Jim
"Your definition of time is at odds with Galileo's inclined plane, because Galileo had no definition of time"
My definition cannot be "at odds" with something that apparently did not exist, though a proper answer would be, obviously, he did have one, at least in his head.
I do not understand calculus, so I cannot say whether what I am saying contradicts it. I suspect any contradiction revolves around that first point about the occurrence of realities and hence what time is. Because what I have said in terms of a matrix, etc, is precisely what we do (or should be doing) to calibrate spatial position.
"that ideas can be represented as abstract mathematical symbols and then be subject to the rules of math independent of the internal consistency of the ideas themselves"
Only if that corresponds with the reality, otherwise all you have is a metaphysical system. Computers just(!) work something out, in accord with the information/rules applied. I do not understand the purpose of this point. If I remember correctly, my point you are quoting was that consciousness/the subsequent processing of physical input received/whatever you want to call it, has no effect on the physical circumstance.
I have a feeling that you have not altogether grasped what I am saying re reality. Which is partly my problem because I can only use words that usually have other connotations. So consider this:
Take any 'object'. Say that bush in the garden. Now we know it alters, we can, if we watch, see the alteration, and if we put it under an electron microscope we can see even more. In other words, when, physically, is the bush the bush? If there is any form of alteration, then it is different. That is, we are deeming reality in terms of 'objects' which do not actually exist, as defined, because they are being defined on the basis of superficial physical characteristics. The bush is the bush because it fulfils certain manifestations. Indeed, we even contradict ourselves by saying 'it changes'. This being a rationalisation to overcome the incorrect conceptualisation of what is it.
So, where does this all 'stop'? One can 'deconstruct' the bush in terms of its physical existence until one arrives at a state of no alteration. Something we cannot achieve in practical terms because of the vanishingly small degrees of alteration and duration involved, but logically that is where it will lead. Or we can, in more general terms, start with the fact that existence occurs, independently of the mechanisms whereby it is detected, but it also differs. Now, occurrence necessitates definitiveness. Difference necessitates alteration. The only way those can be reconciled is sequence. So, any given reality is a discrete definitive physically existent state of whatever comprises it at that time. Any degree of differential to that is another (the subsequent) reality. One cannot have difference and it be of the same reality. There is no time in any reality.
Consider timing. This is calibrating rate of change, irrespective of what is involved. If you have a quartz timing device, then crystal oscillations are being compared to some other sequence of alteration. The timing devices are referenced to a standard constant (or as near as possible) rate of change (ie they are synchronised) so that the system works and the measurements are expressed in a common, and understandable, denominator.
On the subject of spatial position, the way in which reality occurs is important. Because distance is solely determined by physically existent states, since it is the difference between them in respect of spatial attributes, and differences do not exist physically. So distance can only involve physically existent states which exist at the same time. It is not possible to establish a distance, as opposed to some form of conceptual spatial relationship, between something which exists and something else which does not.
Therefore, any given distance is always unique, since it reflects a definitive physically existent circumstance at a given time. Notions which relate to the quantification of it in terms of space, or duration, and the comparison of one way with the other, are a fallacy, if they involve the presumption that there could be a difference. Whatever quantification methodology, there can only be one result.
However, distance could be conceived as a single example of change, ie a difference. So it can be expressed, conceptually, in terms of duration incurred. The concept being that instead of expressing distance as the fixed spatial quantity which it is, it can alternatively be quantified as the duration which would have been incurred had any given entity been able to travel along it, either way. But it must be understood that there is no duration as such, this is just an alternative to, and the equivalent of, a spatial measure, ie a singular quantity. Failure to understand the absence of elapsed time in a physical reality results in the flawed application of the equation x = vt. Making this mistake reifies change, and hence duration.
Paul
