Dear Akinbo,
I sent this comment yesterday and it appeared on my page, but when I looked today it was no longer there. I am sending it again today in case there was some software problem that caused it to be deleted, etc.
TO FQXI: If it was deleted purposely for some reason, please let me know why in an email to me or in a comment on this page, so I can understand the reason and modify future comments to conform to requirements. I would not intentionally go against the rules, but I realize that the interpretation of rules can often vary between different individuals.
Thank you for your positive comments about my paper. I have tried to look at things from the philosophical perspective and also from the abstract math model perspective, but I have found both to be lacking in some way at least for my uses. The philosophical approach tends to lack depth when analyzing reality, which is extremely deep and complex in structure. The arguments often only scratch the surface of all of the various possibilities concerning a subject, but act as though that surface analysis is all that can possibly be involved. As an example, in your paper, the concept that things don't actually move, but the monad in front of the object is turned into a dimensionless point while a dimensionless point behind the object is turned into a monad to create the illusion of motion. Nothing is mentioned about the mechanism that causes these things to work this way. Also, what substance is a monad composed of and where does that substance go when it is changed into a dimensionless point and where does it come from when a dimensionless point is changed into a monad? Are monads conserved, so that there is always the same number of them in the universe or are they increasing in number as the universe expands, etc.? If they can just appear anywhere at any time, how come we don't see things just randomly start moving around, etc.? These things are just some of the depth that reality based research would lead one to investigate and determine, but philosophical arguments often don't bring to mind because only a very narrow focus is often involved. The math models can have much greater depth, but it is easy to get into thinking only in terms of the perceived beauty of some number sequence or formula, etc. and becoming so preoccupied with the math that contact with reality is lost in the process. I, therefore, have found that a slightly modified version of the scientific method works best for me. It goes something like this:
1. Look at as much observational information about the concept that you are researching as you can and continually update that information in the light of new observational information.
2. Analyze the information:
a. Look for structural patterns that show the similarities and differences in different structures within a structural level and between different levels of construction.
b. Look for the structure of sequences of action and variation or change in structure.
c. Look for valid and invalid operations and sequences of action, etc.
d. Look for the various structural ties or bonds between entities both at the same and other structural levels.
e. There are many other things to analyze, but the above give a beginning idea.
3. Make an hypothesis based on the above analysis to explain the existence and operation of those things which are indicated to exist by the observational information, but either have not yet been proven to exist by the current information or have been proven to exist, but their structure and/or details of the way that they operate are still unknown due to lack of detailed information.
4. Identify current scale and all other limitations on observation and analysis, etc.
5. In accordance with all of the above, generate experiments to test the hypothesis.
6. Acquire or make the necessary test and other equipment needed to carry out and analyze the above mentioned experiments.
7. Do the experiments
8. Analyze the resulting information produced by the experiments to see if the hypothesis is proven or disproven by them:
a. If it is proven, go back to item 1. above to look for more understanding on the research of the same concept or go on to the next concept to be researched.
b. If it is disproven, or neither proven nor disproven, either go to 3. above to make another hypothesis if one is indicated by results of the experiments or go to 1. above to check on the previous analysis of the information for indications that lead to a new hypothesis or analyze all of the information again in light of the new experimental information from the experiments to see if a new hypothesis is indicated.
9. If none of this works you may have to wait for more information to be discovered.
The above is just a rough outline of the procedure. Note that it is continually tied to reality generated observed information.
Of course, math has its place in the development of the understanding of the various relationships between entities and in their quantities, etc. and philosophy is of use in areas where science cannot be applied.
I have studied the discrete verses continuous debate and found that the linear motion of an energy photon could be considered to be continuous. When looking at matter, although each level of structure discovered so far is generally composed of discrete entities; those entities are then composed of still smaller discrete entities. As to whether the smallest level is discrete or continuous, however, cannot be discerned by man at this time because it is not known how many more smaller levels exist and what their structures are. This is because of man's current size scale limitations. Currently man tends to think that matter particles and energy photons are the smallest entities, but they are only the tip of the iceberg. It may be a few hundred years before that knowledge is opened up fully for man in this world, however. At that time life will change drastically for man in a short time. For now though, the continuous/discrete debate is one of those things that can be philosophically debated by man because science cannot be adequately applied due to the current scale limitations.
Sincerely,
Paul B.