Dear Alexey and Lev,
First let me thank you for perusing my essay, but I do hope you did peruse! Thanks are due for pointing me to "Achilles paradox, and Feyman's conclusion", I will hunt down and use appropriately.
I am writing this to contest the comments, assuming that the responders are willing to take the time, and effort to move forward in our understanding.
"You are trying to assign objectivity to concepts like 'information', 'meaning', 'semantics', thus assuming that they exist independently of humans. To follow you, I have to assume that certain semantic units did exist billions years ago. ... Thus, by suggesting the objective information, meaning and semantics you are making a step in the right direction, albeit insufficient; 'meaning' without mind is meaningless."
You made it so utterly clear that the sense and meaning of terms like, 'information' and 'semantics' mean different things to you than what they mean to me. Let's give it a genuine try to resolve the differences, without drawing a battle line (even if friendly) yet.
We set the base line where we may agree to begin with. We both base our views only on scientific methods to establish our points. We do not go back to how universe came into existence, and why the changes in states have a pattern reflecting natural causation. We just trust they are given.
Now, in the first experiment, if an electron was ejected by an interaction at (x,t), the existential state of electron must correlate with this information. An electron does not convey this information to anyone, it just correlates with the information that interaction at (x,t) changed its course. As shown, any test of coherence relation designed to determine if interaction did take place at (x,t) succeeds, and test for any other point except (x,t) fails. This defines the limits of positive and negative correlation range within space and time. We wonder what is the meaning of this coordinate (x,t)? Does the electron know its location and the time of interaction. No, it does not know in the sense we know anything, it just correlates with this information. If this is the difference between our views, then it should settle the issue. But can we deny that the state of the ejected electron correlates with the information of its interaction, e.g. space, time, and a whole lot etc.? As further shown in the experiment that when an electron interacts with an observing device specifically pointed towards (x,t), the resultant state of the observing device does not exclusively correlate with electrons location or time of ejection at (x,t), but it just correlates with the electron's incoming direction and time of observation that is in congruence with (x,t), without being exclusive. If the state of observing device is further tested with a coherence relation among such devices, it shows that it correlates with point of ejection of the electron. So, we infer that a transmission of information takes place at each interaction, in such a manner that a limited history of one interacting entity is passed to another that depends on the observing limits of the observing entity (in this case the device). That is, information processing takes place at each interaction.
I have always requested to take the definition of terms in the essay. That is, even if a reviewer has her/his own definition, it must be shed while reading the text. I define, "An information always conveys a relation, at least with contextual elements." Can we deny that? "Therefore, an information is necessarily semantic in our consideration; here, information refers to the semantic value rather than the quantity. The term 'semantics', as used here, is independent of any language or interpreter; it is synonymous to 'meaning', a value that expresses a relation (an object)."
If someone says semantic information or semantics of information, does not one refer to the value content of the information which is the relation. I have also stated that 'semantics' is synonymous to 'meaning' in this text, which is always conveyed by the relation of the object with the context, its relation with other objects etc. Please think of any object which has an existence or a meaning without having this sense of relation. All objects are necessarily relative in this sense. If you do not succeed in finding an object, simple, complex, or abstract, which could be referred to without referring to its relations, then should not I request you to take the meaning of the term semantic as a reference to these relations.
Therefore, does not the electron carry around the information about context of interaction? In fact, the real picture of the essay begins here, when I show that through a properly arranged interactions, the information of correlation can grow arbitrarily to represent any object simple, complex, or abstract. I have always wished that the reader sees the essay in the this context to take home the point that there is no 'meaning', or 'semantics', or 'information content' that cannot form the information of correlation in this perspective. That is, all our mental thoughts are such correlations of states of neurons with the semantics of information. All mathematics have originated from such processing of information. Please retest my views in the text of the essay, shedding for a moment any a priori consideration we may have. In doing so, when we find the authors claim do not hold, then we also have ready rationality as to why claims do not hold. My essay also resolves the following issues.
1) Neurons do seem to connect and process information in a manner that directly maps to proposed disjunction of conjunction. 2) If information processing was not taking place in the neural domain, then how would we come to have such information about objects that we have? 3) If information is not based on natural correlation of states of matter, then where and how do they exist at all?
"To follow you, I have to assume that certain semantic units did exist billions years ago". No, to follow me, you did not have to assume this, but you did have to retest if there is a natural association of information with the states of matter.
I thank you again for perusing, and hoping that you do take the discussion forward.
Rajiv