding of biological intelligence.  But I’d like to talk about one problem that I think is the holy grail of computational neuroscience and artificial intelligence: the quest for invariance. From a purely scientific and technological perspective I think this is a far more important and interesting problem than anything to do with the “C-word”: Consciousness. 🙂

Human (and animal) perception has an extraordinary feature that we still can’t fully emulate with artificial devices. Our brains somehow create and/or discover invariances in the world. Let me start with a few examples and then explain what invariance is.

Invariance in vision

Think about squares. You can recognize a square irrespective of it’s size, color, and position. You can even recognize a square with reasonable accuracy when viewing it from an oblique angle. This ability is something we take for granted, but we haven’t really figured it out yet.

Now think about human faces. You can recognize a familiar face in various lighting conditions, and under changes of facial hair, make-up, age, and context. How does the brain allow you to do things like this?

Invariance in hearing

Think about a musical tune you know well. You will probably be able to recognize it even if it is slowed down, sped up, hummed, whistled, or even sung wordlessly by someone who is tone-deaf. In some special cases, you can even recognize a piece of music from its rhythmic pattern alone, without any melody. How do you manage to do this?

Think about octave equivalence. A sound at a particular frequency sounds like the same note as a sound at double the frequency. In other words, notes an octave apart sound similar. What is happening here?

What is invariance?

How does your brain discover similarity in the midst of so much dissimilarity? The answer is that the brain somehow creates invariant representations of objects and patterns. Many computational neuroscientists are working on this problem, but there are no unifying theoretical frameworks yet.

So what does “invariance” mean? It means “immunity to a possible change”. It’s related to the formal concept of symmetry. According to mathematics and theoretical physics, an object has a symmetry if it looks the same even after a change. a square looks exactly the same if you rotate it by 90 degrees around the center. We say it is invariant (or symmetrical) with respect to a 90 degree rotation.

Our neural representations of sensory patterns somehow allow us to discover symmetries and using them for recognition and flexible behavior. And we manage to do this implicitly, without any conscious effort. This type of ability is limited and it varies from person to person, but all people have it to some extent.

Back to the examples

We can redefine our examples using the language of invariance.


  • The way human represent squares and other shapes is invariant with respect to rotation, as well as with respect to changes in position, lighting, and even viewing angle.
  • The way humans represent faces is invariant with respect to changes in make-up, facial hair, context, and age. (This ability varies from person to person, of course.)
  • The way humans represent musical tunes is invariant with respect to changes in speed, musical key, and timbre.
  • The way humans represent musical notes is invariant with respect to doubling of frequency ( which is equivalent to shifting by an octave.)

All these invariances are partial and limited in scope, but they are still extremely useful, and far more sophisticated than anything we can do with artificial systems.

Invariance of thought patterns?

The power of invariance is particularly striking when we enter the domain of abstract ideas — particularly metaphors and analogies.

Consider perceptual metaphors. We can touch a surface and describe it as smooth. But we can also use the word “smooth” to describe sounds. How is it that we can use texture words for things that we do not literally touch?

Now consider analogies, which are the more formal cousins of metaphors. Think of analogy questions in tests like the GRE and the SATs. Here’s an example

Army: Soldier :: Navy : _____

The answer is “Sailor”.

These questions take the form “A:B::C:D”, which we normally read as “A is to B as C is to D”. The test questions normally ask you to specify what D should be.

To make an analogy more explicit, we can re-write it this way: “R(x,y) for all (x,y) =  (A,B) or (C,D)”.  The relation “R” holds for pairs of words (x,y), and in particular, for pairs (A,B) as well as (C,D).

In this example, the analogical relationship R can be captured in the phrase “is made up of”. An army is made up of soldiers and a navy is made up of sailors. In any analogy, we are able to pick out an abstract relationship between things or concepts.

Here’s another example discussed in the Wikipedia page on analogy:

Hand: Palm :: Foot: _____

The answer most people give is “Sole”. What’s interesting about this example is that many people can understand the analogy without necessarily being able to explain the relationship R in words. This is true of various analogies. We can see implicit relationships without necessarily being able to describe them.

We can translate metaphors and analogies into the language or invariance.


  • The way humans represent perceptual experiences allows us to create metaphors that are invariant with respect to changes in sensory modality. So we can perceive smoothness in the modalities of touch, hearing and other senses.
  • The way humans represent abstract relationships allows us to find/create analogies that are invariant with respect to the particular things being spoken about. The validity of the analogy R(x,y) in invariant with respect to replacing the pair (x,y) with (A,B) or (C,D).

The words “metaphor” and “analogy” are essentially synonyms for the word “invariant” in the domains of percepts and concepts. Science, mathematics and philosophy often involve trying to make explicit our implicit analogies and metaphors.

Neuroscience, psychology and cognitive science aim to understand how we form these invariant representations in the first place. In my opinion doing so will revolutionize artificial intelligence.


Further reading:

I’ve only scratched the surface of the topic of invariance and symmetry.

I talk about symmetry and invariance in this answer too:

Mathematics: What are some small but effective theses or ideas in mathematics that you have came across? [Quora link. Sign-up required]

I talk about the importance of metaphors in this blog post:

Metaphor: the Alchemy of Thought

I was introduced to many of these ideas through a book by physicist Joe Rosen called Symmetry Rules: How Science and Nature Are Founded on Symmetry. It’s closer to a textbook that a popular treatment, but for people interested in the mathematics of symmetry and group theory, and how it relates to science, this is an excellent introduction. Here is a summary of the book: [pdf]

Relatively recent techniques such as deep learning have helped artificial systems form invariant representations. This is how facial recognition software used by Google and Facebook work. But these algorithms still don’t have the accuracy and generality of human skills, and the way they work, despite being inspired by real neural networks, is sufficiently unlike real neural processes that these algorithms may not shed much light on how human intelligence works.



This post is a slightly edited form of a Quora answer I wrote recently.

In the comments section someone brought up the idea that some invariants can be easily extracted using Fourier decomposition. This is what I said is response:

Good point. Fourier decomposition is definitely part of the story (for sound at the very least), but it seems there is a lot more.

Some people think that the auditory system is just doing a Fourier transform. But this was actually shown to be partially false a century ago. The idea that pitch corresponds to the frequencies of sinusoids is called Ohm’s acoustic law.

From the wiki page:


For years musicians have been told that the ear is able to separate  any complex signal into a series of sinusoidal signals – that it acts as  a Fourier analyzer.  This quarter-truth, known as Ohm’s Other Law, has served to increase  the distrust with which perceptive musicians regard scientists, since it  is readily apparent to them that the ear acts in this way only under  very restricted conditions.
—W. Dixon Ward (1970)

This web page discusses some of the dimensions other that frequency that contribute to pitch:

Introduction to Psychoacoustics – Module 05

There are interesting aspects of pitch perception that render the Fourier picture problematic. For example, there is the Phenomenon of the missing    fundamental: “the observation that the pitch of a complex harmonic tone matches  the frequency of its fundamental spectral component, even if this component is  missing from the tone’s spectrum.”

Evidence suggests that the human auditory system uses both frequency and time/phase coding.

Missing fundamental:  “The brain perceives the pitch of a tone not only by its fundamental frequency, but also by the periodicity of the waveform; we may perceive the same pitch (perhaps with a different timbre) even if the fundamental frequency is missing from a tone.”

This book chapter also covers some of the evidence: [pdf]

” One of the most remarkable properties of the human auditory system is its ability to extract pitch from complex tones. If a group of pure tones, equally spaced in freque ncy are presented together, a pitch corresponding to the common frequency distance between the individual components will be heard. For example, if the pure tones with frequencies of 700, 800, and 900 Hz ar e presented together, the result is a complex sound with an underlying pitch corresponding to that of a 100 Hz tone. Since there is no physical energy at the frequency of 100 Hz in the complex, such a pitch sensation is called residual pitch or virtual pitch (Schouten 1940; Schouten, Ritsma and Cardozo, 1961). Licklider (1954) demonstrated that both the plac e (spectral) pitch and the residual (virtual) pitch have the same properties and cannot be auditorally differentiated.”

The status of Fourier decomposition in vision might be more controversial. Spatial frequency based models have their adherents, but also plenty of critics. One of my professors says that claiming the visual system does spatial Fourier amounts to confusing the object of study with the tools of study. 🙂 We still don’t whether and how the brain performs spatial Fourier decomposition.

A very recent paper reviews this issue:

The neural bases of spatial frequency processing during scene perception

“how and where spatial frequencies are processed within the brain remain unresolved questions.”

Vision scientists I know often talk about how the time domain cannot be ignored in visual processing.

A general point to be made is that even if we have mathematical solutions that are invariant, computational neuroscientists haven’t quite figured out how neural networks achieve such invariant representations. The quest for invariance is more about plausible neural implementation than mathematical description per se.


From Cell Membranes to Computational Aesthetics: On the Importance of Boundaries in Life and Art

My next 3QD column is out. I speculate about the role of boundaries in life and aesthetic experience. (Dopamine cells make a cameo appearance too.)

This image is a taster:

If you want to know what this diagram might mean, check out the article:
From Cell Membranes to Computational Aesthetics: On the Importance of Boundaries in Life and Art

A group composed of brilliant individuals will not automatically be the most brilliant group

Perhaps the whole can be better than the sum of its parts?

I came across a very interesting study on McGill University’s excellent Brain from Top to Bottom Blog.

In this study of collective intelligence, the researchers performed numerous statistical analyses. The most interesting finding that emerged from them, and that went beyond the debate about just what exactly collective intelligence might represent, was that this factor was not highly correlated with either the average intelligence of the groups’ members or with the intelligence of the group member who had scored the highest on the individual-intelligence test. In other words, a group composed of brilliant individuals will not automatically be the most brilliant group.
The psychologists did find some factors that let them predict whether a given group would be collectively intelligent. But to identify three, they had to look at factors associated with co-operation. The first such factor was the group’s overall social sensitivity—the members’ ability to perceive each other’s emotions. The second factor was equality in taking turns speaking during group decision-making. The third factor was the proportion of women in the group. This last finding is highly consistent with other data showing that women tend to be more socially sensitive than men and to take turns speaking more naturally than men do.

via The Collective Intelligence of Groups

What is a biological model? Here’s a useful categorization system for people interested in neuroscience, cognitive science, and biology

I found an excellent classification of models in a paper on neurogenesis: Using theoretical models to analyse neural development.

I think this should be illuminating for anyone interested in theoretical, mathematical and/or computational approaches in neuroscience, cognitive science, and biology.

There are several ways in which models of biological processes can be classified. 

Formal or informal models

Informal models are expressed in words or diagrams, whereas formal models — which this Review is concerned with — are described in mathematical equations or computer instructions. Using formal language forces a model to be precise and self-consistent. The process of constructing a formal model can therefore identify inconsistencies, hidden assumptions and missing pieces of experimental data. Formal models allow us to deduce the consequences of the postulated interactions among the components of a given system, and thus to test the plausibility of hypothetical mechanisms. Models can generate new hypotheses and make testable predictions, thereby guiding further experimental research. Equally importantly, models can explain and integrate existing data.

 Phenomenological or mechanistic models 

Most formal models lie on a continuum between two extreme categories: phenomenological and mechanistic. A phenomenological model attempts to replicate the experimental data without requiring the variables, parameters and mathematical relationships in the model to have any direct correspondence in the underlying biology. In a mechanistic model, the mathematical equations directly represent biological elements and their actions. Solving the equations then shows how the system behaves. We understand which processes in the model are mechanistically responsible for the observed behaviour, the variables and parameters have a direct biological meaning and the model lends itself better to testing hypotheses and making predictions. Although mechanistic models are often considered superior, both types of model can be informative. For example, a phenomenological model can be useful as a forerunner to a more mechanistic model in which the variables are given explicit biological interpretations. This is particularly important considering that a complete mechanistic model may be difficult to construct because of the great amount of information it should incorporate. Mechanistic models therefore often focus on exploring the consequences of a selected set of processes, or try to capture the essential aspects of the mechanisms, with a more abstract reference to underlying biological processes. 

Top-down or bottom-up models 

Formal models can be constructed using a top-down or a bottom-up approach. In a top-down approach, a model is created that contains the elements and interactions that enable it to have specific behaviours or properties. In a bottom-up approach, instead of starting with a pre-described, desired behaviour, the properties that arise from the interactions among the elements of the model are investigated. Although it is a strategy and not a type of model, the top-down approach resembles phenomenological modelling because it is generally easier to generate the desired behaviour without all of the elements of the model having a clear biological interpretation. Conversely, the bottom-up approach is related to mechanistic modelling, as it is usual to start with model elements that have a biological meaning. Both approaches have their strengths and weaknesses.

(I removed citation numbers for clarity.)

One point might be relevant here: a model is neither true nor false — ideally it’s an internally consistent mini-world. A theory is the assertion that a model corresponds with reality.

The Mysterious Power of Naming in Human Cognition

I’ve written a long-form essay for the blog/aggregator site 3 Quarks Daily:

Boundaries and Subtleties: the Mysterious Power of Naming in Human Cognition

Here’s a taster:

I’ve divided up the essay into four parts. Here’s the plan:

  1. We’ll introduce two key motifs — the named and the nameless — with a little help from the Tao Te Ching.
  2. We’ll examine a research problem that crops up in cognitive  psychology, neuroscience and artificial intelligence, and link it with  more Taoist motifs.
  3. We’ll look at how naming might give us power over animals, other people, and even mathematical objects.
  4. We’ll explore the power of names in computer science, which will facilitate some wild cosmic speculation.