Monthly Archives: March 2014

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.

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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.

Is consciousness complex?

Someone on Quora asked the following question: What’s the correlation between complexity and consciousness?

Here’s my answer:

Depends on who you ask! Both complexity and consciousness are contentious words, and mean different things to different people.

I’ll build my answer around the idea of complexity, since it’s easier to talk about scientifically (or at least mathematically) than consciousness. Half-joking comments about complexity and consciousness are to be found in italics.

I came across a nice list of measures of complexity, compiled by Seth Lloyd, a researcher from MIT, which I will structure my answer around. [pdf]

Lloyd describes measures of complexity as ways to answer three questions we might ask about a system or process:

  1. How hard is it to describe?
  2. How hard is it to create?
  3. What is its degree of organization?

1. Difficulty of description: Some objects are complex because they are difficult for us to describe. We frequently measure this difficulty in binary digits (bits), and also use concepts like entropy (information theory) and Kolmogorov (algorithmic) complexity. I particularly like Kolmogorov complexity. It’s a measure of the computational resources required to specify a string of characters. It’s the size of the smallest algorithm that can  generate that string of letters or numbers (all of which can be  converted into bits). So if you have a string like  “121212121212121212121212”, it has a description in English — “12  repeated 12 times” — that is even shorter that the actual string. Not very complex. But the string “asdh41ubmzzsa4431ncjfa34” may have no description shorter than the string itself, so it will have higher Kolmogorov complexity. This measure of complexity can also give us an interesting way to talk about randomness. Loosely speaking, a random process is one whose simulation is harder to accomplish than simply watching the process unfold! Minimum message length is a related idea that also has practical applications. (It seems Kolmogorov complexity is technically uncomputable!)

Consciousness is definitely hard to describe. In fact we seem to be stuck at the description stage at the moment. Describing consciousness is so difficult that bringing in bits and algorithms seem a tad premature. (Though as we shall see, some brave scientists beg to differ.)

2. Difficulty of creation: Some objects and processes are seen as complex because they are really hard  to make. Komogorov complexity could show up here too, since simulating a string can be seen both as an act of description (the code itself) and an act  of creation (the output of the code). Lloyd lists the following  terms that I am not really familiar with: Time Computational Complexity; Space Computational Complexity; Logical depth;  Thermodynamic depth; and “Crypticity” (!?).  In additional to computational  difficulty, we might add other costs: energetic, monetary, psychological, social, and ecological. But perhaps then we’d be  confusing the complex with the cumbersome? 🙂

Since we haven’t created a consciousness yet, and don’t know how nature accomplished it, perhaps we are forced to say that consciousness really is complex from the perspective of artificial synthesis. But if/when we have made an artificial mind — or settled upon a broad definition of consciousness that includes existing machines — then perhaps we’ll think of consciousness as easy! Maybe it’s everywhere already! Why pay for what’s free?

3. Degree of organization: Objects and processes that seem intricately structured are also seen as  complex. This type of complexity differs strikingly from computational complexity. A string of random noise is extremely complex from an information-theoretic perspective, because it is virtually incompressible — it  cannot be condensed into a simple algorithm. A book consisting of totally random characters contains more information, and is therefore more algorithmically complex, that a meaningful  text of the same length. But strings of random characters are typically interpreted as totally lacking in structure, and are therefore in a sense very simple. Some measures that Lloyd associates with organizational complexity include: Fractal dimension, metric entropy, Stochastic Complexity and several more, most of which I confess I had never heard of until today. I suspect that characterizing organizational structure is an ongoing research endeavor. In a sense that’s what mathematics is — the study of abstract structure.

Consciousness seems pretty organized, especially if you’re having a good day! But it’s also the framework by which we come to know that organization exists in nature in the first place…so this gets a bit Ioopy . 🙂

Seth Lloyd ends his list with concepts that are related to complexity, but don’t necessarily have measures. These I think are particularly relevant to consciousness and, to the more prosaic world I work in: neural network modeling.

Self-organization
Complex adaptive system
Edge of chaos

Consciousness may or may not be self-organized, but it definitely adapts, and it’s occasionally chaotic.

To Lloyd’s very handy list led me also add self-organized criticality and emergence. Emergence is an interesting concept which has been falsely accused of being obscurantism. A property is emergent is if is seen in a system, but not in any constituent of the system. For instance, the thermodynamic gas laws emerge out of kinetic theory, but they make no reference to molecules. The laws governing gases show up when there is a large enough number of particles, and when these laws reveal themselves, microscopic details often become irrelevant. But gases are the least interesting substrates for emergence. Condensed matter physicists talk about phenomena like the emergence of quasiparticles, which are excitations in a solid that behave as if they are independent particles, but depend for this independence, paradoxically, on the physics of the whole object.  (Emergence is a fascinating subject in its own right, regardless of its relevance to consciousness. Here’s a paper that proposes a neat formalism for talking about emergence: Emergence is coupled to scope, not level. PW Anderson’s classic paper “More is Different” also talks about a related issue: pdf )

Consciousness may well be an emergent process — we rarely say that a single neuron or a chunk of nervous tissue has a mind of its own. Consciousness is a word that is reserved for the whole organism, typically.

So is consciousness complex? Maybe…but not really in measurable ways. We can’t agree on how to describe it, we haven’t created it artificially yet, and we don’t know how it is organized, or how it emerged!

In my personal opinion many of the concepts people associate with consciousness are far outside of the scope of mainstream science. These include qualia, the feeling of what-it-is-like, and intentionality, the observation that mental “objects” always seems to be “about” something.

This doesn’t mean I think these aspects of consciousness are meaningless, only that they are scientifically intractable. Other aspects of  consciousness, such as awareness, attention, and emotion might also be shrouded in mystery, but I think neuroscience has much to say about them — this is because they have some measurable aspects, and these aspects step out of the shadows during neurological disorders, chemical modulation, and other abnormal states of being.

However…

There are famous neuroscientists who might disagree. Giulio Tononi has come up with something called integrated information theory, which comes with a measure of consciousness he christened phi. Phi is supposed to capture the degree of “integratedness” of a network. I remain quite skeptical of this sort of thing — for now it  seems to be a metaphor inspired by information theory, rather than a measurable quantity. I can’t imagine how we will be able  to relate it to actual experimental data. Information, contrary to popular perception, is not something intrinsic to physical objects. The amount of information in a signal depends on the device receiving the signal. Right now we have no way of knowing how many “bits” are being transmitted between two neurons, let alone between entire regions of the brain. Information theory is best applied when we already know the nature of the message, the communication channel, and the encoding/decoding process. We have only partially characterized these  aspects of neural dynamics. Our experimental data seem far too fuzzy  for any precise formal approach. [Information may actually be a concept of very limited use in biology, outside of data fitting. See this excellent paper for more: A deflationary account of information in biology. This sums it up: “if information is in the concrete world, it is causality. If it is abstract, it is in the head.”]

But perhaps this paper  will convince me otherwise: Practical Measures of Integrated Information for Time-Series Data. [I very much doubt it though.]

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I thought I would write a short answer… but I ended up learning a lot as I added more info.

View Answer on Quora