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I love reading articles like this, and I think they are always better while I'm drinking! Sadly, I was reading this article early in the morning, with nothing but coffee to accompany it!
https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/
...the need for a new mathematical language that could “liberate” physicists from infinite precision.
***
The bold below is something I added:
Say the value of x is 0.4999, where further digits unfurl in a choice sequence. Maybe the sequence of 9s will continue forever, in which case x converges to exactly ½. (This fact, that 0.4999… = 0.5, is true in standard math as well, since x differs from ½ by less than any finite difference.)
But if at some future point in the sequence, a digit other than 9 crops up — if, say, the value of x becomes 4.999999999999997… — then no matter what happens after that, x is less than ½. But before that happens, when all we know is 0.4999, “we don’t know whether or not a digit other than 9 will ever show up,” explained Carl Posy, a philosopher of mathematics at the Hebrew University of Jerusalem and a leading expert on intuitionist math. “At the time we consider this x, we cannot say that x is less than ½, nor can we say that x equals ½.” The proposition “x is equal to ½” is not true, and neither is its negation. The law of the excluded middle doesn’t hold.
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“Information is destroyed as you go forward in time; it’s not destroyed as you move through space,” Oppenheim said. The dimensions that make up Einstein’s block universe are very different from one another.
https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/
...the need for a new mathematical language that could “liberate” physicists from infinite precision.
***
The bold below is something I added:
Say the value of x is 0.4999, where further digits unfurl in a choice sequence. Maybe the sequence of 9s will continue forever, in which case x converges to exactly ½. (This fact, that 0.4999… = 0.5, is true in standard math as well, since x differs from ½ by less than any finite difference.)
But if at some future point in the sequence, a digit other than 9 crops up — if, say, the value of x becomes 4.999999999999997… — then no matter what happens after that, x is less than ½. But before that happens, when all we know is 0.4999, “we don’t know whether or not a digit other than 9 will ever show up,” explained Carl Posy, a philosopher of mathematics at the Hebrew University of Jerusalem and a leading expert on intuitionist math. “At the time we consider this x, we cannot say that x is less than ½, nor can we say that x equals ½.” The proposition “x is equal to ½” is not true, and neither is its negation. The law of the excluded middle doesn’t hold.
***
“Information is destroyed as you go forward in time; it’s not destroyed as you move through space,” Oppenheim said. The dimensions that make up Einstein’s block universe are very different from one another.