I’m personally interested in building mathematical models of the brain, and due to the vast complexity of the brain we are forced to make major simplifications in our models of it.  This book gives great information on potentially relevant aspect of neural functioning, which helps a modeler make informed decisions about which simplifications can / should be made.

In addition to a mathematical / computational perspective, the book also more generally gives a great description of what we know about how the brain works at a low level.

LaTex converts text markup (which is relatively simple) into beautifully-formatted formulas, and there are many great, free implementations of it.  You can learn about it generally at http://www.latex-project.org/ and there is a good free implementation at http://miktex.org/.  As an example I’ve also included the LaTex source and resulting pdf for my math study guide.

The most critical piece I was missing is that neural synchronization does not necessarily mean that a group of neurons are all firing in sychrony (i.e. every neuron in the group firing in every cycle of the oscillation).  Instead, it could be that the membrane potential of the synchronized neurons are oscillating together.  This would effectively result in a synchronized group varying in how excitable (likely to fire) they were, together - giving windows when the neurons were all easily excitable, and periods where they were not very excitable at all.  This would allow neurons to be synchronized and still have the information that gets transmitted be interesting – a spike could still mean something beyond “we are all synchronized”.

Another mistaken idea I thought I had heard was that “synchronization allows neurons to communicate / transmit information.”  This didn’t make sense to me because it doesn’t seem like you need synchronization to communicate – a single neuron can fire and send out an action potential to other neurons regardless of what other neurons are doing.  The missing piece was that synchronization isn’t needed for communication per se, but rather synchronization might allow for selective communication.  There is a vast anatomical connectivity between neurons, and it seems likely that only certain subsets of neurons need to be communicating at a given time.  If a “sending” and “receiving” group are oscillating together, then there will be periodic “windows” when the receiving neurons are excitable enough to receive information.  At other points in the cycle, the receiving neurons would likely be unresponsive to input because they would be at a “trough” in their excitability (they would be hyperpolarized).  Thus, only neurons which were synchronized with the receiving neurons would be able to send to them.

From the above sources, a few of the possible functions of synchronization might be:

• “Binding” disparate information together.  If neurons in separated areas representing related information are synchronized, and if another group of neurons which is “interested” in this information is also synchronized with them, then the “interested” area can receive information only from the related, relevant areas, and not receive information from other currently unrelated neurons which have anatomical connections to it.
• Selective communication.  As mentioned above (and in some ways similar to the first point), synchronization could generally allow groups of neurons to selectively communicate and filter out the “noise” of unrelated but anatomically connected other neurons.
• Greater impact.  Since in many cases it takes many post-synaptic potentials to cause a neuron to fire, the effect of one or a few neurons firing an action potential at a target neuron may have little effect on the target.  However, if many neurons are synchronized and fire at the same time, they can have a much greater chance of pushing the target over firing threshold.
• Facilitating synaptic changes / plasticity.  There is evidence to suggest that some / many aspects of synaptic plasticity require many incoming post-synaptic potentials in a very short time window in order to occur.  Many “upstream” synchronized neurons firing at the same time would likely have a much greater chance of effecting synaptic changes than more spread out, unsynchronized firing.

A few other interesting points I noticed:

• Relativley high frequency oscillations seem to be used for small groups of synchronized neurons, and lower frequency / slower oscillations may be used for larger synchronized groups.  This may be due to the mechanics of synchronization such as longer axonal transmission times over longer distances, more “links in the chain”, etc.
• One of the potential challenges to synchronization is that, in order to stay “in phase”, the transmission time from each sending neuron to each receiving neuron needs to be very close to the same.  Amazingly, some evidence suggests that some networks seem to be tuned so that longer-distance axons are more heavily myelinated, resulting in faster conduction speeds for longer distances, and thus very close latency between closer and further connections (such as from the thalamus to the cortex) (Salami et al., 2003).
• Magnetoencephalography is one useful tool for measuring synchronization, since it has the time resolution needed to detect the rapid voltage changes.

References

Buzsaki, G. (2006). Rhythms of the brain. New York: Oxford University Press.

Fries, P. (2005). A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence. TRENDS in Cognitive Sciences, 9, 474-480.

Salami, M. et al. (2003). Change of conduction velocity by regional myelination yields constant latency irrespective of distance between thalamus and cortex. Proceedings of the National Academy of Sciences of the United States of America, 100, 6174-6179.

Schnitzler, A., & Gross, J. (2005). Normal and pathological oscillatory communication in the brain. Nature Reviews Neuroscience, 6, 285-296.

Singer, W. (1993). Synchronizatoin of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349-374.

Emotions are complicated, and both of these views are probably right to a degree – we can experience more than one emotion at a time, but there are also likely to be situations where feeling certain emotions makes it less likely to feel other emotions.

This is more than just a theoretical question – it is relevant to understanding ways of regulating our emotions, ways of changing our emotions when they are unhealthy.  For example, when we are stressed out and worried about something, it would be nice to be able to get rid of that anxiety.  Similarly, if we are angry or depressed, we might like to change those feelings.

Could the intensity of a negative emotion be reduced by getting ourselves to feel a different, “incompatible” emotion?  In particular, could sadness be incompatible with anxiety?  Recently, when I have been especially anxious about something, I’ve been trying to imagine that “the worst possible outcome” (my fear) has already happened, and then to get myself to feel sad about it.  Sometimes this has had little effect on the anxiety, but more than a few times the resulting sadness has been accompanied by my anxiety going away and a sense of calm.

My guess about this is that there are differences between the emotional “circuits” responsible for dealing with things you can do something about vs. things you can’t do anything about.  Once there is “nothing that can be done”, the “sadness circuits” take over, and the “anxiety circuits” stop being active.  The truth is probably more complicated than this, but there might be something to it.

In some cases the need for synchronizatoin seems clear – for example rhythmic movements (such as walking) seem like they would require rhythmic, synchronized neural firing.  But synchronization seems to be much more prevalent than that, and likely plays a critical role in many / most aspects of brain functioning.  As I’m writing this I haven’t read much on synchronization, and am about to read “Rhythms of the Brain” by Gyorgy Buzsaki, which looks to be a great introduction to neural synchronization, to try to get some sense of what we know about this.

One of the initial questions I have is (from an information perspective), if many neurons are firing in the same pattern, don’t we lose information?  In other words, isn’t much of the firing redundant?  I’m interested to find out how synchronization fits into an information processing framework.

• Therapist:  As a therapist, relatively little math seems required, although some basic statistics might be helpful to be able to understand the results of research articles.
• Clinical / social / experimental psychology researcher:  These areas require some knowledge of statistics in order to correctly design and analyze experiments.  In some cases more involved statistical knowledge is necessary for building more complex statistical models, such as structural equation modeling or mediation / moderation relationship modeling.
• Computational brain modeling:  This is an area I’ve gotten more interested in / involved with lately, and I’ve found that it can require extensive math, as it involves modeling complex physical systems.
• Neuroscientist:  Potentially extensive math, depending on type of research.  At some level, models involve, for example, complex differential equations governing the different mechanisms involved.  Additionally, math can be involved in analyzing brain imaging data, such as data from fMRI.
• General cognitive science researcher:  This is a broad area, but may involve mathematical models of perceptual and cognitive processes, with or without explicit modeling of the brain.

I recently came across a classic article that addresses this point directly, Jacob Cohen’s “Multiple Regression as a General Data-Analytic System” (1968).

Cohen has written many articles on the proper use of statistics in psychological research (and in research in general).  Statistics clearly plays an important role in correctly designing and analyzing experiments, but many researchers quite naturally are not statisticians, and there is often a gap between statistical knowledge (of statisticians) and the everyday application of statistics by researchers in other fields.  Cohen has made many contributions to address this divide, by bringing a knowledge of mathematical statistics to bear on research practices.

In this article Cohen shows that analysis of variance, analysis of covariance, and other statistical techniques can be converted into equivalent cases of multiple regression.  Once he has given details about how this can be done (including how to carry out the requisite hypothesis tests, etc.), he goes on to discuss why multiple regression is ultimately a more flexible and powerful technique, and thus can be viewed as a “general linear model”.

One of the main advantages of multiple regression is that it can accommodate a wide range of situations easily – interval/ratio variables, categorical variables, interactions, and so forth – all in a single model.  ANOVA and other specific techniques (such as t tests) are specialized in that they can only handle a fairly limited range of situations.  Multiple regression, on the other hand, can handle many different cases, all at the same time in a single model.

Reference

Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426-443.

This is still a work in progress, but I now have an initial version that models input and two of the brain areas, V4 and IT.  The simulation also displays graphs of the resulting firing rates over time for each simulated neuron.  The Matlab files are available here.

The biggest issue I’ve come across so far has been optimizing performance.  In my initial version of the simulation, solving the equation system took a prohibitive amount of time – simulating 5 neurons for 3 milliseconds of model time took several minutes, and the system ultimately needs to model around 250 neurons for 3000 milliseconds.  Ultimately the problem turned out to be the differential equation solver algorithm.  I initially used Matlab’s default “ode45″ solver, since the model appeared to be simple and I didn’t expect the system to be “stiff”, but switching to the “ode15s” solver (a “stiff” solver) drastically reduced the execution time.

Reference

Hamker, F. H. (2005). The reentry hypothesis: The putative interaction of the frontal eye field, ventrolateral prefrontal cortex, and areas V4, IT for attention and eye movement. Cerebral Cortex, 15, 431-447.

To give some background, one line of thought views “concepts” as ethereal and as existing in some sense independently of any individual thinker.  This is very close to Plato’s “forms”, and posits some “essence” which makes a concept what it is.

Enter modern science and the view that everything is ultimately describable by the patterns of physics.  Under this view, the idea of essences is incorrect, and must be replaced by some mechanistic description of what is happening when someone thinks about a concept.

As controversial as this later view may be in popular culture, I would argue that it is accepted by most scientists, and in my view, likely to be correct.  But we then have the question – if concepts are not made of “essences” but of physical mechanisms, what kind of physical mechanisms are involved?

This book attempts to give a possible answer to this question.  Lakoff and Johnson argue that most of our concepts are “embodied”, meaning that they are directly or indirectly based on our bodies and the movement of our bodies through space.  Of course, some of our concepts / language are clearly and directly based on the body – being cold or hot, or moving forward or backward, for example.  But they argue that much or most of our language is based metaphorically on body concepts.  For example, we conceive of time as moving forward or backward, and we speak of time as *looking* forward or backward – “we’ll see what happens”, etc.

They lay out these basic ideas, and then spend much of the book describing how specific abstract concepts might be based on body metaphors – self, free will, morality, time, etc.

Although the book constantly refers to “the findings of second-generation cognitive science”, it is relatively light on actual experimental evidence supporting their claims.  Much of the value of the book lies, in my opinion, not on the science, but on plausible outlines of how concepts might come to have meaning in physical systems.  In this respect, I think the ideas in the book might truly be as groundbreaking as the authors suggest.

Initially, I thought this would be a good idea – a standardized format might make it easier for someone unfamiliar with the model to really understand the model and to be able to implement it themselves.  However, on second thought, one of the benefits of computational models is that it makes you physically implement your model, forcing you to deal with all of the details of the model – and the devil is, quite often, in the details.  Since the devil is in the details, you could probably never completely specify the model without providing all of the code.  Additionally, newer innovations in model design might not fit in with an existing standardized format.

So my thoughts are that “guidelines” might be more appropriate than any kind of standardized model.  A few thoughts on possible guidelines:

1) Be clear about how much of the model you’re providing in a research paper.  If you say you’re including the whole model, really include everything, including all parameter values used, etc.  More specialized papers may focus on only one or several aspects of a model.

2) If relevant, describe any computational “shortcuts” taken in the implementation.  Were significant numerical approximations made?

3) If possible, do provide the code, most likely on a website.

I imagine that being able to clearly communicate computational models will become increasingly important in the future, as models will need to build on each other, and there will likely be larger-scale models that incorporate multiple smaller-scale models, in modeling larger systems.

Traditionally in psychology, there is heavy emphasis on “doing experiments”, and rightfully so.  The history of psychology contains much that was divorced from science, based on speculation or personal experience instead of on empirical science, such as phrenology or much of “psychodynamic” thinking, for example.  And I think psychology has been right to be wary of “armchair theorizing” that is only loosely based, if at all, on scientific data.

However, in some respects I think psychology has neglected theorizing that is based on empirical data.  Don’t get me wrong – there are hundred of theories proposed to explain the many experimental phenomena that have been discovered – proposing that the brain is performing serial vs. parallel search in a search situation, or describing the role of “self-esteem” in drug abuse, or hypothesizing about what the encoding of memory might look like.  And these theories are useful and important.

However, it seems that although we do theorize, the theories are usually local to the specific phenomenon studied, and (and this is not a very rigorously scientific opinion!) sometimes it “feels like” the theories serve largely as a way to generate more experiments, with the experiments themselves being treated as the important thing.

I’m all for experiments, but I think that there is a need for an increased focus on theorizing, and on theorizing that crosses experimental paradigms.  Such theorizing may attempt to “put together” different pieces of the tremendous amount of existing empirical data that exists.  In other words, just as there are theoretical physicists who focus primarily on theory, there may be a place for “theoretical psychologists” who focus primarily on theories of how the brain / mind works.  The perhaps scandalous opinion I have is that I believe such a person could make important contributions to psychology potentially even without performing any original experiments.  I think the important thing is that theorizing should be based on empirical data, and not that the theorist and experimenter be the same person.

Practically speaking, new theories about the structure underlying old data will almost certainly suggest new experiments, and back-and-forth between theory and experiment is often a natural progression, and it is unlikely for there to be a strong division between “theoretical” and “experimental” psychologists.  But as we gather more and more data, the challenge may not so much be discovering specific properties of the brain / mind, but rather figuring out how to put these specifics together, and thus “theoretical” psychology may become increasingly important.

One question is whether higher-level models are even capable of accurately / usefully modeling brain activity.  In other words, is there in some sense inherent low-level complexity in the brain that does not exhibit interesting, high-level regularities?  I recently started reading “Theoretical Neuroscience” (Dayan & Abbott, 2001), and came across this related quote in the preface (p. xiii):

It is often difficult to identify the appropriate level of modeling for a particular problem.  A frequent mistake is to assume that a more detailed model is necessarily superior.  Because models act as bridges between levels of understanding, they must be detailed enough to make contact with the lower level yet simple enough to provide clear results at the higher level.

Dayan and Abbott (2001) go on later to discuss two classes of neural network models – the more detailed and complex “spiking neuron” models, and the simplified “firing rate” models, where each neuron is modeled as a firing rate, without explicitly modeling spike timing or internal electrical mechanisms.  They argue that both types of models are needed, and that in many cases the firing rate models may even be better for modeling network behavior than the more detailed spiking neuron models.  A summary of (some of) their points about the tradeoffs between model types:

1. Firing rate models are much easier to implement and interpret. Spiking neuron models present many practical difficulties – due to their sheer size and complexity, they can require tremendous computational resources.  And even when they are successfully modeled, the amount of data produced is often challenging to interpret.
2. Firing rate models have fewer “free parameters” to estimate.  Setting the large number of free parameters in spiking neuron models can be difficult.
3. Neural firing may be largely stochastic.  Neural firing appears to be in some sense stochastic – in other words (I think), many “important” aspects of neural firing patterns depend on a probabilistic tendency to respond in certain ways over time, and not so much on the specific details of each spike’s timing.  Thus, we may gain little (in a practical sense) from modeling the details of individual spike timing.  Additionally, in cases where individual spike timing is important, it is likely to be difficult to accurately model them (in spiking neuron models) without knowing specific details of the many variables that go into determining the individual timings.
4. Firing rate models cannot capture some potentially important aspects.  Firing rate models, however, cannot model important correlations between spike timings in a larger network (such as firing synchronization), and they cannot model any other cases where timing is important.

Reference

Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press.

Basic components of the simulation:

• Neurons in several populations, modeled as firing rates
• Input, consisting of populations of neurons with firing rates driven by simulated experimental visual stimuli
• An externally-controlled variable which tells the model Prefrontal Cortex areas whether to “memorize” certain stimuli.  This is set depending on the task
• Output, consisting of saccade times and I think locations, which are triggered based on a threshold for the modeled FEF movement neurons.  Once firing rate threshold is crossed, a saccade is initiated 30ms later
• A set of differential equations describing changes in firing rates over time
• Initial firing rates for all neurons at t = 0

To analyze what the model is doing, will want to potentially monitor:

• Firing rates of all neurons over time
• Simulated experiment condition (visual stimuli over time)
• Saccade occurrences and locations

Will need to implement:

• All relevant variables and set of differential equations governing evolution
• Correctly modeling input over the experiment duration, and initial firing rates

References

Chelazzi, L., Duncan, J., Miller, E. K., & Desimone, R. (1998). Responses of neurons in inferior temporal cortex during memory-guided visual search. Journal of Neurophysiology, 80, 2918-2940.

Hamker, F. H. (2005). The reentry hypothesis: The putative interaction of the frontal eye field, ventrolateral prefrontal cortex, and areas V4, IT for attention and eye movement. Cerebral Cortex, 15, 431-447.

In addition to the “intelligent machines becoming self-aware” scenario however, there is another related scenario.  As technology improves, and our understanding of cognition (both natural and artificial) increases, it may become possible to create relatively “dumb” machines which could go out into the “real world” and cause problems.  Such machines could be “insect-like” in that they might not have any kind of higher “intelligence”, and yet still able to get around quite well in the world.

The type of people who write computer viruses could then potentially escape the confines of existing computers and computer networks, and build self-contained, embodied “virus” machines that could survive out in the “real world”.  Such viruses could, say, take pictures or recordings, be physically destructive (as some computer viruses are), or even potentially create copies of themselves.  Not the happiest thought, but not out of the realm of possibility if technology continues to improve at its current pace.

There has been interest in modeling cognition with production systems.  One example is the highly developed ACT-R framework (Anderson, 1983; Anderson & Lebiere, 1998) which is based on production systems, and another is the Soar framework created by Allen Newell (Newell, 1994).  Lovett and Anderson (2005) give a good overview of modeling cognition with production systems, and Gray (2005) has examples of many productions system applications.  Anderson and Lebiere (1998) even went so far as to call productions one of “the atomic components of thought”.

On one hand, I greatly admire the production system models of cognition.  As Anderson and Lebiere (1998) mention, two of the main goals for a theory of cognition are precision and complexity.  Implementing a model physically (on a computer) requires you to be precise about exactly what you mean in your theories – you can’t implement something which is vaguely defined.  And, as the brain is extremely complex, accurate models of cognition will probably have to be complex to accurately describe the workings of the brain, and prodution systems models are typically more complex than most psychological theories (by specifying all of the details).  Additionally, many production system models are integrated in the sense that they combine perception, cognition, and action in a single model, which I think is important for understanding the brain at a large scale.

However, lately I’ve been questioning some aspects of production system models, especially in light of other, non-production system models based on more detailed knowledge of the brain (such as Hamker 2005, Itti & Koch, 2001, and Lanyon & Denham, 2009).  Such models incorporate specific knowledge of the brain, such as neural connectivity between different brain areas, and firing rate patterns obtained from single-cell neural recordings.  Some of these models have been very successful in explaining certain phenomena, and seem to be much more reflective of the underlying neural structure than the relatively abstract production system models.

While traditionally production systems have not incorporated many neural details in their models, more recently Anderson (2007) has strongly recommended using brain imaging to guide model development.  One question I have is then – how “generic” is cognition?  In other words, are a few basic mechanisms responsible for cognition (as production systems theories might suggest), or does the neural structure of the brain result in a larger variety of mechanisms?

Production systems are also extremely powerful in the sense that they can be made to do almost anything.  Post’s (1943) canonical systems are computationally equivalent to Turing machines, and are thus capable of computing effectively anything that can be computed.  The production systems used in modeling cognition are typically more limited than Post’s (such as in ACT-R), but are still quite powerful.  So another question is then – are production systems too powerful for modeling the brain?  Since we could build production system models which do almost any task in almost any way, do production system frameworks themselves really tell us anything about how cognition works?

My current thought is that we’re ultimately going to have to incorporate more details of neural structure into our models of cognition than are found in many existing production system models.  I also think that our models will have to be more constrained than most production system models if they are to be informative.  But taking a step back, I also think the higher-level aim of many production systems models is excellent – to build relatively complete, well-specified computational models of cognition.

References

Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press.

Anderson, J. R. (2007). Using brain imaging to guide the development of a cognitive architecture. In W. D. Gray (Ed.), Integrated models of cognitive systems (pp. 49-62). New York: Oxford University Press.

Anderson, J. R., & Lebiere, C. (1998). The atomic components of thought. Mahwah, NJ: Lawrence Erlbaum.

Gray, W. D. (Ed.). (2007). Integrated models of cognitive systems. New York: Oxford University Press.

Hamker, F. H. (2005). The reentry hypothesis: The putative interaction of the frontal eye field, ventrolateral prefrontal cortex, and areas V4, IT for attention and eye movement. Cerebral Cortex, 15, 431-447.

Itti, L., & Koch, C. (2001). Computational modelling of visual attention. Nature Reviews Neuroscience, 2, 194-203.

Lanyon, L. J., & Denham, S. L. (2009). Modelling attention in individual cells leads to a system with realistic saccade behaviors. Cognitive Neurodynamics.

Lovett, M. C., & Anderson, J. R. (2005). Thinking as a production system Cambridge handbook of thinking and reasoning, 401-430 DOI: 10.2277/0521531012

Post, E. L. (1943). Formal reductions of the general combinatorial decision problem. American Journal of Mathematics, 65, 197-268.

In so doing, Minsky covers much of the classic ground of what is traditionally studied as “computation” – Turing machines, finite state machines, simple neural network models, the “halting problem”, and so forth.  There are many books which cover these topics, but where I think this book stands out is that it doesn’t just dive into the details.  Instead, throughout the book Minsky steps back and tries to address the bigger picture.  He asks questions such as “What is a machine?”  “What is computation?”  “What could be meant by a description (in the context of ‘describable numbers’)?”

I think this is important because we haven’t really settled these more fundamental questions yet.  For example, we haven’t yet settled the question of what the Church-Turing thesis might mean about what can and can’t happen in the physical world (see a previous post for more explanation of this).  This book is good introduction to some of these questions.  Thinking about what computation means and what its limitations are is also becoming increasingly important, as we model the mind more and more with computational models.

As a side note, Minsky has also authored a number of other books, including another of my favorites, “Society of Mind” (1986) in which he lays out his basic thoughts about the nature of the mind.

References

Minsky, M. (1967). Computation: Finite and infinite machines. Englewood Cliffs, NJ: Prentice-Hall.

Minsky, M. (1986). Society of mind. New York: Simon and Schuster.

The first article (Vanni-Mercier et al., 2009) looks at the role of the hippocampus in computing (or representing) uncertainty.  Different areas of the brain are known to process uncertainty, but this study gives evidence that the hippocampus is also involved in representing uncertainty.  Vanni-Mercier et al. measured local field potentials in the hippocampi of three epileptic patients (who had electrodes implanted pre-surgically).  They had the patients estimate the reward payoff probability for different simulated slot machines.  They performed event-related potential (ERP) analysis of the local field potentials, and found a negative ERP which had an amplitude that had an “inverted U” shaped relationship with the probability of payoff – with the largest amplitude when the probability was 50% (the most uncertainty).

The second article (Hsu et al., 2005) looks at differences between what they call “risk” uncertainty and “ambiguous” uncertainty.  Risk uncertainty occurs when an outcome is unknown, but the probabilities are known – for example, when flipping a coin you don’t know whether it will be heads or tails, but you do know there is a 50% chance of each.  Ambiguous uncertainty occurs when you do not have a clear sense of probabilities – for example, in trying to predict something like a terrorist attack it’s difficult to assign any probability with any real confidence.  In this article, Hsu et al. argue that there are distinct representations in the brain for both kinds of uncertainty.  They reached this conclusion by using brain imaging on subjects while they performed various tasks involving different types of uncertainty, and they found different brain activation patterns for “risk” vs. “ambiguous” uncertainty.

Most experiments that I’ve come across looking at uncertainty (including these), have looked at uncertainty from a relatively “bottom-up” or associative learning perspective.  Or, they have given explicit information about probabilities (or lack of probability information), such as “this deck of cards has 30% red cards” or “this deck of cards contains red and blue cards in some unknown proportion”.  But it seems likely that in many cases, uncertainty calculations could be much more involved.  For example, take the case of someone who is on a diet but is faced with an opportunity to eat a piece of chocolate cake.  There are at least several different kinds of uncertainty here:

• How much impact will eating the cake have on the goal of losing weight?  Everything else being equal, what difference would one piece of cake have on losing weight?
• My friend Janet said eating cake is okay as long as you just eat the frosting.  Is she right?
• What related actions will I engage in in the future?  The outcome depends not only on this decision, but also on what future behaviors might be engaged in.  For example, if I eat the cake but skip dinner, eating the cake might have less of an impact.
• Which is really more “important” – enjoying something bigger in the long term, or enjoying something smaller in the short term?  Where does the trade off lie?
• How likely is it that the cake will actually be as enjoyable as I predict?  We’ve all been disappointed, it could happen this time.  And how much better would my life be if I lost weight?
• If I don’t eat the cake, will I be in a grumpy mood and perform poorly on my job interview later in the day?

Thus it seems like there are many different places uncertainty can play a role in decisions.  It would be interesting to look at how many different types / representations of uncertainty occur in the brain, and whether there is one relatively all-encompassing “uncertainty system”, or whether uncertainty is calculated differently in different areas.

It would also be interesting to see how uncertainty differentially affects different possible action “contenders” during a decision.  As discussed previously, there are likely to be several different systems that calculate value, which are then integrated in some form.  It is likely that uncertainty plays a role in weighting different systems.  For example, if a given system is very certain about its valuation, then it seems to make adaptive sense that it would have more input into a decision than in cases where it is less certain.

References

Hsu, M., Bhatt, M., Adolphs, R., Tranel, D., & Camerer, C. F. (2005). Neural Systems Responding to Degrees of Uncertainty in Human Decision-Making Science, 310 (5754), 1680-1683 DOI: 10.1126/science.1115327

Vanni-Mercier, G., Mauguiere, F., Isnard, J., & Dreher, J. (2009). The Hippocampus Codes the Uncertainty of Cue-Outcome Associations: An Intracranial Electrophysiological Study in Humans Journal of Neuroscience, 29 (16), 5287-5294 DOI: 10.1523/JNEUROSCI.5298-08.2009

Now, think about being able to see an object and reach for it accurately.  In spite of having images “shrunken” or condensed when wearing my glasses, I seem to have no trouble reaching for things and having my hand go right to where they are.  Certainly, reaching can be guided by visual feedback, which would allow accurate reaching regardless of stretching of the image.  But I also have a spatial sense of where objects are, and I’ve tried closing my eyes and reaching for something I was just looking at and am pretty accurate – both with my glasses on, and with them off.

The brain almost certainly maintains some sort of spatial map about where objects are in the environment.  The interesting thing is that this spatial map seems to maintain its accuracy even when the “input signal” of the images hitting the retina are stretched or condensed dynamically – i.e., when I put on or take off my glasses.

I haven’t searched for research about this (I’m assuming someone has a good idea of why this is), but, like most other abilities, this can’t “come for free”, and it would be interesting to know what the underlying mechanisms are.

In particular, doing the work of approaching research questions from many different angles may be important.  As an example, I recently read Michael Posner and Yael Cohen’s article “Components of Visual Orienting” (1984), in which they first discussed what was to become known as the “inhibition of return” phenomenon, a famous aspect of visual attention that has received a large amount of further research.

In the article, they approach this topic from many different angles:

• Literature review:  thorough review of related concepts and previous experiments
• Behavioral experiments:  many different behavioral and reaction time experiments, exploring when the phenomena occur and ruling out alternative explanations
• Theory:  details of potential underlying mechanisms, relationships to other theories, and more fundamental questions about the nature of cognitive science, such as, “One of the goals of cognitive psychology is to account for complex cognitive phenomena in terms of simpler elementary mental operations that can, in turn, be related to neural systems” (p. 532)
• Relation of the phenomena to larger systems:  exploration of the relationship with the eye movement system
• Physiological evidence:  discussion of evidence from different neuroscience methodologies, including single-cell neural recording and lesion studies
• Relation to other tasks:  discussion of how this might affect reading, and relevant reading studies

Each of these things individually might not be unusual, but I was impressed by how many angles they approached the problem from, which, in addition to “inspiration”, probably required quite a bit of hard work.

Reference

Posner, M. I., & Cohen, Y. (1984). Components of visual orienting. In H. Bouma & D. G. Bouwhuis (Eds.), Attention and performance X (pp. 531-556). Hillsdale, NJ: Lawrence Erlbaum.

To start with, it’s not clear what the question really means.  It could mean, “What do people mean when they use the word ‘intelligence’?”  This amounts to a conceptual analysis.  In other words – when the man on the street, or a villager in some remote tribal culture, or a psychologist, uses the word “intelligence”, what exactly do they mean?  This is an interesting question in its own right (especially from an anthropological or cultural psychological perspective), but I don’t imagine this is what most people have in mind when asking this question.  In other words, if there is a culture which has a word which is roughly translated as “intelligence”, and which happens to include “ability to speak to the gods” as part of its meaning, this is interesting – but probably not what we were after (unless we’re specifically studying these things).

The word “intelligence” is just a word, and we can of course attach any concept we would like to the word.  The better questions to ask are (almost always, in my opinion), “What is the world like?” and, “What is the most useful way to conceptualize it?”  When the question is asked in this way, instead of being focused on a word or a concept, we’re focused on the world, which is usually what we’re most interested in.  We start with the world, and then adjust our concepts according to what we find.

I think that when we ask a question like “What is intelligence?” we might really want to know something like:

We have a word, “intelligence”, that corresponds to a vague concept that we use in different ways in different contexts.  It seems that there is something to this idea of “intelligence”, even if we can’t define it exactly.  For example, we often use it (for better or worse) as a way to predict success in a job or at school.  Let’s try to figure out “what the world is like” in this area – what cognitive abilities do humans have, and in what ways do these abilities differ from person to person?  Then we can reformulate our concepts to be more appropriate once we have a better understanding of the world – perhaps keeping something similar to our current sense of “intelligence”, or perhaps replacing it with something else if it better reflects what we find.

This is exactly the approach taken by science generally.  For example, physics does not ask “What is work?” or “What is power?” (two technical terms that are used in physics), but rather investigates the world first, and then devises concepts that match the way the world seems to be.

I like this text because it explains the concepts fully in their “full-strength” versions.  I’ve found many textbooks seem to assume that the reader won’t understand the “real material”, and so they water it down in an attempt to make it easier to understand, which (at least for me) sometimes ends up making it harder to understand.

On the other side of the coin, it also gives explanations of why the material is important and how it fits into the bigger mathematical picture, instead of jumping right into the details without a discussion of the larger context.

Finally, the scope is very broad, teaching many basic mathematical topics that could be helpful to someone trying to get a basic math foundation, in addition to strictly “calculus” topics.  For example, it covers vector algebra, linear algebra, complex numbers, and basic real number axioms.

You can find the two volumes on Amazon here:

http://www.amazon.com/Calculus-Vol-One-Variable-Introduction-Algebra/dp/0471000051/

http://www.amazon.com/Calculus-Vol-Multi-Variable-Algebra-Applications/dp/0471000078/

On one hand, he says that this research is important and is making many valuable contributions to our understanding of behavior.  On the other hand, he asks the question How can all of this research fit together into a larger, unified understanding of the mind? He is concerned that, by only following the above paradigm, we may never get to a “big picture” understanding of how all of these phenomena are produced by a single system.

Interestingly, over 20 years later (in 1990), he still felt such a change in focus was called for, as he describes in his book “Unified Theories of Cognition” (1990).

I’ve taken away two main points:

1) Asking binary questions and doing experiments to investigate them is valuable, but we should keep in mind that the ultimate goal is not just answering these questions, but developing good models of how the mind works.  Thus the focus should perhaps shift from answering questions, to building models (and answering questions can serve as a way to help build models).

2) Psychology is ultimately interested in how the total system of the mind works.  So there could be more work done on integrating findings from different areas, and perhaps there should be less isolation in looking at individual phenomena without thinking about the larger system of the brain / mind in which they take place.

You can find the paper on the web here:

http://www-psychology.concordia.ca/fac/deAlmeida/COGSCI/Newell-1973-TwentyQuestions.pdf

References

Newell, A. (1973). You can’t play 20 questions with nature and win: Projective comments on the papers of this symposium. In W. G. Chase (Ed.), Visual information processing (pp. 283-308). New York: Academic Press.

Newell, A. (1990). Unified theories of cognition. Cambridge, MA: Harvard University Press.

For extremely simple organisms, there can be simple stimulus-response mechanisms whereby given situations in the environment are always responded to with a given behavior. Once there are multiple incompatible behaviors, however, there must be a mechanism to adaptively determine which actions to execute in a given situation. This is the problem of action selection, and this page attempts to describe one possible model of the way action selection might work.

One fundamental question when developing a model of action selection is what gets selected? What are the components of action, and at what level is selection made? In other words, how is action structured, and how could an action selection mechanism specify an action? The next section explores this question, but it basically argues that fundamental components of action can be combined in various ways to form higher-level units of action. These action units (AU’s) are what the action selection mechanism operates on.

The rest is available here:  http://coggr.com/action-selection-ideas/

In other words, does action selection look like this:

Or more like this:

* An emotional system vs. a cognitive system
* Top-down vs. bottom-up systems
* Automatic / unconscious vs. voluntary / conscious

I think there is value in such characterizations, and it seems likely that there is organization at a high level in the brain (i.e. at a level above individual neurons and neural circuits).  It also seems likely that high level systems can in some way be said to interact with each other at a system level, or compete with each other at a system level.  However, the brain is extremely interconnected, and it seems unlikely that there would be truly isolated systems in the brain, especially when we’re talking about such large-scale systems as “emotional” systems, “cognitive” systems, etc.

Therefore, it seems likely that the true picture may be more complicated than just two systems.  A paper I recently came across briefly explores this question, and argues that 1) things must be more complicated than simple two-system models, even though there can be some truth to such models, and 2) computational models are a good way to explore and model this increasing complexity (Frank, Cohen, & Sanfey, 2009).

Why are computational models appropriate for this purpose?  They give two main reasons:

1) They give us precise, well-defined models that avoid the differences and ambiguities in terms used by different researchers.

2) As the underlying mechanisms are likely to be complicated, they allow the models to be complex in a way that ordinary language models can’t often be.

They say about computational models: “…by using the explicit language of mathematics, these models can help researchers avoid vague terminology and permit them to explore complex neural-system dynamics, in an attempt to elucidate their functional roles” (p. 73).

They later go on to say that computational models “offer a way to formalize the functioning of and interactions among these systems in a common mathematical language, which can then be translated back into words” and that such models can serve in “paving the way to replace vague terminology with functional and mechanistic principles” (p. 76).

Reference

There are representations of many things, in many places in the brain – retinotopic maps of visual stimuli, maps of sensory information from body parts, models of the world as it is and as it might be.  Many of these representations are not part of consciousness.  What consciousness consists of, is when many different representations occur together and relationships between the representations are represented as well.  For example, a conscious “experience” of “seeing a red apple” might consist of a representation of red and other colors at a certain location in space, a representation of a body located in space (your own), a representation of the possible motor actions that could be undertaken to reach the apple, a representation of taste sensations that might occur if the apple was eaten, etc.

A central point of the paper is that there is no “magical place” where “consciousness exists” – there are just different representations occurring in relationship to each other and in relationship to actions that could be taken in the world, etc.

Another excellent point of the paper is that there is no need of any special “essence” to describe consciousness – and that there need not be any qualitative difference between consciousness and other aspects of the nervous system other than organizational differences.  Quoting from a paragraph I thought particularly relevant (p. 246):

“The properties of things describe what happens when things interact.  A thing cannot have an absolute property (in vacuo) any more than a sensation can have an absolute quality. … All properties are interactive.  Just as figure could not exist without ground, so some context with potential for interaction is always needed to enable anything to manifest any of its properties.  Thus it is a property of neurons to generate awareness when they interact, although the neuron is not conscious.  Properties that manifest when components of a system interact have been called ‘emergent’.  …  Emergence is no more or less mysterious than the organization of the physical world in general, and to characterize consciousness as emergent … in no qualitative way distinguishes it from anything else in the world.”

I really appreciated this discussion of “emergence” because I have never quite understood what people mean when they say something is “emergent”, especially when it is implied that this is in stark contrast to something being “reductive”.

Reference

I initially found the article through ScienceCentric, which has a good discussion of it here:

http://www.sciencecentric.com/news/article.php?q=09032416-astrocytes-help-separate-man-from-mouse

You can also view the article itself online here:

http://www.scribd.com/doc/13767802/Uniquely-Hominid-Features-of-Adult-Human-Astrocytes-Oberheim-et-al

Reference

Oberheim, N. A., Takano, T., Han, X., He, W., Lin, J. H., Wang, F., et al. (2009). Uniquely hominid features of adult human astrocytes. The Journal of Neuroscience, 29, 3276-3287.

There is reasonably good evidence that all sequences of numbers which could “naturally be regarded as being computable” can be computed by a Turing machine (the Church-Turing Thesis) – namely, that no one has been able to come up with anything which seems to be “computable” which couldn’t be computed by a Turing machine.  But does this mean that Turing machines are appropriate for modeling the brain?  I have two questions about this:

1) Turing machines produce sequences of numbers (or equivalently, calculate functions) – is this adequate to describe a physical system (like the brain) in general?  Might there be aspects of a physical system not describable via number sequences or functions?

2) As we are ultimately trying to model a physical system (the brain), what is “naturally regarded” as being computable seems less important than what is physically computable.  Reformulations of the Church-Turing Thesis saying that a Turing machine is capable of computing anything which could be physically computed, are known as Physical Church-Turing Theses (and I say theses instead of thesis because there are several different versions).  Thus I would argue that the Church-Turing thesis as originally stated is ultimately less interesting than some form of Physical Church-Turing Thesis.

A paper giving a good perspective on the differences between the classical Church-Turing Thesis and different forms of the Physical Church-Turing Thesis (Piccinini, n.d.) is located here:

http://www.umsl.edu/~piccininig/CT%20Modest%20or%20Bold%205.htm

Bottom line:  it seems that we don’t yet know whether there might be aspects of physical systems (e.g. the brain) that can’t be modeled with a Turing machine, and we don’t yet know whether some form of Physical Church-Turing Thesis is correct.

However, my guess is that whether or not standard computation (Turing machines) ends up being capable of modeling everything relevant to our understanding of the brain, it will turn out to model at least a very significant portion of it.

Piccinini, G. (n.d.). The physical Church-Turing thesis: Modest or bold? Retrieved April 18, 2009 from http://www.umsl.edu/~piccininig/CT%20Modest%20or%20Bold%205.htm

Turing, A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42, 230-265.

1) Describing a phenomenon – details about what happens, in which situations, and what the effects of changing different variables are

2) Proposing or providing evidence for a conceptual model (i.e. a verbal description) of the processes that might underlie a phenomenon

3) Proposing or providing evidence for a computational model (i.e. a rigorously defined model) of the processes that might underlie a phenomenon, at a relatively high level that does not include a detailed neural implementation

4) Proposing or providing evidence for a computational model of the processes underlying a phenomenon, which does include a detailed neural implementation