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Since “Infinity” seemed to play a prominent role in a few recent CNPS presentations, it’s good that a forum discussion has been opened on that topic. Greg Volk has long been a strong advocate for making sure that terminology is used correctly and that when people discuss a topic, they agree on the key terminology, so that they are not talking at cross purposes. Throughout the ages, infinity was discussed by philosophers and mathematicians. The formal definition of “infinity” as an abstract math construct was popularized by Georg Cantor at the end of the 19th century and is the definition accepted by Academia. Basically, it says that “infinity is greater than any integer”. Admittedly, “infinity” can be used in an informal, watered down, colloquial way such as meaning “boundless”, “endless” or “an extremely large number of something”. However, I will stick with the formal, academic meaning of infinity as an abstract math construct.
As such, by definition, “infinity” is not a valid construct for describing the real, physical world. I used to think, in an offhand way, that “time” might the one exception and might be considered “infinite”, however, I later realized that view was doubly invalid. However, if one uses “infinity” in the informal, colloquial sense, then the terms “infinity” can be used in physics, but one must make clear exactly what one’s personal use of the term means and that one is NOT using the formal academic definition of “infinity”.
I see below that Andy has thought about this topic for many years, indeed decades, and has thought about it deeply. If I misrepresent him, Andy can correct me. However, it seems to me that Andy came to the same conclusion that I did, namely, one cannot use the formal definition of “infinity” and apply it to the physical world. In fact, he says that “infinity” is so inherently meaningless for the physical world, that it must be redefined for use in physics. So his redefinition of “infinity’ is along the lines of “infinity” means “an extremely large number of something”, but Andy provides much more rigor than that colloquial phrase. I have suggested to Andy that it might be clearer if he gave his “new” construct a new name rather than redefining “infinity”.
However, before putting the above online, I thought it prudent to ask Dennis Allen, a retired math professor and author of “The Reality Oriented Mathematician”, if he thought “infinity” was applicable to physics and his view was 100% in sync with my view. Further, I spoke with a most respected member of the CNPS and that person agreed with my view as well.
So, as critical thinkers, we must be sure to give proper analysis to this topic regardless of how firmly bound to one view or another we may be AND we must be clear about the meaning of the term “infinity” that we are using.
Incidentally, as far as I have found, the term “infinitesimal” is defined in terms like:
Adjective: extremely small (e.g., nanoscopic, barely perceptible, invisible to the naked eye
OR
Noun (MATHEMATICS) : an indefinitely small quantity; a value approaching zero.
Thus, unless one is using the term “infinitesimal” with some other definition, “infinitesimal” is unrelated to the formal meaning of “infinity”.