Is cancer due to bad luck?

A few weeks ago, a Science paper about cancer was relayed in all newspapers, as a study showing that most cancers are due to random factors rather than to either genes or environmental factors. I was highly skeptical. Many cancer scientists were apparently critical too. But I'm not a cancer scientist, and the reason for my skepticism was firstly epistemological: how do you prove that something is due to chance, rather than to any unknown factor? By definition, you cannot quantify what you don't know. So when I read: two cancers out of three are due to pure chance, I frowned. But again I'm not a cancer scientist; so maybe I was just missing some key element.

There was so much press coverage about this story that I finally decided to read the original paper. You do not need to be a cancer scientist to understand the study and its methodology. It is actually quite simple (conceptually). It is known that different types of tissues (e.g. brain, stomach) have widely different risks of cancer. Why? This could be for example because environmental factors target more some tissues than others. The authors' hypothesis was simply that cells (specifically stem cells) in different tissues have different division rates. Indeed, cancer-causing mutations are introduced during cell division, and so you would expect that there are more cancers in tissues where cells divide more. And so that's exactly what they found: 0.8 correlation between cell division rate and cancer risk across different types of tissues.

I suppose this is certainly quite an interesting result for cancer research. But how did journalists interpret that as cancers being mostly due to bad luck? Well this time, it seems that authors are to be blamed. I quote the ending sentence of the paper: “For [a subset of] tumors, primary prevention measures are not likely to be effective”. It is pretty clear what it means, and it goes way beyond the results of the study.

Let me restate: the study shows that differences in average risk between types of tissues is highly correlated with stem cell division rate. In other words: statistically, variations in average risk between different tissues can be explained essentially by different division rates. This has nothing to do with the variation in risk between different people! Let me just give you a simple example. Imagine that the risk of developing a cancer is the product of cell division rate, which is tissue-specific, and of an environmental factor, which impacts all tissues in the same way (to simplify). To make my point even simpler, imagine this factor is either 0 or some fixed quantity, depending on whether the person smokes or not. Then in this case, the average risk in a tissue is completely explained by the tissue's cell division rate (correlation is 1), since environmental factors affect all tissues equally. Does this mean that cancers are only due to chance? Of course not, since the risk for a person is either 0 for a non-smoker or a fixed value for a smoker. Now in the light of this example, I find the article's conclusion that “primary prevention measures are not likely to be effective” very worrying, since in this case primary prevention would entirely eradicate the disease.

A quick summary: the study shows that the risk of cancer, averaged across all individuals, varies between types of tissues mainly because those tissues have different average cell division rates (I'm being optimistic here since the study showed correlation and not causality). That's all. It says exactly zero about whether prevention is helpful or not, or about the influence of genes. I have to say the interpretation made by the authors is rather apalling.

Modern panpsychism: about the integrated information theory of consciousness

In the last decade, a number of neuroscientists have become interested in the question of consciousness. For example Christof Koch, Stanilas Dehaene, Gerald Edelman, and many others. There have been a number of interesting new insights on this old subject, mostly focused on the so-called “neural correlates of consciousness”, that is, the properties of neural activity that are associated with conscious states, as opposed to say coma. However, to my mind there is no convincing theory that explains what is consciousness, why we are conscious at all and why we feel anything at all (phenomenal consciousness). But there have been attempts. A recent one is the integrated information theory (IIT) proposed by Tononi, which proposes that consciousness is a property of all systems that have a high level of “integrated information”. In a nutshell, such a system is a dynamical system that cannot be divided into smaller independent (or weakly dependent) systems. The term “information” should be understood in the sense of information theory: how much information (uncertainty reduction) there is in the state of a subsystem about the future of another subsystem. In a nutshell, the problem with this theory is that it is as much about consciousness as information theory is about information.

Christof Koch is a notorious fan of IIT. He describes the theory in a popular science article entitled “Ubiquitous minds” (available on his web page). I should point out that it is not an academic paper, so maybe my criticisms will seem unfair. So to be fair, let us say that what follows is a criticism of the arguments in that article, but perhaps not of Koch's thought in general (admittedly I have not read his book yet).

Koch correctly presents IIT as a modern form of panpsychism, that is, the idea that lots of things are conscious to some level. Animals, of course, but also any kind of system, living or not, that has high “integrated information” (named “phi”). On his blog, Scott Aaronson, a theoretical computer scientist, gives an example of a matrix multiplication system that has this property and therefore should be highly conscious according to IIT if it where physically implemented. Now Tononi and Koch do not see this counter-intuitive implication as a problem with the theory, but on the contrary they embrace it as a highly interesting implication. Koch speculates for example that the internet might be conscious.

Koch starts by describing the naïve version of panpsychism, which indeed can easily be dismissed. Naïve panpsychism states that everything is conscious, to different levels: a brain, a tree, a rock. This immediately raises a big problem (refered to as the “problem of aggregates” in the article): you might claim that everything is conscious, but then you need to define what a “thing” is. Is half a rock conscious? Then which half? Is any set of 1000 particles randomly chosen in the universe conscious? Is half of my brain plus half of your stomach a conscious entity?

IIT is more restricted than naïve panpsychism, but it suffers from the same problem: how do you define a “system”? Wouldn't a subsystem of a conscious system also be conscious, according to the theory? As Koch writes, the theory offers no intrinsic solution to this problem, it must be augmented by an ad hoc postulate (“that only “local maxima” of integrated information exist”). What puzzles me is that the paper ends on the claim that IIT offers an “elegant explanation for [the existence of] subjective experience”. What I have read here is an interesting theory of interdependence in systems, and then a claim that systems made of interdependent parts are conscious. Where is the explanation in that? A word (“consciousness”) was arbitrarily put onto this particular property of systems, but no hint was provided at any point about a connection between the meaning of that word and the property those systems. Why would this property produce consciousness? No explanation is given by the theory.

If it is not an explanation, then it must simply be a hypothesis; the hypothesis that systems with high integrated information are conscious. That is, it is a hypothesis about which systems are conscious and which are not. As we noted above, this hypothesis assigns consciousness to non-living things, possibly including the internet, and definitely including some rather stupid machines that no one would consider conscious. I would consider this a problem, but tenants of IIT would simply adopt panpsychism and consider that, counter-intuitively, those things are actually conscious. But then this means admitting that no observation whatsoever can give us any hint about what systems are conscious (contrary to the first pages of Koch's article, where he argues that animals are conscious on those grounds); in other words, that the hypothesis is metaphysical and not testable. So the hypothesis is either unscientific or wrong.

Now I am not saying that the theory is uninteresting. I simply think that it is a theory about consciousness and not of consciousness. What about is it exactly? Let us go back to what integrated information is supposed to mean. Essentially, high integrated information means that the system cannot be subdivided in two independent systems – the future state of system A depends on the current state of system B and conversely. This corresponds to an important property of consciousness: the unity of consciousness. You experience a single stream of consciousness that integrates sound, vision, etc. Sound and vision are not experienced by two separate minds but by a single one. Yet this is what should happen if there were two unconnected brain areas dealing with sound and light. Thus a necessary condition for a unique conscious experience is that the substrate of consciousness cannot be divided into causally independent subsets. This is an important requirement, and therefore I do think that the theory has interesting things to say about consciousness, in particular what its substrate is, but it explains nothing about why there is a conscious experience at all. It provides a necessary condition for consciousness – and that's already quite good for a theory about consciousness.

But that's it. It does not explain why an interdependent system should be conscious – and in fact, given some examples of such systems, it seems unlikely that it is the case. What is missing in the theory? I hinted at it in my introduction: the problem with integrated information theory is that it is as much about consciousness as information theory is about information. The word “information” in information theory has little to do with information in the common sense of the word, that is, something that carries meaning for the receiver. But information theory is actually better described as a theory of communication. In fact, one should remember that Shannon's seminal paper was entitled “A Mathematical Theory of Communication”, not of information. In a communication channel, A is encoded into B by a dictionary, and B carries information about A insofar as one can recover A from B. But of course it only makes sense for the person sitting at the receiving end of the communication channel if 1) she has the dictionary, 2) A already makes sense to her. “Information” theory says nothing about how A acquires any meaning at all, it is just about the communication of information. For this reason, “integrated information” fails to address another important aspect of consciousness, which in philosophy is named “intentionality”: the idea that one is always conscious of something, i.e. consciousness has a “content” - not just a “quantity of consciousness”. Any theory that is solely based on information in Shannon's sense (dictionary) cannot say much about phenomenonal consciousness (how it feels like).

For the end of this post, I will simply quote Scott Aaronson:
“But let me end on a positive note. In my opinion, the fact that Integrated Information Theory is wrong—demonstrably wrong, for reasons that go to its core—puts it in something like the top 2% of all mathematical theories of consciousness ever proposed. Almost all competing theories of consciousness, it seems to me, have been so vague, fluffy, and malleable that they can only aspire to wrongness.”

Why does a constant stimulus feel constant? (I)

What is the relationship between neural activity and perception? That is, how does the quality of experience (qualia) relate with neural activity? For any scientist working in sensory neuroscience, this should be a central question – perhaps THE question. Unfortunately the obsession of the community for the question of “neural coding”, which is about relating neural activity with externally defined properties of sensory stimuli, does not help much in this regard. In fact, very naïve philosophical assumptions about this question seem to pervade the field. A popular one is that the perceived intensity of a stimulus corresponds to the firing rate of the neurons that are sensitive to it, in particular sensory receptor neurons. This was indeed an idea proposed by Lord Adrian in the 1920s, and the basic argument is that the firing rate of sensory neurons generally increases when the strength of the stimulus is increased. Clearly the argument is very weak (only an observed correlation), but I will try to refute it explicitly, because it triggers some interesting remarks. To refute it, I will turn the perspective around: why is it that a constant stimulus feels constant? In fact, what is a constant stimulus? This is a very basic question about qualia, but it turns out that it is a surprisingly deep one.

Let us start by listing a few sensory stimuli that feel constant, in terms of perceptual experience. A pure tone (e.g. the sound produced by a diapason or a phone) feels constant. In particular its intensity and pitch seem to be constant. Another example could be a clear blue sky, or any object that you fixate. In the tactile modality, a constant pressure on a finger. For these stimuli, there is a perceived constancy in their qualities, ie, the color of the sky does not seem to change, the frequency of the tone does not seem to change. Attention to the stimulus might fade, but one does not perceive that the stimulus changes. In contrast, neural activity is not constant at all. For a start, neurons fire spikes, and that means that their membrane potential always changes, but we do not feel this change. Secondly, in sensory receptor neurons but also in most sensory neurons in general, the frequency of those spikes changes in response to a constant stimulus: it tends to decrease (“adapt”). But again, a blue sky still feels the same blue (and not darker) and the pitch and intensity of a pure tone do not decrease. There appears to be no such simple connection between neural activity and the perceived intensity of a stimulus. Why is it that the intensity of a pure tone feels constant when the firing rate of every auditory nerve fiber decreases?

In response to this question, one might be tempted to propose a homunculus-type argument: the brain analyzes the information in the responses of the sensory neurons and “reconstructs” the true stimulus, which is constant. In other words, it feels constant because the brain represents the outside world and so it can observe that the stimulus is constant. As I noted a number of times in this blog, there is a big conceptual problem with this kind of argument (which is vastly used in “neural coding” approaches), and that is circular logic: since the output of the reconstruction process is in the external world (the stimulus), how can the brain know what that output might be, as it is precisely the aim of the reconstruction process to discover it? But in fact in this case, the fallacy of this argument is particularly obvious, for two reasons: 1) whereever the representation is supposed to be in the brain, neural activity is still not constant (in particular, made of spikes); 2) even more importantly, in fact what I called “constant stimulus” is physically not constant at all.

Physically, a pure tone is certainly not constant: air vibrates at a relatively high rate, the acoustic pressure at the ear fluctuates. The firing of auditory nerve fibers actually follows those fluctuations, at least if the frequency is low enough (a phenomenon called phase locking), but it certainly doesn't feel this way. Visual stimuli are also never constant, because of eye movements – even when one fixates an object (these are called fixational eye movements). In fact, if the retinal image is stabilized, visual perception fades away quickly. In summary: the sensory stimulus is not constant, neurons adapt, and generally neural activity is dynamic for any stimulus. So the question one should ask is not: how does the brain know that the stimulus is constant, but rather: what is it that make those dynamic stimuli feel perceptually constant?

Rate vs. timing (XXII) What Robert Rosen would say about rates and spikes

Robert Rosen was an influential theoretical biologist, who worked in particular on the nature of life. He made the point that living organisms are very special kinds of natural systems, in that they are anticipatory systems, which is the name of one of his most important books. He spends a substantial part of that book on epistemological issues, in particular on what a model is. The following figure is in my opinion a brilliant illustration of what a model is:

modeling relation

The natural system is what is being modeled. For example, the brain or the solar system. The formal system is the model, for example sets of differential equations describing Newtonian mechanics. The model has state variables that represent observables of the natural system. The mapping from the natural system to those state variables is called “encoding” here – it corresponds to measurement.  Decoding is the converse process. Causality describes changes occurring in the natural system, while implication describes changes in the formal system. A good model is one that is such that this diagram commutes. That is, causality in the natural system corresponds to implication in the formal system.

Let us apply this framework to the debate at hand: rate-based vs. spike-based theories of the brain. The question then is: can there be a good rate-based model of the brain, i.e., a model in which observables are rates, or is it necessary to include spikes in the set of observables? The question has little to do with the question of coding (how much information there is in either spike timing or rates about some other observable). It has to do with whether rates, as observables, sufficiently characterize the natural system so that the evolution of a formal system based on them can be mapped to the evolution of the natural system. In other words: do rates have a causal value in the dynamics of neural networks? It is easy to imagine how spikes might, because neurons (mainly) communicate with spikes and there are some biophysical descriptions of the effect of a single spike on various biophysical quantities. It is not so easy for rates. The problem is that in our current biophysical understanding of neurons, spikes are observables that have a causal role (e.g. the notion of a postsynaptic potential), but rates are primarily described as observables (averages of some sort) with no causal nature. To support rate-based theories is to demonstrate the causal nature of rates. As far as I know, it has not been done, and I have heard no convincing reason why rates might have a causal nature.

In fact, given that a rate is an observable that is defined on top of another observable, spikes, the question reduces to a more formal question, about relations between two formal systems: can a spike-based model of the brain be approximated by a rate-model? (in the same sense as depicted on the figure above) This is an interesting remark, because now the question is not primarily empirical but formal, and therefore it can be addressed theoretically. In fact, this question has already been addressed. This is precisely the goal of all studies trying to derive mean-field descriptions of spiking neural networks. So far, the results of those studies are that 1) it is not possible in the general case; 2) it is possible under some specific assumptions about the structure of the spiking model, which are known not to be empirically valid (typically: random sparse connectivity, independent external noise to all neurons).