Posts Tagged ‘mistakes’

About The Limits of Reason

Sunday, August 3rd, 2008

You can always find an infinite amount of equations that fits a finite set of points.

When the set of points changes the equation changes. This represents a major problem when you want to find a general pattern. The solution is to assume that the pattern behind the set of points has to be a Simple Equation (or a Simple Law).

A  theory has to be simpler than the data it explains, otherwise it does not explain anything.

To define Simplicity we have to define a tool that measures the simplicity of an equation. Mathematicians have tried to solve this problem in many different ways. The problem seamed unsolvable until computers and software-languages were invented.

A law of nature is a piece of software, a computer algorithm, and instead of trying to measure the complexity of a law via the size of an equation, we now consider the size of programs, the number of bits in the software that implements a theory.

If every theory is represented by a string of bits we are able to analyze what a computer (our “thinking mind”) is able to represent. The problem is transformed to the problem of representation. Behind this problem lies the problem of Compression.

Our Reality is represented by the simplest equation (the shortest (most compressed) binary set) that when it is expanded represents the most complex binary set that represents our reality.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz

One of the conditions we have to add is the condition of “understand ability”. Perhaps the expression exists but we are unable to grasp the law. Leibniz calls this law the principle of sufficient reason.

Leibniz formulated this principle as follows: “Dieu a choisi celuy qui est… le plus simple en hypotheses et le plus riche en phenomenes” (God has chosen that which is the most simple in hypotheses and the most rich in phenomena)”. “Mais quand une regle est fort composée, ce qui luy est conforme, passe pour irrégulier” (But when a rule is extremely complex, that which conforms to it passes for random)”.

The interesting point in the statements of Leibniz is de term “irrégulier“. It is translated by the term “random“. This term can be interpreted in many ways. In the world of Statistics it means that a certain event is unpredictable. In algorithmic terms it means that we are unable to find a pattern behind the pattern we observe. A random pattern is an essential pattern. It cannot be compressed.

Science ends when we have found randomness and have reached the Limits of Reason.

Everybody has a Limit of Reason and this limit expands in time but for every mind that will be born there is an absolute limit of Reason. When we have reached this limit we will know there are still patterns to find but we will be unable to prove they are real patterns.

Gregory Chaitin
Gregory Chaitin

Gregory Chaitin is the expert of the Limits of Reason and he is highly influenced by Leibniz.

By running a program you can eventually discover that it halts, if it halts. When it halts you have found a theory. The problem is to decide when to give up on a program that does not halt.

A great many special cases can be solved, but Turing showed that a general solution is impossible. No algorithm, no mathematical theory, can ever tell us which programs will halt and which will not.

We are never certain that we have found a theory because when we wait a little longer (collect more facts) we find the final theory that explains what we want to explain (if we understand the theory).

We could use a computer to search for patterns (this happens already) but the computer presents an incomprehensible theory (this happens already) or it has to search a little longer. A computer could run “for ever” when there is enough energy but a human has a fixed lifetime. The halting problem shows that we will not know how long “for ever” is. We also will not have enough minds to analyze the output. The Halting problem is proved to be unsolvable.

Chaitin defined a constant Ω that shows our progress in reaching the Limit of Reason. It shows our progress to reach the Incomprehensible.

We still have a long way to go.

The Halting Problem cannot be solved because we (the Humans) are unable to define the Limits of Reason. Even the Brightest Minds will not be able to understand all the patterns that are available in Our Universe. Even Mechanical Devices programmed by the Brightest minds will not solve the Mystery. Somewhere we will make a Mistake.

The Mistake will start a new process of Inquiry and New Theories will be created that will always contain a Mistake. We will be Busy until Enternity to Create because we are not perfect. Only Perfect Solutions are Impossible.

I want to close this blog with a statement of Leibniz: ”Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien”(Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything)”.


George Chaitin about the Principle of Sufficient Reason

About  Geometry and Fractal Patterns

About Formal Languages and Mistakes 

About the Quest for the perfect language (A Talk of Chaitin about the book of Umberto Ecco)

Leibniz forgot to mention the role of the Artist

About Leibniz and Deleuze

About Turing Machines

Why Conflicts Solve Many Security Problems: About Attacks and Mistakes

Tuesday, November 20th, 2007

One of the most interesting jobs in my career was the management of the Security in a big bank. It was an interesting job but also a very stressful job.

When you are responsible for Security you are always fighting against two forces. The first force is the Outside Attacker. The other force is your Boss.

When “Things Go Terribly Wrong” your Boss will be very angry.

When “Nothing is Happening” he will reduce your budget or he will tell you to stop “boddering people” with all the things you do to “Prevent that Terrible Things will Be Happening”.

People don’t like Security Measures.

One of the most spectaculair activities was “The Simulated Attack“. We paid people to attack our Systems and we hoped we could stop them. I can tell you one thing. They always succeeded! Personnally I am convinced it will be much easier to attack a bank than 10 years ago. I still know “How They Did It” and I know it is almost impossible to prevent “This to Happen”.

If you know a little bit about the way payments are processed the only thing you have to do is to change a software-program. “This” can be done on many levels in the IT-Infrastructure. When you do “this” on a “deep level” you need a lot of technical expertise. You can also do it in a simple way. Just sell yourself as a programmer to a contracter or sub-contracter.

The funny things is that you can also Attack a Bank without the intention to Attack the Bank. Just “Make a Vital Mistake” and Complete Systems Stop Working. Soon I discovered that “Preventing Small Mistakes” was much more important than “Preventing a Big Attack”.

The most important reason is that when somebody wants to Attack a Bank you just cannot stop them without Stopping the Bank.

You need to take so many “Counter-Measures” that everybody (Personel and Customers) is simply stopped in everything they want to do.

One of the people that inspired me the most was Prof.dr. Willem Albert Wagenaar. He showed me that it is almost impossible to prevent mistakes.

When you want to Prevent a Mistake you Have to  Change the System Not the People.

Many Security systems are Symbolic Systems. You are not allowed to exceed a speed-limit when you drive a car. It would be much easier to block the car to exceed the limit.

The only thing you can do is to “design” systems that are resistant to the things “you don’t want to happen”. But Beware of the “Total Blocking Effect”.

A very effective way to do this is to “Create a Conflict”.

When you don’t want somebody to spend money without permission make Two persons responsible for the decision to spend the money. When you want to prevent that your personnel is treated badly make one person responsible for the Care of the personnel and another for the Use of the personnel. When you want High Quality and Speedy Delivery make one person responsible for Quality and the other for Speed.

The most important thing you have to do to make this work is to give them Equal Power. When you don’t do this one of them will become the Slave of the Other. When you give them Equal Power they have to Negociate the Two Conflicting Forces.

A Projectmanager needs a Very Special Expert to reach his goals in time and the Expert is very tired or sick or his father is dying. The  solution is to talk with the Customer and explain the problem to him. Perhaps he wants to postpone the project for a few days.

A bad solution is to waste the Expert (he will make mistakes) or to use an unexperienced employee (he will make mistakes). When they make mistakes the project has to be postponed and the Customer will loose his faith in your competence.

When the Opponents are unable to solve the conflict give a third party (The Wise Judge) the Power to Decide and write down “How He Solved the Conflict”.

This will prevent the next one.