The magic of cognition

I would like to tell you about the most powerful computers on the face of earth, maybe in the entire universe. Those who know me can guess that I am referring to the humid, squishy, pinky, convoluted material apparently messy and not very elegant, that most of us wear hanging in between our shoulders and above our noses. Our brains. The famous British writer Oscar Wilde sentenced: “The great events of the world take place in the brain”. Our brains allow us to communicate, to think, to feel, they enabled our ancestors with the ability to distinguish friend from foe, to search for food, they allowed us to develop mathematics and prove Fermat’s theorem among many others, to synthesize antibiotics, to go to the moon and to explore other planets and also to fabricate those artificial and rudimentary computers that are so entertaining to us. Our brains have changed the course of natural evolution.

How is it possible that a soft biological tissue, composed of nothing more and nothing less than moving organic and inorganic molecules, can give rise to the magic of cognition? The fundamental basis for the study of the brain was established by a Spaniard, Ramon y Cajal. A giant. He wanted to become an artist. His parents told him “no way” and forced him to study medicine. He combined tradition and passion by devoting his life to observing and drawing the main cells of the brain: the neurons. The secret of the brain is hidden within the complex neural networks that connect millions of neurons. Our memories, our decisions, our feelings are codified in the patterns of connection and communication among neurons.

Let us consider an example. What does it mean to see and recognize the face of a friend? Light is reflected in that face and reaches our eyes, our retinae, and is converted into electrical signals, almost like pixels in a digital camera. From there, those electrical signals travel, in a binary format, essentially fancy sequences of zeros and ones, moving at enormous speeds, passing from one neuron to another, extracting relevant features from that face, and transforming those pixels into new codes, new formats and thus building a reality, an interpretation of the world. What we perceive is nothing more and nothing less than our interpretation, our own way of building our internal world in a code formed by zeros and ones. In a small fraction of a second, in less time than it takes to blink, we can compare those electrical pulse sequences with our memories and recognize the person in front of us.

This may not seem too surprising. After all, any kid can recognize his family and friends without having to study advanced calculus. And yet, those other computers, the artificial ones, still cannot do this very well. In fact, those tasks that seem difficult to us, such as computing the square root of 7 are very easy to execute for artificial computers. In contrast, those common sense tasks that are so intuitive to us such as identifying a friend and understanding their jokes, can be extremely difficult to teach to an artificial computer.

During the last couple of years, we have developed new tools that enable us to interrogate the brain at unprecedented resolution. We are beginning to characterize and describe the neural circuits within our brains in a large scale. Maybe in the not too distant future we may have brain diagrams similar to the ones used by electrical engineers to design computers. We are also beginning to listen how ensembles of neurons converse with each other. Elucidating how the brain works is changing history. Understanding neural circuits will enable us to alleviate the devastating conditions that afflict the brain. Imagine a world without Parkinson’s disease and without Alzheimer’s disease. Deciphering the biological codes in neuronal circuits will also enable us to build robots that are smarter than us, with tremendous consequences in almost every domain. Imagine a world where robots can paint better than Picasso, compose more beautiful music than Bach and develop theories better than Einstein. The first ultra-intelligent machine is the last invention that man need ever make. Because that machine will be able to make the rest. And perhaps more importantly, decoding the magic of cognition will allow us to understand who we are.

Brain causality, emergence and how to predict the future

Neuroscientists study the brain at multiple scales, ranging from the detailed structure of ion channels (those proteins in the neuronal membrane that let ions in and out of the cell) all the way to inferring brain function by examining behavior. There is also a similarly wide range of temporal domains from the sub-millisecond processes that govern the movement of ions up to the consequences of aging over the years.

We all hope that one day we will be able to navigate smoothly across all of these scales, in the same way that we can transition from subatomic particles all the way to galaxies (or can we?). A term that often arises when discussing different scales is the concept of emergence. Sometimes, it is useful to consider macroscopic properties of a system where “… the whole is more than the sum of its parts…” It is useful to use temperature to describe the property of an object even when there is no direct temperature in each of its atoms. There is a whole arena of Physics where we relate macroscopic thermodynamic properties such as temperature to the statistical properties of the microscopic components and their interactions.

We may expect the evolution of a similar niche in Neuroscience where we can relate the macro and micro worlds. The notion of emergence in brain circuits is not new. Ultimately, every aspect of brain function emerges from the interactions of a large number of interconnected neurons. Yet, the problem of how to rigorously define and study emergence in neural circuits has been quite elusive. Recently, Giulio Tononi’s group made a significant leap forward in an elegant manuscript that was published before the close of 2013.

The authors started by quantifying how well one could predict future states from previous states, a measure they refer to as effect information. In a nutshell, the effectiveness by which causal interactions in a system can be described depends on the degree of determinism and degeneracy. Determinism is a measure of how much noise there is. If the system is so noisy that the future is completely random and unrelated to the present, then predictability will be low. Degeneracy refers to the number of ways in which a future state can be reached from the present.

Skipping a few technical details, for any spatial or temporal level of analysis, it is possible to go through all possible states and evaluate how well future states can be predicted from the present state. In principle, it is possible to perform this analysis at multiple different coarse graining scales. We can ask about how well we can predict future states based on the flow of ions, or upon considering action potentials, or studying local field potentials, or even at the behavioral level. It turns out that it is not always the case that the most reductionist version of the system is necessarily the most informative one in terms of future states. This observation holds even though the system is perfectly “supervenient”, that is, the macroscopic states are perfectly dictated by the microstates and the mechanisms that group microelements into macro ones. In other words, there is no new magic in the macroscopic states.

The manuscript provides a series of elegant and simple examples where causal emergence arises due to an increase in determinism and/or a reduction in degeneracy upon spatial and/or temporal coarse graining at the macro scale. In this way, the authors provide a series of definitions to rigorously evaluate the optimal level to characterize and predict the behavior of the system, the level that “carves nature at its joints”.

Brining these definitions to bear on real brains is far from trivial. One of the difficulties resides in the exponential growth in the number of states and possible interactions. Even for simple organisms with a relatively small number of neurons, the number of possible microscopic and macroscopic states is so large that we cannot really compute these quantities in any simple way. Yet, not all hope is lost. The formalism defined in this study may help look for simplifications and feasible comparisons among macroscopic states or network motifs that can be characterized.

The simple and well-thought theoretical foundation established in this study opens the doors to a serious discussion and quantification of causality and emergence in neural circuits. In turn, the quantification of causal emergence may find implications for deciding upon what kind of measurements to make to study neural systems, for deciding how to best make use of neural data for practical applications such as prosthetic devices and, most importantly, for bridging different levels of analyses that can transform our understanding of brain circuits.

Hoel EP, Albantakis L, Tononi G (2013) Quantifying causal emergence shows that macro can beat micro. Proceedings of the National Academy of Sciences of the United States of America 110:19790-19795.

You want proof?

An image is worth a thousand words. And an equation is worth a thousand images. Yet, the value of pictorial proofs is astounding. I was reminded of this fact upon reading a delightful monograph by a brilliant mind, Sanjoy Mahajan, “Street-Fighting Mathematics”.

Let us examine one example (this comes from one of the exercises in Sanjoy’s book).

Consider the following sum:

You probably know that the general formula is: n(n+1)/2

But do you know why? Try it with a couple of examples to make sure that it works:

1+2+3=3x4/2=6

1+2+3+4+5=5x6/2=15

Proof 1: Group the first and last term, the 2^nd term and the one before last, etc.

q.e.d.

 (This is assuming that n is even. If n is odd, the last term in the second line is (n+1)/2+(n+1)/2).

Proof 2: By induction.

It is trivial to verify that S1=1.

Assume that 

is correct.

Then

q.e.d.

You probably have seen Proof 1 and/or Proof 2 at school at some point. And you may have forgotten about them. Here comes a neat graphical proof. Try to forget this one!

Proof 3: Pictorial

Here is another example.

You probably know Pythagoras theorem for right triangles:  where a,b are the sides and c is the hypotenuse. But do you remember the proof? Here is a pictorial proof. No words.

References

Sanjoy Mahajan. Street-Fighting Mathematics. The Art of Educated Guessing and Opportunistic Problem Solving. MIT Press. Cambridge, MA

Individuals with highly superior autobiographical memory have false memories too

The ability to remember events from the past constitutes one of the quintessential components of who we are. Take a moment to consider you and your life without those revered moments. Forming memories is likely to have played a central role during evolution by conferring species the power to learn from mistakes and to recall useful information such as directions to food sources.

Individuals differ significantly in their abilities to recall information. In particular, recent studies have identified elite players in the particular domain of autobiographical memories. How superior are these creatures in remembering their past? The results are quite impressive. For example, an investigator asked about the events that happened on October 19, 1987. If you are like me, I would not be able to report anything at all. After scrutiny, I would be able to report events that happened that year, and perhaps even pinpoint some of those events to specific months by combining memory and reconstructive logic. One of these individuals with superior autobiographical memory responded: “It was a Monday. That was the day of the big stock market crash and the cellist Jacqueline du Pre died that day.” Wow.

Intriguingly, these superior autobiographers are not better than you and me on normal non-autobiographical laboratory tests. For example, if you give them a long list of words and you test them an hour or a day later, their recall rate would be similar to that of age and gender-matched controls. Perhaps superior autobiographers keep amazingly detailed diaries, which they scrutinize over and over on a routine basis but this does not seem to be the case for all of them.

An elegant recent study examined individuals with superior autobiographical memories in tasks that involve the formation of false memories. Several studies have documented that memories are malleable and can be distorted. In one of the multiple paradigms developed to study false memories, subjects are presented with a series of slides that describe a story. After a delay of approximately one hour, subjects are presented with a narrative of the same story that introduces misinformation. Subsequently subjects are queried in terms of the story and they often report “having seen” events that were never shown during the slides but were falsely reconstructed from the narrative. It happens to the best of us. The formation of false memories has been a serious issue in court, where witnesses may faithfully believe that they remember events that never happened.

Back to the superior autobiographers, it stands to reason that if somebody can remember that the 19^th of October of 1987 was a Monday, that person will not be easily fooled into buying misinformation. Well, it turns out that this logical hypothesis is quite wrong. Individuals with superior autobiographical memories are as prone to form false memories (in laboratory tests of non-autobiographical information) as controls. They report remembering words that were never shown, they report seeing events that never happened and they may even tell you that they have seen footage of news events that does not exist.

Our memories are reconstructions, with a significant component of reality, and a few sprinkles of added fantasy, logical deduction, embellishment, emotional distortions and other tricks. Investigators can manipulate the formation of false memories by astutely implanting a few seeds of misinformation here and there. And to this date, nobody has found individuals who are immune to such memory distortions. Even amazing people who have extraordinary autobiographical recollections can make mistakes. Even if you can remember that the violinist Josephine du Pre died on Monday, October 19^th, 1987, you can be prone to forming false memories.

Reference:

False memories in highly superior autobiographical memory individuals.

Patihis L, Frenda SJ, Leport AK, Petersen N, Nichols RM, Stark CE, McGaugh JL, Loftus EF. Proc Natl Acad Sci U S A. 2013 Dec 24;110(52):20947-52. doi: 10.1073/pnas.1314373110. Epub 2013 Nov 18.