Hey, great read as always, really insighful how you connected Bostrom's trichotomy, but I'm still trying to wrap my head around whether the 'simulated minds outpace base-layer inhabitants' scenario neccessarily means we are already in one, or just that the odds approach 1 in the future.
Thank you for your kind words! It's great to have some feedback :)
To answer your question:
According to Nick Bostrom's argument, the odds that we live in a simulation approach 1, which means, we nearly 100% live in a simulation. The reason is: assuming that (1) in the future simulated minds are significantly more than base-layer minds, (2) and assuming we have no special privilege, i.e. we are a random pick from the distribution of all minds, then it's way more likely that we live in a simulation. In fact, the more simulated minds we assume, the more likely we are in a simulation.
A nice follow-up: recently, Nick Bostrom's argument has been disputed by physics from the University of British Columbia. Their thesis is that, because of Gödel’s incompleteness theorem, there exists a paradoxical statement that is true but whose truthfulness cannot be computed using logic. Imagine for example a statement such as, "This true statement is not provable." If it were provable, the statement would be false—a contradiction; if it were false, it'd be another contradiction. This implies that the universe can never be a simulation, as not all information can be computed.
This argument is similar to common criticism of the world-famous cosmologist Max Tegmark's thesis called "mathematical universe hypothesis"—which, if you ask me, strongly resembles Galileo Galilei's statement that "Il gran libro della natura è scritto in caratteri matematici" (The great book of nature is written in mathematical characters). Max Tegmark's idea is that the universe is a mathematical object and that every mathematical object must exist somewhere in the universe—in other words, Platonism, or, if you prefer, Pythagoreanism.
This hypothesis has been ruled inconsistent with Gödel's theorem because of the reasons mentioned above. Tegmark's response is very lean and, although unintentionally, also defeats any simplistic disregard of the simulation hypothesis. In short, Tegmark says that only Gödel-complete mathematical structures have physical existence. Quoting Wikipedia, "Tegmark goes on to note that although conventional theories in physics are Gödel-undecidable, the actual mathematical structure describing our world could still be Gödel-complete, and "could in principle contain observers capable of thinking about Gödel-incomplete mathematics, just as finite-state digital computers can prove certain theorems about Gödel-incomplete formal systems like Peano arithmetic.""
Hey, great read as always, really insighful how you connected Bostrom's trichotomy, but I'm still trying to wrap my head around whether the 'simulated minds outpace base-layer inhabitants' scenario neccessarily means we are already in one, or just that the odds approach 1 in the future.
Thank you for your kind words! It's great to have some feedback :)
To answer your question:
According to Nick Bostrom's argument, the odds that we live in a simulation approach 1, which means, we nearly 100% live in a simulation. The reason is: assuming that (1) in the future simulated minds are significantly more than base-layer minds, (2) and assuming we have no special privilege, i.e. we are a random pick from the distribution of all minds, then it's way more likely that we live in a simulation. In fact, the more simulated minds we assume, the more likely we are in a simulation.
A nice follow-up: recently, Nick Bostrom's argument has been disputed by physics from the University of British Columbia. Their thesis is that, because of Gödel’s incompleteness theorem, there exists a paradoxical statement that is true but whose truthfulness cannot be computed using logic. Imagine for example a statement such as, "This true statement is not provable." If it were provable, the statement would be false—a contradiction; if it were false, it'd be another contradiction. This implies that the universe can never be a simulation, as not all information can be computed.
This argument is similar to common criticism of the world-famous cosmologist Max Tegmark's thesis called "mathematical universe hypothesis"—which, if you ask me, strongly resembles Galileo Galilei's statement that "Il gran libro della natura è scritto in caratteri matematici" (The great book of nature is written in mathematical characters). Max Tegmark's idea is that the universe is a mathematical object and that every mathematical object must exist somewhere in the universe—in other words, Platonism, or, if you prefer, Pythagoreanism.
This hypothesis has been ruled inconsistent with Gödel's theorem because of the reasons mentioned above. Tegmark's response is very lean and, although unintentionally, also defeats any simplistic disregard of the simulation hypothesis. In short, Tegmark says that only Gödel-complete mathematical structures have physical existence. Quoting Wikipedia, "Tegmark goes on to note that although conventional theories in physics are Gödel-undecidable, the actual mathematical structure describing our world could still be Gödel-complete, and "could in principle contain observers capable of thinking about Gödel-incomplete mathematics, just as finite-state digital computers can prove certain theorems about Gödel-incomplete formal systems like Peano arithmetic.""
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