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Updated: May 15, 2025
We are, therefore, under an illusion if we assume the factor c to represent anything of what velocity implies in outer cosmic reality. The truth is that c represents a spatial distance just as s does, with the difference only that it is a certain unit-distance. Just as little does real time enter into this formula nor does it into any other formula of mathematical physics.
Position, figure, motion, are contingent properties of body; they presuppose that it is extended or spatial; they are modi extensionis, as feeling, volition, desire, representation, and judgment are possible only in a conscious being, and hence are merely modifications of thought. Extension is the essential or constitutive attribute of body, and thought of mind.
Deduction, then, does not work unless there be spatial intuition behind it. But we may say the same of induction. It is not necessary indeed to think geometrically, nor even to think at all, in order to expect from the same conditions a repetition of the same fact.
Number is driven to the heart of phenomena and nature dissected with this delicate scalpel. Speaking in more general terms, we adopt spatial relation as the perfect example of intelligible relation. I do not wish to deny the use of such a method now and again, the services it may render, or the beauty of construction peculiar to the systems it inspires.
In order to have inertia, one must also have spatial properties which make the existence of inertia possible.
This is the process of assimilation of carbon from the carbon dioxide of the air. If we leave aside the change in the chemical combination which the carbon undergoes, there remains the picture of the plant drawing this matter to itself from its environment and at the same time subjecting it to a spatial condensation.
To this kind of observation nothing is accessible, we know, except spatial displacements of single point-like entities. Hence we find Bacon and Hooke already attributing the sensation of warmth to minute fast-moving particles of matter impinging on the skin. Some time later we find Locke taking up the same picture. We see from this how little the mechanical theory of heat owes to empirical facts.
Bergson gives the name "space" to the form which belongs to abstractions but not to actual facts: abstractions, he says, are "spatial," but facts are not. This use of the word "space" is peculiar and perhaps unfortunate.
A new approach, called a spatial database engine, creates intuitive objects from standard geospatial databases and uses commercial databases to add attributes to the objects. It is particularly useful for distributed databases such as one would find on a network. Modeling and simulation is also benefiting from object-oriented technologies. Simulations were once stand-alone codes.
In the same way the particular condition 'σ' required for the definition of an event-particle must be looked for beyond the mere notion of extension. The same remark is also true of the particular conditions requisite for the other spatial elements.
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