Dear Sir,
We congratulate you for your brilliant essay. We assume that when we talk about brain, you imply consciousness that is involved in perception. Since brain is also a material object, we find it convenient to use the other term. By perception we mean the result of measurement, which in turn means comparison between similars.
We fully agree that "the mind's conception of a thing is not the same as the thing itself". These belong to two distinct categories. The conception is stored in the memory and is retrieved by giving it a name, while the other is a material object or related to a material object.
We have a different interpretation for Goldstick's interpretation of a hole and a bump. A bump can come into being only when a hole is dug somewhere and the totality of the surface area of all holes and bumps are equal. This interpretation has an important place in our theory. We have a different notion of infinity and number sequence that has been discussed briefly in our essay. Regarding how a set would appear to different observers, our view is as follows:
Let us presume that we are sitting in a room separated from another room by a screen. A person moved from the other room to our room through the screen. This action will be described by the people in the other room as "exit", whereas we would describe it as "entry". Since both these terms are descriptions of the same action by different observers, and since each of these observations are correct, it appears that the terms "exit" and "entry" do not have any fixed meaning and can have relative meanings only with reference to the set of observers in a particular frame of reference. This is an example of the concept of relativity.
Now, let us analyze this concept scientifically using number theory as described in our book. The description of the movement of the person from one room (a frame of reference) to another room (another frame of reference) has been given by two sets of observers with reference to their frames of reference only. If there is an observer, who occupies a vantage position (all embracing biggest frame of reference) from where he could observe both the rooms (individual frames of reference) equally clearly, he would not describe this movement as either exit or entry. Similarly, if the screen is removed and both groups of observers could observe the entire movement simultaneously (from the same bigger frame of reference), then they would not describe this movement as either exit or entry. This is because all actions are confined to a frame of reference. Even where two objects join or disjoin due to some action, such action takes place within a frame of reference. If we separate these two frames of references, then the motion from the first room leads to the space beyond it, which de-links the person from the previous frame of reference. Since the two frames of reference are not linked, it cannot be an action involving both entry and exit. This is known as destructive non-existence without an end. Hence, subsequently it cannot lead to entry, which is a beginning. Similarly, his movement inside our room would have started from the space beyond the second frame of reference, which is known as the initial non-existence. Hence it could not have a prior existence as exit from the previous frame of reference. In both instances, the motion would have a fixed meaning as the action is confined within the frame of reference.
If the motions in both frames of reference are related, then our description of the motion must be with reference to a bigger frame of reference, which includes both the smaller frames of reference. In such event, we would describe the motion as "movement from point A to point B or movement of n meters from point A in the x direction through the screen to the point B". Both these descriptions are universally valid and there is no question of any ambiguity. The relative concept introduced earlier, thus, is due to a wrong description. Such wrong descriptions have been described by describes class constriction as non-relational description of similar and related objects. Here the two rooms (frames of reference) not only belonged to the same class (with similar characteristics), but also are related to make the motion possible. Describing the motion relating both frames of reference without describing the relation between the frames of reference is erroneous.
In one there cannot be many, implying, there cannot be a set of one element or a set of one element is superfluous. There cannot be many without one meaning there cannot be many elements, if there is no set - they would be individual members unrelated to each other, as is a necessary condition of a set. Thus, in the ultimate analysis, a collection of objects is either a set with its elements or individual objects, which are not the elements of a set. There is no contradiction in either case. The above description has been re-invented by Russell as the Russell's Paradox. This concept of can be proved mathematically through the Russell's Paradox of Set theory.
The Set theory as developed by Cantor and Dedekind defines set as "a collection into a whole of definite well distinguishable objects of our intuition or thought". This has been refuted by Kronecker and Russell by a contradiction known as the Russell's paradox. Ultimately, mathematicians agreed to leave the term "set" as undefined. Thus, the set theory goes against the basic premises of mathematics relating to unambiguous exactitude. Hence it is not mathematics, even though it is widely used by modern science. According to our theory, in a set, the elements merge their individual identity. Simultaneously, the set has no individual existence beyond these elements. Thus, while considering the relation between individual elements of a set, the concept of one and many are not applicable. The true picture will emerge only when we treat the biggest collection of elements as the set and examine the relationship between the elements against the back drop of such a biggest set. This principle has been presented as the Russell's paradox in set theory.
The examples cited by Einstein and others to illustrate the relativity concept would show that, the descriptions suffer from the defect class constriction. Class is defined as the cause for similar perception or non-differentiation. The action of the man standing on the platform watching the receding train is neither of the same class (element of the set, bringing in the problem of "x x") as the action of the train or the passenger of the train is not related to the man standing on the platform nor the platform is related to the motion of the train, except that the train runs near it and then crosses it. The only relationship between both is the "observation" by one of the action of the other, as it appears to him. Observation relates to conscious action - the act of knowing. Knowledge is the result of measurement. Measurement is the process of comparison between similars. What we "observe" is not decided by the object itself, but by the totality of the valence electrons of the object, which create a disturbance in the adjacent space due to their continuous pulsation. This disturbance travels through space to reach our eye and excite the valence electrons there. This disturbance is transmitted by the neurons to our brain, which compares it with other disturbances stored in our memory. When it matches some stored disturbance, we "know" that it is the "same object that we had seen before". Thus, the whole process is dictated by the disturbance created by the valence electrons and not the object as a whole. Since there is no possibility of distinguishing between two valence electrons, and the disturbance created by them always travels at the velocity of light, the velocity of the moving object is irrelevant for its perception. However, since the radiations from the two ends of an object moving with a high velocity reach us at slightly different times, their total effect at any point will be slightly different, which can be easily carried out by elementary geometry and it turns out to be 1/(1-v2/c2). But this is only the totality of the disturbances created by the valence electrons of the observed body, which does not change the physical shape of the body.
It should be noted that the passenger of the train, who is actually observing the action of the train and is related to the train will not notice any time dilation or length contraction in the moving train. Thus, the observation of the man on the platform, who is not related to the action of the train, has to be apparent observation. That such observation is apparent and sometimes a myth has been proved by the example of the mirage. The traveler looking at the flowing waters of the mirage does not make the desert flush with water. This is because the observation of the traveler is apparent and not related to the spot, where he sees water. A man standing at that spot (related to the spot) will not see any water there, which is the reality. More on the length contraction observed in the changes of the Bohr radius of an atom will be discussed later.
Regards,
basudeba.
