On Saturday, August 16, 2014 8:45:30 PM UTC+10, Liz R wrote: > > On 16 August 2014 16:48, Pierz <[email protected] <javascript:>> wrote: > >> I assert this confidently on the basis of my intuitions as a programmer, >> without being able to rigorously prove it, but a short thought experiment >> should get halfway to proving it. Imagine a lookup table of all possible >> additions of two numbers up to some number n. First I calculate all the >> possible results and put them into a large n by n table. Now I'm asked what >> is the sum of say 10 and 70. So I go across to row 10 and column 70 and >> read out the number 80. But in doing so, I've had to count to 10 and to 70! >> So I've added the two numbers together finding the correct value to look >> up! I'm sure the same equivalence could be proven to apply in all analogous >> situations. >> >>> >>> But if your table gives the results of multiplying them, you get a > slightly free lunch (actually I have a nasty feeling you have to perform a > multiplication to get an answer from an NxN grid ... to get to row 70, > column 10, don't you count N x 70 + 10?) > > So suppose your table gives the result of dividing them, I'm sure you're > getting at least a cheap lunch now? > > Sorry this is probably complete nitpicking. I can see that the humungous > L.T. needed to speak Chinese would require astronomical calculations to > find the right answer, which does probably prove the point. >
Actually it's not nit-picking. My first thoughts on this were wrong. It's clear some lookup tables aren't worth the computational cost of looking them up, e.g, a lookup table of addition, whatever the precise computational cost (you can jump rows without having to count through each cell, so I think the cost is still linear on the size of the table). However, we can imagine a table of cubes or powers of 796.0584304 and see that the lunch gets very cheap if you have the memory resources for it. It's a trade-off of time versus space. Actually I think you can show that the LT saves work so long as the program doesn't actually disregard any of the information passed to it and does some real work on it. Why is this even interesting? Because if you can use lookup tables more efficiently than doing the computations themselves, then maybe you can make a philosophical zombie through the careful selection of recordings. However, I think you can show this won't work. Firstly, the machine won't be a *complete* zombie because it will have to work hard and therefore somewhat intelligently in selecting the correct records, so then we have the situation of a "partial" zombie, which is absurd vie the fading qualia argument. But also, we have to recognise that to completely recreate the program/person, we can't only record overt behavioural outputs, but also internally reportable states to cater for the possibility of someone asking, "what are you thinking now?" etc. That means our lookup table needs to record each step of each calculation, not only the outputs, and that means no compression is achieved at all. To locate the machine's state, we can't just look up a result from an input, but we have to go down the rabbit hole of the computation itself, which will involve as many, and the same, computations as the original program. Maybe it's possible that some compression could be achieved because not all machine states can be interrogated. An "output" is after all merely an accessible machine state. Inaccessible machine states could be compressed into a lookup table or cache, but the interesting possibility here is that * maybe they already are* and that is why they are unconscious and inaccessible. Perhaps we turn often repeated computations into recordings and that is why they are unconscious, because no true computation is being carried out any more. Ah gad, that's enough on that. I'm thinking out loud more than anything else, sorry! -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
