Objectivism Online Forum

# Abhijeet Melkani

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1. ## Measurement-omission in mathematical models - also my take on dimensions

Let me further elaborate my position: The same physical entity can be classified into the different categorical concepts of ... -> furniture -> chair -> rocking chair ... according to the level of measurements you choose to retain/omit. Similarly, a physical entity can be treated, in science, as a member of different categorical concepts/mathematical models depending on what level of coarseness of information we are interested in. ...-> ideal-gas-molecule -> molecule-with-internal-properties-like-magnetic-moment -> many-body-quantum-system-of-n-dimensions -> ... Dimension then becomes the number of different measurements/quantifiers associated with that model. Now, to your reply (as far as I could follow it): The key idea is that objects are quantifiable to varying degrees and the degree determines the model by which it would be treated. Such that in the ideal gas model, all molecules of the gas are equivalent no matter what their energetic state may be. It is exactly the same as making statements such as: "My furniture is ugly." or "The tables are not that flat." When a particular existent is being treated as furniture as opposed to table there is only so much that you can say about it.
2. ## Measurement-omission in mathematical models - also my take on dimensions

Measurement-omission in mathematical models.Mathematical models are special kind of models and they too involve particular measurement omissions and the preservation of generalities of special-case events/objects of reality.These measurement omissions in the physical context must be dictated essentially by the scale of time and change-magnitude:1) The lower bound of the energies that can be measured. Eg: The fine structure of hydrogen-spectrum can be omitted.2) The lower bound to the frequency of recurrence of events that can be measured. Eg: The rotation of the earth about its axis is too slow we may consider our laboratories to be inertial frames. 3) The upper bound to the frequency of recurrence of events that can be measured. Eg: The motion of gas molecules is too fast, the precise knowledge of momentum-impinges on a surface can be sacrificed for one measurement: pressure.Any given mathematical model has a precise number of parameters required to describe a particular instance of it. This is its dimension. (One can also use a model described by a function over the real numbers - in that case the dimension is infinite. An example for that is the temperature distribution of a rod modeled as a straight line-segment. But in this case we are constraining our system more than we have information about it. After all one cannot measure upto arbitrary precision.)A model is only an abstracted essence as a tuple of numbers can only describe one level of information of the actual object. For example, an actual physical triangle is more than just the side lengths, it has material properties, etc.According to the physical context, a new model is constructed by including new parameters (to make finer distinctions), for example, in expressing the state of a molecule we may either choose to only keep track of the velocity coordinates of its center of mass, or we may include coordinates describing its vibrational modes or its rotational motion, etc increasing the dimension of the model as we include more complexity. The new model may even omit the previous parameters (in the sense that the parameters do have particular values but may have any of the permissible values) if they are assumed to have no bearing in the working of the considered details. For example, in the wave-function description of the molecule one is unconcerned with the motion of the molecule as a whole. Prior to Einstein, it was believed that one can use purely spatial models for dynamics plugging in time independently.
3. ## Life is the necessary value - but why is it sufficient?

For some time I have been having qualms about how Objectivist ethics was formulated by Ayn Rand.Her argument starts with the idea that the fundamental choice, without which no other choice is even possible, is the choice of life over death. (Since only a living being can make any further choices). But I do not see how that makes life the ultimate value - in the sense of the exclusive standard of morality. Life is, granted, necessary for the pursuit of any other values, but is life (and all other values based on the standard of life) sufficient? In other words, after having achieved that which sustains life, because that is a precondition, what dictates that there are no other values - like, say, knowledge for the sake of it - to be sought?Her answer for that seems to be based along the line that happiness is the moral purpose of life and that biologically it's function is as a pointer/guide to life-achieving fulfillments. So that, life-achieving actions capture the entirety of happiness which makes life a sufficient standard. In other words, the two additional premises that happiness is the purpose of life and that biologically "it is the successful state of existence" (A.R.) closes the argument that life is a sufficient value to be sought. [Is what I have stated correct so far?] A problem arises when you realize that an organism is biologically built not just to sustain itself but also to propagate its own species further. In fact, many biologists argue that the primary function (biological motivation) of any organism is to sustain itself till puberty only to mate and reproduce its own kind. In that case, happiness is not just a successful state of (the individual's own) life maintenance. It follows also, one may argue, from sex and taking care of your young ones.Now, does it really go against Objectivist ethics? One may say that the desire for sex is not just a desire for any kind of indiscriminate sex/reproduction but the search for the fittest mating partner (fit according to your standard) - a quest for the same set of values based on the standard of life. The desire to raise young ones may also be a desire to nurture the same kind of values. But I think the question remains - a desired sexual partner, although embodies the life-achieving values, is not necessary for the achievement of life at all. Not any more than any trader, of whichever sex, which embodies the same values. So, is the quest for a sexual partner/healthy and happy children consistent with happiness being the pointer to only the individual's life and well-being? Are we not biologically tailored to be happy in not just achieving our individual life but also the life of our species? Human life in general? In short, does Objectivism depend on the biological argument that happiness is a pointer to life-achieving fulfillments? And if it does, does it not fall prey to the arguments that the biological motivations(happiness essentially) of individuals is not just their individual survival but the propagation of their species? [Thank you for reading this far. I have tried to be clear but I am not very happy with my wording. Please bear with me.]
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