Another painting completed today, one last touched in 2022 too, making this the 4th completed work of the week: 'You Know How It Is When You Remember A Friend':
As with the other works, this was envisaged as part of a series, so I paused to wait for those plans, as a series can benefit from the unity of having matching underpainting colours. After 2 years though, I'm keen to finish things. The only painting officially in progress now is the Rene Descartes painting, though there is one with a title/theme about Social Media Paranoia that was underpainted but abandoned.
Today was a first long day of painting. I don't feel like immediately starting on Descartes and may pause to plan new paintings first.
In the night I thought about the Continuum Hypothesis; in partcular considering the set of integers and, say, integers divisible by two. Both are infinite, but you could think of the latter as 'half the size' of the former. I thought that this was a ridiculous, and that both sets are the same, differing only in the language used for the numbers, not the content (1, 2, 3, etc. vs. 2, 4, 6, etc.).
This reminded me that zero or infinity do not (and can not) exist in the real universe and that any mathematical description of the universe cannot be accurate if it involves the use of zero or infinity. In an earlier idea, I thought about eliminating multiplication and division, but that's not necessary; all that is needed is to exclude zero and infinity.
We could use a new symbol for zero which is simply very small, and in all practical application the same as zero, but it is not. The same applies to infinity, which we could call that 1/zero. A new symbol for 'near-zero', perhaps a z with a line though it, can be this tiny number, 'ideally infinitesimal', as small as small can be, but not zero. The number is defined as the smallest physically measurable value, or smallest definable quantity of a function of, nature. I hypothesize that this number, when applied to the physics of the universe, was larger in the past than now.
I'm reminded that the philosophy of mathematics is often self referencing and divorced from practicality. If a maths or any system exists to describe and predict things in the real world, it must primarily equate to it; it must feature the limits (and perhaps imperfections) of reality.
