What is computational neuroscience? (XXII) The whole is greater than the sum of its parts

In this post, I want to come back on methodological reductionism, the idea that the right way, or the only way, to understand the whole is to understand the elements that compose it. A classical rebuttal of methodological reductionism is that the “whole is greater than the sum of its parts” (Aristotle). I feel that this argument is often misunderstood, so I have thought of a simple example from biology.

Cells are enclosed by membranes, which are made of lipids. A membrane is a closed surface that defines an interior and an exterior. No part of a membrane is a membrane, because it is not a closed surface. You could study every single lipid molecule that forms a membrane in detail, and you would still have no understanding of what a membrane is, despite the fact that these molecules are all there is in the membrane (ontological reductionism), and that you have a deep understanding of every single one of them. This is because a membrane is defined as a particular relationship between the molecules, and therefore is not contained in or explained by any of them individually.

There is another important epistemological point in this example. You might want to take a “bottom-up” approach to understanding what a membrane is. You would start by looking at a single lipid molecule. Then you could take a larger patch of membrane and study it, building on the knowledge you have learned from the single molecule. Then you could look at larger patches of membrane to understand how they differ from smaller patches; and so on. However, at no stage in this incremental process do you approach a better understanding of what a membrane is, because the membrane only exists in the whole, not in a part of it, even a big part. “Almost a membrane” is not a membrane. In terms of models, a simple model of a cell membrane consisting of only a small number of lipid molecules arranged as a closed surface captures what a membrane is much better than a large-scale model consisting of almost all molecules of the original cell membrane.

This criticism applies in particular to purely data-driven strategies to understand the brain. You could think that the best model of the brain is the one that includes as much detailed empirical information about it as possible. The fallacy here is that no part of the brain is a brain. An isolated cortex in a box, for example, does not think or behave. A slice of brain is also not a brain. Something “close to the brain” is still not a brain. A mouse is a better model of a human than half a human, which is bigger and physically more similar but dead. This is the same problem as for understanding a membrane (a much simpler system!): the methodologically reductionist strategy misses that it is not the elements themselves that make the whole, it is the relationship between the elements. So the key to understand such systems is not to increase the level of detail or similarity, but to capture relevant higher-order principles.

What is computational neuroscience? (XXI) Lewis Carroll and Norbert Wiener on detailed models

The last published novel of Lewis Carroll, Sylvie and Bruno (1893 for the second volume), contains a passage that explains that a high level of detail is not necessarily what you want from a model. I quote it in full:

“What a useful thing a pocket-map is!” I remarked.

“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

In other words: if the model is nearly as complex as the thing it applies to, then it is no more useful than the thing itself. This theme also appears in a 1945 essay by Arturo Rosenblueth and Norbert Wiener, “The Role of Models in Science”:

“The best material model for a cat is another, or preferably the same cat. In other words, should a material model thoroughly realize its purpose, the original situation could be grasped in its entirety and a model would be unnecessary. […] This ideal theoretical model cannot probably be achieved. Partial models, imperfect as they may be, are the only means developed by science for understanding the universe. This statement does not imply an attitude of defeatism but the recognition that the main tool of science is the human mind and that the human mind is finite.”

The last sentence is the most important: a model is not something that is meant to mimic reality; it is something that is constructed by and for the human mind to help it grasp complex aspects of reality.

What is computational neuroscience? (XX) What is a realistic model?

What is a realistic neuron model? There is a hierarchy among neuron models, which goes like this: least realistic model is the integrate-and-fire model, which is phenomenological; then the single-compartment Hodgkin-Huxley model; then multicompartmental Hodgkin-Huxley models (this hierarchy is questioned by a recently accepted paper that I wrote, but I will discuss it when the paper is out).

But what is meant exactly by “realistic”? Take two models of a plane: a toy plane made of wood, and a simple paper plane. The first model certainly looks more like a plane. It has different recognizable elements of a plane: wings, helixes, a cockpit. One might say that this model is more realistic. The second model doesn’t have a cockpit, and in fact doesn’t really look like a plane. However, unlike the first model, it flies – definitely an important characteristic of planes. So which one is more realistic?

There are generally two types of answers to justify the fact that the Hodgkin-Huxley model (HH) is more realistic than the integrate-and-fire model (IF). One is: the HH model has ionic channels, the IF model doesn’t. Another one is: the HH model has been proven right with experiments.

Let us start with the first type of answer. Strictly speaking, the HH model does not have ionic channels. Ionic channels are proteins. The HH model is a set of equations. There are parts of these equations that we identify with properties of proteins, but they are not the real things. Saying that the HH model has ionic channels is like saying that the wooden plane has a helix: there is something we call a “helix”, yes, but functionally it is not a helix, it is a nice-looking piece of wood. Specifically, in the HH model, the sodium gating variable (m) has no biophysical counterpart in the actual sodium channel. The sodium current in the HH model corresponds to something that can be physically measured, but it is described as proportional to the third power of gating variable m, only because exponent 3 was the best fit to their data. We call it “gating” variable only because it is part of a story in which it is a gating variable: the story that there are three independent gates that must all be open for the channel to be open. It is an attractive story, but we now know that this is not what happens with the sodium channel. So the model is consistent with a story in which there is a neuron with sodium channels, but the story is not an accurate description of reality. We might call this “wooden plane realism”.

The second of type of answer is more scientific in its expression. However, it is a bit ambiguous. What Hodgkin and Huxley proved is that their model was an accurate description of the electrical behavior of a giant squid axon, which was space-clamped with a metal wire. But when we claim that the HH model is realistic, we mean something more general than that. We mean that the same “kind” of model would successfully account for electrical behavior of other neurons. It would not be exactly the same model, because parameters and ionic channels would be different, and would have to be properly adjusted. So in fact it is rather the HH theory or formalism that is meant to be more realistic. However, for a given neuron, the HH “model” is only more realistic if the structure and parameters of the model are properly adjusted for that given neuron.

These remarks touch on several epistemological concepts that have been described by Karl Popper (The logic of scientific discovery, 1935). The first one is the notion of “empirical content” of a theory, which is defined as the set of possible falsifiers of the theory. In short, for a model, it is the type of (non-tautological) predictions that a model can make. For example, the integrate-and-fire model can make predictions about the membrane potential and the spike times, as a function of the input current. The HH model can additionally make predictions about the sodium and potassium currents. This is just about the logical structure of the models, in their articulation with empirical data, not about whether the models are accurate or not. We can consider greater empirical content as a more satisfying way to rephrase the idea that the HH model is more realistic because it “has” ionic channels. But it is a mistake to identify realism with empirical content: a theory can have a very large empirical content and make predictions that turn out to be all completely wrong.

Related to this notion is the “levels of universality”. Consider these two statements (taken from Popper): all orbits of planets are ellipses; all orbits of heavenly bodies are ellipses. The second statement is more universal, because planets are heavenly bodies. So in this sense it is a better theory. HH theory has this quality of being quite universal: it is meant to apply to spiking and non-spiking neurons, for example.

Finally, a theory can be characterized by its “degree of precision”. Taking again an example from Popper: all orbits of planets are circles; all orbits of planets are ellipses. Independently of the empirical validity of these two statements, the first one is more precise than the second one, because all circles are ellipses. Applied to models, this is related to the number of parameters that are left unspecified. For example, multicompartmental models have a greater empirical content than single-compartment models, because they can make predictions about membrane potential at different locations on the dendritic tree. However, they are not necessarily more realistic because they are less precise: there are many unspecified parameters, and the additional empirical content is only accurate if these parameters are properly set.

So in fact there are two aspects of realism that can be discussed about models. One has to do with the logical structure of the model: what cases it is meant to apply to (empirical content, universality), how precise it is in its predictions (precision); in other words: the ambition of the model. On this dimension, one seeks models with greater universality, greater empirical content, greater precision. Another way to phrase it is to say that a useful model is one that has many opportunities to be wrong. It is less easy than we might think to compare HH and IF models on this dimension: on one hand the HH model is more universal, but on the other hand it is less precise than the IF model (for example, a HH model does not necessarily spike).

This first aspect has nothing to do with how accurate the model is, with respect to empirical observations. It only has to do with the logical structure of the model. The second aspect has to do with empirical validity: how accurate the model predictions are. For example, we could well imagine that a phenomenological model produces more accurate predictions than a biophysical model, which has a greater empirical content. In this case the biophysical model makes more predictions, but they do not match empirical observations as well as the phenomenological model. Which model is more realistic?

What is computational neuroscience? (XIX) Does the brain process information?

A general phrase that one reads very often about the brain in the context of perception is that it “processes information”. I have already discussed the term “information”, which is ambiguous and misleading. But here I want to discuss the term “process”. Is it true that the brain is in the business of “information processing”?

“Processing” refers to a procedure that takes something and turns it into something else by a sequence of operations, for example trees into paper. So the sentence implies that what the brain is doing is transforming things into other things. For example, it transforms the image of a face into the identity of the face. The coding paradigm, and more generally the information-processing paradigm, relies on this view.

I will take a concrete example. Animals can localize sounds, based on some auditory cues such as the level difference between the two ears. In the information processing view, what sound localization means is a process that takes a pair of acoustic signals and turns it into a value representing the direction of the sound source. However, this not literally what an animal does.

Let us take a cat. The cat lives and, most of the time, does nothing. Through its ears, it receives a continuous acoustic flow. This flow is transduced into electrical currents, which triggers some activity in the brain, that is, electrical events happening. At some moment in time, a mouse scratches the ground for a second, and the cat turns its eyes towards the source, or perhaps crawls to the mouse. During an extended period of time, the mouse is there in the world, and its location exists as a stable property. What the cat “produces”, on the other hand, is a discrete movement with properties that one can relate to the location of the mouse. Thus, sound localization behavior is characterized by discrete events that occur in a continuous sensory flow. Behavior is not adequately described as a transformation of things into things, because behavior is an event, not a thing: it happens.

The same remark applies to neurons. While a neuron is a thing that exists, a spike is an event that happens. It is a transient change in electrical properties that triggers changes in other neurons. As the terms “neural activity” clearly suggest, a spike is not a “thing” but an event, an action on other neurons or muscles. But the notion of information processing implies that neural activity is actually the end result of a process rather than the process itself. There is a confusion between things and events. In a plant that turns trees into paper, trees and papers are the things that are transformed; the action of cutting trees is not one of these things that are transformed. Yet this is what the information processing metaphor says about neural activity.

There are important practical implications for neural models. Traditionally, these models follow the information-processing paradigm. There is an input to the model, for example a pair of acoustical signals, and there is an output, for example an estimate of sound location (I have worked on this kind model myself, see e.g. Goodman & Brette, PLoS Comp Biol 2010). The estimate is generally calculated from the activity of the neurons over the course of the simulation, which corresponds to the time of the sound. For example, one could select the neuron with the maximum firing rate and map its index to location; or one could compute estimate based on population averages, etc. In any case, there is a well-defined input corresponding to a single sound event, and a single output value corresponding to the estimated location.

Now try to embed this kind of model into a more realistic scenario. There is a continuous acoustic flow. Sounds are presented at various locations in sequence, with silent gaps between them. The model must estimate the locations of these sounds. We have a first problem, which is that the model produces estimates based on total activity over time, and this is clearly not going to work here since there is a sequence of sounds. The model could either produce a continuous estimate of source location (the equivalent of continuously pointing to the source), or it could produce an estimate of source location at specific times (the equivalent of making a discrete movement to the source), for example when the sounds stop. In either case, what is the basis for the estimate, since it cannot be the total activity any more? If it is a continuous estimate, how can it be a stable value if neurons have transient activities? More generally, how can the continuous flow of neural activity produce a discrete movement to a target position?

Thus, sound localization behavior is more than a mapping between pairs of signals and direction estimates. Describing perception as “information processing” entails the following steps: a particular time interval of sensory flow is selected and considered as a thing (rather than a flow of events); a particular set of movements is considered and some of its properties are extracted (e.g. direction); what the brain does is described as the transformation of the first thing into the second thing. Thus, it is an abstract construction by an external observer.

Let me summarize this post and the previous one. What is wrong about “information processing”? Two things are wrong. First (previous post), the view that perception is the transformation of information of some kind into information of another kind is self-contradictory, because a signal can only be considered “information” with respect to a perceptual system. This view of perception therefore proposes that there are things to be perceived by something else than the perceptual system. Second (this post), “processing” is the wrong term because actions produced by the brain are not things but events: it is true at the scale of the organism (behavior) and it is true at the scale of neurons (spikes). Both behavior and causes of behavior are constituted by events, not things. It is also true of the mind (phenomenal consciousness). A thing can be transformed into another thing; an event happens.

What is computational neuroscience? (XVIII) Representational approaches in computational neuroscience

Computational neuroscience is the science of how the brain “computes”: how it recognizes faces or identifies words in speech. In computational neuroscience, standard approaches to perception are representational: they describe how neural networks represent in their firing some aspect of the external world. This means that a particular pattern of activity is associated to a particular face. But who makes this association? In the representational approach, it is the external observer. The approach only describes a mapping between patterns of pixels (say) and patterns of neural activity. The key step, of relating the pattern of neural activity to a particular face (which is in the world, not in the brain), is done by the external observer. How then is this about perception?

This is an intrinsic weakness of the concept of a “representation”: a representation is something (a painting, etc) that has a meaning for some observer, it is not about how this meaning is formed. Ultimately, it does not say much about perception, because it simply replaces the problem of how patterns of photoreceptor activity lead to perception by the problem of how patterns of neural activity lead to perception.

A simple example is the neural representation of auditory space. There are neurons in the auditory brainstem whose firing is sensitive to the direction of a sound source. One theory proposes that the sound's direction is signaled by the identity of the most active neuron (the one that is “tuned” to that direction). Another one proposes that it is the total firing rate of the population, which covaries with direction, that indicates sound direction. Some other theory considers that sound direction is computed as a “population vector”: each neuron codes for direction, and is associated a vector oriented in that direction, with a magnitude equal to its firing rate; the population vector is sum of all vectors.

Implicit in these representational theories is the idea that some other part of the brain “decodes” the neural representation into sound's direction, which ultimately leads to perception and behavior. However, this part is left unspecified in the model: neural models stop at the representational level, and the decoding is done by the external observer (using some formula). But the postulate of a subsequent neural decoder is problematic. Let us assume there is one. It takes the “neural representation” and transforms it into the target quantity, which is sound direction. But the output of a neuron is not a direction, it is a firing pattern or rate that can perhaps be interpreted as a direction. So how is sound direction represented in the output of the neural decoder? It appears that the decoder faces the same conceptual problem, which is that the relationship between output neural activity and the actual quantity in the world (sound direction) has to be interpreted by the external observer. In other words, the output is still a representation. The representational approach leads to an infinite regress.

Since neurons are in the brain and things (sound sources) are in the world, the only way to avoid an external “decoding” stage that relates the two is to include both the world and the brain in the perceptual model. In the example above, this means that, to understand how neurons estimate the direction of a sound source, one would not look for the “neural representation” of sound sources but for neural mechanisms that, embedded in an environment, lead to some appropriate orienting behavior. In other words, neural models of perception are not complete without an interaction with the world (i.e., without action). In this new framework, “neural representations” become a minor issue, one for the external observer looking at neurons.

What is computational neuroscience? (XVII) What is wrong with computational neuroscience?

Computational neuroscience is the field that aims at explaining the neural mechanisms that underlie cognitive abilities, by developing quantitative models of neural mechanisms that are able to display these cognitive abilities. It can be seen as the “synthetic” approach to neuroscience. On one hand, it is widely believed that a better understanding of “how the brain does it” should allow us to design machines that can outperform the best computer programs we currently have, in tasks such as recognizing visual objects or understanding speech. On the other hand, there is also a broad recognition in the field that the best algorithms for such tasks are always to be found in computer science (e.g. machine learning), because these algorithms are specifically developed for these tasks, without the “burden” of having to explain biology (for example, support vector machines or hidden markov chains). In fact, part of the work done in computational neuroscience aims at connecting biological mechanisms with preexisting computer algorithms (e.g. seeing synaptic plasticity as a biological implementation of ICA). Given this, the belief that better algorithms will somehow arise from a better understanding of biology seems rather magical.

What is wrong here is that, while it is proposed that new generation computers should take their inspiration from brains, the entire field of computational neuroscience seems to invert this proposition and to take the computer as a model of the brain. I believe there are two main flaws with the computer analogy: 1) the lack of an environment, 2) the idea that there is a preexisting plan of the brain.

 

1) The lack of an environment

Neural models that address cognitive abilities (e.g. perception) are generally developed under the input-output paradigm: feed data in (an image), get results out (label). This paradigm, inspired by the computer, is also the basis of many experiments (present stimulus, observe behavior/neural activity). It follows that such models do not interact with an environment. In contrast with this typical setting, in a behaving animal, sensory inputs are determined both by the outside world and by the actions of the animal in the world. The relationship between “inputs” and “outputs” is not causal but circular, and the environment is what links the outputs to the inputs. In addition, the “environment” of neural models is often only an abstract idealization, often inspired by a specific controlled lab experiment. As a result, such models may be able to reproduce results of controlled experimental situations, but it is not so clear that they have any explanatory value for ecological situations, or that they can be considered as models of a biological organism.

A corollary of the absence of environment is the lack of autonomy. Such neural models do not display any cognitive abilities since they cannot “do” anything. Instead, the assessment of model performance must rely on the intervention of the external observer, as in the coding paradigm: models are designed so as to “encode” features in the world, meaning that the external observer, not the organism, decodes the activity of the model. This weakness is an inevitable consequence of the strong separation between perception and action, as the “output” of a sensory system is only meaningful in the context of the actions that it drives. This issue again comes from the computer analogy, in which the output of a program is meaningful only because an external observer gives it a meaning.

These criticisms are in fact very similar to those expressed against traditional artificial intelligence in the 80s, which have given rise in particular to the field of behavior-based robotics. But they do not seem to have made their way in computational neuroscience.

 

2) The plan of the brain

There is another criticism of the computer analogy, which has to do with the idea that the brain has been engineered by evolution in the same way as a computer is engineered. A computer has a program that has been written so as to fulfill a function, and the brain has a structure that has evolved so as to fulfill a function. So in virtually all neuron models, there are a number of parameters (for example time constants) whose values are either chosen “because it works”, or because of some measurements. It is then assumed that these values are somehow “set by evolution”. But genes do not encode parameter values. They specify proteins that interact with other chemical substances. The “parameter values”, or more generally the structure of the brain, result from all these interactions, in the body and with the environment.

The structure of the brain is highly dynamic, most obviously during development but also in adulthood. Synaptic connections are plastic, in strength, structure, conduction delay. But almost everything else is plastic as well, the density and location of ionic channels, the morphology of dendrites, the properties of channels. Activity can even determine whether a neuron becomes excitatory or inhibitory. Therefore what the genes specify is not the structure, but an organization of processes that collectively determine the structure. Humberto Maturana pointed out that what characterizes a life form is not its structure, which is highly dynamic, but its self-sustaining organization. This is a fundamental distinction between engineered things and living things.

 

A different approach to computational neuroscience could take biological organisms, rather than the computer, as models. The first point is that neural models must be embedded in an environment and interact with them, so that the external observer is not part of the cognitive process. This implies in particular that perceptual systems cannot be studied as isolated modules. The second point is to focus on organizational mechanisms that guarantee sustainability in an unknown environment, rather than on a structure that specifies a particular input-output function.

What is computational neuroscience? (XVI) What is an explanation?

An explanation can often be expressed as the answer to a question starting with “why”. For example: why do neurons generate action potentials? There are different kinds of explanations. More than 2000 years ago, Aristotle categorized them as “four causes”: efficient cause, material cause, formal cause and final cause. They correspond respectively to origin, substrate, structure and function.

Efficient cause: what triggers the phenomenon to be explained. Why do neurons generate action potentials? Because their membrane potential exceeds some threshold value. A large part of science focuses on efficient causes. The standard explanation of action potential generation in biology textbooks describes the phenomenon as a chain of efficient causes: the membrane potential exceeds some threshold value, which causes the opening of sodium channels; the opening of sodium channels causes an influx of positively charged ions; the influx causes an increase in the membrane potential.

Material cause: the physical substrate of the phenomenon. For example, a wooden box burns because it is made of wood. Why do neurons generate action potentials? Because they have sodium channels, a specific sort of proteins. This kind of explanation is also very common in neuroscience, for example: Why do we see? Because the visual cortex is activated.

Formal cause: the specific pattern that is responsible for the phenomenon. Why do neurons generate action potentials? Because there is a nonlinear voltage-dependent current that produces a positive feedback loop with a bifurcation. Note how this is different from material cause: the property could be recreated in a mathematical or computer model that has no protein, or possibly by proteins that are not sodium channels but have the required properties. It is also different from efficient causes: the chain of efficient causes described above only produces the phenomenon in combination with the material cause; for example if sodium channels did not have nonlinear properties, then there would not be any bifurcation and therefore no action potential. Efficient causes are only efficient in the specific context of the material causes – i.e.: the efficient cause describes what happens with sodium channels. The formal cause is what we call a model: an idealized description of the phenomenon that captures its structure.

Final cause: the function of the phenomenon. Why do neurons generate action potentials? So as to communicate quickly with distant neurons. Final causes have a special role in biology because of the theory of evolution, and theories of life. According to evolution theory, changes in structure that result in increased rates of survival and reproduction are preferentially conserved, and therefore species that we observe today must be somehow “adapted” to their environment. For example, there is some literature about how ionic channels involved in action potentials have coordinated properties that ensures maximum energetic efficiency. Theories of life emphasize the circularity of life: the organization of a living organism is such that structure maintains the conditions for its own existence, and so an important element of biological explanation is how mechanisms (the elements) contribute to the existence of the organism (the whole).

A large part of physics concerns formal cause (mathematical models of physical phenomena) and final cause (e.g. expression of physical phenomena as the minimization of energy). In the same way, theoretical approaches to neuroscience tend to focus on formal cause and final cause. Experimental approaches to neuroscience tend to focus on material cause and efficient cause. Many epistemological misunderstandings between experimental and theoretical neuroscientists seem to come from not realizing that these are distinct and complementary kinds of explanation. I quote from Killeen (2001), “The Four Causes of Behavior”: “Exclusive focus on final causes is derided as teleological, on material causes as reductionistic, on efficient causes as mechanistic, and on formal causes as “theorizing.””. A fully satisfying scientific explanation must come from the articulation between different types of explanation.

In biology, exclusive focus on material and efficient causes is particularly unsatisfying. A good illustration is the case of convergent evolution, in which phylogenetically distant species have evolved similar traits. For example, insects and mammals have a hearing organ. Note that the terms “hearing organ” refers to the final cause: the function of that organ is to allow the animal to hear sounds, and it is understood that evolution has favored the apparition of such an organ because hearing is useful for these animals. However, the ears of insects and mammals are physically very different, so the material cause of hearing is entirely different. It follows that the chain of efficient causes (the “triggers”) is also different. Yet it is known that the structure of these organs, i.e., the formal cause, is very similar. For example, at a formal level, there is a part of the ear that performs air-to-liquid impedance conversion, although with different physical substrates. The presence of this air-to-liquid impedance conversion stage in both species can be explained by the fact that it is necessary to transmit airborne sounds to biological substrates that are much denser (= final cause). Thus, the similarity between hearing organs across species can only be explained by the articulation between formal cause (a model of the organ) and final cause (the function).

In brief, biological understanding is incomplete if it does not include formal and final explanations, which are not primarily empirical. At the light of this discussion, computational neuroscience is the subfield of neuroscience whose aim is to relate structure (formal cause = model) and function (final cause). If such a link can be found independently of the material cause (which implicitly assumes ontological reductionism), then it should be possible to simulate the model and observe the function.

What is computational neuroscience? (XV) Feynman and birds

“Philosophy of science is about as useful to scientists as ornithology is to birds”. This quote is attributed to Richard Feynman, one of the most influential physicists of the 20th century. Many other famous scientists, including Einstein, held the opposite view, but nonetheless it is true that many excellent scientists have very little esteem for philosophy of science or philosophy in general. So it is worthwhile reflecting on this quote.

This quote has been commented by a number of philosophers. Some have argued, for example, that ornithology would actually be quite useful for birds, if only they could understand it – maybe they could use it to cure their avian diseases. This is a funny remark, but presumably quite far from what Feynman meant. So why is ornithology useless to birds? Presumably, what Feynman meant is that birds do not need the intellectual knowledge about how to fly. They can fly because they are birds. They also do not need ornithology to know how to sing and communicate. So the comparison implies that scientists know how to do science, since they are scientists, and this knowledge is not intellectual but rather comes from their practice. It might be interesting to observe after the fact how scientists do science, but it is not useful for scientists, because the practice of science comes before its theory, in the same way as birds knew how to fly before there were ornithologists.

So this criticism of philosophy of science entirely relies on the idea that there is a scientific method that scientists master, without any reflections on this method. On the other hand, this method must be ineffable or at least very difficult to precisely describe, in the same way as we can walk but the intellectual knowledge of how to walk is not so easy to convey. Otherwise philosophy of science would not even exist as a discipline. If the scientific method is not something that you learn in an intellectual way, then it must be like a bodily skill, like flying for a bird. It is also implicit that scientists must agree on a single scientific method. Otherwise they would start arguing about the right way to do science, which is doing philosophy of science.

This consensual way of doing science is what Thomas Kuhn called “normal science”. It is the kind of science that is embedded within a widely accepted paradigm, which does not need to be defended because it is consensual. Normal science is what scientists learn in school. It consists of paradigms that are widely accepted at the time, which are presented as “the scientific truth”. But of course such presentation hides the way these paradigms have come to be accepted, and the fact that different paradigms were widely accepted before. For example, a few hundred years ago, the sun revolved around the Earth. From times to times, science shifts from one paradigm to another one, a process that Kuhn called “revolutionary science”. Both normal science and revolutionary science are important aspects of science. But revolutionary science requires a critical look on the established ways of doing science.

Perhaps Feynman worked at a time when physics was dominated by firmly established paradigms. Einstein, on the other hand, developed his most influential theories at a time when the foundations of physics were disputed, and he was fully aware of the relevance of philosophy of science, and philosophy in general. Could he have developed the theory of relativity without questioning the philosophical prejudices about the nature of time? Here are a few quotes from Einstein that I took from a paper by Howard (“Albert Einstein as a philosopher of science”):

“It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why then should it not be the right thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing to do at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are so well established that waves of doubt can’t reach them; but it cannot be right at a time when the very foundations of physics itself have become problematic as they are now. [...] Concepts that have proven useful in ordering things easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as “necessities of thought,” “a priori givens,” etc. [...] A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is - in my opinion - the mark of distinction between a mere artisan or specialist and a real seeker after truth.”

In my opinion, these views fully apply to computational and theoretical neuroscience, for at least two reasons. First, computational neuroscience is a strongly interdisciplinary field, with scientists coming from different backgrounds. Physicists come from a field with strongly established paradigms, but these paradigms are often applied to neuroscience as analogies (for example Hopfield’s spin glass theory of associative memory). Mathematicians come from a non-empirical field, to a field that is in its current state not very mathematical. Physics, mathematics and biology have widely different epistemologies. Anyone working in computational neuroscience will notice that there are strong disagreements on the value of theories, the way to make theories and the articulation between experiments and theory. Second, computational neuroscience, and in fact neuroscience in general, is not a field with undisputed paradigms. There are in fact many different paradigms, which are often only analogies coming from other fields, and there is no accepted consensus about the right level of description, for example.

Computational neuroscience is perhaps the perfect example of a scientific field where it is important for scientists to develop a critical look on the methods of scientific enquiry and on the nature of scientific concepts.

What is computational neuroscience? (XIV) Analysis and synthesis

I would like to propose another way to describe the epistemological relationships between computational and experimental neuroscience. In acoustics, there is a methodology known as “analysis-synthesis” of sounds (Risset & Wessel, 1982) to understand what makes the quality (or “timbre”) of a sound (see in particular Gaver (1993), “How do we hear in the world?”). A first step is to examine the sound by various methods, for example acoustic analysis (look at the spectrum, the temporal envelope, etc), and try to extract the salient features. A second step consists in synthesizing sounds that display these features. One then listen to these sounds to evaluate whether they successfully reproduce the quality of the original sounds. This evaluation step can be made objective with psychoacoustic experiments. The results of the synthesis step then inform the analysis, which can then focus on those aspects that were not correctly captured, and the procedure goes through a new iteration. The analysis can also be guided by physical analysis, i.e., by theory. For example, the perceived size of a sounding object should be related to the resonant frequencies, whose wavelengths correspond to the dimensions of the object. The type of material (wood, metal) should be related to the decay rate of the temporal envelope. By these principles, it is possible to synthesize convincing sounds of impacts on a wood plate, for example.

There is a direct analogy with the relationship between computational and experimental neuroscience. Experimental neuroscience aims at identifying various aspects of the nervous system that seem significant: this is the analysis step. The object of experiments is a fully functional organism, or a piece of it. The empirical findings are considered significant in relationship with the theory of the moment (perhaps in analogy with physical analysis in acoustics), and with the chosen method of analysis (type of measurement and experimental protocol). By themselves, they only indicate what might contribute to the function of the organism, and more importantly how it contributes to it. For example, if the attack of a piano sound is removed, it doesn’t sound like a piano anymore, so the attack is important to the quality of the piano sound. In the same way, lesion studies inform us of what parts of the brain are critical for a given function, but this doesn’t tell us how exactly those parts contribute to the function. Computational neuroscience, then, can be viewed as the synthesis step. Starting from nothing (i.e., not a fully functional organism), one tries to build a drastically simplified system, informed by the analysis step. But the goal is not to reproduce all the pieces of empirical data that were used to inform the system. The goal is to reproduce the function of the organism. In analogy with sound: the goal is not to reproduce detailed aspects of the spectrum, but rather that the synthesized signal sounds good. If the function is not correctly reproduced, then maybe the features identified by the analysis step were not the most relevant ones. In this way the synthesis step informs the analysis step.

This analogy highlights a few important epistemological specificities of computational neuroscience. Most importantly, computational neuroscience is primarily about explaining the function, and only secondarily the empirical data. Empirical experiments on the auditory system of the barn owl aim at explaining how the barn owl catches a mouse in the dark. Computational studies also aim at explaining how the barn owl catches a mouse in the dark, not at reproducing the results of the empirical experiments. Another way to put it: the data to be explained by the theory are not only what is explicitly stated in the Results section, but also the other empirical piece of evidence that is implicitly stated in the Methods or the Introduction section, that is, that before the experiment, the barn owl was a fully functional living organism able to catch a prey in the dark. Secondly, computational neuroscience, as a synthetic approach, aims at a simple, conceptually meaningful, description of the system. Realism is in the function (how the signal sounds), not in the amount of decoration aimed at mimicking pieces of empirical data.

This discussion also brings support to the criticism of epistemic reductionism. Imagine we can measure all the components of the brain, and put them together in a realistic simulation of the brain (which already implies some form of methodological reductionism). This would correspond to fully analyzing the spectrum of a sound, recording it in complete details, and then playing it back. What is learned about what makes the quality of the sound? A second point is methodological: suppose we collect all necessary data about the brain, but from different individual brains, and perhaps a bunch of related species like mice. Would the result sound like a piano, or would it sound like a cacophony of different pianos and a violin?

What is computational neuroscience? (XIII) Making new theories

Almost all work in philosophy of science concerns the question of how a scientific theory is validated, by confronting it with empirical evidence. The converse, how a theory is formulated in the first place, is considered as a mysterious process that concerns the field of psychology. As a result of this focus, one might be led to think that the essence of scientific activity is the confrontation of theories with empirical facts. This point stands out in the structure of biology articles, which generally consist of a short introduction, where the hypothesis is formulated, the methods, where the experiments are described, the results, where the outcome of the experiments is described, and the discussion, where the hypothesis is evaluated in regard of the experimental results. The making of theory generally makes a negligible part of the articles.

Let us consider the problem from a logical point of view. At a given point of time, there is only a finite set of empirical elements that can be taken into account to formulate a theory. A theory, on the other hand, consists of universal statements that apply to an infinite number of predictions. Because the empirical basis to formulate a theory is finite, there are always an infinite number of possible theories that can be formulated. Therefore, from a purely logical point of view, it appears that the making of a theory is an arbitrary process. Imagine for example the following situation. One is presented with the first two observations of an infinite sequence of numbers: 2, 4 and 6. One theory could be: this is the sequence of even numbers, and the empirical prediction is that the next number is 8. Another theory would be: this is the beginning of a Fibonacci sequence, and so the next number should be 10. But it might also be that the next number is 7 or any other number. So no theory is a logical consequence of observations.

If what is meant by “scientific” is a process that is purely based on empirical evidence, then we must recognize that the making of a theory is a process that is not entirely scientific. This process is constrained by the empirical basis, and possibly by Popper’s falsifiability criterion (that the theory could be falsified by future experiments), but it leaves a considerable amount of possibilities. Whether a theory is “good” or “bad” can be partly judged by its consistence with the empirical evidence at the time when it is made, but mostly the empirical evaluation of a theory is posterior to its formulation. Thus, at the time when a theory is formulated, it may be considered interesting, i.e., worth investigating, rather than plausible. Therefore the choice of formulating one theory rather than another is determined by non-empirical criteria such as: the elegance and simplicity of the theory; its generality (whether it only accounts for current empirical evidence or also makes many new predictions); its similarity with other fruitful theories in other fields; its consonance with convincing philosophical point of views; the fact that it may generalize over preexisting theories; the fact that it suggests new experiments that were not thought of before; the fact that it suggests connections between previously distinct theories.

Thus, theoretical activity reaches far beyond what is usually implicitly considered as scientific, i.e., the relationship with empirical evidence. Yet there is no science without theories.