the value of this memory card, was worth more than the rest of the entire observable universe minus the card
I doubt this would be true. I think the value of the card would actually be close to zero (though I’m not completely sure). It does let one solve the halting problem up to 10,000 states, but it does so in time and space complexity O(busy_beaver(n)). In other words, using the entire observable universe as computing power and the card as an oracle, you might be able to solve the halting problem for 7 state machines or so. Not that good… The same goes for having the first 10,000 bits of Omega. What you really want are the bits of Tau, which directly encode whether the nth machine halts. Sure you need exponentially more of them, but your computation is then much faster.
the value of this memory card, was worth more than the rest of the entire observable universe minus the card
I doubt this would be true. I think the value of the card would actually be close to zero (though I’m not completely sure). It does let one solve the halting problem up to 10,000 states, but it does so in time and space complexity O(busy_beaver(n)). In other words, using the entire observable universe as computing power and the card as an oracle, you might be able to solve the halting problem for 7 state machines or so. Not that good… The same goes for having the first 10,000 bits of Omega. What you really want are the bits of Tau, which directly encode whether the nth machine halts. Sure you need exponentially more of them, but your computation is then much faster.