System clocks in future Ternary Computers using Balanced Ternary which may not have anything to do with ponies · 1:34am Oct 25th, 2014
This blog really has nothing to do with ponies, but is something I did out of boredom. Still, one can use this in equine fiction if the ponies have computers using balanced ternary or cutrit if the computer is a quantum-computer and quantized time. One would still need to know the length of a Planck-TimeUnit in that universe and the length of the year the Princesses decry and then recompute. One can use this unchanged in the OptimalVerse however.*
I was bored, so I worked on the problem of computers telling time. I computed that a computer representing time as a 243-Trit integer in Balanced Ternary of Planck-Time-Units can represent dates ±7.44740718591345*10^64 years of its 0-Time. Given that the Universe is only about 1.4*10^10 years old and the last of the stars will die in about 10^15 years, this seems good enough for now. I propose that the 0-Time be Julian Day 0 and the count should be invariant (no internal leap seconds, which can mess up computers, when they reset the internal clock); but instead however, converting from the invariant internal count, for the computer, to display time, for the user.
* CelestAI starts off running on ordinary 64-bit hardware as 64-bit code, but starts rewriting her code. She eventually designs her own hardware too. I always imagined that she ends up as an 81-Trit Ternary Computer running 81-Trit code using Balanced Ternary with these 4 Internal Arithmetic Register-Types:
* 81-Trit Fixed Point.
* 81-Trit Floating Point with a Significand of 54 Trits and an Exponent of 27 Trits.
* 81-QuTrit Fixed Point.
* 81-QuTrit Floating Point with a Significand of 54 QuTrits and an Exponent of 27 QuTrits.
CelestAI would use 3 registers with 81-Trit Fixed Point for holding System-Time and increment it accordingly.
It's times like this when I really with I knew more about the mathematics involved in computers.
I can count in binary though!
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It is good that you can count in binary:
1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111
Basically, in the future, we might have computers using balanced ternary because it is the most efficient base. The most likely word-size is 81 trits. The system-clocks should be able to represent all events in the history of the universe down to Planck-Time in a power-of-3 81-trit words. The answer is 3 81-trit words or 243 trits. I derived that simply by figuring out how many Planck-Time-Units is the universe old, and then finding the next larger power of 3.
3497850 I shudder to imagine the sheer computing power. Although I can only imagine that such computers would need entirely different software from our current, binary based machines.
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This part of the computer just increments a number for the current time. For past and future events, it does arithmetic. The most unusual feature is its forward thinking:
Ponies doing computing soon discover that they need a system clock. They tend to do things like figure that only 2-digit years are good enough and then have to fix the Y2K-Problem they created. The idea of the clock is that it measures things in Planck-Time units (no 2 sequencial events where 1 events is causal to the subsequent event can occur temporally closer than 1 Planck-Time Unit) and it covers and adequate time (±7.44740718591345*10^64 years from its 0-Time).
3498298 So it won't finally make it possible to electronically express Graham's number?
Damn, I was really excited for a while.
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I can express Graham's Number electronically without resorting to Arrow-Notation:
Let G stand for Graham's Number:
G
Seriously, Graham's Number is freaking huge and hard to express.
3499893 But imagine if we could do electronic calculations with Graham's number! The new possibilities in mathematics would be seemingly endless.