The title of the project is…

An Investigation in to the Relationship Between Lower and Higher Order Cellular Automata Problems when Solved with Evolutionary Search Heuristics

Basically I’m going to be looking at how search methods inspired by Evolution can be used to solve problems in Cellular Automata and how different solutions to similar problems are related (if at all).

What the frig are Cellular Automata?

Cellular Automata are systems built up of many simple individual cells. Each of the cells is in one of a small number of states at any given time. A cell decides which state it is in by following some simple rules based upon the current state of its neighbours. Cellular automata are interesting to computer scientists (among others) because the simple rules at the micro-level (individual cells) can lead to very complex behaviour at the macro-level (the whole system).

One of the most famous cellular automata is Conway’s Game of Life, this simple model of a population of cells has demonstrated many interesting global behaviours. Earlier this month, the first replicating creature was demonstrated in the game. Previously the game has been shown to be able to model a Universal Turing Machine, meaning it is potentially capable of computing anything that can ever be computed. Not bad for some blinking blobs.

What the double frig is an Evolutionary Search Heuristic???

Evolutionary Computing is a field of computer science that looks at ways of solving problems inspired by biological evolution. Consider all the organisms in the world as being different solutions to the problem of survival. Every plant, animal, snottite and what-not, manages to survive using different strategies all developed by evolution. In computing, there are problems that cannot be solved using traditional, algorithmic, approaches. Perhaps the number of possible answers are too many to search one-by-one, or the solution is not very well defined. In cases like these, we can search for a good answer, not necessarily the best answer, but good enough. This is a Heuristic.

A simplified model of biological evolution can be applied to computer search problems. We can model potential solutions with a series of parameters, analogous to DNA. The potential solutions are tested against one another, the best are combined to produce another set of solutions. As the process is repeated, only the best solutions ‘survive’. this is known as a Genetic Algorithm. A similar process can be used to develop computer code to perform some function, this is called Genetic Programming.

Oh, I see. So what are you doing?

I’m going to be applying Evolutionary Heuristics to Cellular Automata, to find a set of simple micro-scale rules that can produce solutions to macro-level problems. Then I’ll look at whether or not these rules can be applied to other, related problems.

Evolutionary heuristics are known to produce good solutions to problems, but it can take a lot of effort to get there. For every new problem, you have to search from scratch. I’m interested in finding any ‘shortcuts’ between solutions, which would save time.

I’m going to be working on this over the next year or so. I’ve every intention to keep this blog updated with my progress and other related bits and bobs. But we’ll see how that pans out.

Laters…

The Brain is Not a Computer

I actually think the brain is a computer, if you define “computer” quite broadly as an information processing machine. And if you define “information”, “processing” and “machine” quite broadly too. What I’m actually saying it that the metaphor of the brain being like a desktop computer isn’t a very good one.

It is a useful metaphor to understand the difference between the brain and the mind (brain being the “hardware” and mind being the “software”), but that’s as far as it’ll take you. Beyond this, in any way you’d care to compare them, the brain and a computer are different.

Computers are mostly serial processors, they do one thing at a time, in a pre-defined sequence. Parallel processing is becoming more and more common, but a quad-core processor is hardly comparable to the 100’000 plus processing units of the brian – neurons.

Computer memory is designed to store data accurately, for a long time. There are checksums and recovery processes built in to computers to ensure that the data stays the same as it’s moved between hard disks, RAM and across networks. Human memory is nothing like this. Information in our brians degrades over time.  It is recalled, reviewed and rebuilt in many different ways, all the time. When we fist ‘make’ a memory, it’s already inaccurate. We don’t remember everything we see or hear, only the bits we find interesting at the time, or more accurately, the bits our brains tell us are probably the most interesting. When we recall memories the gaps are smoothed over by intuition and guesswork.

Computers break. They break a lot. For no apparent reason a computer can just stop working. This doesn’t happen to our brains,  if parts of our brain has problems other parts can step in. Studies on amputees have shown that ‘unused’ parts of the motor cortex can be reused by neighbouring parts. This can give peculiar sensations like feeling a feather on a missing hand when it’s brushed against the cheek.

There’s three reasons, but there’s countless more. In nearly every way brains are good at the things that computers are bad at, and vice-versa. I’m not saying that computers can’t be programmed to act like brains, artificial neural network models are more common than you might think. But computers are also used to model, engine parts, bridges, traffic flow, economic strategies, wars and a ton of other things, none of which we compare to being ‘like’ computers.

So that’s my theory. ACCEPT or REJECT?

]]> http://www.craig-russell.co.uk/its-only-my-theory/feed/ 0 http://www.craig-russell.co.uk/gravity-goblins-and-confirmation-bias/ http://www.craig-russell.co.uk/gravity-goblins-and-confirmation-bias/#comments Fri, 02 Oct 2009 15:39:52 +0000 Craig http://www.craig-russell.co.uk/?p=305 I’ve got a theory about gravity, not just a theory, an explanation for how gravity works. I can tell you, dear reader, exactly why bodies of mass are drawn together. My theory is clear, simple and above all correct. I know this because I have proven it. The proof is all around, as clear as sky. Allow me to explain…

My theory of gravity is simple, all objects on this earth have invisible pieces of string attached to them, upon the oppisite end of which little invisible goblins hang off. That’s correct – invisible goblins.

What do you mean you don’t believe me? Fine, I’ll prove it to you…

Pick up a pencil (or any other object you have to hand) hold it at arms length over the floor and prepare to release it (being mindful of any children or animals below). Now if my theory is correct, when you release the pencil, the Gravity Goblin (as I have christened them) will pull upon the invisible string, drawing the pencil towards the floor.

Ready…?

Release…!

Theory proven. I thank you.

Obviously, this is bollocks. But I tell it to illustrate a key part of the scientific process – falsification. Falsification allows us to differentiate between Gravity Goblins and Isaac Newton. Any monkey can “prove” a hypothesis (I’m using the more scientifically appropriate term now), finding evidence in support of a hypothesis is easy. Just pick any phenomena you fancy and make up some bullshit to connect cause and effect.

Soap bubbles in the washing up bowl? – Microscopic scuba elves.

Crystal Healing? – Energy flow and focusing and karma and that…

Homeopathic Remedies? – Diluted sub-molecular chemical memory or something…

The massive diversity of life on Earth and the subtle interactions and behaviours therein? – God.

For a hypothesis to be scientifically tested (and hence logically robust) you’ve got to attempt to prove it wrong. You’ve got to be prepared to say “if my hypothesis is correct, I can hit it with the sledgehammer of reason and it won’t crack”. Suggest a way to break it and invite others to try, if it stands up, well done, you’ve got yourself a robust theory.

Despite what you may (or may not) have thought, this kind of thinking doesn’t come naturally to our human brains. We have a habit of favouring evidence that supports our beliefs while giving less weight to the opposing evidence. Psychologists call this effect ‘confirmation bias’.  Understanding our natural tendency towards confirmation bias makes it all the more clearer why a scientific, rational approach to exploring ideas is so powerful.

Without knowing how to properly test our ideas, how to prove them wrong, we’d never be able to develop our ideas, to differentiate fact from superstition. Without falsification, we could all be believing in Gravity Goblins.

Here ’tis…

Passive dynamics is a form of locomotion where the mechanics of the device allow it to be driven forward from it’s own inertia, with minimal energy input. Formally, passive dynamics was described by McGeer (1990), but it is inspired by gravity powered toys dating back to the 1800′s (Fallis 1888). These early bipedal toys were able to walk down gentle inclines, with no energy input other than the gravitational force. The mechanics of these designs caused the toy to rock laterally from side to side, allowing one foot to swing in front of the other, producing a forward walking motion.

McGeer(1990) studied these early toys, building upon these ideas to develop a laterally stable robot with four legs and knee joints, which better approximated a human-like gait. He formalised this mathematically as the ‘rimless wheel model’ and then the ‘synthetic wheel model’. Whereby a two legged device with curved feet would approximate the motion of a wheel rolling down an incline as each foot is laid down in front of one another. He notes that with a little modification to provide power to the device in the place of gravity, this mechanism would also function on a flat surface.

It’s this approach that defines passive dynamic robotics from actively powered robotics. Actively powered robots require powered control at every point in the walk cycle, and are developed to be powered from the outset. Passively dynamic robots utilise the mechanical properties of the robot to perform the walk cycle, electronic control systems can be added later to extend the range or refine the model. McGeer(1990) draws an analogy to the development of powered flight, early flying machines were simple gliders, only later having developed a solid understanding of aerodynamics, was power source added for sustained flight.

Since this time many more researchers have developed passive dynamic robots, building upon gravity powered devices to more sophisticated motor/piston driven walkers. Collins et. al (2005a) describes the development of two such robots.

The first, built at Cornell University, was designed for minimal energy use. The first phase of development for this robot was to built a gravity powered device that was able to walk stably down a slope. The design has joints at both the hips and the knees, and is one of the first of this type to include arms. The arms are mechanically connected to the opposite leg, the swing of the arms helps to laterally stabilise this robot while walking. From this original design, a second powered robot was built. This robot is powered by electrical motors, and added spring powered joints at the ankles to provide a push off from the trailing foot. To compare the efficiency of walking between robots and with humans Collins et. al. (2005a) used a value called the specific cost of transport, this is a unit less value which gives the energy consumed per unit weight per unit distance. For a human this value is 0.2, for the Cornell biped, discussed above, this is also 0.2. Whereas for Honda’s ASIMO, a robot designed with precise joint control, this figure is much higher at 3.2.

A second robot, built at MIT, was designed to use an adaptive control mechanism which allowed the robot to maintain a stable walking gait over changing level terrain (bricks, wooden tiles and carpet). The robot makes random adjustments to it’s control parameters at each step, and measures the change in it’s performance. And a learning algorithm aims to optimise the performance gradient. This robot was able to rapidly adapt to changes in terrain. Collins et. al. (2005a) argue that the learning mechanism used in this robot is ‘biologically plausible’ as there is evidence that it may describe biological motor learning.

Another robot worthy of mentioning is RunBot, built at the University of Sterling (Geng, T 2006). RunBot has four actuated joints, two hips and two knees, there are, however, points during the walk cycle where the robot continues to move forwards without actuation. The robot is supported by a boom connected with a universal joint to a central column, causing the robot to walk a circular path. RunBot is novel in it’s use of a neural network control system. The network receives input from sensors on the hips, feet and two on each knee, and provides output to the actuators on each joint. The network allows RunBot to adapt to changing conditions in real time. RunBot is able to change walking speed and walk on irregular terrain while maintaining a stable walking gait. RunBot was designed to walk at a relative speed equivalent to that of a human. Relative speed is measured in leg lengths per second. RunBot achieves a maximum of 3.5 leg lengths per second, comparable to the fastest human walking and making RunBot one of the fastest biped robots.

The close relationship between passive dynamic robots and human locomotion has been demonstrated by Bauby and Kuo (2000). They studied the variability of human foot placement during walking and compared this to a passive dynamic biped model. Their findings suggest that human walking ‘may harness passive dynamic properties of the limbs’.

Hansen and Gard (2007) have begun to study the effect of natural (passive) dynamics on prosthetics. They have developed prosthetic feet which mimic the flexible roll of human feet and have planned to investigate any improvement in efficiency.

I find it fascinating that some of the robots described here, have already approached human levels in their respective abilities. The Cornell robot is a as efficient as a human in it’s energy use, and Runbot is able to walk (relatively) as fast. Also, the relationship of this paradigm to human mechanics is already influencing the development of prosthetic limbs. In my view, this is an exciting field that will continue to surprise as it develops in the future.

References

Bauby, C. Kuo, A. (2000) Active Contol of Lateral Balance in Human Walking. Journal of Biomechanics, 33 (11), pp. 1433-1440

Collins, S et. al. (2005a) Efficient Bipedal Robots Based on Passive-Dynamic Walkers. Science, 307 (Feb), pp. 1082-1085

Collins, S et. al (2005b) Supporting Online Material for Efficient Bipedal Robots Based on Passive-Dynamic Walkers. [WWW] Science. Available from http://www.sciencemag.org/cgi/content/full/307/5712/1082/DC1 [Accessed 22/09/09]

Collins, S et. al (2001) A Three-Dimensional Passive-Dynamic Walking Robot with Two Legs and Knees. The International Journal of Robotics Research, 20 (7), pp. 607-615

Collins, S. Ruina, A. (2005) A Bipedal Robot with Efficient and Human-Like Gait. [PDF] Cornell University. Available from http://ruina.tam.cornell.edu/research/topics/locomotion_and_robotics/papers/efficient_bipedal_robots/bipedal_walking_robot_cornell.pdf [Accessed 22/09/09]

Fallis, G. (1888) Walking Toy. United States Patent Office, Patent No. 376588

Geng, T et. al. (2006) Fast Biped Walking with a Sensor-driven Neuronal Controller and Real-time Online Learning. The International Journal of Robotics Research, 25 (3), pp. 243-259

Hansen, A. Gard, S. (2007) Effects of Prosthetic Foot Rocker Radius on Gait of Prosthesis Users. [WWW] Northwestern University. Available from http://www.medschool.northwestern.edu/depts/repoc/sections/research/projects/ambulate/foot_rocker_radius.html [Accessed 22/09/09]

McGeer, T. (1990) Passive Dynamic Walking. The International Journal of Robotics Research, 9 (2), pp. 62-82

Why do this you may ask? Well, I’ve come to realise that there is little point attempting to get anyone to abandon their belief system for the sake of (what appears to them to be) a minor intellectualist point. And anyway, I don’t want to be that guy. If your god makes you happy, and your not hurting anyone, I’ve got no issue there. I can, however, appeal to every bit of human reason and logic that you have to demonstrate to you that belief in evolution is not ‘the same’ as belief in divine creation. Evolution is a rational, logical process, not a superstition.

So, here goes…

Oh, one more thing. I am just a layman, my understanding of the subject comes solely from GCSE science (about 10 years ago) and a few popular science books. I welcome any corrections or further discussions.

So, again, here goes…

Evolution requires two basic assumptions: a population of replicating entities (we’ll call them Blobs), and some non-random selection process for stopping some Blobs from replicating.

These blobs simply clone themselves, we’re not going to bother with the intricacies of sexual reproduction, or the artificial randomisation in evolutionary algorithms. The selection process must be non-random as this is the guiding force of evolution, a farmer selecting for larger cows will get larger cows, an algorithm selecting for optimisation will achieve higher efficiency.

As no copying process is perfect, there will occasionally be a Blob that is slightly different from it’s parent. Over time, a population of Blobs will eventually show variety across the board. The selection process (whatever it may be) will eliminate some blobs, preventing them from replicating. The remainder of the population will continue to clone themselves (with the occasional error), and the population as a whole will move towards the ideal defined by the selection process. If only the fastest are selected, the population will get faster. If only the smallest are selected, the population will get smaller.

That is evolution in a nutshell.

…which may seem a bit far removed from “the reason for the diversity of life on earth”, but it’s not really. In the natural world, the selection process is the attainment of resources, If you don’t succeed in getting food, you die. And there are many different food resources out there each requiring specialist abilities to take advantage of. The natural world allows for life* to diversify and specialise in surviving on some of the resources available. Don’t forget too that life too is a resource to be consumed, which inevitably some organisms evolved to take advantage of. so there are actually many different ‘selection pressures’ driving evolution in different directions.

Evolution is also useful in fields other than the natural sciences, the basic principles of evolution have been knowingly put to use in industry, creating optimisation algorithms for complex machinery; like aircraft carriers, stealth bombers and nuclear reactors. These control systems have far too many variables to exhaustively explore all the configurations, so evolutionary principles have been applied to find the settings for optimum operation.

I don’t mind that you don’t believe that evolution ‘actually happened’. I don’t mind if you choose to believe that it was all made by some divine being,  I don’t want to take that from you. But evolution is not impossible. I hope to have shown that from a few basic assumptions, what logically follows is a powerful, beautiful, creative process.

*if you haven’t worked it out by now, that’s the Blobs