>>4
Mathematical objects are just things defined by abstract rules, they always `existed' and will always `exist', you're merely discovering what happens if you take some rules (axioms) and try to go with them and see the resulting true statements in the system (theorems).
Will natural numbers suddenly stop existing if you forget how to count? What about if everyone in the world does? Just because you forgot how a system acts within a set of rules doesn't mean that the next time you think of that arbitrary set of rules you'll get different results.
A particular instance/implementation of a mathematical structure into a physical system capable of computation (which can only implement a restricted class of such mathematical structures) is not equivalent to the structure itself. Destroying the physical implementation that you created doesn't mean that the axioms would lead to different theorems next time you try to look at them.
Now assume the universe (multiverse or whatever you wish) is such a consistent mathematical structure, maybe it's a simple computable object, or maybe it's some weird thing allowing computation with infinities (this (real numbers or other infinite objects) would annoy me a bit as it would imply that each quanta of time it would compute an infinity of simpler calculations, but I'll leave my personal predictions out of this). If you could look at this presumably simple object defined by some simple axioms and within it you could find the information defining you right this moment. If you could put time t=current time (along with whatever other parameters would be required) into this equation and you had a way of calculating it (highly unlikely as you'd probably need more information than this universe can hold), you could see the instance of yourself sitting on the computer right now and posting on /prog/.
>>6
I'm not talking about it as a physical thing, but I know you're incapable of contemplating the abstract.
I merely mean it in the form that if someone considers a set of definitions for some system, they will always get the same conclusions within that system. Not only this, but there can true statements within some axiomatic system which cannot be proven or reachable from the axioms themselves, yet whenever you test the statements on concrete values, you'll always see that they are true, and you may even be able to prove that you cannot prove that they are true or false.
As for the mathamatical object being "physical", you could try to imagine an universe which is a computer simulation (possibly with a "brain-in-a-vat" scenario, if you don't want to emulate the mind as well within the simulation). The other question that you may ask is that if current trends are completed, we may reach a "theory of everything" that describes the entire existence of this universe as a mathematical object (hence if you could simulate or compute it, you would get the exact same world). Even if you think obtaining a ToE is impossible for whatever reason, the regularity we have observed in physics make it most likely that the fundamental nature of reality can be expressed as a mathematical object, and when/if you reach that conclusion you'll ask the question "why these equations?", if/when you do, I ask you to read that paper I linked.
>>5 Will natural numbers suddenly stop existing if you forget how to count? What about if everyone in the world does?
That's what reality is all about.
>>8
What if you reinvent natural numbers independently (it's not that hard to axiomatize them and even a child can take a bucket and throw rocks in it to get an intuition for it), do you think you'll find different rules? You could even try to make a computer program which tries out various sets of axioms (after you formalize a way of describing them; there are already a few such ways), and for each set of axioms you can't have a different set of theorems from the ones you forgot about (in this thought experiment we assumed everyone forgot natural numbers) - we might not be able to know all of them, but if we were to reach them, you'll see that all the old theorems still hold regardless if you know of them or not.
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Anonymous2011-05-17 3:01
A total lack of exact quantity language did not prevent the Pirahã from accurately performing a task which relied on the exact numerical equivalence of large sets. This evidence argues against the strong Whorfian claim that language for number creates the concept of exact quantity. […] Instead, the case of Pirahã suggests that languages that can express large, exact cardinalities have a more modest effect on the cognition of their speakers: They allow the speakers to remember and compare information about cardinalities accurately across space, time, and changes in modality. […] Thus, the Pirahã understand the concept of one (in spite of having no word for the concept). Additionally, they appear to understand that adding or subtracting one from a set will change the quantity of that set, though the generality of this knowledge is difficult to assess without the ability to label sets of arbitrary cardinality using number words. (emphasis added)[2]
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Anonymous2011-05-17 3:03
Being concerned that, because of this cultural gap, they were being cheated in trade, the Pirahã people asked Daniel Everett, a linguist who was working with them, to teach them basic numeracy skills. After eight months of enthusiastic but fruitless daily study with Everett, the Pirahã concluded that they were incapable of learning the material and discontinued the lessons. Not a single Pirahã had learned to count up to ten or even to add 1 + 1.[11]
Everett argues that test-subjects are unable to count for two cultural reasons and one formal linguistic reason. First, they are nomadic hunter-gatherers with nothing to count and hence no need to practice doing so. Second, they have a cultural constraint against generalizing beyond the present which eliminates number-words. Third, since, according to some researchers, numerals and counting are based on recursion in the language, the absence of recursion in their language entails a lack of counting. That is, it is the lack of need which explains both the lack of counting-ability and the lack of corresponding vocabulary. Everett does not claim that the Pirahãs are cognitively incapable of counting.
>>10-11
This only shows that there can be civilizations having languages that make it hard to think abstract thoughts in them. It does not show that such a thing would be common or that it represents a typical human culture.
>>14
Where do they claim that? I may have a different opinion about certain things than them, but I never seen anyone of them claim anything as ridiculous.
There is the famous quote "Any sufficiently advanced technology is indistinguishable from magic.", but that is only to be taken as the fact that to someone who doesn't understand some advanced technology and has no change of understanding it, they may as well regard it as magic. On the other hand, it is possible to construct a thought experiement using a simulation argument ( http://simulation-argument.com/ ) and some form of (possibly strong, but doesn't have to be) AI having write access to the simulation as being more or less equivalent to any universe allowing ``magic'' or various forms of theistic gods, which would be a great way to make the quote explicit.
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Anonymous2011-05-17 4:21
Any sufficiently complex C++ program is indistinguishable from Prime Intellect. It just grows magic and begins to understand itself, using quantum homosexuality. And then it just grows robotic arms out of the monitor and yudkovsky passes the bong to it.