**Abstract**: A mathematical convenience truncates real analysis and discussion of the transformation nexus between the finite and infinite. A short-term trick became a long-term solution to ignore the most fundamental transition that defines our universe. The first challenge is to define the infinite in a way that respects its beingness yet opens possibilities for new analyses. Although initiated back in 1971, that three-part description — continuity (order), symmetry (relations) and harmony (dynamics) — is re-engaged to test to see if all words can satisfactorily be used to describe an aspect or face of the infinite.

This body of this document will finally be written as a result of these studies of the finite-infinite relation and renormalization outlined here.

**Planckspheres**.** **Within this model the Planck spheres are being generated one at a time, just as imaged above. That is the sole action of the first notation and the piling on as imaged with its sequences happens as part of the notational activity over time.

**References**:

- https://en.wikipedia.org/wiki/Renormalization
- https://en.wikipedia.org/wiki/Renormalization_group
- https://en.wikipedia.org/wiki/Scale_invariance
- https://en.wikipedia.org/wiki/Transformation_(function)
- https://en.wikipedia.org/wiki/Matrix_theory_(physics)

- https://81018.com/2017/11/04/infinitude/
- https://81018.com/2018/03/14/hawking-pi/
- https://81018.com/pi-day/
- https://81018.com/pi2/
- https://81018.com/view/

Schrödinger_equation:

https://en.wikipedia.org/wiki/Schrödinger_equation

Not to be confused with *Schröder’s* equation:

https://en.wikipedia.org/wiki/Schröder%27s_equation

**The Net Advance of Physics: RENORMALIZATION**

- http://web.mit.edu/redingtn/www/netadv/Xrenormali.html
- Baez: “…assume you vaguely know what a Lagrangian for a quantum field theory looks like.” http://www.math.ucr.edu/home/baez/renormalization.html
- Feynman,
*QED: Strange Theory of Matter and Light*: https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter *A Quantum Pioneer Unlocks Matter’s Hidden Secrets*by Elizabeth Gibney (*Nature*, Sept. 2017): “What if each quantum critical point is just the beginning of another generation? …probing the boundaries around those states could reveal more phases, and studying the boundaries of those could reveal yet more, with discoveries unfolding in a fractal manner.” https://en.wikipedia.org/wiki/Gilbert_George_Lonzarich

- On the Revolutions of the Internal Spheres:A New Theory of Matter and the Transmission of Light, K. Troy.
- https://81018.com/derivative/
**An infinite number of symmetry groups**are possible within the first-64 notations.- key conceptual transitions https://81018.com/beyond/ https://81018.com/overview/
- https://81018.com/functions/
- https://en.wikipedia.org/wiki/Growing_block_universe
- Michael Tooley (in 1997) and Peter Forrest (in 2004).
- Tooley, Michael (1997).
*Time, Tense, and Causation*(pdf). Oxford University Press. ISBN ;9780198235798. - Bourne, Craig (2002). “When am I?”.
*Australasian Journal of Philosophy*. ;**80**(3): 359–71. doi:10.1080/713659472. hdl:2299/8627. - Braddon-Mitchell, David (2004). “How do we know it is now now?”.
*Analysis*.**64**(283): 199–203. doi:10.1111/j.0003-2638.2004.00485.x. - Forrest, Peter (2004). “The real but dead past: a reply to Braddon-Mitchell”.
*Analysis*.**64**(284): 358–62. doi:10.1111/j.0003-2638.2004.00510.x. - Merricks, Trenton (2006). Zimmerman, Dean, ed.
*Good-Bye Growing Block*(pdf). Oxford Studies in Metaphysics.**2**. Oxford University Press. p. 103. ISBN 9780199290598. - https://en.wikipedia.org/wiki/Growing_block_universe
- External Links: https://www.iep.utm.edu/time/ (excellent references at the end) Bradley Dowden, California State University, Sacramento