User talk:Robert Adams: Difference between revisions

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Without a very careful presentation, it is very possible that the CZ community will not accept this article as meeting its standards. [[User:John R. Brews|John R. Brews]] 16:20, 21 July 2013 (UTC)
Without a very careful presentation, it is very possible that the CZ community will not accept this article as meeting its standards. [[User:John R. Brews|John R. Brews]] 16:20, 21 July 2013 (UTC)


== Article has been moved here for storage ==
TITLE: The Rules Of Physics


This article is clearly not of encyclopedic standards.  I have moved your text here for the moment.  I will ask a Constable to delete the remaining articles. [[User:Hayford Peirce|Hayford Peirce]] 17:39, 22 July 2013 (UTC)


1.0   ABSTRACT.
1.0     ABSTRACT.
Physics is a study of repeatable measurements which are for all intents and purposes made by light. Each observer "owns" the light beams associated with his observations and measurements and the velocity of light is independent of the relative velocity of object being observed.
Each observer has access to exactly one coordinate system, his own. Access to another observer's coordinate system is made by a communication instrumentation process which is accomplished by light. 
Finally, mathematics is the language that defines the communication between observers. It is not an expression of the truth from absolute point of view.
I believe that these are the rules that define the field of physics. Furthermore, I believe these rules may result in the discovery that an object can have a velocity greater than light.


Physics is a study of repeatable measurements which are for all intents and purposes made by light. Each observer "owns" the light beams associated with his observations and measurements and the velocity of light is independent of the relative velocity of object being observed.
2.0    DETAILED DISCUSSION
2.1    PHYSICS IS A STUDY OF REPEATABLE MEASUREMENTS


Each observer has access to exactly one coordinate system, his own. Access to another observer's coordinate system is made by a communication instrumentation process which is accomplished by light.  
Is sound generated from a tree falling down in the forest if there is nobody there to hear it?  This is an interesting question which I heard a long time ago, probably in my first years of college.


Finally, mathematics is the language which provides a convenient communication between observers, not an expression of the truth from absolute point of view.
How do we know that sound is generated if there is nobody there to hear it? Most assuredly, the generation of sound and listeners to hear the sound are irretrievably connected. Consequently it is impossible to logically answer the above question.


I believe that these are the rules that define the field of physics. Furthermore, I believe these rules will result in the discovery that an object can have a velocity greater than light.
I believe that there is a simple response to above question and this response will provide a profoundly simple definition of the field of physics. Namely, if there is no listener, nothing can be said about the generation of sound.
Historical speaking, the field of Physics is the study of repeatable observations and measurements. Everything in the field of physics that we know today is the result of a long sequence of experiments performed over several hundred years.
2.2    PHYSICISTS ALSO HAVE BELIEFS
The human being needs to believe in something. The many religions would not exist if this was not so. Physicists have their own unique set of beliefs. One of these beliefs had important historical consequences.


2.0  DETAILED DISCUSSION
2.3    THE ETHER BELIEF
As early as 1600, it was known that light could travel in a vacuum. There was a strong belief that light like sound needed a media for its transmission. This gave birth to very undetectable transmission media called the "Ether".


2.1  DEFINITION OF PHYSICS
Fresnel originally proposed the velocity of the earth and that of the Ether relative to the World Coordinate System were different. In 1845, Stokes proposed that the Ether was attached to the earth. Later, Maxwell proposed that the Ether was attached to the World Coordinate System.


Is sound generated from a tree falling down in the forest if there is nobody there to hear it?.  How do we know that sound is generated if there is nobody there to hear it?
The resulting intense research effort was motivated by the possibility that measurements of light in a refractive media would help them measure the velocity of the earth relative to the World Coordinate system
 
Most assuredly, the generation of sound and listeners to hear the sound are irretrievably connected. Consequently it is impossible to logically answer the above question.
 
There is a simple answer to above question and this answer will provide a profoundly simple definition of the field of physics.
 
Historical speaking, the field of Physics is the study of repeatable observations and measurements. Everything in the field of physics that we know today is the result of a long sequence of experiments performed over several hundred years.
 
The subject question is not valid. The field of physics requires the presence of the observer and sound is one of the observer's means of observation.
 
2.2  THE ETHER BELIEF
 
As early as 1600, it was known that light could travel in a vacuum. There was a strong belief that light like sound needed a media for its transmission. This gave birth to very undetectable transmission media called the "ether".
 
Fresnel originally proposed the velocity of the earth and that of the ether relative to the World Coordinate System were different. In 1845, Stokes proposed that the ether was attached to the instrument. Later, Maxwell proposed that the ether was attached to the World Coordinate System.
 
The resulting intense research effort was motivated by the possibility that measurement of light in a refractive media would help them to measure the velocity of the earth.


This research effort was terminated in 1881 by the Michaelson-Morley experiment which clearly demonstrated that one could not measure the velocity of the earth from the behavior of light within a moving coordinate system.
This research effort was terminated in 1881 by the Michaelson-Morley experiment which clearly demonstrated that one could not measure the velocity of the earth from the behavior of light within a moving coordinate system.


At this time, the ether and the world coordinate system, the baseline for Newtonian Physics, became obsolete.
At this time, the Ether and the World Coordinate System, the baseline for Newtonian Physics, became obsolete.


 
2.4    THE POSTULATES OF EINSTEIN
   
   
2.3  THE POSTULATES OF EINSTEIN
Einstein proposed that 1) the laws of physics are the same for all observers independently of the relative velocity between the observers and 2) the velocity of light is independent of the velocity of the source relative to the observer.
Einstein proposed that 1) the laws of physics are the same for all observers independently of the relative velocity between the observers and 2) the velocity of light is independent of the velocity of the source relative to the observer.


These postulates were not consistent with the Newtonian equations of motion as they were understood during this period. Einstein proceeded to modify the Newtonian equations of motion so that they would be consistent with these postulates. His effort resulted in the Special Theory of Relativity.
These postulates were not consistent with Newtonian Physics as they were understood during this period.  
Einstein proceeded to modify Newtonian Physics so that it would be consistent with these postulates. His effort resulted in the Special Theory of Relativity.  
2.5    THE SPECIAL THEORY OF RELATIVITY


If we accept the historical fact that the field of Physics is the study of repeatable observations and measurements, then we must update our understanding of Einstein's two postulate.
The Special Theory of Relativity is basically a system of equations which relates the observations made by two observers in terms of the relative velocity between them.


Specifically, the observer basically "owns" the light beams defining his observations. Two observers, looking at the same object, will not "share" the light beams. Consequently, an observer cannot directly "look through the eyes of" another observer.
These observations included position, time and velocity. The velocity of light was made independent of velocity of the source relative to either observer. Consequently, the velocity of light is independent of the relative velocity between the two observers. 
   
The Special Theory of Relativity supports the statement that field of Physics is the study of repeatable observations and measurements. The numbers associated with these equations (position, time, velocity, etc) are the results of these measurements.
2.6    MATHEMATICS AS A LANGUAGE
2.6.1  MATHEMATICS AS A "TRUE" STATEMENT?
"The word comes first and the word is true" is a relatively common religious statement.  It requires that the associated statement is accepted without question. These statements are the foundation of the associated belief.
The human being needs to believe in something. The many religions would not exist if this was not so. Physicists have their own unique set of beliefs. Can the mathematics of Theoretical Physics be considered a statement of beliefs that can be accepted without question? Will it ever be?
I think not.


The only way that an observer can share his observations with another is through a communication process. Communication is a very complex measurement process involving one or more languages.  One of the best languages for the field of physics is the mathematical expression.
These mathematical equations are used to communicate and explore the results of continuing research programs. If the results of these experiments are not consistent with the associated mathematical equations, the differences are carefully examined and the associated mathematics is updated.


2.4  MATHEMATICS AS A LANGUAGE
The Special Theory of Relativity and Quantum Mechanics are important historical examples of this update process and there is no reason to assume that this will not occur again.


2.4.1 MATHEMATICS AS A "TRUE" STATEMENT?
I believe that a re-examination of the Special Theory Of Relativity and its defining Einstein Postulates will enable the next major discovery.
3.0    MY RE-EXAMINATION
3.1    LORENTZ TRANSFORMATION
The Special Theory of Relativity and the associated Lorentz Transformation attempts to define the differences between two observations based on the differential velocity between the two associated observers.
From an observer point-of-view, the Special Theory of Relativity has not been thoroughly tested.  Even with our manned space travel activities, the relative velocity between observers is negligibly small relative to the speed of light.
3.2     EINSTEIN POSTULATES RE-EXAMINATION
From an observer point-of-view, the Einstein's Postulates have also not been thoroughly tested.   Again, the relative velocity between observers is negligibly small relative to the speed of light.
Assuming that these postulates are unconditionally valid, what can we learn by re-examining them. My re-examination has resulting in the following conclusions.


"The word comes first and the word is true" is a relatively common religious statementIt requires that the associated statement is accepted without question. These statements are the foundation of the associated belief.
3.2.1  SPEED OF LIGHT RE-EXAMINATION
   
Einstein's second postulate states that the velocity of light is independent of the velocity of the source relative to the observer. This will be the case for multiple observers receiving light from the same source.


How much "truth" is contained in these religious statements? These statements originated a long time ago and were usually written in an ancient languageA significant amount of interpretation and translation was required resulting in many opportunities for inaccuracies in the communication process.
I have some serious problems with Einstein's second postulate where there are multiple observers with large relative velocities.  
   
Specifically, I have difficulty accepting the constancy of the speed of light where the multiple observers are using the same light beam to observe the same source.
The only way that I can resolve this issue is to make the assumption that the multiple observers can not share the light beams from the source being observed. In essence, each observer must have his own light beam from the common source.


The human being needs to believe in something. The many religions would not exist if this was not so. This need is also present in field of Theoretical Physics. Please keep in mind that it took over 30 years to discard the belief in the "ether".
As a consequence, each observer has access to only one coordinate system, his own. The only way that an observer can share his observations with another is through a communication process.


Can the mathematics of Theoretical Physics be considered a statement of the "truth"? I think not. I believe that I might have found a "Goedel's Incompleteness Theorem" problem in one of my personal research efforts.
3.2.2  RELATIVE SOURCE VELOCITY QUESTION
   
My re-examination has resulting in an interesting final question. Einstein's second postulate does not appear to place any limitations on the relative velocity between the source and observer.


2.4.2 TIME-DEPENDENT DIFFERENTIAL EQUATION
Can this relative velocity be greater than the speed of light?


During this research effort (Sections 4.1, 4.2) I found a significant problem in a time-dependent differential equation.
You say no and you have a large amount of theoretical physics research and the resulting mathematical equations to back it up!
But wait a minute! These mathematical equations resulting from Einstein's postulates relate a set of numeric measurements with another. These equations are not a definition of fundamental truths.


Time is basically defined by a periodic process commonly referred to as a clock.  
Let's assume for the present that this might be possible.
 
The clock consists of a oscillator, a zero detector, and a counter. The zero detector issues a "tick" whenever the state (velocity, position) of the oscillator is zero. The counter, incremented with each tick, presents the passage of time.
Let us assume that an object moves from the left towards the observer, passes very close to the observer, and then moves to the right away from the observer. Let us also assume that this object emits light along the way.  
 
Let there be two clocks. Let the frequency of the second oscillator clock be a integer multiple (n) of the frequency of the first one. Then every n'th tick of the second clock will coincide with the ticks of the first one, There are an infinite number of unique second clocks that will have coincidental ticks with the first clock.
3.2.2.2 LESS_THAN_LIGHT
Let us assume that the velocity of the object is less than the speed of light. Then when the object is approaching the observer, the light will arrive at the observer before the object. The observer will see the object move towards him from the left, pass by him, and then move away from him to the right.
3.2.2.3 GREATER_THAN_LIGHT


Let us assume that the velocity of the object is greater than the speed of light. Then when the object is approaching the observer, the object will arrive at the observer before the light.
The observer will not see the object approaching him. Instead, the observer will see two objects travelling on the same line, one moving away from him to the left, and the other moving away from him to the right.
 
3.2.2.4 EXPANDING UNIVERSE
   
   
Time appears to be a countably infinite variable.  Continuous numbers are uncountably infinite. As a consequence, the time dependent derivative may not be sufficiently valid to render the associated differential equation a statement of "truth".
There have been many measurements that suggest that the universe is expanding.
 
Finally, I believe that it is impossible to prove that time is either continuous or discrete (Section 4.3). I think that this could be a "Geodel Incompleteness Theorem" problem. If so, theoretical physics and the associated mathematics may not be capable of defining the universe.
 
2.4.3 VALUE OF MATHEMATICS
 
We must now ask the question: "What is the true value of Mathematics"?
 
Communication is a complex and imperfect instrumentation process by which humans share their experiences and ideas. Each society has a unique language that facilitates their unique communication process.
 
Mathematics is the language of the society of physicists. In this society, it is a very efficient communication tool.
 
3.0  CONCLUSIONS
 
3.1  ROLE OF MATHEMATICS


Mathematics is the primary language used by physicists to communicate with each other and to prepare a historical record of their work.
Is it truly expanding? Perhaps there are objects with relative velocities greater than light which gives us the impression of an expanding universe?
 
3.2  ROLE OF LORENTZ TRANSFORMATION
 
The Special Theory of Relativity and the associated Lorentz Transformation attempts to define the differences between two observations based on the differential velocity between the two associated observers.
 
From an observer point-of-view, the Special Theory of Relativity has not been thoroughly tested.  Even with our manned space travel activities, the relative velocity between observers is negligibly small relative to the speed of light.
 
3.3  OWNERSHIP OF LIGHT
 
For all observers, the speed of light is independent of the relative velocity of the object being observed. Each observer "owns" the light beams defining his observations.
 
The act of making an observation or the number of observers making the observation does not restrict the behavior of object being observed.
 
Although there is no evidence of this time, Einstein's second postulate does not seem to restrict the relative velocity of the object being observed to less than the speed of light. 
 
3.4  PROPOSAL
 
A major potential opportunity may be present if we can accept the Rules of Physics as presented in this document. Specifically, it may be possible for an object to have a velocity relative to an observer greater than the speed of light.
 
Let us assume that an object moves from the left towards the observer, passes very close to the observer, and then moves to the right away from observer. Let us also assume that this object emits light along the way.
 
Let us assume that the velocity of the object is less than the speed of light. Then when the object is approaching the observer, the light will arrive at the observer before the object. The observer will see the object move towards him from the left, pass by him, and then move away from him to the right.
 
Let us assume that the velocity of the object is greater than the speed of light. Then when the object is approaching the observer, the object will arrive at the observer before the light.
 
The observer will not see the object approaching him. Instead, the observer will see two objects, one moving away from him to the left, and the other moving away from him to the right.
 
3.4.4 CONCLUDING REMARKS
 
There have been many measurements that suggest that the universe is expanding.


Is it truly expanding? Are there objects with relative velocities greater than light that give the impression of an expanding universe?
Only time and additional research will answer these questions.


Only time and additional experimentation will answer these questions.
==References==
==References==
<references/>
<references/>

Revision as of 19:40, 4 December 2013

Welcome to Citizendium, the Citizens' Compendium! We hope you will contribute much and well. You will probably want to read the help pages. Again, welcome and have fun! John Stephenson 15:07, 16 July 2013 (UTC)

Rules of physics: some suggestions and queries

Hi Robert:

I am unclear what your objective is with the blank article RULES OF PHYSICS and the more extensive version: The Rules Of Physics. You may be unaware of the existing article Physics or have in mind some elaboration of the subject that is not explained at the beginning of your piece.

There are some CZ conventions in article construction you will have to follow. Neither of your titles follows CZ custom, which would be in the form The rules of physics with only the lead word and proper nouns capitalized. The use of an abstract is common in technical publications, but not on CZ, where an introductory few lines explains the subject. You can look at some example articles like Physics or Speed of light to get the idea.

The outline provided in the abstract to The Rules Of Physics appears to state your personal conception of the topic. I'd hazard that this approach will not fly without supporting references and a clear presentation of the objectives of the article, and whether this is (in your opinion) a personal point of view or a presentation of an established view.

Although CZ prides itself upon being constructed by experts, no author here is felt to be such an expert that their unsupported opinion is sufficient basis for assertions. References are provided using footnotes and a References section. If you click the Edit indicator at the top right of a page like Metre (unit) and scroll through the text you will see how these notes and sources are provided in a CZ article that uses this formatting.

It appears that your article is a work under construction. Perhaps you would find it more comfortable to develop it on a user page until it reaches a more mature form? That can be done by moving your work to a new page like User:Robert Adams/The rules of physics.

Hope to see your efforts grow and prosper as you learn more about CZ. John R. Brews 03:59, 21 July 2013 (UTC)

Some additional observations

Below are some remarks I have placed on the Talk page for your article. I'm repeating them here in the event you move this page to user space and they become lost.

Faster than the speed of light

Robert: As you know, the speed of light plays a key role in special relativity. Apparently you wish to discuss this matter in this article. There are, of course, two aspects to it: the logical framework of the theory and its various propositions, and the empirical observations used to support it.

You wish, it seems, to establish that objects can in fact travel faster than the speed of light. As I understand the matter, there is no experimental evidence of this fact that is widely accepted. Recent observations of neutrino motion have been deemed not to provide evidence about this matter. Of course, a logical formulation different from the special theory could lead to this prediction, which then must await experimental confirmation.

Any attempt to upset the credibility of the special theory faces an uphill battle. I think the best you can do in this article is to cite various published objections to the theory and their basis. You will have to conclude with the assessment of these objections by the scientific community at this time.

A different title is advisable because The rules of physics does not convey its subject, which is more along the lines of Alternatives to the special theory of relativity.

Without a very careful presentation, it is very possible that the CZ community will not accept this article as meeting its standards. John R. Brews 16:20, 21 July 2013 (UTC)

TITLE: The Rules Of Physics


1.0 ABSTRACT.

Physics is a study of repeatable measurements which are for all intents and purposes made by light. Each observer "owns" the light beams associated with his observations and measurements and the velocity of light is independent of the relative velocity of object being observed.

Each observer has access to exactly one coordinate system, his own. Access to another observer's coordinate system is made by a communication instrumentation process which is accomplished by light.

Finally, mathematics is the language that defines the communication between observers. It is not an expression of the truth from absolute point of view.

I believe that these are the rules that define the field of physics. Furthermore, I believe these rules may result in the discovery that an object can have a velocity greater than light.

2.0 DETAILED DISCUSSION 2.1 PHYSICS IS A STUDY OF REPEATABLE MEASUREMENTS

Is sound generated from a tree falling down in the forest if there is nobody there to hear it? This is an interesting question which I heard a long time ago, probably in my first years of college.

How do we know that sound is generated if there is nobody there to hear it? Most assuredly, the generation of sound and listeners to hear the sound are irretrievably connected. Consequently it is impossible to logically answer the above question.

I believe that there is a simple response to above question and this response will provide a profoundly simple definition of the field of physics. Namely, if there is no listener, nothing can be said about the generation of sound.

Historical speaking, the field of Physics is the study of repeatable observations and measurements. Everything in the field of physics that we know today is the result of a long sequence of experiments performed over several hundred years.

2.2 PHYSICISTS ALSO HAVE BELIEFS

The human being needs to believe in something. The many religions would not exist if this was not so. Physicists have their own unique set of beliefs. One of these beliefs had important historical consequences.

2.3 THE ETHER BELIEF

As early as 1600, it was known that light could travel in a vacuum. There was a strong belief that light like sound needed a media for its transmission. This gave birth to very undetectable transmission media called the "Ether".

Fresnel originally proposed the velocity of the earth and that of the Ether relative to the World Coordinate System were different. In 1845, Stokes proposed that the Ether was attached to the earth. Later, Maxwell proposed that the Ether was attached to the World Coordinate System.

The resulting intense research effort was motivated by the possibility that measurements of light in a refractive media would help them measure the velocity of the earth relative to the World Coordinate system

This research effort was terminated in 1881 by the Michaelson-Morley experiment which clearly demonstrated that one could not measure the velocity of the earth from the behavior of light within a moving coordinate system.

At this time, the Ether and the World Coordinate System, the baseline for Newtonian Physics, became obsolete.


2.4 THE POSTULATES OF EINSTEIN

Einstein proposed that 1) the laws of physics are the same for all observers independently of the relative velocity between the observers and 2) the velocity of light is independent of the velocity of the source relative to the observer.

These postulates were not consistent with Newtonian Physics as they were understood during this period.

Einstein proceeded to modify Newtonian Physics so that it would be consistent with these postulates. His effort resulted in the Special Theory of Relativity.

2.5 THE SPECIAL THEORY OF RELATIVITY

The Special Theory of Relativity is basically a system of equations which relates the observations made by two observers in terms of the relative velocity between them.

These observations included position, time and velocity. The velocity of light was made independent of velocity of the source relative to either observer. Consequently, the velocity of light is independent of the relative velocity between the two observers.

The Special Theory of Relativity supports the statement that field of Physics is the study of repeatable observations and measurements. The numbers associated with these equations (position, time, velocity, etc) are the results of these measurements.

2.6 MATHEMATICS AS A LANGUAGE 2.6.1 MATHEMATICS AS A "TRUE" STATEMENT?

"The word comes first and the word is true" is a relatively common religious statement. It requires that the associated statement is accepted without question. These statements are the foundation of the associated belief.

The human being needs to believe in something. The many religions would not exist if this was not so. Physicists have their own unique set of beliefs. Can the mathematics of Theoretical Physics be considered a statement of beliefs that can be accepted without question? Will it ever be?

I think not.

These mathematical equations are used to communicate and explore the results of continuing research programs. If the results of these experiments are not consistent with the associated mathematical equations, the differences are carefully examined and the associated mathematics is updated.

The Special Theory of Relativity and Quantum Mechanics are important historical examples of this update process and there is no reason to assume that this will not occur again.

I believe that a re-examination of the Special Theory Of Relativity and its defining Einstein Postulates will enable the next major discovery.

3.0 MY RE-EXAMINATION 3.1 LORENTZ TRANSFORMATION

The Special Theory of Relativity and the associated Lorentz Transformation attempts to define the differences between two observations based on the differential velocity between the two associated observers.

From an observer point-of-view, the Special Theory of Relativity has not been thoroughly tested. Even with our manned space travel activities, the relative velocity between observers is negligibly small relative to the speed of light.


3.2 EINSTEIN POSTULATES RE-EXAMINATION

From an observer point-of-view, the Einstein's Postulates have also not been thoroughly tested. Again, the relative velocity between observers is negligibly small relative to the speed of light.

Assuming that these postulates are unconditionally valid, what can we learn by re-examining them. My re-examination has resulting in the following conclusions.

3.2.1 SPEED OF LIGHT RE-EXAMINATION

Einstein's second postulate states that the velocity of light is independent of the velocity of the source relative to the observer. This will be the case for multiple observers receiving light from the same source.

I have some serious problems with Einstein's second postulate where there are multiple observers with large relative velocities.

Specifically, I have difficulty accepting the constancy of the speed of light where the multiple observers are using the same light beam to observe the same source.

The only way that I can resolve this issue is to make the assumption that the multiple observers can not share the light beams from the source being observed. In essence, each observer must have his own light beam from the common source.

As a consequence, each observer has access to only one coordinate system, his own. The only way that an observer can share his observations with another is through a communication process.

3.2.2 RELATIVE SOURCE VELOCITY QUESTION

My re-examination has resulting in an interesting final question. Einstein's second postulate does not appear to place any limitations on the relative velocity between the source and observer.

Can this relative velocity be greater than the speed of light?

You say no and you have a large amount of theoretical physics research and the resulting mathematical equations to back it up!

But wait a minute! These mathematical equations resulting from Einstein's postulates relate a set of numeric measurements with another. These equations are not a definition of fundamental truths.

Let's assume for the present that this might be possible.

Let us assume that an object moves from the left towards the observer, passes very close to the observer, and then moves to the right away from the observer. Let us also assume that this object emits light along the way.

3.2.2.2 LESS_THAN_LIGHT

Let us assume that the velocity of the object is less than the speed of light. Then when the object is approaching the observer, the light will arrive at the observer before the object. The observer will see the object move towards him from the left, pass by him, and then move away from him to the right.

3.2.2.3 GREATER_THAN_LIGHT

Let us assume that the velocity of the object is greater than the speed of light. Then when the object is approaching the observer, the object will arrive at the observer before the light.

The observer will not see the object approaching him. Instead, the observer will see two objects travelling on the same line, one moving away from him to the left, and the other moving away from him to the right.


3.2.2.4 EXPANDING UNIVERSE

There have been many measurements that suggest that the universe is expanding.

Is it truly expanding? Perhaps there are objects with relative velocities greater than light which gives us the impression of an expanding universe?

Only time and additional research will answer these questions.

References

4.0 REFERENCES

4.1 CONFERENCE ARTICLE 1

IMACS 11'th WORLD CONGRESS on System Simulation and Scientific Computation, 1985, Oslo, Norway: "Statistical Mechanics Simulation Experiments On The Personal Computer".

4.2 CONFERENCE ARTICLE 2

IMACS EUROPEAN CONGRESS on Simulation, 1987, Prague, Czechoslovakia: "Phase Space -- Continuous or Discrete".

4.3 CONFERENCE ARTICLE 3

IMACS EUROPEAN CONGRESS on Scientific Computation, 1988, Paris, France: "Goedel's Incompleteness Theorem -- A Practical Application".