What\'s Ultimately Possible in Physics by Paul N Butler

Hello dear Paul,

Happy to see you on the contest .

Personally I prefer don't participate for several reasons .

I read your essay ,we see always your faith and the christianity .

It's so spiritual .Congratulations for your universality .

The conscious is a driving force of the evolution towards harmony ,physical .

We see too a real understanding of the rule of human like a catalyzer of the love ,the truth .

Take care

Steve

Cristinel,

Sorry it took so long to get back to you. I have been very busy recently. I will just answer your comment to me after mine at this time so this does not get exceptionally large (well, ok it already is, sorry). I notice that you tried to get away from math, but couldn't completely do it. I understand that it is hard to change information transfer formats when you get used to using one most of the time.

If we assume that reality remains the same, (always continues to follow the same rules and laws, etc.), then a theory of everything that completely describes current reality has always existed and will always exist at least as long as reality exists. The problem is to find it and recognize it from all other lesser theories that do not completely describe reality as it is. The true theory of everything would, of course, be a member of the set of all possible theories. Our problem is that we do not have a global perspective that would allow us to examine the complete set of all possible theories to search for the true one in it. We have a local perspective that only allows us to generate some of the theories in the complete set at any given time. They are the theories that fit our current set of known observable data. As later observations increase our set of known data, some of the current theories will be proven wrong and drop away, but we will also then be able to generate new theories (actually we gain access to some of the theories that already exist as members of the set of all possible theories) that fit the new expanded data set. These new theories were in existence already as members of the set of all theories, but they were hidden to us in the past because of our lack of data at that time. Moreover because of our limited local perspective, some of the observed data may prove to be wrong by later more refined observations. This can cause the generation of theories that are not part of the set of all possible theories if we restrict the set to observed data that is valid. From our limited local perspective we see old theories abandoned and new theories being developed to replace them even though the new theories could be considered as already existing in essence as parts of the set of all possible theories, if the current data set is completely valid. You are right that we cannot know from observation if a current theory is the theory of everything even if it agrees with all of the known data because we cannot be sure that we will not later gain new data from subsequent observation that will disprove it. We see a limited continually changing window of current observed data and theories that attempt to explain the data. It is entirely possible that current observed data could indicate that a proposed theory is wrong. Such a theory could be abandoned. Later new data could suggest that it was true all along. So far there has never been a theory in this world that has actually described all of the observed data at that time. If such a theory ever is generated and if much time goes by without the discovery of any new data that cannot be explained by it, such a theory might be considered more likely to be the true theory of everything. If at the same time man can no longer find new things to observe for a long time so that no new observed data is generated, this would add credibility to that belief (faith). You are right that man would still not know for sure in the absolute sense that it really was the theory of everything because man may just have overlooked something. In such a case even though we would not be sure that we knew about everything, there still might not be much for people of that time to do to search for new data if no one could think of any new experiments or if any new experiments always had results that agreed with the established theory. It is likely that if such conditions continued for a long time, man's faith in the current theory would gradually become a closed faith in the minds of most if not all people, so that man would eventually stop looking for new data and new theories and accept the current theory as the theory of everything whether it was so in truth or not. The only way that man would know for sure is if somehow he gained a global perspective or if it was given to man to know by someone with a global perspective (God).

I generally use men's math only when it is absolutely necessary in communications with others in this world because it adds another layer of abstraction to an already abstract language. What often happens is that people who use math a lot tend to begin to leave off the descriptions of the meanings of variables, constants, and other terms that may just be represented by a letter or some other symbol and most never describe the math rules used, to allow those without high level math training to understand what they are saying.

My purpose is to be able to describe what can often be very difficult concepts to as many others as possible in a way that they can understand, so they can gain knowledge and understanding of such things to the greatest degree possible. I have found that using high-level math, especially when it's not necessary, tends to limit the audience to a much smaller group, which is contrary to my goal. I don't even like to use mnemonics as short cuts like TOE instead of theory of everything because some reader that is new to the subject may not know what is being talked about unless it is described at some point in the communication. I see many papers in which people use math formulas with constants and variables or mnemonics without making any reference in the paper as to their meanings. If I find it desirable to use such things for some reason, I try to always define such terms at their first use and if the paper is long I might define them again later also. I do understand that such short cuts and math structures can be very useful to use when one is attempting to understand a concept that is readily convertible to manipulation in that way, however. I am not against math usage. It can be most useful when communicating with those that you know have the knowledge of the mnemonics, constants, and variables, etc. already, so they can gain from the use of the various shortcuts and structured rules that math offers. It is likely to be less useful (if not detrimental) when communicating with those who do not possess such knowledge. Generally if you cannot explain a concept without the use of math, you do not have a good understanding of it or you do not have a good understanding of the language that you are using to describe it. Math can often express a concept in a more concise and well defined or limited way that can eliminate ambiguities, but only if the problem is well structured and both those who generate the math structure to describe the problem and those who read it are well versed in the level of the math structures used, the structural definitions of the rules contained within it, and the meaning of all variables constants and operators, etc. that are used in the structure. You may have noticed that we are not made to interface directly with reality on the base mathematical level. We generally interface on a much higher hierarchical level with visual sensors that do not generate mathematical formulas in our conscious minds for shape formations, combinations of structures, and other relationships, etc. Instead our mind translates such things internally in its structure and generates output information in a form of recognized objects and their relationships with each other, etc. to our conscious mind. Because man's conscious mind works on this level, it is usually easier to transfer information to man through communication at this level. Man's languages generally are based on words that label these objects and their observed relationships with other such objects. Because objects we see can come in various quantities or levels of quantity and the rules of relationships between them can also possess quantitative aspects, mathematics is built into the world. The understanding of math concepts (beyond basic understandings of quantities, etc.) are not built into man's conscious mind internally, so that man can just automatically perform math operations, but instead they need to be developed through extrapolation from higher-level processes. It is generally easier to stay with those higher-level language structures that man is familiar with than to use math structures that are only understood by a more limited subset of man that has either developed or studied them. Another problem with using math to transfer information is that it adds a greater level of abstraction. Languages allow the transfer of information and come in two basic types and various combinations of those types. They are literal languages and abstract languages. If I desire to transmit information to you about what a car is, I could just show an actual car to you. That would be using a literal information transfer because the information was transferred to you from the actual object involved (light being the media of transfer). On the other hand if I wrote a description of a car in the English language on a piece of paper and gave it to you I would be giving you information in an abstract form because you could not possibly come to understand anything about a car from it just by looking at the various shapes and patterns of the letters on the paper. You would have to learn that the various patterns of letters between spaces represent words and that the words represent things such as the car or relationships between them. You would have to learn the specific meanings of the words that I used in my communication to you and their various contexts when used together in the manner in which I used them. It can be seen that the use of an abstract language requires that both the sender and the receiver of the information possess the knowledge of the specific set of rules used to represent the information elements and their interrelationships. In the English language, the letters used and their positions within a given word generally remain the same, so that a word can be readily recognized once it has been learned. One problem can come when a group of words is shortened into a mnemonic in order to attempt to shorten the communication. A mnemonic such as PDE could mean partial differential equation to one person and Pride International Inc's stock ticker symbol, or the Pennsylvania Department of Education to another. Math carries the amount of abstraction to a greater level because the letters and symbols used in one formula will likely represent completely different things or concepts than the same letters and symbols when used in a different formula. This abstract variability of terms requires that the meaning of such mnemonics and math entities be described in plain language at least once (preferably at its first use) in each communication to insure that the information is understood properly by the receiver unless it is directed only to a receiver that has already become familiar with its specific localized use. There are, of course, various levels of modified literal and modified abstract language structures and the whole subject of information and information transfer methods would take many volumes to adequately describe in a coherent and comprehensive manner. I have tried to give only a small amount of relevant information to keep this post from getting too long. One of the most interesting things that I have observed in my quest to understand this world is that it is made in the form of a very complex written hierarchical language structure that starts out as an abstract language and transfers (translates) through it hierarchical levels into a literal language structure.

Dear Paul,

Thanks for your answer. In large, the second paragraph of your comment contains partially what I tried to express in my comments, so I will agree with it. It seems to me that you object only to the way I expressed things, and not to the content.

As for the last phrase of the second paragraph, "The only way that man would know for sure is if somehow he gained a global perspective or if it was given to man to know by someone with a global perspective (God).", I agree with the first part of this phrase, but not with the second. The only way someone can be sure about the truth is by having the "global perspective". If this is given by God, that's fine, but I think that the only way to be "given to man to know" by God, is if God gives to man the "global perspective" itself, and not just His testimony about the "global perspective".

You say "I see many papers in which people use math formulas with constants and variables or mnemonics without making any reference in the paper as to their meanings."

Yes, I find this also a difficulty in communication, but I learned that a self-contained paper tend to become a book, most times in more volumes. Why not just referring to such volumes which are already written? I agree that when we try to understand such papers you need to look up, and we end up by consulting several books just to understand a four-page article on fundamental physics. This can be related to my observation referred by Giovanni as "the nightmare principle". You say "Generally if you cannot explain a concept without the use of math, you do not have a good understanding of it or you do not have a good understanding of the language that you are using to describe it." I find this observation unjustified. How do you know if someone used math because he cannot explain without it? How do you know that he hasn't understood? He may have simply chosen to use fewer words. We can at most say that it is difficult for us to understand what he said.

You are right, my comment could be expressed without symbols like E(Dt). But I do not think that such shortcuts really are more mathematical than your own description. They only are briefer. Replacing such symbols by the definitions I gave in words result in a little longer comment, which is not more mathematical than your comment. I don't understand your objection.

All words in a natural language are also placeholders, some you learn from context, others are defined in term of the first ones, and so on. Neither English, nor the mathematics we use is Mind's native language. The assumption that when we read math we need to translate in English to understand it, is not that true. It is like saying that French people discuss in French, but secretly translate from/to English in their minds. Or that we are secretly translating to the limited vocabulary we had at the age of three, since everything else is defined in terms of those words. Many don't know math, and even mathematicians don't know all math, but they translate in what they know only until they learn the new stuff. Like when you learn English as your native language, you "develop" all the placeholders you use, until you learn them, and use them as such.

To resume:

- I did not see in your comment objections to the content of my comment, only to its form.

- Just because I used placeholders that contain brackets doesn't mean that my comment is mathematical.

- I do not agree that mathematics is less natural or less intuitive than the so-called "natural languages". It is a matter of training.

- I agree that if the same thing can be said without mathematics, without affecting very much the length, it is desirable to say it. I would add that if you can draw a picture instead, or even show the real thing, it is even better.

Best regards,

Cristi

Cristinel,

Note: It looks like the subscripts will be removed from the formulas in transmission to FQXI.

You are very perceptive in that we do pretty much agree on many of the concepts that you presented. There are just a few minor details that you presented one of which was that the experimental data set will only increase and not decrease when in fact man's known acceptable experimental data set can decrease due to new experimental observations (that later prove to be false) that cause man to discard previously observed experimental data that is actually true, until the new false data is later found to be false or lacking thus allowing the discarded data to be restored to man's accepted experimental data set. The new false data would also temporarily add its data to the accepted experimental data set until it was proved to be false at a later time when it would then be deleted from the set thus reducing it in size. These kinds of fluctuations of the data set due to erroneous data that is accepted as true for some time would need to be considered. The set of all possible theories (your E) that can be derived from and be compatible with the observed experimental data set (your D) at any given time (t) will be based on both the true data and also the false data that is contained in that experimental data set at that time. This means that the assumption that the data set only increases with time is not completely true and all of the concepts based on that assumption would need to be modified to be compatible with that understanding.

You are right that if God appeared and gave man the complete data set of all observable data from the global perspective we would still have to have faith that he was telling us the truth and not trying to deceive us, but if it explained all of our observed data set completely and no one found any exceptions for a prolonged time in any new observed data, it would likely become a closed faith and man would likely accept it as fact at some point. From an absolute point of view it is impossible to ever completely know that we have the complete and true data set or theory of everything because even if God appeared and took you up to where you could see the world from a global perspective, you would not know that it was not just an illusion. You might just be a computer box on someone's desk with all that you observe being fed into you over some cable with a program running in you that interprets that data to be what you observe. In the end we all live by faith whether that faith is in God or just in the belief that what we see is what we get (the belief that what we observe is actually connected to and represents reality).

I am glad that you have seen and understand the problems of undefined data in papers. In today's Internet world you could put a link to the book in your paper, but I have found that if you just make a reference, most people will never look it up. They will just try to make what they can from what is presented and may get off of the track and not understand what is given. As a matter of fact some people use this tactic to present information that they do not want people to understand by including a reference to a law, etc. in a contract knowing that the person will likely sign the contract without ever looking up the law that might say they would be bound in some way that they would not agree to if they understood it. The nightmare principle is not quite as bad as it may appear on the surface because a given man does not need to know and completely understand the complete set of presently known observed data to add new observed data to it or to process that data for pattern recognition to generate new theories, etc. He can just specialize into a more and more narrow portion of the whole set to advance that portion as the set grows due to new additions. With many men working on different portions, the set could ultimately be completed even if it was too complicated for any one man to understand it all. This was made possible when man developed written language so that the set could be recorded outside of any given individual so that it could grow beyond any one man's ability to fully store and comprehend and so that it could be accessed by any man at any time. Of course, man in this world has not presently organized all observed data into an easily searchable format that can be easily understood. I did not say that a man could: 1. understand what he is talking about and, 2. be able to explain it without math and, 3. not still be able to make the choice to use math. As a matter of fact I said that it is appropriate to use math to get a point across to someone else if that one is known to also be expert in the level of math used so that they can also take advantage of the shortcuts and structured rules that are a part of the math at that level. I do believe that it would be an unwise choice to use high-level math to try to get your point across to a general audience that may not be able to understand it at that level. The person who does so may understand the concept and the language so that he could explain it without the use of math, but may have just made an unwise choice to try to communicate to a general audience at a level that is beyond their ability to understand, unless it was his desire that he not be understood for some reason.

First, let me congratulate you on a comment that is almost completely free from the use of math and math symbols, but still makes sense. As a reward I will include a few in my response to you to make you feel a little more at home while still trying to explain in English also for any that it would help, if I don't get carried away in the math myself in the process. The use of the E(Dt) could have been just used as a somewhat awkward name, but it appeared to me that you were actually using it to represent a set of all possible theories (the E) based on and compatible with the set of all known (or accepted) experimental data (the D) at a certain time (the t). This plus other subsequent manipulations of it and additions to it (the K) are parts of set theory math. It is fine to use this method as long as you can expect that all of your readers have an understanding of set theory rules and its method of presentation or if you completely describe it also in a way that can be understood by those that do not have that understanding. The total presentation would have likely been somewhat confusing to someone that did not know set theory, especially because you first said that you were going to use the symbols as short names and not as equations, but later you used Kt:=K(E(Dt)) which is a form of an equation. What I found confusing is that you started out talking about the set of E(Dt) as the set of all theories that are compatible with the experimental data set at a time t. Later you said that set E(Dt) contained all possible theories even those theories contained in the set of all theories E that are compatible with the set of experimental data at a later time t'. The assumptions here is that all of the data in the experimental data set at time t would also be in the set at a later time t' and that any new theory that would be compatible with the experimental data set at time t' would also have to be compatible with the data set at time t. Even if the first assumption is true and as mentioned above it might not be so, the lack of the data in the set of experimental data at time t that was later added by the time t', would exclude some theories from being considered compatible with the experimental data set at time t because those theories would need to be substantiated by the experimental data that was not yet available at time t to be considered valid theories that were compatible with the current set of experimental data at that time. For example, at the time that experimental data was limited so that it was possible from that data set to generate theories that describe matter as being composed of atoms, but the then current experimental data gave no indication that atoms were not the ultimate smallest building blocks of matter, it would not have been reasonable to say that a theory that described atoms as composed of sub-atomic particles was a valid part of the set of all theories that are compatible with the experimental data set at that time t because the experimental data set of that time did not contain the data required to substantiate that theory. The lack of that data would actually imply the opposite conclusion that the atom was the smallest building block of matter and theories that went along with that concept would be the only ones that would be compatible with that experimental data set at that time. It seems that you went from a local concept of compatibility with the experimental data at a specific time t to a global concept that included all theories compatible with the experimental data of all times described as t'. Though you only mentioned t' as one certain time later than time t, if the argument would hold for that time it could be extended to all times later than t. If you stick to the concept that you first introduced that the set of E contains only those theories that are compatible with the set of experimental data at time t, then if time t is that time when the experimental data set contains only data that indicates that the atom is the smallest building block of matter then set E(Dt) contains only theories that are compatible with the concept that the atom is the smallest building block of matter. If time t' is that later time when additional experimental data has been obtained that indicates that atoms are not the smallest building blocks of matter, but are composed of sub-atomic particles, then set E(Dt') contains only theories that contain the concept that atoms are not the smallest building blocks of matter, but are composed of sub-atomic particles. As you can see even a constantly increasing set of experimental data can generate a set E at one time that contains only theories that are opposite in some way to those that are contained in set E at a later time. If on the other hand, you are considering the set of E that contains the set of all theories that are compatible with the ultimate set of all possible experimental data at all times, your argument may be right, but we do not have access to all the elements of that set (namely any elements for any time after the present), so it is not of much practical use to us. It looks like you started out using a localized set E that contained only theories that were compatible with the experimental data at any chosen single time t. The theories in this set at any chosen time t would only include those that were compatible with the then present experimental data set (described or explained reality in accordance with the then present experimental data). It would not include any theories that were not supported by observations in that data set, such as those that would say that atoms were composed of sub-atomic particles in a time t in which the experimental data set only included data that supported the concept that the atom was the most basic particle and could not be subdivided. In this local structure, the set E(Dt) would definitely not contain all possible theories, but only the limited set of theories that were compatible with the experimental data set at the specific time t that was chosen. You assume that experimental data only increases with time (new data is only added into the set and no data is ever deleted from it), which is not necessarily true as explained above. If your assumption were true, you might be justified in believing that for any time t that was before a later time t' the experimental data set at time t would also be included in the experimental data set at time t', but this does not mean that the theories in set E(Dt) would be included as valid theories in E(Dt') because new data added into the experimental data set from time t to time t' could make acceptable theories at time t obsolete by time t'. Also, theories compatible with the experimental data set at time t' would not necessarily be compatible with theories in set E(Dt) because the lack of the new data added between time t and time t' might cause that more limited data set to indicate or support only theories that were even opposite in some or all respects from those that were indicated and supported by the later larger data set of the later time t' as noted above. In the example that I gave above, the later data set would support the concept that atoms were divisible into smaller particles, but would not support the concept that they were indivisible. The earlier data set would support the concept that atoms were indivisible, but would not support the concept that atoms were divisible into smaller particles. These are opposing principles that would make the theories contained in the two sets mutually exclusive. Therefore E(Dt) would not contain E(Dt') and E(Dt') would not contain E(Dt) in the above example.

The abstract set of all theories is a global set that we do not have access to beyond the present point in time t that we are in due to our local perspective. The parts about it and the limited knowledge set pertaining to it is pretty good.

So far, my research into man suggests that if theory were to completely describe all observed experimental data for a prolonged time, man's faith in it would become set and man would then stop looking for new observed data and would accept that total theory as the theory of everything whether it was or not in much the same way you accept that you are not just a computer on someone's desk as I described above.

You are right that both English and math are abstract constructs used to communicate information entities and their relations with and to each other from one person or object to another and neither is the mind's native language. Both contain information entities (words and punctuation symbols in English) and (letters or other symbols in math) that possess meaning (information). In either case you must learn the relational symbols (punctuation in English) and (relational symbols like , =, and -, etc. in math) and basic rules of application of those symbols and the information entities to make and transmit information to others and take in and understand information provided by others in those forms. It is not that it is necessary to translate all math into English for it to be understood if the audience that you are transmitting the math to has an understanding of the math at the level contained in your transmission. I have found that most people have some understanding of English (or their native language) and how to read and understand it reasonably well. A much smaller number have high-level math skills. If I am transferring information to an unknown audience it is, therefore, more likely that a larger number will understand me if I use English rather than math. I generally desire to pass on information to as many as possible to have the greatest chance that someone will understand it and assimilate it into the culture so I can track acceptance thresholds and advancement potentials, etc. If, on the other hand, you wish to limit your communication to only those who posses a certain level of math skill, you could use math at that level as a filter, but that is not usually my task. Man's math is generally harder to understand than a language such as English because it adds an additional layer of abstraction. Most words in English have a limited meaning or information set attached to them, but the same letter or symbol in math may mean a completely different thing in one math application than it does in another. The letter E may mean energy in one formula (E=MC^2) and electromotive force (voltage) in another one (E=IR). This can make transmission of math formulas without descriptions of the meanings of their information entities difficult if not impossible for the reader to understand unless he is well acquainted with what the writer is communicating. This means that it is sometimes necessary to communicate the meanings of such math entities in English or some other language known by the reader so he will not be confused as to their meanings.

I looked at the content of your previous post and talked about it above.

That is true, but it is evident that the brackets were used as part of set theory math structures.

You are right. It just takes more training to deeply understand high-level math, so most don't bother to get it unless it is needed for some reason.

That is a very good insight because the picture or the real thing would communicate the meaning in one of the mind's native literal information acquisition languages without the additional internal translation that must be applied to abstract language forms.

Paul,

Let me restate what I tried to show in that comment on Nov. 7, 2009 @ 03:02 GMT. The point was that, even if we don't know a theory fitting all the observable data, such a theory may exist. In that comment, I gave a concrete but oversimplified example, consisting in guessing the formula for a real function. The purpose was not to discuss the universe as a mathematical structure, but to show that experimental data can, in principle, be fit by some rule. I considered my comment in direct relation to Giovanni's essay, in which it is stated that the search of the TOE is based on faith. I just tried to show that it is not so unconceivable to find a rule fitting all the data, and in fact the number of such rules may be infinite. The set of such theories (=rules) can be refined by new data. Eventually, we will have a nonempty set of theories describing all the data. Such a theory is the TOE, so it is very plausible that a TOE exists. Note, I do not claim that we will find it, or that the theories are mathematical in nature. Of course they are, but I will not argue about this :-). Science is finding the rules. There is no more leap of faith in searching for the rules (i.e. doing Science), than to believe that these rules must be consistent with one another.

You give three objections to my argument:

1. You say that I use set theory, implicitly. Yes, and you also use sets in your previous comment from Nov. 26. I said "I do not think that such shortcuts really are more mathematical than your own description", and I stick with this. And what you called formula it was in fact a definition.

Sorry, but I consider that there are little chances that someone is interested about TOE, and don't understand elementary stuff like a set is included in another, and cannot look it up.

2. You say that the experimental data may decrease, by being discarded, and later reloaded etc. In the image I presented, all the data is kept. Problems may arise when we interpret the data, but the data is considered true. My purpose was not to describe how we are doing science in the real world - e.g. by ignoring the data which contradict our hypothesis. My purpose was just to show that there is always a nonempty set of theories fitting the data until that time. I did not say that we know those theories; just that they exist, like you know that the number pi exists, although you don't know its value. And I did not consider that we can discard any data, because a TOE must account for all the data. I just approximated by not discussing the possibility that the data records can be destroyed or lost. In fact, there is not even needed to give a temporal development of the process of finding the TOE, to sustain my argument, but I developed it temporally because I wanted to make it more accessible.

3. You say that not all the theories fitting the present data can fit the data available in antiquity. Probably here is the source of the misunderstanding. The theories fitting the present data must fit the data available at any time before. You assumed that the theory must fit the data as is interpreted by the humans living at that time. It is your assumption, and I never said that. Data is data, and the way is interpreted is another story. Tycho Brahe's observations fit well Kepler's laws, Newton's theory, and Einstein's theory, although these theories occurred later. Particle theory (example you gave) does not conflict with the data of XIXth century, it is compatible with that data.

We can see the theories as algorithms used to compress the experimental data. For example, Newton's equation contains Kepler's laws in a more condensed form, which in turn contain Tycho Brahe's observations in a very compressed form. Viewed like this, it is clear that any nonrandom data can be compressed by some algorithm (the random data in general cannot be compressed more). Science searches in fact compression algorithms for the data. These algorithms contain the rules, and the rules can be used to make predictions. A TOE is nothing but a compression algorithm, which compresses all experimental data.

I think that it is desirable to have theories as compression algorithms which don't use conditional expressions ("if ... then ... else"). Such expressions mean that there are exceptions. If we have good theories for different domains, (e.g. quantum field theory and the standard model, and general relativity), we can combine them by conditional expressions, and we obtain a TOE only if their domains cover all the data (which is not the case at present). But a good TOE will make no use of conditional expressions. In this respect, it is more difficult to find a TOE, although not impossible. In fact, it is always possible to find a compression algorithm which doesn't use conditional expressions, and makes the job of another one which uses such conditional expressions.

Cristinel,

Yes a theory that fits all observable data may exist. (It actually does exist if you are considering the global set of all observable data or if you are only considering the true data in a local observable data set). I think we can agree on that. Yes your example was oversimplified (which in essence was all that I was saying). Not a bad beginning guess. Guesses usually need to be refined with additional input to get a final fully valid form. It is really a much more difficult problem than either of us was presenting. I only introduced a couple of minor incremental complexities. I stayed away from more difficult levels such as the possible roll of random structures, etc. That is one of the real questions, can all experimental data be explained by a rule or set of rules or is some of it just random in nature with no discernable rules. I believe your assumption is right, but if quantum physics were right, that concept might not hold. Giovanni is right because the search for anything is based on faith. It is only after you have found what you are searching for, fully understand it, and can absolutely prove its existence to be as you observe it to be that you can say that faith is no longer needed. Man has not found any way to absolutely prove anything, so we really all live in faith in all things. It may be faith based on evidence, but it is faith nevertheless. In reality the ultimate theory of everything will be a very complex and large hierarchical set of interacting rules. What man would like to find is a single base theory or set of theories from which all others expand or follow to explain the complete world. If the world was created by an intelligent being that would be the most likely case. If the world came from random happenings, it would more likely have many bases from which different parts of the world sprang due to many chance happenings over time. In that case a single base theory or set of theories would only expand to describe a part of the world. One would then have to understand all of the sets of base theories and all of their interrelationships (interactions with each other) to get a fully expanded understanding of the world. These are concepts that are well beyond what you presented though, so I will go back to basics so as not to cloud the issue any further. I also believe (have faith) that there is a set of rules in the absolute sense that completely describe the world and I believe that there is just a single base. That is one reason that I said that we are in close agreement in many ways. From man's local perspective, it is likely that man could obtain a close approximation of the absolute set of rules through the level of fifth vector structuring given enough time. The structural disconnect will prohibit man's observation of higher structural levels. If the assumption that the world is completely based on a set of structural rules is true (not random structure), then there is a set of actual rules that describe it and of which it is actually composed. It would therefore likely be possible to make a representation of that set in some other form unless it is infinite, which is not likely although I will not go into why at this time. The world is composed of motions and motions at their simplest level are relatively simple information structures. They mainly possess position, direction, and motion amplitude. These can all be described in man's mathematical terms, so you are right that the world can be explained in man's mathematical terms. It just becomes very difficult to work with in some large-scale interactive structuring descriptions. You do bring up a good point that all of the rules need to be consistent with each other to avoid destructive consequences. This is an argument for the likelihood of a single base structure rather than many randomly generated bases. Within our local perspective, positive observable evidence of something does tend to make it more believable than if no evidence is present, but the belief that the evidence that is observed represents actual reality always requires the same amount of faith in all observations in the long run because we can never prove it absolutely. From what we can see from our local perspective though, the world's construction appears to be based on a very intelligently designed set of rules that starts with some relatively simple structures based on some simple basic rules and then combines them together hierarchically in more and more complex ways to generate the total world that we live in.

Now concerning your perception of three objections from me. In reality I merely throw concepts out to encourage deeper thought.

1. You are right that we both did use set theory in our respective comments. I expressed mine in English and you expressed yours in more of a mathematical form replacing names with letters and placing them in parentheses suggesting a relationship between them according to some rule or rules. I am not saying that it was a real big problem because you did define what each letter meant. As I said the main thing that might have been confusing to some was that you said you would use such symbols as short names, not equations and then later used Kt:= K(E(Dt)) which is in the form of an equation. You may have meant it to be only a name, but a name that looks exactly like an equation could be confusing. Mainly I just wanted to see if you could communicate intelligently without the math abstraction and you have done well. I notice that this comment is completely math free. Very good.

You may be right, but I wouldn't count on it. There are many people in the world that would like to know generally about scientific concepts, but don't want to or don't have the time or money to spend getting all of the tools such as math expertise, etc. to be able to actively participate in science. There wouldn't be so many books or television shows like NOVA, etc. designed for such people if they weren't there. Some are still too young to have attained to a high level of math knowledge and the right motivation of learning about something new and interesting in a form that they can understand could make the difference of career choice for them. Ultimately the amount of money available for science in this world is at least somewhat determined by how many non-scientists believe it is worth the money and will vote for it.

2. I saw that you first talked about what appeared to be a local set of theories that were compatible with the local set of experimental data that existed at just a specific time because you said "for each set of data there is a set of possible theories of reality, E(Dt), compatible with that set of data." The implication here is that one set of observable data has a set of theories that describe it and another (say later) set of observable data would have its own set of theories that might differ from those in the first set of observable data because of the difference in the data in the two observable data sets. Later I saw that you appeared to be talking about the ultimate set of all theories that are compatible with the ultimate set of all observable data because you said that E(Dt) should contain all theories, which implies that the global set of all possible theories that could be compatible with the observed data from any possible time would be considered as compatible with all possible observed data sets from all possible times, but it was not clear how you got from the one to the other. I believe part of the problem was that we were applying the word compatible in different ways. I was considering that compatible meant that the compatible theories would be in correspondence with the data so that the compatible theories would explain the complete set of data and no more. In that way of looking at it, the data set generates the theories by informing the theories with the data elements that are then explained by the theories. Such theories would not contain extraneous descriptions of things that were not in the data set at that time because there would be no reason to believe from the then current data set that such extraneous descriptions would have any basis in reality. A theory that contained explanations for things that were not in the current data set would not be compatible with it because those things would not correspond with the data in the data set. You seem to have looked at it with the idea that any possible theory that was compatible with any data set would also be compatible with all other data sets (all sets that were both forward and backwards in time from the compatible set) because you considered theory elements that would be extraneous at one time, but valid at a later time due to added new data as still compatible with the theories from previous times when the data set would have no need for them to completely describe the then current data set. Your approach could be valid in an abstract way considering the abstract global sets and their theories, but it seems that it would not work very well in a real world search for the ultimate theory of everything because even if you achieved the goal of obtaining the complete observable data set, and used it to generate the theory of everything that completely explained the data set, you would also have to consider as still valid any theories that added any additional extraneous descriptions of imagined additions that went beyond reality even if there was no evidential basis for them in the data set. Since reality is likely only a small subset of the set of all things that could be imagined to be parts of reality, the theory of everything would just continue to grow over time with more and more nonsensical additions given to explain things that don't really exist. It sort of sounds somewhat like string theory. Very interesting. Although it can be interesting to think about global and absolute concepts that may or may not exist, but are beyond our ability to observe or prove, such things are only useful to man when they are brought down to man's local level of observation. Of course, that is where man's interactions with them can modify their outcomes and results. This interaction does make for more complex structures to fully comprehend, but if you do, the knowledge is much more useful in the real world, which is the one that we live in after all. In the real world the possibilities exist that data believed by man can be either true or false at any given time and that man can be led by the data to only generate theories that agree with the data and not see possibilities that new data will lead them to later even if the new theories could be said to be an extension of current data. It is evident that there is a possible description of everything in the world because it is already recorded in the world to make it up. It is very likely that it can be recorded (a literal or abstract image of its rules can be made) in some other form also. It is also evident that there are at least a large number of possible false or partly false theories of everything. The problem is that there is only one completely true explanation, but many false ones. The useful concept would be one that would point to the true theory and point away from all the false ones. Since time is a part of the world, removing it from consideration would only go farther away from reality making it less useful.

3. Again, as I said in my last post, you are right from a global perspective, but we don't have a global perspective so it does us very little good in any practical way. We can look back and say that at the time that observed data agreed with the concept of the existence of the atom as the smallest known particle of matter and gave no indication that anything smaller existed, the data did not preclude that smaller particles could exist and make up atoms, but those who looked at that data would have no reason to believe that such smaller particles existed so there would be no reason for them to make up theories that included what to them would be imaginary particles that were not needed to describe the world as it was then known. In reality it is not the possible theories that matter, it is the theories that man actually comes up with or can access based on the observed data at the time that determine man's progress. In the long run I think that the problem is that you are looking at the problem from an overall generalized global perspective of how it would look if we could see all of the possible observational data in reality and all of the possible theories that could attempt to describe the data during all possible times and I am looking at the same problem from the local perspective of what man can actually achieve in his path through all of those times with the observational data that he has access to in each of those times to generate theories that come as close as possible to describing the known data to work toward the time when we could hope that the complete data set would be obtained and a complete theory that would explain completely all of the data and would not require any other data beyond the observed set for a complete understanding of reality would be obtained. Not that I expect man to fully attain to that goal, but much will be gained in the attempt.

Algorithms are sets of instructions or operations that are performed according to predefined rules and/or by rules that are contained within the set of the algorithm. You are right that they can be used to compress or decompress data. In terms of what we are talking about here they are very useful in modeling the data and its rules in a way that simulates reality. Depending on what type of data is involved it is often not possible or at least not practical to use data in its most compressed format. It must often be decompressed to its native format before practical use. The same problem can appear in some theories that contain complex math structures because a math structure such as an equation may contain a symbol that represents a whole series of other math operations on data in other equations, which may also contain symbols that in turn represent more math structures, etc. If the problem were to be worked by a man he would have to unpack the structures do the operations then repack the results to feed the next level of structure. Of course, with computers, the computer can be programmed to do the decompression and recompression along with the data operations at each level, so it only slows things down somewhat, but would likely still be faster than typing the complete uncompressed data structure into the computer.

The if, then, and else, etc. operators are just ways of showing dependencies, relationships, or interactions between entities. Dependencies and interactions are built into and are parts of the world that we live in. They can be expressed in other ways, but they are the same thing no matter how you express them. I can say, if the resistance decreases or the voltage increases then the current in the circuit will increase or I can say I=E/R. In either case I am just showing that there is a dependency relationship between voltage, current, and resistance in an electric circuit, so that a change in one will cause a change in another. The I=E/R is a conditional expression that expresses the same dependency relationships as does the if, then statement. (I only showed one of several if-then statements that would fully show the complete dependency relationship). You could only eliminate all statements in the theory of everything that show that the condition of one thing is dependant on the condition or action of another thing if you eliminated all interactions between all things because an interaction is basically a change in one entity caused by another entity (it could be mutual changes to each other). Another way of saying the same thing is that the condition of one entity is dependant or conditional on an interaction with another entity. The whole world is based on dynamic interactions between entities within it. It's cause and effect in action. If this cause happens then that effect results.

I see that our conversation has been moved to my forum.

To everyone:

If anyone reads Cristinel Stoica's conversation with me here and wants to see the beginning of it you can find it in Giovanni Amelino- Camelia's forum under his paper "The Fairness Principle and the Ultimate Theory of Everything. It starts somewhere around October 25, 2009.

Paul,

>> "Yes your example was oversimplified (which in essence was all that I was saying)."

I simplified it to the bare bones, but I kept the essence of my argument (abstraction).

>> "Giovanni is right because the search for anything is based on faith."

Giovanni seems to believe that TOE is based on faith. I said that TOE is based on faith, like the rest of physics.

>> "Man has not found any way to absolutely prove anything, so we really all live in faith in all things."

So we agree.

It is interesting the perspective you have on the knowledge we can have about the physical laws. I think that you make more assumptions than I did, but I do not find here a reason of controversy.

At the point 2, it seems that you understand what I say, but you consider that

"it seems that it would not work very well in a real world search for the ultimate theory of everything because ..."

My purpose, as I said, wasn't to help finding the TOE, just to argue for its existence. And I see now that the example of f(x) (which is not high math, even for nova watchers, is just a real function, everybody learn it in school) was better than explaining only in words. In that example, it is clear what I said. The function f is compatible with the data (x1, y1), (x2, y2), ..., (xn, yn) if yi=f(xi) for all i between 1 and n. This doesn't mean that the domain of f must be limited to the set { x1, x2,..., xn}, and not even to the real numbers.

>>"...even if you achieved the goal of obtaining the complete observable data set..."

Again, it was not the purpose of my argument to teach people how to find TOE, only to show that it exists. An existence proof does not necessarily put in our hands the thing whose existence is proven. All your discussion seems to miss this point. It was a counterargument to Giovanni's claim against TOE. TOE may be simple or complicated, may contain elements which we can't verify, I don't know. What I said is that, after gathering all the data, it remains a nonempty set of theories fitting our data. It will indeed contain incredibly complicated solutions, as well as nonverifiable solutions. If we will find one solution, it may not be the ultimate, or the simplest. Maybe we will find several, and we will chose using Occam's razor. Maybe later we will find that our Occam's razor based choice is wrong. It can be speculated ad infinitum. I just argued for the existence of TOE, that's all. I had a modest purpose.

>> "Since time is a part of the world, removing it from consideration would only go farther away from reality making it less useful."

Of course. I did not say to remove it from the search of TOE, I just said:

"there is not even needed to give a temporal development of the process of finding the TOE, to sustain my argument, but I developed it temporally because I wanted to make it more accessible"

To summarize: I presented an argument for the existence of a TOE. You objected the form, and said that it is of no practical use. I tried to make it logically closed, not to answer all questions which are not directly related to its purpose. My argument was only for the existence of TOE. And this is practical, since many try to find a TOE in the real world. My argument doesn't help in finding the TOE, I know, and this was not its purpose. But it is important, even for practical viewpoint, to know whether what you are searching exists or not.

By "theories as compression algorithms which don't use conditional expressions ("if ... then ... else")" I meant theories based on universal laws, not different laws for different domains. It was just an observation, not related to your comment.

Cristinel,

Good to see that you made the transfer from forum set G to set P. It renews my faith in man's ability to adapt to change (at least a little, one out of many is not much, but it can make that one more important and shows it is possible).

I am aware that your purpose was to give the generalized concept that a theory of everything exists or at least is possible and that belief in that concept requires no more faith than belief in other scientific concepts. We both agree on these things. I find it refreshing to find someone that understands that faith is a part of everything that we do and is willing to admit it. Too many people in science today try to paint science as completely separate from and somehow better than faith while at the same time painting every one that has a belief in God as basing it only on blind faith without any logical thought process or evidence involved. Their point, of course, is to try to make science look to be a more reasonable path to follow (that is a version of science that denies the possible existence of God) while at the same time to make religion (the belief in God) look as though it is foolish (basically it's a political anti God movement). Those who understand the true limitations and necessary relationships and joining together of both science and faith in both science and religion understand it all to be just a political game that is being played by many to the detriment of both science and religion in the long run. I always like to add some new information to provoke thought, but I will now try to get back to your point.

I agree that Giovanni seems to lean more toward the belief of separation of faith from science, but not as completely as some that I have seen (at least not as ardently as some).

Yes I think we can agree that man has not found any way of getting around the problem of the lack of a global perspective preventing the absolute knowledge of anything.

It may be that I make more assumptions than you do. I doubt that spending the time to really check that out would gain much that is of any real value in the overall scheme of things though. Like faith, assumptions are a necessary part of the acquisition of knowledge at least according to man's current scientific method. The general method is to first look at past-observed data and look for patterns that might indicate some scientific rule behind the observed patterns. At this point an assumption (hypothesis) is made that (if true) explains the generation of the observed patterns. Then experiments are designed and carried out to test the assumption to try to determine if it is a true cause of the observed patterns. It is not a matter of whether you use assumptions or not or whether you use more or fewer than others that is important. The important thing in the long run is whether they ultimately lead to a better understanding of reality or distract people from reality to believe and live a lie.

To argue for the existence of something that exists is good. To find and prove it is better and a natural progression from arguing for it in the first place. Personally I find that the farther away I get from observed reality into abstract thought the more likely I tend to make errors or overlook details, etc., so I try to stay away from the use of math and other abstract forms unless they are necessary to gain an understanding of some facet of the subject. It may be the opposite with you. If it is, we might work well together. I could develop the concepts and you could develop the math models for them.

Though your purpose was modest it is a good purpose to try to understand as much as you can about the world that we live in. I encourage you to continue in that endeavor. It is much more likely that the theory of everything will be approached gradually by amassing large amounts of data and slowly putting it all together to culminate in the complete understanding (or as complete an understanding as man can achieve) of the theory of everything than to find it like a needle in a hay stack and then use it to extrapolate everything else, although that would result in much less total work.

It was good that you left the time component in, but time is not what most people think it is. It is not a physical fourth dimension as many think (just another bit of additional data for thought).

Why does man always think of things in terms of extremes, for or against, agree or object, friend or enemy, etc.? If one can believe man's psychology even natural middle positions must be looked at in comparison to extremes. The cup must be either half full or half empty. I wonder how a psychologist would respond to someone that said the cup contains liquid to the center of its range. My purpose was not to be against you, but just to encourage you to continue and go deeper to the point that you could not only convince others that the theory of everything exists, but also contribute what you can to finding it. It should be evident to anyone that if the world is completely based on and described by rules (if its programmed to proceed in certain paths by cause and effect, etc.) then there is an existent theory of everything because it would have to exist (be recorded) in the world within its structure in order for the world to proceed according to those rules. The main question is: Do any truly randomly generated structures exist that proceed without any rules? If such structures exist there cannot be a complete theory of everything because the individual outcomes of such structures could not be predicted and accounted for by the theory. Secondary to that question is: Can man find and connect together all of the rules in the proper way to generate and understand the complete theory of everything in his mind, whether individually or at least as mankind as a whole.

Yes the problem of whether there is a single base theory or set of theories or several with each based on its own set of rules that do not connect to the others except perhaps by interactions is a valid question as I described in previous posts.

To a great degree the answers to these questions are likely determined by the source of the creation of this world. If the source was an intelligent being, then it is very likely that the world is based on and proceeds according to a set of logical rules because intelligent beings (man is the best local example) tend to solve complex problems by generating structures (sub-assemblies) that function according to specific logical rules and connecting them together into greater serial, parallel, or hierarchical structures to accomplish an overall end purpose. It would be likely that there would just be one beginning base to all structure upon which all other structure would be built. The functions performed by the individual sub-assemblies are often abstract to the overall purpose of the complete structure. As an example, a car has the primary purpose of transporting passengers, etc. from one place to another. The gas tank in the car has the purpose of containing gasoline, which seems on the surface to have very little connection to the overall purpose of the car. It is only after tracing the flow of the gasoline from the tank through the fuel pump, fuel injection system, and various other engine components that you come to the point that you find that the gasoline is not to be just stored in the car, but is meant to be combusted. Again exploding the gasoline does not seem to be connected to the purpose of moving the car to transport passengers, etc. until you follow the path of the energy produced by the explosion through many parts in the engine, transmission, axle/wheel assemblies, etc. to the point that you see that it is channeled into turning the wheels to cause the car to move. When you look at many of the sub-assemblies, their individual purposes (functions) do not seem to be connected to the purpose of the structure as a whole until you follow through to see how they are joined to the overall structure and how their actions affect other sub-assemblies both directly and also indirectly through their affects on other sub-assembly's actions. The world seems to follow that type of pattern. If the world came about from some chance happening, however, it would be likely that there would be more than just one such happening over time thus generating many base structures. Chance happenings tend to generate structures that are not based on complex rules of action and the actions of the generated structures also generally generate random actions. The aggregate results of a large number of the actions of such structures tend to work toward the center of the range (averaging) of possible values of action (entropy) rather than being programmed to work for some other value for some purpose. If the possible values can be from one through nine, the average result of a large number of actions will tend toward an average result of five because by chance alone it is just as likely that one number will happen as it is that any other action will happen. This would tend to produce an equal number of each possible result over a long time. And the average of a large number of results with an equal number in all possible values in the range is the average (middle) value of the range. On the one hand the world is evidently based and constructed on and functions according to an extremely complex set of interacting rules with many levels of hierarchy with abstract lower levels with translation to literal structures at the higher levels. On the other hand the higher levels do not produce new such structures, but instead tend to produce results that overall follow the averaging effect of entropy. Moreover, its structure is slowly deteriorating or wearing down due to entropy. It looks like a device that was constructed by a very intelligent being to be just a temporary structure for some purpose that has an end or completion after which the device will no longer be needed. The fact that motions do not cancel out in interactions, but are conserved, leads one to the conclusion that entropy was more designed into the structure than a necessary part of or an inherent limitation of it. Looking at the kinds of logic used to design this world and the structure of the rules and their interactions with each other to discern patterns that can be generalized to describe the world as a whole and its purpose(s) can likely increase the chance and decrease the time needed to find the theory of everything or at least as close as we can come to obtaining it. The current political structure of the scientific community will not likely encourage that process, however, with its insistence on only looking for a random natural basis for the structure of the world. Just more food for thought not related to your comment.

Dear Paul,

I am glad to see again how much we agree, but I also like that we have different views at some points, because this gave a reason to the dialogue. I like that you take seriously and thoughtfully the discussions.

Best Regards,

Cristi

Cristinel,

I am glad that you see our areas of agreement. What would you say is the greatest area where we have different views and what are yours in that area. It is always good to examine differing views because that is often how we learn new things or at least flesh out new details in our understandings of each other, the world we live in, and its and our purpose. I try to take these things seriously and thoughtfully because discovering those purposes and fulfilling them is what life is all about after all. It is always better to know who you are meant to be and what you are supposed to do to make the world a better place to live in and how to recognize and help those who need help so that they can be the same, than to stumble around in the dark all your life, just being a victim of lack of knowledge and understanding. I trust that this is an area that we agree in.

I look forward to working with you toward the fullness of that understanding if it is according to your will.

Paul

Paul,

> What would you say is the greatest area where we have different views and what are yours in that area.

I cannot think now at important differences, probably because I feel great about the differences between various views. But if I would want to make a suggestion, this would be that fundamental physics can be understood better by understanding the underlying mathematics. Before this step is taken, we may think that mathematics is just the quantitative expression of physics; only after this step is taken can become clear how apparently unrelated pieces of the puzzle fit in harmony.

Cristi

Cristinel,

I have seen this concept that reality is founded upon mathematics as though there are underlying math formulas that somehow generate the reality that we observe. If we look at physics as the study of the structure of observed reality with the intent to understand its basic underlying structure and rules of behavior, we find that the most fundamental basic structure that exists in observed reality is motion. A single one-dimensional motion is a simple structure that contains only a small amount of information. It mainly possesses three pieces of information, which are position, direction, and motion amplitude level. Each of these pieces of information could be looked at as a quantity. You could number each position within the dimension so that each position would be assigned its own specific number that was different from the numbers assigned to all other positions within the dimension. You could also assign a number to the motion's direction so that one direction would be labeled direction 1 and the other direction would be called direction 2. You could also think of a specific motion amplitude as a quantity of motion with a specific value. When you actually look at a motion, you do not actually see these quantities, however. What you actually see is the motion existing at a position in space that changes in a specific direction at a rate that depends on its motion amplitude. The motion is not generated by the numbers or numeric quantities. Instead, the numbers are generated by man to allow him to quantify and study the motion's observed effects. The numbers allow man to follow the motion's information variabilities that exist as parts of the makeup of the motion. The motion is the fundamental entity. The motion's motion amplitude is a direct attribute of the motion alone. The motion's position and direction are attributes that come from the interaction of the motion with the information structures of the dimensional system that the motion exists in. All of these attributes are stored within the motion as parts of its makeup. The numbers are a step of abstraction away from the actual motion's existence. As an example, the motion amplitude is a continuously variable structure. In order for man to generate the numbers he must first divide that structure into a scale with numbers applied to various scale points in that continuous variability. This involves the creation of a unit that equals a certain specified amount or level of motion amplitude. Twice that level would then equal 2 units of motion amplitude, etc. It is still possible to see the continuous nature of the structure by using partial units, such as 9.898 units of motion amplitude, but man likes to make things simple, so actual tests and examples would more likely use whole units as much as possible, which can distract one from the continuously variable nature of the structure and make one begin to think of it more as a structure divided into discrete steps of motion amplitude. The scale and numbers are not actual attributes of the structure, but are artificial attributes imposed on the structure by man to allow him to more easily follow the effects of its variations to aid in the study of the structure. Mathematics is just a part of man's language structure and as such it contains the same types of advantages and disadvantages as any other part of man's language, but man's language that describes observed reality is not the same as the language that actually composes reality. It is at best just an image of it.

That being said, it is true that observed reality is built up from basic structural rules and understanding those rules and being able to express them in some language form can be of great help in increasing ones knowledge and understanding of observed reality. It is also true that those rules that contain quantitive relationships or aspects can often be expressed more simply in mathematical forms. Even in those cases, however, one could instead express the rules in English or other languages without the use of math. It would just possibly be more cumbersome to do so. You are right that if you express in math form those things that can be more simply expressed in mathematics, it can make it easier to see relationships between quantities than it might be if it is expressed in another form. As an example, D=RT where D=distance, R=rate, and T=time does show relationships between distance and time that can give one a good understanding of part of the nature of time. Of course, one must first understand that it is easier to replace the rate with the motion amplitude, which is basically the same thing in a different form (it is easier to see and understand this in a visual form rather than through math) to get D=MT (where M=motion amplitude) or T=D/M. This is the formula that describes how periods are generated and the period concept is considered part of the definition of time. Basically the length of a period increases with increases in distance traveled and decreases with increases in motion amplitude. A specific period is the result of or generated by a motion with a specific motion amplitude traveling through a specific distance (of course, there are many combinations of distance traveled and motion amplitude that generate the same period). This aspect of time is therefore derived from and its existence is dependant on motions traveling through distances. If all motion in the universe went away, there would be no periods of time in the universe. In addition to that, there would be no sub-energy, energy, or matter either in the universe since they are composed of motions. Conversely, this means that as long as motion exists in the world, periods of time will also exist. Periods of time are used to compare motions that have different motion amplitudes to each other. We would not really need the concept of time periods if motion only came in one amplitude level because that level could be considered the unit of motion amplitude, so that T=D/M would equal T=D/1 or T=D. This means that time and distance would be the same equivalent concept. Then if someone asked you when you would arrive, it would make perfect sense to say, "I will be there in 10 miles", which would be easily understandable by anyone who had previously traveled 10 miles.

Food For thought

These things apply to observed reality, but may not completely apply to the level of structure behind observed reality that generates it. At this time man is not yet ready to accept that level though. It is well beyond man's present maximum acceptance threshold. To get the image, think: the characters on the television screen are not ready to think about the internal workings of the television set that generates them. I won't go into that any more now. You have to wait until the time (the end of that particular period of motion through distance) for the release of basic dimensional structuring concepts to get that introduction. Don't expect that very soon though.

Sometimes observing things in detail in reality, comparing the observations of two or more things in reality, or using the visualization of things that are similar to what you are trying to understand in your mind (good when you can't actually observe the object of study) can also allow you to see how apparently unrelated pieces of the puzzle fit in harmony. Some things yield their secrets more easily in one way and others do so in another way. The real key is to be able to discern which method is most appropriate for your current investigation and to have the skills to use that (and all other) method(s) effectively. That is what structural pattern analysis is all about. Too bad that concept has not yet been understood to be important in this world (although there have been some who have figured some aspects of it out for their own use and have contributed much to man's understanding).

I will not be available to answer comments until about the last week of January 2010. Feel free to make them to me though and if I can stay in this world, I will answer them when I return to this place. If you get one in by Sunday, I may be able to answer it before I go, but no guarantee.

Peace be unto you.

Paul,

You seem to identify mathematics with numbers, which is a very limited concept of mathematics. In fact, I even warned against this mistake in my small comment. What I said is just that you can understand better some phenomena in physics by understanding some chapters of mathematics. I did not say that everything in the world should be understood by mathematics, and certainly not just by numbers.

Your intuition about the limitations of using numbers to represent coordinates is good. It is no wonder that mathematicians know it, and insist on it. If you read about differential manifolds, you can see that the coordinates are not the fundamental objects, and the true objects used by mathematicians are coordinate-free. And motion is a relation between the position (more generally in phase space or in configuration space) and time. It is mathematics.

Food For thought

To know how a foreign country really is, you have to visit it, and to spend some time there. Then, you are in a good position to discuss with a native about his country. A vacation is a good opportunity to explore new places.

Enjoy your trip.

Cristi

Cristinel,

Yes, a large part of what currently would come under the definition of mathematics has to do with the interrelationships or interactions of quantities of or numbers of things with one another. I do realize that there are branches of mathematics that can deal with things on a non-quantitative basis such as much of set theory and path flow structuring, etc. (I like to connect most of those areas more under the heading of logic than math, but that is just my personal method). I also realize that there are areas of math that deal more in the area of spatial structuring such as much of geometry, etc. Even these areas often include quantitative elements in their structure and definitions of things. For example, in Euclidian Geometry part of the definition of a triangle might be that it contains 3 straight lines that intersect to form an enclosed structure with 3 sides and 3 internal angles and that the 3 internal angles thus created total 180 degrees of rotation (one half of a rotation) on a scale where 360 degrees equals one complete rotation around a central point. Notice that there are numbers of lines and angles, and a quantity of amount of rotation involved. We both agree that some things can be easier to understand from a mathematical point of view and that there are also some things that can be understood more easily by other means.

So you won't have to believe that I am attacking your positions on things or trying to undermine you in some way let me explain some of my information gathering techniques and my reasons for using them. First my main reason for communicating with you (or even man in general) is to see if you are or can become compatible to work with, share, and hopefully enjoy together a common fellowship based on development of common understandings without mutually exclusive concepts hindering our progress. For that to happen we both need to get to understand each other's beliefs and understandings about the world and work through any disagreements or at least recognize and find ways around them. When we make statements, they are often based on much study of information, but we tend to give very minimal summaries rather than the whole understanding and often over generalize, so it is not possible to get the complete understanding of the concept that is being covered. In your statement "fundamental physics can be understood better by understanding the underlying mathematics" you do not limit the concept to just some of fundamental physics, so the natural assumption is that it applies to all fundamental physics. The concept presented is that there exists mathematics that underlies or is the basis for or possibly produces fundamental physics. The term fundamental physics would most likely refer to basic concepts in physics and I assumed that you meant that. It also could refer to concepts of any level of complexity about fundamental levels of the worlds structure studied as a part of physics, such as particle physics or the study of electromagnetic energy photons, etc. Since you did not go into the extent or depth of your meaning of the underlying mathematics of fundamental physics, I had two easy methods to get that information from you. First I could just ask you what you meant in that respect. This method can work, but tends to be slow because it can take many communication turnarounds to get much information. Secondly I could look at the whole range of belief that I have found so far in man in that concept and give one extreme or the other and then explain where my belief is in respect to it, so I pass on to you my belief and allow you to respond with a more detailed response of where you are at on the topic and whether you are in agreement with me on it or to give your reasons if you disagree in some point(s). This allows simultaneous communication to you while at the same time you would tend to think that I believed that you had the extreme position that I mentioned and give me your belief in a more detailed way (unless you actually held the extreme position). If you haven't yet seen anyone with that extreme position, it also passes the information on to you that some do believe that way. Of course, I can't work that way with everyone because some who are weak either from much rejection or just from timid personalities might be either offended or discouraged easily by it and that is not my goal, but you have shown the ability to respond effectively to it. It allows me to mention many of the concepts that I would like to know your viewpoint on in more detail and at the same time show you my understandings about them for your observation and comment. In your response you changed from "fundamental physics" to "some phenomena in physics" and from "understanding the underlying mathematics" to understanding some chapters of mathematics (which I presume to mean understanding some specific applicable types of mathematic processes or maybe also the possession of knowledge at some certain necessary levels of complexity of those processes to use them successfully to aid in the understanding of the phenomena). We agree on these things. My point about the quantitative relationships or aspects is that phenomena that involve numbers or quantities of things are more likely to be the ones that are better understood by use of mathematics. This is not to imply that there are not any that do not have anything to do with numbers or quantities that could be easier to understand by the use of some mathematical processes that do not involve numbers or quantities.

I am glad to see that you understand the problems of manmade coordinate systems. Reality is not coordinate-free, however. The fact that things exist in specific local positions in respect to each other creates natural local coordinates. Because man cannot get out of the world and look at the whole world at once from that global perspective he does not know if global coordinates exists. It is only known that no indications of such global coordinates have been observed from man's limited local perspective, but that is not very surprising. You will have to give me more information about your belief that motion is generated by position and time. Generally those who believe that time is a physical dimension tend to believe that in some way our three dimensional world and/or the objects in it travel through the time dimension (or at least that they have a motion in it) and time is in one way or another the observed result of that travel. Of course, that travel would be motion, so it seems like motion would have to generate time even in that type of system rather than the other way around, but there are a multitude of different beliefs and explanations that I have seen, so in this case I will just ask you to elaborate on how you understand it to work. Of course, position can be said to be connected to motion because motion by definition is a change in position, but even there, the position is not usually considered to cause an object in it to move or change to another position. Instead, the objects motion is considered to cause its change in position or at least to be equal to that change in position

A very long time has been spent in the foreign place and much observation has been done of the natives. The discussions are now begun. Tell me, how would you describe particle, nuclear, and atomic physics and chemistry to a native in a small village in Africa who only understands a language that does not even have words adequate to describe the basic concepts? It is an interesting problem, but not insurmountable if the native really wants to know. Of course, you have to decide whether you really want that native to have all the information needed to make a nuclear bomb, etc. Yes vacations can be very good. There are so many interesting places to see in the world and some of the more interesting ones are very new.

Thank you, I will try to enjoy it.

Paul,

I wanted to give some examples of fundamental physics, which cannot be truly understood in a non-mathematical fashion. You may read very good popular books and get the impression that you understood them, but you really understand them when you understand them geometrically. I started to compile a list, and then I realized that the list will be difficult to read, and you will pick up some details and contradict them, without trying what I say. Moreover, as you said, my statement was about fundamental physics in general. Therefore, I think that it would be better that you pick some phenomenon of fundamental physics, which is today understood, of course, and which you think that you can fully understand without mathematics. According to my statement, I should be able to show you that you can understand it better if you understand it mathematically. But the only way I can show this to you is by telling you what to study to obtain this understanding (assuming that I understand this phenomenon myself and I can guide you). Otherwise, our long discussion reduces to me telling you how good is a special recipe of ice cream, and you providing philosophical arguments supporting the idea that you will not miss anything by not tasting it.

You say "Reality is not coordinate-free, however." I disagree. A coordinate-free object doesn't remain the same by changing the coordinate, but rather it's "shape" remains the same. If you want to understand what mathematical physicists know about coordinates, and by coordinate-free objects, you can read something on differentiable manifolds, special and general relativity, and gauge theory.

About motion. Motion is change in time. Change of what? Of a state, or of a configuration. All possible states, or all possible configurations of a system, in a particular theory, form an abstract space. Motion is change of the state in time. Therefore, motion is a curve in the space of all configurations or states, parameterized by time. Any physical phenomenon which is currently understood has such a description. Can you think at a different kind of physical motion, which is not completely describable like this? For the motion, I would recommend something on Lagrangian and Hamiltonian mechanics, Schrodinger equation, and perhaps dynamical systems in general.

On your observation about time as a fourth dimension, I would say that explaining time as a moving 3D-space in the 4D-space is wrong, and this is not the way time is understood as a fourth dimension (or at least those who understand it like this are wrong). The first idea is that all the equations describing physical phenomena happening in space have as solutions fields, which can be defined equivalently as time-evolving space fields, or as space-time fields. Therefore, all the information is contained in the space-time fields. The second, and most important reason for viewing time as a fourth dimension, is due to Lorentz transformations, which rotate space components into time components and time components into space components. These two clues suggest that, at least as a representation, time as a fourth dimension satisfies all the physical needs. Mathematics explains relations. Some may disagree, but can they show a physical phenomenon which is not describable with time as a fourth dimension?

You say:

"Tell me, how would you describe particle, nuclear, and atomic physics and chemistry to a native in a small village in Africa who only understands a language that does not even have words adequate to describe the basic concepts? It is an interesting problem, but not insurmountable if the native really wants to know."

It depends on how much they want to know. If they want to have an idea, popular science books can be enough. If they really want to know, I am sorry, but they will need to learn a lot of mathematics and physics. And the mathematics is not just for being fancy, it is necessary. I respect your thoughts, this is why I did not come to you and tell you that you need to learn math. It was you who came to me and told me not to use math. I cannot show you the importance of math in physics, if you don't jump and swim. It is your choice, I don't want to insist at all. The discussion was continued because you asked me to resolve some of your doubts. But if the doubts keep coming, there is only one solution: go and see. Take a particular phenomenon and explore it. But it's up to you.

You cannot describe with words a symphony to someone, the only way is for him to listen that symphony (or you can show him the sheet, if he can read it).

Cristi

Cristinel,

I saw your comment, but don't have time to go over it in detail now, as I am getting ready to go on my trip. It looks like one thing that we have in common is the understanding that math can sometimes make it easier to understand things about the world around us. Why don't we start by taking a couple of basic concepts and explain what the math shows us about the nature of the world that we live in. Lets say we start with a simple geometry example say the Pythagorean Theorem where you can get the size of the side that is not a part of the 90 degree angle (hypotenuse) by squaring each of the other two sides and adding the 2 results together and then taking the square root of the result. In the next three weeks while I am gone you can think about it and tell me in your next comment all that you can see from the math of it that explains things about the real world and how the world works as an example of how math can be helpful in giving understanding about the real world. We might also try one a little more difficult like E=MC^2 if you have time. When I get back I will give what I see in them also and we can then compare notes and see if we can maybe add to each other's understanding or maybe you can help me to understand if I am completely wrong on it, etc. I think it would be an interesting first step together and maybe help each of us to get to know the other better.

Paul,

My claim was not that, in order to understand physics, you need to know all mathematics, so there is no reason to start with a math topic and search for applications. What I said is that "fundamental physics can be understood better by understanding the underlying mathematics". If you disagree, and consider this an "extreme position", you can pick a phenomenon in fundamental physics, at your choice, then you explain it without understanding mathematics, and I will try to show you how mathematics can make it clearer.

But perhaps you agree. Or maybe you are not interested in doing this, and that's fine, you can tell me, because I don't want to insist; we can stop our discussion at any time.

Have a nice trip,

Cristi

Cristinel,

I am not sure where you got the idea that I was implying that one would have to know all mathematics to understand physics or that I was in some way claiming that you were implying that. If that were the case, no one could understand physics because it is obvious by the existence of currently unexplainable mathematical paradoxes that man's mathematical skills are still incomplete or lacking in some areas. Moreover, if I believed that you were implying that, I would have had to ask you to present all math and then to tell me how it in total gave a better understanding of fundamental physics. I think we can agree that this is not necessary because the world is designed such that individual parts of it can be understood (at least in part) without having to understand it in total. As a matter of fact it is only by gaining understandings of such parts and assembling these bits of knowledge together that we have any hope of gaining a total understanding of the world that we live in. As I said before, I think we are in agreement that mathematics can be an aid (a useful tool) to gain understanding of some things in the world. My point is that the mathematics is best used in conjunction with observations of the world around us to help us to better understand the things that we observe in the world around us and to possibly guide us to look for things (make certain new specific observations) that may help us to see and understand the world to a greater extent or at a deeper level. It is the combination of mathematics with real world observations that truly allows us to get the best understanding of how the world works and, therefore, also gives us a better understanding of physics because (properly applied) it is a part of the study of the world and our attempt to get a better understanding of it. My reason to start with a simple geometric example (the Pythagorean theorem) was to start in an area of math that I believe you are expert in (geometry), about which we can both agree that the math can lead to a better understanding and to work together in it to see what we can understand better from the math and how we can combine the math of the theorem with other observations of how the world works to get the most out of it that we can by seeing where the math and other observations lead us. I believe that you might be better at explaining what the math tells us about the world and I may be better at combining that knowledge with other observations to arrive at a more complete total understanding of the subject and where it leads us or to see new areas of thought that the math leads us to explore. You may be the one to develop the new math to describe these new areas of thought. Of course, I may be wrong about that, but we will not know either way unless we try. I asked you to start by giving the math and what you see as the better understanding that comes from it because the math is the initial focus that leads us to specific thought patterns and observations for expansion into new understandings. This is the natural way to start if you want to show how the math leads to a better understanding of the subject because the observables and thought paths that result can be easily traced back to the beginning math source. If I, on the other hand, began by explaining in English from the dimensional viewpoint what the Pythagorean theorem tells us and why it works the way that it does, the benefits of the concise form of the math formula or the geometric expression of it might not be as apparent. In other words, I chose the subject to allow both of us to not only prove our points, but also to allow us to work together by allowing each of us to contribute to the final result according to our individual strengths and to compensate for each other's weaknesses. For me to pick an area where math would be of no or limited benefit would not be a valid choice to encourage us to work together, which is my goal, if it is agreeable to you. My viewpoint is not that the world can be best understood by either the exclusive use of math or by the exclusion of math, but by the proper joining together of math with other methods of thought expression and with observations of the world that we live in, to allow us to develop thought patterns that give us deeper insights into the structure of the world and how it works. I think that to make it easier we should limit our first discussion to the Pythagorean theorem and leave E=MC^2 for later. I would still like you to begin from the math point of view first if it is agreeable to you, but if you feel uncomfortable doing it that way; I can give it from an English description of observables first. Of course, I would need to use some numbers, etc. because there are some quantitative aspects to be understood. You can either just present it from the math perspective in your next comment or let me know if you want me to do it from the other angle first.

I am interested in doing this if you are. Just let me know how you want to proceed with it in a way that we will be working together and not against each other.

Thank you. The trip went well.