Registered: Feb 2004
Posts: 152

Objective: This thread will illustrate various aspects of randomness and their implication for the modeling of biomedical phenomena with CA.
--------------------------------------------------------------------------

Cellular automata (CA) provide simple models for evaluating interesting philosophical questions. Here is a simple teaser:

The definition of a cellular automaton (CA) excludes randomness. Nevertheless S. Wolfram applies random numbers as initial states for his CA. What an inconsistency! Rather he ought to use CA for generating initial states, and ban the term “Randomness” from his models. You might apply the term “Pseudo-randomness” to a given state provided that you specify the CA (or CA set) which generated it, and the number of iterations to reach it. Wolfram uses a CA for generating pseudorandom sates, yet does not specify their two crucial attributes {CA set, number of iterations}.

Why do I dislike randomness? As a physician I am flooded with medical statistics based on the Normal Distribution and its derivatives. The Normal Distribution is the hallmark of randomness in science. However, in Medicine (like in Love) nothing is really random. Life and randomness is a medical oxymoron, which causes medically induced diseases known as Iatrogenesis.

More teasers in my site: http://www.what-is-cancer.com/papers/ca/ca01.htm

G. Zajicek gzajice@what-is-cancer.com

Last edited by Gershom Zajicek M.D. on 04-22-2006 at 10:42 AM

Report this post to a moderator | IP: Logged

Registered: Aug 2003
Posts: 712

The distinction between "pseudo random" and "random" assumes there is a real physical process that qualifies as the latter rather than the former. Which is at best debatable. The NKS book has an extensive discussion of forms of randomness - from page 299 to 326 -

http://www.wolframscience.com/nksonline/section-7.2

The whole of chapter 6 is about the behavior of simple programs from random initial conditions. But be clear about this - the systems examined there are completely deterministic in their evolution from their initial condition. There is no "inconsistency" with "the definition" of CAs. There is no coin-flipping at each step along the way, only different starting conditions. Each step below is always exactly the same for a given starting condition.

If you want to enumerate all possible initial conditions up to a certain width you can look at those instead of random initial conditions. You will find it rather hard once you get to a modest initial width, since the number of possible initial conditions rapidly exceeds the number of particles in the universe. Inevitably, you sample to look at the behavior of wider initial patterns.

You either sample random patterns to see how wider ones typically behave, or you sample contrived ones you have generated through some more simplified procedure. In the latter case, however, you will have no idea whether the results you see are representative of the zillions of otherwise similar cases that do not have the simplified initial structure you provided them.

In NKS Explorer, you can conduct the experiments yourself and try different initial conditions. The random number seed is one of the fields you can change, and is fully displayed. The procedure used to generate the initial condition from that seed is also fully specified in Mathematica - it is based on rule 30. Provide your own copy of the program the same seed, and naturally it gives the same initial condition.

There are 133 index entries about randomness in the NKS book. Notes about it are found from page 967 to 977 and again on page 1067-6, covering the history of definitions of it, practical means used to generate it and how they actually work, and its use in models. It is a broad and interesting subject.

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

Nature presents itself to us as change. We distinguish between two kinds of change: Change which is explained by a theory, and unexplained change, which we call Randomness. Randomness is not an inherent (ontological) property of nature. It is our way to describe it.

In linear models randomness is represented by a separate term, called error, which has to be minimized. Here R-square expresses the adequacy of a linear model. In other words, R-square stands for the fraction of the observations explained by the theory , and 1-Rsquare stands for randomness or error.

Neural Nets start from a random initial state and converge to a (non random) solution. Thus Neural Nets are processes (algorithms) which eliminate randomness. On the other hand, chaotic CA systems lack this property. If they start from a random initial state they will propagate randomness, and even amplify it. Above all, such models can not be reproduced, since being sensitive to initial conditions. For this reason their initial states ought to be non random and uniquely specified.

Life never starts from randomness. Two cells, the sperm and the ovum unite to form a (non random) zygote, which evolves into what we are. This is why Life and Randomness is a medical oxymoron, and a meaningful model of Life has to exclude Randomness.

More on this topic in my site: http://www.what-is-cancer.com/papers/ca/ca01.htm

G. Zajicek gzajicek@what-is-cancer.com

Report this post to a moderator | IP: Logged

Registered: Aug 2003
Posts: 712

Of course they can be reproduced. Start them from the same exact initial condition - e.g. by specifying the same random number seed - and you get the exact same pattern every time.

As for whether there is randomness in the sense of uncaused, probabilistic underlying events, it is an open philosophic and physical theory question. The NKS view is that underlying deterministic systems can produce all the apparent randomness we see, without requiring underlying stochastic processes. So far as that is your main point - that you'd like to see more use of deterministic simple program models rather than stochastic, statistical ones, particularly in biology - fine I agree with you. That is part of the point of NKS.

But NKS still speaks of randomness, not where determinism is lacking but where computational reducibility is lacking. The randomness driving the economy of Las Vegas does not depend on whether underlying physical theory is eventually grounded in a deterministic NKS type model, or a stochastic QM type model. Either way, there is phenomenal randomness, for practical purposes.

One can define the terms in various ways. It seems to me the meaning ascribed to "randomness" should not beg relevant open questions, either about what "can" exist or about what sort of model does account for phenomena we see. It should also stay close enough to ordinary usage, that what average speakers refer to as random in everyday life, are still called random.

In common speech, we call things random when our ordinary methods of analysis cannot "crack" them or exhaustively reduce their behavior to a simplified structure. We call, for instance, the digits of pi random, when they are a fully specified constant of nature that cannot be otherwise, which we can determine by any of a number of different, exact mathematical formulas.

We don't mean that we can't know the millioneth digit of pi. We just mean before we calculate it, we have no confidence it will be (say) "4" rather than "7". We wouldn't accept a bet for one rather than the other offering only 2:1 odds, if we haven't calculated the right answer beforehand. We would if the odds were 50:1 - provided the amount at stake was livable if we lost.

Following your link one question you had is whether CAs can model systems like flames, which have direction and structure as well as seemingly chaotic elements. Look at the java applet on the CA FAQ page linked below. It is using a CA to generate those images, though I don't know the underlying details enough to say whether it uses any explicit randomizing steps or not. I hope it is of some interest.

http://cafaq.com/bibliography/index.php

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

We ought to distinguish between Random and Pseudo Random initial conditions. The first obviously cannot be reproduced. Pseudo Random initial conditions meet my requirements provided that one specifies how they were generated. I don’t recall that in his examples Wolfram specifies how the pseudo random initial conditions were generated.

While disliking Randomness, Pseudo Randomness is closer to my heart since I know how it is generated. While Randomness and CA is an oxymoron, pseudo randomness and CA, is not. My point is that in the world of CA, Randomness is meaningless, and should not be used. The same applies to biology and medicine.

I agree with you that one can define terms in various ways. However in medicine such terms have profound implication on therapy and may harm the patient. This issue is dealt with in my site under the heading: A New Kind of Medicine. (you might abbreviate it as NKM) http://www.what-is-cancer.com/paper...wmedicine0.html

Thanks for the link depicting CA flames. I would appreciate if you find out how the program looks like, particularly it’s CA portion.

G. Zajicek gzajicek@what-is-cancer.com

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

The Central Limit Theorem (CLT) states, that any sum of many independent identically distributed random variables is approximately normally distributed. http://www.worldhistory.com/wiki/C/...mit-theorem.htm
For instance if dice are rolled repeatedly, the frequency distribution will resemble more and more the Normal Distribution. You may check it experimentally at the following site:
http://www.stat.sc.edu/~west/javahtml/CLT.html

The CLT is the hallmark of Randomness, which underlies many statistical procedures. Does it apply also to the world of CA? You may create a pseudorandom set of initial conditions, and let the CA evolve. When small they may obey the CLT, yet when larger they do not. More precisely, when the distance between the CA is such that they remain isolated, CLT works. When overlapping, it fails, and in chaotic CA it is useless.
CLT works only in linear systems whose elements do not interact and are isolated. In other words CLT thrives on Randomness which CA lack. Farewell to linear statistics.

Life also lacks the two prerequisites of CLT. Neither are its elements isolated nor independent. Unfortunately, epidemiologists ignore this common wisdom and base their statistics on the CLT. They take the human being and simplify his attributes until the CLT requirements are met. Yet this simplified creature is a far cry from that which was created in Genesis. Epidemiology thus nurtures medically induced diseases known as Iatrogenesis. By now you might understand why I dislike randomness.

To learn more on the distortions of medical statistics visit my site at:
http://www.what-is-cancer.com/paper...tsgenetics.html

G. Zajicek gzajicek@what-is-cancer.com

Last edited by Gershom Zajicek M.D. on 02-11-2004 at 02:15 PM

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

The Random Walk is another manifestation of the Randomness concept. It is a stochastic process like Brownian motion, and serves among other to describe the stock market and exchange rates. The Efficient Market Theory says that the prices of many financial assets, such as shares, follow a random walk.

Random walk may explain why the stock market won’t make you rich. However it fails to explain why some brokers got rich. No wonder, since the stock market is more than a sum of random walks. It is a living system, and as such cannot be modeled by random walks. Economists don’t like this idea because they do not know how to model living systems. They reduce and simplify the humans which make the stock market tick, to faceless points, until they meet the prerequisites of random walks.

Yet all these amazing guys who made a fortune, are not at all faceless as economists suggest. They are simply creative, and since economists do not know how to model creativity, they ignore it. It seems as if CA might be a good tool for modeling creativity. An example of what is meant is given in my site: http://www.what-is-cancer.com/papers/ca/ca3.htm

I wonder whether a CA model of the stock market would help me to reduce my overdraft.

G. Zajicek gzajicek@what-is-cancer.com

Last edited by Gershom Zajicek M.D. on 02-29-2004 at 04:54 AM

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

Nature presents itself to us as change. We may distinguish between rapid change, like a torrent, and a slow change, which is called variation. Prior to Darwin, variation was regarded as God’s creation. Some even believed that God whose nature is incomprehensible, presents himself to us as variation.
In 1859, Darwin published “The Origin of Species” in which he explained variation in a novel way. Variation evolves. He distinguished between three kinds of variation:
1. Spontaneous, known today as genetic mutation, or crossover.
2. The outcome of competition between species.
3. Resulting from the selection of entities which will survive by the environment, known as “Survival of the Fittest.”
Evolution is a random process. Its objects are powerless to alter their fate. They are shuffled in the hyperspace representing nature like dice. Yet life is more than that! It is creative, exclaimed Henri Bergson in his book “Creative Evolution”. http://www.what-is-cancer.com/papers/Bergson.html

He was ignored as an esoteric Vitalist. Today Darwin’s theory gained the status of a religion: “Nothing in Biology makes sense except in the Light of Evolution” said Theodosius Dobzhansky. Modern Darwinists ignore that there may be other more sophisticated ways to model evolving variation.

The crudeness of Darwin’s model is evident in Genetic Algorithms (GA) which apply it for classifying and generating various solutions,. They manipulate their objects in the same way as Darwinists would suggest. Despite some impressive achievements, GA hardly ever generalize. Above all they are not creative.

They better be called Creationistic GA, since their proper function requires a programmer god (demiurge), whose task is to select proper fitness spaces, define fitness measures, and crossover modes. GA illustrate the major weakness of Darwin’s theory, it is based on Randomness which by its very nature cannot be creative.

I dislike Darwinism for two main reasons: 1. Social Darwinism promotes discrimination, and 2. Medicine applies Darwinism to describe cancer progression. As cancer evolves, it becomes fitter than its host (the patient), and gradually destroys him . Yet Cancer is more than that! It is a creative process operating in a creative host. More on cancer and host creativity in my site: http://www.what-is-cancer.com

G. Zajicek e-mail gzajicek@what-is-cancer.com

Last edited by Gershom Zajicek M.D. on 02-29-2004 at 04:55 AM

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 6

I've read your post on ANKoS forum. I think you have misunderstood randomness here. Random doesn't mean casual.

"However, in Medicine (like in Love) nothing is really random."
In fact nothing is completely random. That's why probability theory has not only uniform variables but all kinds of distributions, and that's why two different random processes can be correlated or not. I have a certain probability of getting in love, but that probability can be higher if I meet the right girl P(in love|right girl). It's a over simplification to say that random in medicine means "without any rule". In fact, Bayesian modelled diagnosis tools perform quite well, in some cases better than the human doctors that instructed it.

"Nature presents itself to us as change. We distinguish between two kinds of change: Change which is explained by a theory, and unexplained change, which we call Randomness. Randomness is not an inherent (ontological) property of nature. It is our way to describe it."
Randomness is implicit in nature. Quantum physics and the Heisenberg's indetermination principle say that.

"Neural Nets start from a random initial state and converge to a (non random) solution. Thus Neural Nets are processes (algorithms) which eliminate randomness."
Neural nets are usually deterministic you're right (mostly). But what does it mean? They still deal with randomness. The probability theory rules that we use to manipulate random variables aren't random and so? Tools can be random or deterministic, this says nothing. Neural networks are strongly based on probability theory, in fact they are derived from Bayesian classifiers. Randomness does converge, every randomized algorithm for example converges (otherwise we couldn't get d a solution) and they are fundamental in computer science. The CLT say something on that too. But this is not an argument against randomness! It just says that random does not mean that we can't get results from it, and that random doesn't mean casual, inpredictable.

"Life never starts from randomness. Two cells, the sperm and the ovum unite to form a (non random) zygote, which evolves into what we are. This is why Life and Randomness is a medical oxymoron, and a meaningful model of Life has to exclude Randomness."
??? Yes when the sperm and the ovum met they form a zygote. And so? Do they always met? No! They met with some random distribution. By the way without randomness the darwinian evolution simply does not work, so it's lucky that we have randomness all the way down :D

"Life also lacks the two prerequisites of CLT. Neither are its elements isolated nor independent. Unfortunately, epidemiologists ignore this common wisdom and base their statistics on the CLT. They take the human being and simplify his attributes until the CLT requirements are met. Yet this simplified creature is a far cry from that which was created in Genesis. Epidemiology thus nurtures medically induced diseases known as Iatrogenesis. By now you might understand why I dislike randomness."
Sometimes you can misuse a tool and what will that say? That the tool itself is wrong? No maybe it's wrong in that model, maybe the model is oversimplified but that's something that you'll find everywhere in science, we always make simplifications, with random processes and without. Determinism that you advocate is no better. Equations are not more powerful than random models, they are usually worse. Chaotic system could be but it's hard to say. Even Wolfram that was wrote a big book saying many things that where known for decades (he is not the only one, or the first, or the main, CA researcher, and CA are only a subset of all the chaotic models we could use) hasn't found a good way to use them to solve some kind of scientific problem as far as I know. He haven't applied them in the real world, they're just toys, interesting, unoriginal toys. Not a 'new kind of science'. Not even a 'new kind of model' as the model was already widely known.

"The Random Walk is another manifestation of the Randomness concept. It is a stochastic process like Brownian motion, and serves among other to describe the stock market and exchange rates. The Efficient Market Theory says that the prices of many financial assets, such as shares, follow a random walk."
See the reply above... if a model doesn't fit a problem that doesn't make the underlying framework bad. We should only elaborate a more complex model. That more complex model could be random or non random, it depends but that doesn't say anything about how good are random models in general. The fact that they are so widely used, that they are so successful and that there aren't other models in many fields should tell you that they shouldn't be so bad after all... If even with all those simplifications they manage to make good predictions, that means that there is some inherent randomness, who knows what we can make with the same framework and more accurate models!

"The crudeness of Darwin’s model is evident in Genetic Algorithms (GA) which apply it for classifying and generating various solutions,. They manipulate their objects in the same way as Darwinists would suggest. Despite some impressive achievements, GA hardly ever generalize. Above all they are not creative."
Eh!!! GA do generalize, GA are global optimizators, GA are creative! And if we don't use GA we use other random processes to solve global optimization problems, not deterministic ones! There's no useful deterministic global optimization procedure (except maybe tabu search). All the deterministic ones are local, they converge to a local minimum and fail to find a global one. We should be happy that life is dominated by the Darwinian process, otherwise we could fail in one of those local minimums and never evolve further.

"I dislike Darwinism for two main reasons: 1. Social Darwinism promotes discrimination, and 2. Medicine applies Darwinism to describe cancer progression. As cancer evolves, it becomes fitter than its host (the patient), and gradually destroys him . Yet Cancer is more than that! It is a creative process operating in a creative host."
Wrong, wrong, wrong, WRONG. Again and again the same argument. You dislike something because you find that it fails sometimes, in a particular contest (I don't know how good are Social Darwinism or Darwinian cancer evolution, I assume that they are bad, I trust you). If someone writes a bad model using linear equations would you say that linear equations are bad?

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

Thank you for your response. Please remember that the discussion is essentially philosophical. The question is whether Randomness exists as such in (biological) Nature. I claim that it does not. This concept is applied by us for describing (understanding) Nature. Randomness exists solely in the eye of the beholder.

You have to distinguish between reality and the tools we apply to study it. To my understanding, traditional statistical tools, which you mentioned, fail in (non trivial) CA models. Therefore, if we wish to model life with CA, we have to abandon this concept. In the CA universe, Randomness is meaningless. Medicine enters a new era in which tools based on Randomness will have to be replaced with better ones.

By the way I really don’t dislike randomness, I simply ignore it. I mentioned “disliking” only to provoke you. After all, there might be a take home lesson even for you. If you happen to be treated by a doctor who applies randomness, you might ask another one for a second opinion. This is the main message of “The New Kind of Medicine” described in my site:
http://www.what-is-cancer.com/paper...wmedicine0.html

G. Zajicek gzajicek@what-is-cancer.com

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 6

Randomness can or can not exist in nature. I don't think we'll ever know. We are limited in what we can know about reality by our senses. We cannot know something that we haven't created, we never will (at least not if we don't find some recursion at certain point) because there will always be something more subtle or too big for us to measure. And when we can't measure the state of a thing, we don't have even to ask if there's some inherent randomness in it, it will be unknowable for us without probability. Even in probability concepts do not apply to CA (as they do not apply to many other things) when we want to apply CA to nature we have to do some approximation or we have to reason in a probabilitic way. So there's no point in asking ourselves if radomness is or isn't part of the nature, what we can't know should be modelled as a probability.
By the way you haven't posed a 'philosophical' question, you raised pratical, actual arguments against the use of probability as a modelling tool. I answered those statements.

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

You obviously may use any tool for any kind of model, yet when choosing CA as your model you are somewhat limited. Regard modeling as a game. You start with certain rules, and play. The rules of the “CA game”, and Randomness, don’t go together. In CA the present state determines what the next state will be, and in random processes the present state has no effect on the next one. Either you stick to the CA rules, and keep away from using Randomness, or you include Randomness in the “CA game”, whereupon it ceases being a “CA game”. In other words, no CA rule generates Randomness, and vice versa. Inclusion of Randomness in CA models leads to a contradiction.

In my opening statement I wrote: “Cellular automata (CA) provide simple models for evaluating interesting philosophical questions. Here is a simple teaser . . .” I use CA to illustrate a fundamental property of Life. Each state depends on the previous one. Since statistical tools, like the Central Limit Theorem, or Random Walk require that the states of a process be independent from each other, they are inadequate for studying Life (and CA). New tools have to be invented.

More philosophical teasers in my site: http://www.what-is-cancer.com/papers/ca/ca0.htm

G. Zajicek e-mail gzajicek@what-is-cancer.com

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 6

Of course CA are a model and of course they're not probabilistic. They are useful and they model many interesting phenomenons. I don't argue (and haven't argued) this. But what does this tell to us about randomness and nature? You made some strong claims about that, and I replied to those.

"Since statistical tools, like the Central Limit Theorem, or Random Walk require that the states of a process be independent from each other, they are inadequate for studying Life (and CA). New tools have to be invented." Some statistical tools require independancy. Some others do NOT. By the way the fact that some tools are or aren't good doesn't tell us anything about randomness and nature.

Last but not least: "Inclusion of Randomness in CA models leads to a contradiction." LOL! Try to search google about "probabilistic cellular automata"... The fact that Wolfram doesn't mention them into his book does not mean that they don't exist! Wolfram has only made some (too) strong claims on CA, he hasn't invented them.

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 152

The concept of entropy was introduced in 1865 by Rudolf Clausius According to the second law of thermodynamics the total entropy of a thermally isolated system can never decrease. In 1877, Boltzmann defined entropy as a function of the possible microstates in a system. It is a measure of the system’s disorder. In this context the second law of thermodynamics states that the disorder in an isolated system tends to increase.

Which caught the imagination of doom prophets. Since the universe is an expanding closed system, its total disorder increases. Ultimately it will reach a state in which its thermal energy will be homogenously distributed, and die a “heat death”.

Might a rising entropy account also for human death? Obviously not, since the organism is an open dissipative system. In his book “What is Life” Erwin Schrödinger suggested that the entropy of our organism remains low since it feeds on negentropy.

Following Boltzmann’s model, Claude E. Shannon defined entropy as a measure of uncertainty. In the state of randomness, entropy and uncertainty are maximal. Which brings us back to a statement made here in a previous section, that Randomness is ignorance.

Entropy is meaningless when applied to CA for two reasons. 1. In statistical thermodynamics, entropy varies between 0 and 1. Since CA and Randomness are mutually exclusive, CA entropy will never vanish (be zero). Unlike in Information theory or Statistical Thermodynamics, CA entropy is not defined over the entire [0 , 1] interval. 2. CA may be regarded as an open system. An isolated string of numbers will never change by itself. It has to be driven to its next state by a processor. While the string may be regarded as isolated, together with the processor it is an open system in which entropy is meaningless.

More on “unpleasant” properties of CA: http://www.what-is-cancer.com/papers/ca/ca01.htm

Report this post to a moderator | IP: Logged

Registered: Feb 2004
Posts: 6

Mhm I can't reply your last post, but it was out of topic in my opinion. I never argued about the properties of CA. I argued about randomness and nature (the lack of the first in the second). All the other things could be right, but what do they tell to us? What does your last post tell? That CA lacks entropy, ok take that for granted, what so? It is true that randomness is ignorance, but is ignorance something that we can eliminate when we talk about nature (science) or not? I don't think so, I don't think that we could ever know a world that we haven't made down its inner workings. And there are some physical evidence that this is true too, that we can't rely on deterministic tools to study the inner workings of the matter. So the fact that CA lacks randomness is not a good thing 'science-wise' (by the way, as I told you this is NOT TRUE, there are some non-deterministic versions of CA). I don't believe that CA can ever be a new kind of science, to prove that you shouldn't try with so weak philosophical arguments, let's begin to see what they can do in some real 'production' environments...

Report this post to a moderator | IP: Logged