strange loops

The Mitr

Review of I Am A Strange Loop by Douglas Hofstadter – Part 2

Part 1

The toilet flush is one of the simplest and common feedback mechanisms that we find. There is a float which rises with the water level which controls the inflow of water. After a certain height is reached the water inflow is stopped. Do we attribute intentionality to the water flush? We usually do not. And this is the theme that Hofstadter explores in Chapter 4 Loops, Goals and Loopholes.

But what kinds of systems have feedback, have goals, have desires? Does a soccer ball rolling down a grassy hill “want” to get to the bottom? 52

We anthropomorphize objects and impart them our human attributes. Adding a “purpose” or a “goals” to any system is considering it from a teleological perspective. Teleology is the explanation of phenomena by the purpose they serve rather than by postulated causes. Considering examples of variations on this theme, we can say that answer to the above question is not clear cut. There are no black-and-white answers but are judgment calls. We tend to move towards the idea of teleology and intention for a system when the feedback mechanisms are not directly perceptible.
Among other examples, Hofstadter considers plants which in normal time will appear to be static and without any “goals”. But a time-lapse of the same would show that they have “goals” and “intentions” and use strategies to achieve them.

The question is whether such systems, despite their lack of brains, are nonetheless imbued with goals and desires. Do they have hopes and aspirations? Do they have dreads and dreams? Beliefs and griefs? 53

The claim is made that presence of a feedback loop in a system, triggers in us a response which shifts the description from a goalless level of mechanics to a goal-oriented level of some cognitive mechanism. Things have the desire to move!
So far we have considered basic feedback loops. Now we move onto a more complex idea of a positive feedback loop. In a positive feedback loop, a part of the output of the system goes into increasing the output by a certain factor. With each iteration the output increases, which causes the next output to increase even more. A small change in input can cascade into a very large change (exponential) in output.
Perhaps the most common example of a positive feedback loop is the unpleasant, high pitch sound one hears in an auditorium or a meeting. This happens when a microphone gains some of its output as an input and produces an ever increasing pitch and volume of the input sound. An example is given below:

Now one can imagine that due to the exponential nature of growth, any little disturbance in such a system might lead to a sound which will eventually destroy everything.

In theory, then, the softest whisper would soon grow to a roar, which would continue growing without limit, first rendering everyone in the auditorium deaf, shortly thereafter violently shaking the building’s rafters till it collapsed upon the now-deaf audience, and then, only a few loops later, vibrating the planet apart and finishing up by annihilating the entire universe. What is specious about this apocalyptic scenario?

But this is a fallacious argument. The first fallacy is the physical nature of the setup and the amplifier in our scheme of things. If the roof falls, it will destroy the amplifier too! The second case is the nature of the amplifier, it doesn’t amplify in an unlimited way. After a certain gain, due to the physical design, the amplification becomes equal to unity and the system stabilizes at its natural frequency. It so happens that the natural high frequency of an audio amplifier is close to a high pitch scream. This is achieved by the system tends to go towards that pitch in series of rapid iterations. These are the screeching high pitch oscillations that we hear. It seems the systems “wanted” to go there, the stable point of its existence. Thus we see that
Similarly, we can also “see” visual feedback loops, when the output of a camera is given back to the camera. This can be most easily setup by pointing the camera towards a screen which is showing a live output of the camera. The cover image of the book is one such image, captured during Hofstadter’s “experiments” with the visual feedback system. One of the difference, in this case, is that the camera is not an amplifying device, it just transmits. Yet the pictures it produces are bizarre and beautiful. Seeing images of video feedback gives one a sense of mystery and wonder. There is some inherent beauty in it, yet it seems un-natural to watch.

Feedback — making a system turn back or twist back on itself, thus forming some kind of mystically taboo loop — seems to be dangerous, seems to be tempting fate, perhaps even to be intrinsically wrong, whatever that might mean. 57

Shifting gears, we get a Hofstadter’s introduction to Gödel when he was fourteen. What intrigued him was the thought that one could have an entire book about a single book. The book was Nagel and Newman’s Gödel’s Proof, published in 1958. Hofstadter wrote the introduction to the new imprint in 2001. He was fascinated by footnote on formal use of quotation marks.

So here was a book talking about how language can talk about itself talking about itself (etc.), and about how reasoning can reason about itself (etc.). I was hooked! I still didn’t have a clue what Gödel’s theorem was, but I knew I had to read this book. 58

This is something that happens to me too. Some time back (almost a decade now) I had posted about books attracting me. Perhaps it happens to many people.
We next look at famous Russel’s Paradox. One of the examples derived from it is Barber’s Paradox

The barber is the “one who shaves all those, and those only, who do not shave themselves.” The question is, does the barber shave himself? [.]

There is also a loop here and there is contradiction too.

This loophole (the word fits perfectly here) was based on the notion of “the set of all sets that don’t contain themselves”, a notion that was legitimate in set theory, but that turned out to be deeply self-contradictory. 60

Russell tried to overcome this by formally re-defining the concepts of sets to save this, but it didn’t work out well. Rather it became too complex, though built on solid, atomic (in the mathematical sense) ideas.

In Principia Mathematica, there was to be no twisting-back of sets on themselves, no turning-back of language upon itself.  61

But why is self-reference considered problematic? Here Hofstadter quotes from his column Metamagical Themas (an anagram of Martin Gardner’s Mathematical Games) in Scientific American on Self-Referential sentences. But all were not receptive to the idea, some of the readers were sceptical about the utility of self-reference and denied any meaningful output of such activities.
In the next chapter On Video Feedback we explore the theme of video of video feedback and Hofstadter’s experiments with it. He explores and explains many of the images which were made by adding slight things in the image, fox example, truncated corridor, endless corridor, helical corridor etc. The common element in all these video feedback is the repeating of the primary image in scaled down fashion till the resolution of the screen can support (theoretically infinite). During one the experiments, he covers the lens and then removes his hands. During this, the movement of his hand is captured and forms an endless image which is moving, even when the hand is removed. This action has formed a loop and is feeding itself in a cyclic setup.

A faithful image of something changing will itself necessarily keep changing! 67

A similar phenomenon is that of dogs barking in sync. Some dog somewhere, starts to bark for something that is passing near it. Now, other dogs pick up and start barking too. And the chain goes on. Once setup, it doesn’t matter what was the reason for the first dog to bar, it may have gone away. But the chain of barking sustains itself. During one the flights, I have seen this happen with small babies. There were about 5-6 babies on the flight. It so happened that one of them started to cry for some reason. Then the rest joined in one-by-one. Perhaps the others were crying because the heard another one cry. And the event became self-sustaining. This went on for quite some time.
This is one of the core idea of an emergent phenomenon, once

In general, an emergent phenomenons omehow emerges quite naturally and automatically from rigid rules operating at a lower, more basic level, but exactly how that emergence happens is not at all clear to the observer. 68

The video explorations led to some fantastic images, many of which are reproduced in color in the central pages of the book. In the last part of the chapter, Hofstadter drives towards one of the central themes which we will explore in the remaining book. The idea is that strange and robust (self-sustaining) structures can emerge from the process of looping.

Once a pattern is onthe screen, then all that is needed to justify its staying up there is George Mallory’s classic quip about why he felt compelled to scale Mount Everest: “Because it’s there!” When loops are involved, circular justifications are the name of the game. 70

Some of the images I myself have collected are shown below:


The locking-in gives rise to abstract phenomena at higher levels.

In short, there are surprising new structures that looping gives rise to that constitute a new level of reality that could in principle be deduced from the basic loop and its detailed properties, but that in practice have a different kind of “life of their own” and that demand — at least when it comes to extremely finite, simplicity-seeking, new level of description that transcend the basic level out of which they emerge. 71

Whether we will be able to actually do it, or want to do it is another question. This reminds me of the saying: In theory, there is no different in theory and practice, in practice there is.
Here are a few more:


 

The Mitr

Review of I Am A Strange Loop by Douglas Hofstadter – Part 1


I recently finished I Am A Strange Loop by Douglas Hofstadter. The book is an introduction to the core ideas about self, self-reference, feedback loops and consciousness as  an emergent phenomena. The core question that is considered is

What do we mean when we say I?

Hofstadter in the preface indicates his angst at many people missing out on the core ideas of Gödel, Escher, Bach: An Eternal Golden Braid. No doubt GEB is hard to read, and each one makes their own meaning of it.

Years went by, and I came out with other books that alluded to and added to that core message, but still there didn’t seem to be much understanding out there of what I had really been trying to say in GEB. xiii

I Am A Strange Loop is sort of a prequel to GEB, which came afterwards. In the book the focus is on developing an idea of emergent self, in which our consciousness is seen to emerge from feedback that we have by interacting with the world. Hofstadter uses a variety of examples to drive home the point of recursive feedback loops, giving rise to strange phenomena. The central claim is that we, our sense of self, our idea of consciousness derives from recursive interactions and feedback that we get via our senses.
He starts with a dialogue he wrote as a teenager between Plato and Socrates about what is it to be alive and being conscious, this in a way sets the stage for things to come. In the first chapter On the Souls and Their Sizes we are made to think about presence of souls in different foods that we eat (he himself doesn’t partake mammalian meat). We non-chalantly eat a tomato, irritatingly squish a mosquito, but what happens when we eat higher life forms, like chicken, pigs and sheep? Do they have souls? Do all living beings have souls? If so, then does the soul of a human is greater than that of a cow (now here I must be careful, there are people in my country who judge the soul of a cow much much greater than that of a human being), of a pig, of a chicken, of a mosquito of a tomato?

Does a baby lamb have a soul that matters, or is the taste of lamb chops just too delicious to worry one’s head over that? 18

The suggestive answer is  given in a conciousness cone, in which we normal adult humans are at the top and atoms are the start of the cone. But then granted that we have a soul, are we born with a fully developed one? Here Hofstadter takes a developmental approach to the concept of the soul. The idea is that we are born with some essence of what appears to be soul, then gradually over the years it develops. The concept of soul here is used interchageably with “I”. The main take home point in this chapter is whatever this is, we do not get the fully developed version of it from birth. Rather it is a developmental process which takes place in the real world, shaped by experiences. The said developmental changes are in degree, rather than a black/white switch.
In the second chapter This Teethering Bulb of Dread and Dream we look at possible ways of studying the mechanisms of the brain which might potentially shed some light on the puzzle that we are after. In general the idea of studying the hardware of the brain seems to be set in agenda of many neurologists. But Hofstadter argues against this way of studying thinking.

Saying that studying the brain is limited to the study of physical entities such as these would be like saying that literary criticism must focus on paper and bookbinding, ink and its chemistry, page sizes and margin widths, typefaces and paragraph lengths, and so forth. 26

Another analogy given is that of the heart. Just like heart is a pumping machine, brain is a thinking machine. If we only think heart as an aggregate of cells, we miss out on the bigger picture of what the cells do. The heart surgeons don’t think about heart cells but look at the larger structure. Similarly to study thinking the lower level of components may not be the correct level to study highly abstract phenomena such as concepts, analogies, consciousness, empathy etc. This is pointing towards thinking as an emergent phenomena, emerging from the interactions at lower levels which are composed of objects/entities which are not capable of thinking.
Hofstadter then takes philosopher John Searle to task for his views regarding impossibility of thinking arising from non-thinking entities. The analogy of a beer can to a neuron is taken apart. What is suggested by Searle in his thought experiments is equivalent to memory residing in a single neuron. But this certainly is not the case. We have to think of the brain as a multi-level system. But going too deep in these levels we would not get a comprehensible understanding of our thinking.

Was it some molecules inside my brain that made me reshelve it? Or was it some ideas in my brain? 31

Rather it is ideas that make more ideas.

Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to producein toto a burstwise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell. Sperry as quoted on 31-32

Another analogy that is given is that of Thermodynamics and Statistical Mehcanics. Just as atoms interact in a gas at a micro-level to create gas laws which can be observed at a macro-level. The macro-level laws also makes it comprehensible to us, because of the sheer amount of information at mirco level that one would have to analyse to make sense. (Provided that we can in theory solve such a massive set of equations, not considering the quantum mechanical laws.) Similarly the point is made that for understanding a complex organ such as the brain, which contains billions of interacting neurons, we should not look at the hardware at the lowest level, but rather look for macro-level patterns.

Statistical mentalics can be bypassed by talking at the level of thinkodynamics. 34

The perception of the world that we get is from sensory inputs, language and culture. And it is at that level we operate, we do not seek atomic level explanations for the dropping of the atomic bomb. This simplification is part of our everyday explanation, and we choose the levels of description depending on the answers that we are seeking.

Drastic simplification is what allows us to reduce situations to their bare bones, to discover abstract essences, to put our fingers on what matters, to understand phenomena at amazingly high levels, to survive reliably in this world, and to formulate literature, art, music, and science. 35

The third chapter The Causal Potency of Patterns provides us with concrete metaphors to think about emergent phenomena and thinking at levels. The first of such metaphors is a chain of dominoes, which can be thought of as a computer program for carrying out a given computation. In this case finding checking if a number is prime: 641. Now a person watching the domino fall right upto 641 can presumably give two answers, the first one is that the domino before 641 did not fall, while other is 641 is a prime number. These two answers are many levels apart. The second example is of Hofstadter sitting a traffic jam, The reason why you are stuck in traffic, is because the car in front of you is not moving. On the other hand this does not tell you anything about  why the jam arose in the first place, which may be due to a large number of cars going home after a game or a natural disaster of some kind. The main idea is that we can have two (many?) levels of explanation each one looking at the system from a different level of detail, for example, the car ahead of you local,  the reasons for the jam global. As far as the causal analysis goes we can look at answers at different levels.

Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals. 41

Similar example is that of a combustion engine. The designers of the engine do not think about molecular level of interactions, the level that is relevant for them is the thermodynamic level of pressure, temeperature and volume. The properties of individual molecules like their locations, velocities is irrelevant in such a description, though the properties of the ensemble is.

This idea — that the bottom level, though 100 percentresponsible for what is happening, is nonetheless irrelevant to what happens — sounds almost paradoxical, and yet it is an everyday truism. 42

Another example that is given is of listening to music. Lets say you hear a piece of music, and you experience some emotions due to it. Now, consider there was a slight delay before playing started, the actual molecules which vibrated to get you the music, would be different than in the first case. Yet, you would experience the music in the same way even though the molecules that brought you that music were completely different.

The lower-level laws of their collisions played a role only in that they gave rise to predictable high-level events. But the positions, speeds, directions, even the chemical identity of the molecules – all of this was changeable, and the high-level events would have been the same. 42

Thus we can say that a lower level might be responsible for a higher level event and at the same time is irrelevant to the higher level.
 
The next metaphor we consider is that of careenium and simmbalism. (No points for guessing what the intended puns are here!) There are many witty puns throughout the book, and Hofstadter uses them very effectively to make his points. This Gedankenexperiment is referred to many times in the book. Simms (small interacting marbles) are very small marbles, which can crash into each other and bounce off the walls in a frictionless world. They are also magnetic so that if they hit each other with low velocity they can “stick” to each other and form clusters called simmballs. A simmball can be composed of millions of simms, and may loose or gain simms at its boundary. Thus we have tiny and agile simms, and huge and nearly immobile simmballs. All this bashing and boucing happens at frictionless pooltable, the careenium.
After setting this metaphorical system we add another complexiety that external events can affect the simmballs, thus we can have a record of history by reading the configurations of simmballs. Now a reductionist approach to this system would be that we really need to know only about nature of interaction of the simms, rest are just epi-phenomena, which can be explained by behavior of the simms. But such a view isnot helpful in many ways. One of the issues that is raised is that of enormous complexity raised by such approach will render it meaningless. But, whether we can even describe a phenomena in a truly fundamental way, just by using basic laws is itself questionable.
A interesting reading in similar line of though is by Anderson (Anderson, P. W. (1972). More is different. Science, 177(4047), 393-396). He gives examples from physical science which seemingly defy solutions or explanations on basis of the fundamental laws. He strongly argues against the reductionist hypothesis

The main fallacy in this kind of thinking is that the reductionist hypothesis does not by .any means imply a “constructionist” one: The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe, In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, theless relevance they seem to have to the
very real problems of the rest of science, much less to those of society.

Anderson draws three inferences from this 1) Symmetry is of great importance to physics; symmetry the existence of different viewpoints from which the system appears the same. 2) the internal structure of a piece of matter need not be symmetrical even if the total state of it is.

I would challenge you to start from the fundamental laws of quantum mechanics and predict the ammonia inversion and its easily observable properties without going through the stage of using the unsymmetrical pyramidal structure, even though no “state” ever has that structure.

3) the state of a really big system does not at all have to have the symmetry of the laws which govern it; in fact, it usually has less symmetry.

Starting with the fundamental laws and a computer, we would have to do two impossible things – solve a problem with infinitely many bodies, and then apply the result to a finite system-before we synthesized this behavior

Finally Anderson notes:

Synthesis is expected to be all but impossible analysis, on the other hand, may be not only possible but fruitful in all kinds of ways: Without an understanding
of the broken symmetry in superconductivity, for instance, Josephson would probably not have discovered his effect.

Going back to Hofstadter, he considers a higher level view of the Gedankenexperiment with simms, simmballs and careenium. To get a birds eye view of our  have to zoom out both space and time. The view that we will get is that of simmballs, simms would be to small and too fast for us to view at this level. In fast forward of time, the simmballs are no longer stationary, but rather are dynamic entities which change their shapes and positions due to interactions of simms (now invisible) at lower level. But this is not evident at this level, though the simms are responsible for changing the shape and position of simmballs, they are irrelevant as far as description of simmballs.

And so we finally have come to the crux of the matter: Which of these two views of the careenium is the truth? Or, to echo the key question posed by Roger Sperry, Who shoves whom around in the population of causal forces that occupy the careenium? 49

The answer is that it all depends on which level you choose to focus on. The analogy can be made clear by thinking of how billions of interacting nuerons form patterns of thought, analogy, interacting ideas. Thus while trying to think about thinking we should let go of observing a single neuron, or the hardware of the brain itself, it will not lead us to any comprehensible description or explanation of how we think. Nuerons are though responsible for thinking they are irrelevant in the higher order of thinking.