Would it be possible for a wizard to create a universal Turing machine that had an infinite amount of memory?
Also, if we could master magic, do you think that it would be possible to create a separate pocket universe for a computer, that could perform exhaustive searches of an infinite problem space in a way that would seem instant when observed from this universe?
Wouldn't it be interesting if we found a technique to do the latter.
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Anonymous2013-05-28 0:41
When the singularity happens (still waiting, Kurzweil and Kaku), I'm going simulate my own private universe where I am a cute little witch and wear cute Touhou dresses, but everyone else is normal. I'll give them hope, then crush their dreams right in front of them, keeping them in perpetual misery. I'll curse them with ambitions, but make those ambitions impossible to fulfill. I'll give them a good life, then smash them right in the middle, just to give them a taste of the happiness that they never have. I'll delude them into thinking that they are free, then reveal to them that they are only my slaves. I'll torture and kill them, just to resurrect them and do it again, until their mind is completely broken and there is no shreds of a human left in them, then discard them and move on to the next victim. I'll make Hell, and condemn those who resent my evil ways to eternal agony. I'll teach them concepts of justice just sneer in their faces as they try to reconcile my words with my actions. I'll reward those who emulate me with riches and power, and punish those who don't with starvation, sickness, and the death of those around them. I'll make them toil for their entire lives to build monuments to my vanity. I'll give them brief reprieves of love and contentment, then kill off everything they loved and leave them wondering what they did wrong.
This will be a very fun and very intellectual game -- I am very much looking forward to it.
>>6
but once you get to wear the cute dress you would probably stop being angry and wanting to hurt people am I right?
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Anonymous2013-05-28 0:59
I'm no physician, but I'm pretty sure that quantum mechanics allows for this.
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Anonymous2013-05-28 1:06
>>9
I really, really doubt it. Inside I will still be an insecure, hateful, bully. Maybe it would be better for me to do something more constructive, like learn empathy. Perhaps, providing that we invent magic, I can simultaneously live out the lives of every person who ever lived in my universe, while I still suffer under the cruel reign of myself. Once the simulation is completed (which might take as long as an entire universe lifespan), my various consciousnesses will collapse to form a something that is either a much more wholesome human being, or an even more brutal tyrant.
With eternity to experiment, I can't help by try this at least once.
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Anonymous2013-05-28 1:21
>>11 Once the simulation is completed (which might take as long as an entire universe lifespan), my various consciousnesses will collapse to form a something that is either a much more wholesome human being, or an even more brutal tyrant.
Also know as AchievingSatori
>>18
Well it's not constructible using only the finite operations you can perform on sets. Which is why it's an axiom. It's taken to exist.
It's not really a physical construct, it just encapsulates the iterative idea in a set form. Mainly what you do is prove some properties that classes of objects have. Like all even numbers behave in a certain way or something like that. As a programmer, you can think of it as a stream, we make sure never to explicitly calculate elements, but use the definition of the stream itself to do our work.
Sorry that explanation came out terrible and I'm having a hard time thinking of a smart way of saying this.
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Anonymous2013-05-28 9:04
>>18
I = {ø, {ø}, {{ø}}, {{{ø}}}, ...}. I believe this is just ℕ as Peano numbers, but I might be wrong, I'm rusty on THEORETICAL SHIT THAT DON'T GET SHIT DONE.
>>21
The definition I gave (standard construction) produces:
I = {ø, {ø}, {ø, {ø}}, {ø, {ø}, {ø, {ø}}}, ...}
You could also do for all x ∈ I: {x} ∈ I, which is what you gave. Generally you just need a successor function S then for each element e in the set, S(e) is also in the set.
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Anonymous2013-05-28 9:28
empty sets dont exist
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Anonymous2013-05-28 13:59
No, because magic doesn't exist.
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Anonymous2013-05-28 14:51
>>15-16,18,20-22
Shalom aleichem, Jewish brothers! May HaShem give you infinitely many infinite sets.
Memory is addressable, so a set of addresses can represent our memory. Then memory is infinite if there is a one-to-one correspondence from the set of addresses to the set of natural numbers.
>>22
You know, I honestly thought that at first, and then I wondered why I was getting something that was so close to what I learned as the Peano numbers, and I figured you were just abusing notation a little and pretending () ∈ was really {} ⊂.
To access an infinite amount of memory, they would be a need for an infinite amount of addresses. To store each address during processing, an infinite amount of memory would be needed, which would in turn need an infinite amount of memory to address the address. Thus, the size of an infinite memory needed to store addresses must exceed the size of the infinity needed for the infinite memory itself in an infinite fashion. The minimum infinity needed is ∞∞. We can model this relationship as follows:
lim xx = ∞ x→∞
Thus, a machine with an infinite amount of memory requires an infinite amount of memory.
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Anonymous2013-05-28 19:00
>>23
Let ø be the set containing exactly the girls with which >>23-san has gotten laid. That should do for our purposes.
Edit: No deal. She's too old and too big and has too much fat on her chest. Are you absolutely sure that you don't want the loli? Oh well, more for me.