00:18 – Introductory Statement:
“…as far as the propositions of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.”*
– Albert Einstein, 1922
*First published 1921 by Julius Springer (Berlin) https://einsteinpapers.press.princeton.edu/vol7-trans/225
A quote remembered for what it says about the limits of human knowledge, but less remembered for what it says about the peculiar powers of a conscious mind, to perceive perfect certainty, such as mathematical proofs, despite living in an imperfect universe.
00:55 – Introducing myself, Andrew Malcolm, and my host, Dr. Vijayakumar Varadarajan and Ajeenkya D Y Patil University; and providing an overview of the workshop
02:43 – Reading the Music Festival Example:
If you wanted to fill in the details surrounding a memory of an event, like viewing a show at a music festival, what would you do? You could revisit the site of the festival, ask friends you went with to share stories, or see the same show again somewhere else, meet the performers, and ask about their perspectives. But what if you wanted to fill in the details surrounding the memory of a thinking-event, like a fantasy of yourself on the stage instead of the performers? You could repeat the fantasy again, this time with more awareness of what was happening in your mind during the visualization, but how would you know for sure that any of the qualities of the repeated fantasy match those of the first iteration? How would you know for certain you visualized the same sights, the same sounds, or experienced the same affiliated feelings, or even started and ended the fantasy the same way, with the same duration in between? For the memory from real life, you have people, things and events in the external universe that confirm for you the continuity between where the show took place, how long the show lasted, and who or what was involved, but nothing can confirm this kind of continuity for you in terms of your thinking-events. In fact, this experiment leads to an unanswerable question: how do you really know that you had any of the thoughts that you remember having?
04:07 – I state that remembered-thinking-events are defined by uncertainty, and introduce the exercise of comparing the real and fantasy music festival event-memories.
05:02 – Examining the memory of the real life event:
Memories of real events have a beginning and end, they have boundaries, but the boundaries are fuzzy.
The mind recognizes repeated events in the universe, but it also understands that events aren’t repeated perfectly, that repeatability in the external universe is only sort-of there.
We make deductions and inferences about the connections between events in the universe, but we know that are deductions and inferences are vulnerable to criticism from other people, and future evidence that may disprove our deductions.
08:52 – “This interlude presents Section 2 from my essay (“The Pressure of Light: how consciousness creates permanence in an infinite universe”*), which examines the nature of external-events-remembered.
*https://pressureoflight.ca/the-pressure-of-light/
12:29 – Examining the fantasy music festival event-memory:
I may believe that the visualization caused a feeling of excitement, but can’t prove this happened
I can repeat the fantasy over and over, and presume that I’ve done so in precisely the same way without the risk of disproof
I can perceive the boundaries surrounding the thinking event as perfect
15:35 – Summary of examination of each type of memory
The differences are important because our brains would have evolved according to the knowledge-generating nature of each memory-type
17:30 – Seeing a remembered thought, and two thoughts ago, and three thoughts ago, as analogous to nodes of communication in Claude Shannon’s “The Mathematical Theory of Communication”*. A similar increase in uncertainty makes it easier to perceive perfect iterations further and further back, so that infinite iterations are in fact easy to perceive.
*https://archive.org/details/in.ernet.dli.2015.503815/mode/2up
19:55 – “This interlude presents Section 3 from my essay (“The Pressure of Light: how consciousness creates permanence in an infinite universe”*), which examines the nature of internal-events-remembered.
*https://pressureoflight.ca/the-pressure-of-light/
26:10 – Concluding with my thoughts on the introductory quote: “…as far as the propositions of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.”*
– Albert Einstein, 1922
*First published 1921 by Julius Springer (Berlin) https://einsteinpapers.press.princeton.edu/vol7-trans/225
I propose that the nature of remembered-thinking explains how we are able to perceive systems that are perfect, such as what’s contained in mathematics, despite living in a universe not described by mathematics with perfect certainty.