• Posted by Konstantin 16.03.2011 No Comments

    This is a (slightly modified) write-up of a part of a lecture I did for the "Welcome to Computer Science" course last semester.

    Part I. Humans Discover the World

    How it all started

    Millions of years ago humans were basically monkeys. Our ape-like ancestors enjoyed a happy existence in the great wide world of Nature. Their life was simple, their minds were devoid of thought, and their actions were guided by simple cause-and-effect mechanisms. Although for a modern human it might seem somewhat counterintuitive or even hard to imagine, the ability to think or understand is, in fact, completely unnecessary to succesfully survive in this world. As long as a living creature knows how to properly react to the various external stimuli, it will do just fine. When an ape sees something scary — ape runs. When an ape seems something tasty — ape eats. When an ape sees another ape — ape acts according to whatever action pattern is wired into its neural circuits. Does the ape understand what is happening and make choices? Not really — it is all about rather basic cause and effect.

    As time went by, evolution blessed our ape-like ancestors with some extra brain tissue. Now they could develop more complicated reaction mechanisms and, in particular, they started to remember things. Note that, in my terminology here, "remembering" is not the same as "learning". Learning is about simple adaptation. For example, an animal can learn that a particular muscle movement is necessary to get up on a tree — a couple of failed attempts will rewire its neural circuit to perform this action as necessary. One does not even need a brain to learn — the concentration of proteins in a bacteria will adjust to fit the particular environment, essentially demonstrating a learning ability. "Remembering", however, requires some analytical processing.

    Remembering

    It is easy to learn to flex a particular finger muscle whenever you feel like climbing up a tree, but it is a totally different matter to actually note that you happen to regularly perform this action somewhy. It is even more complicated to see that the same finger action is performed both when you climb a tree and when you pick a banana. Recognizing such analogies between actions and events is not plain "learning" any more. It is not about fine-tuning the way a particular cause-and-effect reflex is working. It is a kind of information processing. As such, it requires a certain amount of "memory" to store information about previous actions and some pattern analysis capability to be able to detect similarities, analogies and patterns in the stored observations. Those are precisely the functions that were taken over by the "extra" brain tissue.

    So, the apes started "remembering", noticing analogies and making generalization. Once the concept of "grabbing" is recognized as a recurring pattern, the idea of grabbing a stone instead of a tree branch is not far away. Further development of the brain lead to better "remembering" capabilities, more and more patterns discovered in the surrounding world, which eventually lead to the birth of symbolic processing in our brains.

    Symbols

    What is "grabbing"? It is an abstract notion, a recurring pattern, recognized by one of our brain circuits. The fact that we have this particular circuit allows us to recognize further occurrences of "grabbing" and generalize this idea in numerous ways. Hence, "grabbing" is just a symbol, a neural entity that helps our brains to describe a particular regularity in our lives.

    As time went by, prehistoric humans became aware (or, let me say "became conscious") of more and more patterns, and developed more symbols. More symbols meant better awareness of the surrounding world and its capabilities (hence, the development of tools), more elaborate communication abilities (hence, the birth of language), and, recursively, better analytic abilities (because using symbols, you can search for patterns among patterns).

    Symbols are immensely useful. Symbols are our way of being aware of the world, our way of controlling this world, our way of living in this world. The best thing about them is that they are easily spread. It may have taken centuries of human analytical power to note how the Sun moves along the sky, and how a shadow can be used to track time. But once this pattern has been discovered, it can be recorded and used infinitely. We are then free to go searching for other new exciting patterns. They are right in front of us, we just need to look hard. This makes up an awesome game for the humankind to play — find patterns, get rewards by gaining more control of the world, achieve better life quality, feel good, everyone wins! Not surprisingly, humans have been actively playing this game since the beginning of time. This game is what defines humankind, this is what drives its modern existence.

    Science

    Galelio's experiment

    "All things fall down" — here's an apparently obvious pattern, which is always here, ready to be verified. And yet it took humankind many years to discover even its most basic properties. It seems that the europeans, at least, did not care much about this essential phenomenon until the XVIIth century. Only after going through millenia self-deception, followed by centuries of extensive aggression, devastating epidemics, and wild travels, the europeans found the time to sit down and just look around. This is when Galileo found out that, oh gosh, stuff falls down. Moreover, it does so with the same velocity independently of its size. In order to illustrate this astonishing fact he had to climb on to the tower of Pisa, throw steel balls down and measure the fall time using his own heartbeat.

    In fact, the late Renaissance was most probably the time when europeans finally became aware of the game of science (after all, this is also a pattern that had to be discovered). People opened their eyes and started looking around. They understood that there are patterns waiting to be discovered. You couldn't see them well, and you had to look hard. Naturally, and somewhat ironically, the sky was the place they looked towards the most.

    Patterns in the Sky

    Tycho Brahe

    Tycho Brahe, a contemporary of Galileo, was a rich nobleman. As many other rich noblemen of his time, he was excited about the sky and spent his nights as an astronomer. He truly believed there are patterns in planetary motions, and even though he could not see them immediately, he carefully recorded daily positions of the stars and planets, resulting in a vast dataset of observations. The basic human "remembering" ability was not enough anymore — the data had to be stored on an external medium. Tycho carefully guarded his measurements, hoping to discover as much as possible himself, but he was not the one to find the pattern of planetary motion. His assistant, Johannes Kepler got a hold of the data after Tycho's death. He studied the data and came up with three simple laws which described the movements of planets around the Sun. The laws were somewhat weird (the planets are claimed to sweep equal areas along an ellipse for no apparent reason), but they fit the data well.

    Kepler's Laws

    This story perfectly mirrors basic human pattern discovery. There, a human first observes the world, then uses his brain to remember the observations, analyze them, find a simple regularity, and come up with an abstract summarizing symbol. Here the exact same procedure is performed on a larger scale: a human performs observations, a paper medium is used to store them, another human's mind is used to perform the analysis, the result is a set of summarizing laws.

    Isaac Newton

    Still a hundred years later, Isaac Newton looked hard at both Galileo's and Kepler's models and managed to summarize them further into a single equation: the law of gravity. It is somewhat weird (everything is claimed to be attracted to everything for no apparent reason), but it fits the data well. And the game is not over yet, three centuries later we are still looking hard to understand Gravity.

    Where are we going

    As we play the game, we gradually run out of the "obvious" patterns. Detecting new laws of nature and society becomes more and more complicated. Tycho Brahe had to delegate his "memory" capabilities to paper. In the 20th century, the advent of automation helped us to delegate not only "memory", but the observation process itself. Astronomers do not have to sit at their telescopes and manually write down stellar positions anymore — automated radar arrays keep a constant watch on the sky. Same is true of most other science disciplines to various extents. The last part of this puzzle which is not fully automated yet is the analysis part. Not for long...

    Part II. Computers Discover the World

    Manufactured life

    Vacuum tube

    The development of electricity was the main industrial highlight of the XIXth century. One particularly important invention of that century was an incredibly versatile electrical device called the vacuum tube. A lightbulb is a vacuum tube. A neon lamp is a vacuum tube. A CRT television set is a vacuum tube. But, all the fancy glowing stuff aside, the most important function of a vacuum tube turned out to be its ability to act as an electric current switcher. Essentially, it allowed to hardwire a very simple program:

    if (wire1) then (output=wire2) else (output=wire3)

    It turns out that by wiring thousands of such simple switches together, it is possible to implement arbitrary algorithms. Those algorithms can take input signals, perform nontrivial transformations of those signals, and produce appropriate outputs. But the ability to process inputs and produce nontrivial reactions is, in fact, the key factor distinguishing the living beings from lifeless matter. Hence, religious, spiritual, philosophical and biological aspects aside, the invention of electronic computing was the first step towards manufacturing life.

    Of course, the first computers were not at all like our fellow living beings. They could not see or hear, nor walk or talk. They could only communicate via signals on electrical wires. They could not learn — there was no mechanisms to automaticaly rewire the switches in response to outside stimuli. Neither could they recognize and "remember" patterns in their inputs. In general, their hardwired algorithms seemed somewhat too simple and too predictable in comparison to living organisms.

    Transistors

    But development went on with an astonishing pace. The 1940's gave us the most important invention of the XXth century: the transistor. A transistor provides the same switching logic as a vacuum tube, but is tiny and power-efficient. Computers with millions and billions of transistors became gradually available. Memory technologies caught up: bytes grew into kilobytes, megabytes, gigabytes and terabytes (expect to see a cheap petabyte drive at your local computer store in less than 5 years). The advent of networking and the Internet, multicore and multiprocessor technologies followed closely. Nowadays the potential for creating complex, "nontrivial" lifelike behaviour is not limited so much by the hardware capabilities. The only problem left to solve is wiring the right program.

    Reasoning

    The desire to manufacture "intelligence" surfaced early on in the history of computing. A device that can be programmed to compute, must be programmable to "think" too. This was the driving slogan for computer science research in most of the 1950-1980s. The main idea was that "thinking", a capability defining human intellectual superiority over fellow mammals, was mainly related to logical reasoning.

    "Socrates is a man. All men are mortal. => Hence, Socrates is mortal."

    As soon as we teach computers to perform such logical inferences, they will become capable of "thinking". Many years of research have been put in to this area and it was not in vain. By now, computers are indeed quite successful at performing logical inference, playing games and searching for solutions of complex discrete problems. But the catch is, this "thinking" does not feel like being proper "intelligence". It is still just a dumb preprogrammed cause-and-effect thing.

    The Turing Test

    Alan Turing

    A particular definition of "thinking" was provided by Alan Turing in his Turing test: let us define intelligence as a capability of imitating a human in a conversation, so that it would be indistinguishable from a real human. This is a hard goal to pursue. It obviously cannot be achieved by a bare logical inference engine. In order to imitate a human, computer has to know what a human knows, and that is a whole lot of knowledge. So, perhaps intelligence could be achieved by formalizing most of human knowledge within a powerful logical inference engine? This has been done, and done fairly well, but sadly, this still does not resemble real intelligence.

    Reasoning by Analogy

    Optical character recognition

    While hundreds of computer science researchers were struggling hard to create the ultimate knowledge-based logical system, real-life problems were waiting to be solved. No matter how good the computer became at solving abstract logical puzzles, he seemed helpless when faced with some of the most basic human tasks. Take, for example, character recognition. A single glimpse at a line of handwritten characters is enough for a human to recognize the letters (unless it is my handwriting, of course). But what logical inference should the computer do to perform it? Obviously, humans do not perform this task using reasoning, but rely on intuition instead. How can we "program" intuition?

    The only practical way to automate character recognition turned out to be rather simple, if not to say dumb. Just store many examples of actual handwritten characters. Whenever you need to recognize a character, find the closest match in that database and voila! Of course, there are details which I sweep under the carpet, but the essence is here: recognition of characters can only be done by "training" on a dataset of actual handwritten characters. The key part of this "training" lies, in turn, in recognizing (or defining) the analogies among letters. Thus, the "large" task of recognizing characters is reduced to a somewhat "smaller" task of finding out which letters are similar, and what features make them similar. But this is pattern recognition, not unlike the rudimentary "remembering" ability of the early human ancestors.

    The Meaning of Life

    Please, observe and find the regularity in the following list:

    • An ape observes its actions, recognizes regularities, and learns to purposefully grab things.
    • Galileo observes falling bodies, recognizes regularities, and leans to predict the falling behaviour.
    • Tycho Brahe observes stars, Johannes Keper recognizes regularities, and learns to predict planetary motion.
    • Isaac Newton observes various models, recognizes regularities, and develops a general model of gravity.
    • Computer observes handwritten characters, recognizes regularities, and learns to recognize characters.
    • Computer observes your mailbox, recognizes regularities, and learns to filter spam.
    • Computer observes natural language, recognizes regularities, and learns to translate.
    • Computer observes biological data, recognizes regularities, and discovers novel biology.

    Unexpectedly for us, we have stumbled upon a phenomemon, which, when implemented correctly, really "feels" like true intelligence. Hence, intelligence is not about logical inference nor extensive knowledge. It is all about the skill of recognizing regularities and patterns. Humans have evolved from preprogrammed cause-and-effect reflexes through simple "remembering" all the way towards fairly sophisticated pattern analysis. Computers now are following a similar path and are gradually joining us in The Game. There is still a long way to go, but we have a clear direction: The Intelligence, achieving which means basically "winning" The Game. If anything at all, this is the purpose of our existence - discovering all the regularities in the surrounding world for the sake of total domination of Nature. And we shall use the best intelligence we can craft to achieve it (unless we all die prematurely, of course, which would be sad, but someday some other species would appear to take a shot at the game).

    Epilogue. Strong AI

    There is a curious concept in the philosophical realms of computer science — "The Strong AI Hypothesis". It relates to the distinction between manufacturing "true consciousness" (so-called "strong AI") and creating "only a simulation of consciousness" (the "weak AI"). Although it is impossible to distinguish the two experimentally, there seems to be an emotional urge to make the distinction. This usually manifests in argumentation of the following kind: "System X is not true artificial intelligence, because it is a preprogrammed algorithm; Humans will never create true AI, because, unlike us, a preprogrammed algorithm will hever have free will; etc."

    Despite the seemingly unscientific nature of the issue, there is a way to look at it rationally. It is probably true that we shall never admit "true intelligence" nor "consciousness" to anything which acts according to an algorithm which is, in some sense, predictable or understandable by us. On the other hand, every complex system that we ever create, has to be made according to clearly understandable blueprints. The proper way of phrasing the "Strong AI" question is therefore the following: is it possible to create a system, which is built according to "simple" blueprints, and yet the behaviour of which is beyond our comprehension.

    Cellular automaton

    The answer to this question is not immediately clear, but my personal opinion is that it is a strong "yes". There are at least three kinds of approaches known nowadays, which provide a means for us to create something "smarter" than us. Firstly, using everything fractal, cellular, and generally chaotic is a simple recipe for producing uncomprehensibly complex behaviour from trivial rules. The problem with this approach, however, is that there is no good methodology for crafting any useful functions into a chaotic system.

     

    The second candidate is anything neural — obviously the choice of Mother Nature. Neural networks have the same property of being able to demonstrate behaviour, which is not immediately obvious from the neurons or the connections among them. We know how to train some types of networks and we have living examples to be inspired by. Nonetheless, it is still hard to actually "program" neural networks. Hence, the third and the most promising approach — general machine learning and pattern recognition.

    The idea of a pattern recognition-based system is to use a simple algorithm, accompanied by a huge dataset. Note that the distinction between the "algorithm" and the "dataset" here draws a clear boundary between two parts of a single system. The "algorithm" is the part which we need to understand and include in our "blueprints". The "data" is the remaining part, which we do not care knowing about. In fact, the data can be so vast, that no human is capable of grasping it completely. Collecting petabytes is no big deal these days any more. This is a perfect recipe for making a system which will be capable of demonstrating behaviour that would be unpredictable and "intelligent" enough for us to call it "free will".

    Think of it...

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  • Posted by Konstantin 07.12.2008 7 Comments

    Logic versus Statistics

    Consider the two algorithms presented below.

    Algorithm 1:

       If, for a given brick B,
          B.width(cm) * B.height(cm) * B.length(cm) > 1000
       Then the brick is heavy

    Algorithm 2:

       If, for a given male person P,
          P.age(years) + P.weight(kg) * 4 - P.height(cm) * 2 > 100
       Then the person might have health problems

    Note that the two algorithms are quite similar, at least from the point of view of the machine executing them: in both cases a decision is produced by performing some simple mathematical operations with a given object. The algorithms are also similar in their behaviour: both work well on average, but can make mistakes from time to time, when given an unusual person, or a rare hollow brick. However, there is one crucial difference between them from the point of view of a human: it is much easier to explain how the algorithm "works'' in the first case, than it is in the second one. And this is what in general distinguishes traditional "logical" algorithms from the machine learning-based approaches.

    Of course, explanation is a subjective notion: something, which looks like a reasonable explanation to one person, might seem incomprehensible or insufficient to another one. In general, however, any proper explanation is always a logical reduction of a complex statement to a set of "axioms". An "axiom" here means any "obvious" fact that requires no further explanations. Depending on the subjective simplicity of the axioms and the obviousness of the logical steps, the explanation can be judged as being good or bad, easy or difficult, true or false.

    Here is, for example, an explanation of Algorithm 1, that would hopefully satisfy most readers:

    • The volume of a rectangular object can be computed as its width*height*length. (axiom, i.e. no further explanation needed)
    • A brick is a rectangular object. (axiom)
    • Thus, the volume of a brick can be computed as its width*height*length. (logical step)
    • The mass of a brick is its volume times the density. (axiom)
    • We consider the density of a brick to be at least 1g/cm3 and we consider a brick heavy if it weighs at least 1 kg. (axiom)
    • Thus a brick is heavy if its mass > width*height*length > 1000. (logical step, end of explanation)

    If you try to deduce a similar explanation for Algorithm 2 you will probably stumble into problems: there are no nice and easy "axioms" to start with, unless, at least, you are really deep into modeling body fat and can assign a meaning to the sum of a person's age with his weight. Things become even murkier if you consider a typical linear classification algorithm used in OCR systems for deciding whether a given picture contains the handwritten letter A or not. The algorithm in its most simple form might look as follows:

       If \sum_{i,j} a_{ij} \mathrm{pixel}_{ij} > 0
       Then there is a letter A on the picture,

    where a_{ij} are some real numbers that were obtained using an obscure statistical procedure from an obscure dataset of pre-labeled pictures. There is really no good way to explain why the values of a_{ij} are what they are and how this algorithm gets the result, other than to present the dataset of pictures it was trained upon and state that "well, these are all pictures of the letter A, therefore our algorithm detects the letter A on pictures".

    Note that, in a sense, such an "explanation" uses each picture of the letter A from the training set as an axiom. However, these axioms are not the kind of statements we used to justify Algorithm 1. The evidence they provide is way too weak for traditional logical inferences. Indeed, the fact that one known image has a letter A on it does not help much in proving that some other given image has an A too. Yet, as there are many of these "weak axioms", one statistical inference step can combine them into a well-performing algorithm. Notice how different this step is from the traditional logical steps, which typically derive each "strong" fact from a small number of other "strong" facts.

    So to summarize again: there are two kinds of algorithms, logical and statistical.
    The former ones are derived from a few strong facts and can be logically explained. Very often you can find the exact specifications of such algorithms in the internet. The latter ones are based on a large number of "weak facts" and rely on induction rather than logical (i.e. deductive) explanation. Their exact specification (e.g. the actual values for the parameters a_{ij} used in that OCR classifier) does not make as much general sense as the description of classical algorithms. Instead, you would typically find general principles for constructing such algorithms.

    The Human Aspect

    What I find interesting, is that the mentioned dichotomy stems more from human psychology than mathematics. After all, the "small" logical steps as well as the "big" statistical inference steps are all just "steps" from the point of view of maths and computation. The crucial difference is mainly due to a human aspect. The logical algorithms, as well as all of the logical decisions we make in our life, is what we often call "reason" or "intelligence". We make decisions based on reasoning many times a day, and we could easily explain the small logical steps behind each of them. But even more often do we make the kind of reason-free decisions that we call "intuitive". Take, for example, visual perception and body control. We do these things by analogy with our previous experiences and cannot really explain the exact algorithm. Professional intuition is another nice example. Suppose a skilled project manager says "I have doubts about this project because I've seen a lot of similar projects and all of them failed". Can he justify his claim? No, no matter how many examples of "similar projects" he presents, none of them will be considered as reasonable evidence from the logical point of view. Is his decision valid? Most probably yes.

    Thus, the aforementioned classes of logical (deductive) and statistical (inductive) algorithms seem to directly correspond to reason and intuition in the human mind. But why do we, as humans, tend to consider intuition to be inexplicable and thus make "less sense" than reason? Note that the formal difference between the two classes of algorithms is that in the former case the number of axioms is small and the logical steps are "easy". We are therefore capable of representing the separate axioms and the small logical steps in our minds somehow. However, when the number of axioms is virtually unlimited and the statistical step for combining them is way more complicated, we seem to have no convenient way of tracking them consciously due to our limited brain capacity. This is somewhat analogous to how we can "really understand" why 1+1=2, but will have difficulties trying to grasp the meaning of 121*121=14641. Instead, the corresponding inductive computations can be "wired in" to the lower, unconscious level of our neural tissue by learning patterns from experience.

    The Consequences

     There was a time at the dawn of computer science, when much hope was put in the area of Artificial Intelligence. There, people attempted to devise "intelligent" algorithms based on formal logic and proofs. The promise was that in a number of years the methods of formal logic would develop to such heights, that would allow computer algorithms to attain "human" level of intelligence. That is, they would be able to walk like humans, talk like humans and do a lot of other cool things that we humans do. Half a century has passed and this still didn't happen. Computer science has seen enormous progress, but we have not found an algorithm based on formal logic that could imitate intuitive human actions. I believe that we never shall, because devising an algorithm based on formal logic actually means understanding and explaining an action in terms of a fixed number of axioms.

    Firstly, it is unreasonable to expect that we can precisely explain much of the real world, because, strictly speaking, there exist mathematical statements that can't in principle be explained. Secondly, and most importantly, this expectation contradicts the assumption that most "truly human" actions are intuitive, i.e. we are simply incapable of understanding them.

    Now what follows is a strange conclusion. There is no doubt that sooner or later computers will get really good at performing "truly human" actions, the trend is clear already. But, contradictory to our expectations, the fact that we shall create a machine that acts like a human will not really bring us closer to understanding how "a human" really "works". In other words, we shall never create Artificial Intelligence. What we are creating now, whether we want it or not, is Artificial Intuition.

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