I don't think it is. I think the idea that the natural numbers go on forever is a concept in your brain that is associated with a Platonic romantic dream of logic that doesn't hold in reality. If the total energy content of the universe was saturated into pure intelligence, there would still be a limit to the highest natural number and most sophisticated mathematical structure it could process. And since it is the largest possible to be realized in any real consciousness, in my opinion it is the highest level of mathematics that is truly real.
Is the number of natural numbers/mathematical objects really infinite?
- Thread starter nanocosm
- Start date
What prevents you from adding 1 to the number is that at the limit of the nervous firings that process numbers there is no possible new way of firing to process a next number. Since you can use hyperoperation notation for larger and larger numbers, it is so large that its impossible to start to think about it...but you would reach it eventually, and not go further.
Pardon?
What evidence do you have for this?
Or this?
How would such a thing work?
If I see the "absolutely maximum number" written down you're claiming that my brain will somehow freeze up and prevent me incrementing it by 1?
This must be false since, to give an example, if that number (regardless of how large it actually is) ends in, say 3, then what is to prevent me from ignoring the rest of that number and simply changing that "3" to a "4"? Or an "8"? :shrug:
in base ten 9 is the limit of natural whole numbers . All others can be considered larger groups of the same 9 numbers . But that is just one aspect of mathematical objects . There are many mathematical fixtures that are not real numbers .
so here you go all the natural whole numbers
123456789
246813579
369369369
483726159
516273849
639639639
753186429
876543219
999999999
o.k. thats it , all is a repeat after that to infinity . The power of nine . You can fold up every whole number and it will fall in that pattern in its precise group of power . Kind of like counting by ten over and over again but not really . The thing is all factors of whole numbers follow the rule you see right there . Multiples of 4 will follow multiples of 13 with the same pattern .
It is quite remarkable to Me . It still blows my mind . I try not to think about it . It can be very distracting when you start seeing the implications , or better to say the weird congruences in the segregation . Don't that just blow your mind ? God I don't know why that would not . I just can't get use to it all working out like that .
Edit : O.K. it is Monday morning and you all are bad for making think about the math . Bad People !!! I got things to do besides think about math .
It don't matter how big the number is it will be a product of the above posted pattern . If it was 19191919191919.191919 the multiples would still follow the first row . By reduction if the number i just displayed is x thenx1, x2,x3,x4,x5,x6,x7,x8,x9 would still be 1,2,3,4,5,6,6,8,9
or if x was 134 then x1,x2,x3,x4,x5,x6,x7,x8,x9 would still be 8,7,6,5,4,3,2,1,9.
It just blows my mind ! Can you believe that shit ? Don't you think that is unbelievable .
It gets worse!
The interval is all perfect from 0 . The distance relationship from 0 is in perfect harmony in its bigger form . You that 7 and 25 for example . Lets call them blue. We got 0 ,7,14 ,21 = x0,x1,x2,x3 . Now we got 0,25,50,75= 0,x1,x2,x3. Now by reduction what do we got ? We got the 7 pattern of the master list above that I posted . You go to the 7 list of 7,5,3,1,8,6,4,2,9 and both are congruent by reduction .
I know you all think that might be all no big deal cause of how all multiples of 9 reduce to 9 , but I can not get past the completeness of occurrence. It don't matter how big a number it is its multiples will be of just those forms above .
so here you go all the natural whole numbers
123456789
246813579
369369369
483726159
516273849
639639639
753186429
876543219
999999999
o.k. thats it , all is a repeat after that to infinity . The power of nine . You can fold up every whole number and it will fall in that pattern in its precise group of power . Kind of like counting by ten over and over again but not really . The thing is all factors of whole numbers follow the rule you see right there . Multiples of 4 will follow multiples of 13 with the same pattern .
It is quite remarkable to Me . It still blows my mind . I try not to think about it . It can be very distracting when you start seeing the implications , or better to say the weird congruences in the segregation . Don't that just blow your mind ? God I don't know why that would not . I just can't get use to it all working out like that .
Edit : O.K. it is Monday morning and you all are bad for making think about the math . Bad People !!! I got things to do besides think about math .
It don't matter how big the number is it will be a product of the above posted pattern . If it was 19191919191919.191919 the multiples would still follow the first row . By reduction if the number i just displayed is x thenx1, x2,x3,x4,x5,x6,x7,x8,x9 would still be 1,2,3,4,5,6,6,8,9
or if x was 134 then x1,x2,x3,x4,x5,x6,x7,x8,x9 would still be 8,7,6,5,4,3,2,1,9.
It just blows my mind ! Can you believe that shit ? Don't you think that is unbelievable .
It gets worse!
The interval is all perfect from 0 . The distance relationship from 0 is in perfect harmony in its bigger form . You that 7 and 25 for example . Lets call them blue. We got 0 ,7,14 ,21 = x0,x1,x2,x3 . Now we got 0,25,50,75= 0,x1,x2,x3. Now by reduction what do we got ? We got the 7 pattern of the master list above that I posted . You go to the 7 list of 7,5,3,1,8,6,4,2,9 and both are congruent by reduction .
I know you all think that might be all no big deal cause of how all multiples of 9 reduce to 9 , but I can not get past the completeness of occurrence. It don't matter how big a number it is its multiples will be of just those forms above .
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I know it's not his usual subject, but this thread just screams "reiku."
DonQuixote
Registered Senior Member
Ha-hum... well, nothing, but with these operations you will always end up with a definite, non-infinite number... Jou just start counting and come back and tell us when you have reached infinity!
Nah, Reiku would have tried to link it to quantum mechanics and thrown in something like
"And so the conciousness wavefunction is $$\int_{\Omega}|\psi|^{2} dx = 1$$ with gauge connection $$D = \partial + ie A_{\mu}$$ for Wely spinor $$\chi_{s}$$ and so we can conclude neutrinos go faster than light!"
then proceed to throw his toys out the pram when someone points out his incorrect spelling of Weyl and the complete non-sequitor nature of his post.
Ha-hum... well, nothing, but with these operations you will always end up with a definite, non-infinite number... Jou just start counting and come back and tell us when you have reached infinity!
The concept of 'infinity' as applied to numbers remains interesting to me. That a species of demonstrably finite life expectancy would contemplate such a concept which, by logic, seems impossible to verify, is an exercise in futility, IMO. :bugeye:
I think this is about as succinct a refutation as you can get.
The philosophy of mathematics is a subject for the Philosophy subforums, not Physics & Math.
DonQuixote
Registered Senior Member
The concept of 'infinity' as applied to numbers remains interesting to me. That a species of demonstrably finite life expectancy would contemplate such a concept which, by logic, seems impossible to verify, is an exercise in futility, IMO. :bugeye:
It is interesting. Personally, I'm not convinced by the "you can always add one"-argument, since when you do, you always end up with a completely ordinary number. I think it is a mistake to equal "indefinetly" with "infinitely".
I think we can safely disregard the original poster's idea that this has something to do with neurons. If anything, our finite brains seems to have no problem with the concept of infinity. But I do think the use of infinity is, or at least can be, problematic.
There is no doubt that infinity may be useful sometimes, but I think it is mostly shorthand for "a very big number".
There are all sorts of difficult philosophical questions here. What kind of reality do we ascribe to a number, any number, not to mention infinity? If "number" is a concept anyway, why should "infinity" be less real? What is the relation between mathematics and physics?
Many mathematicians would not be offended by being called platonists. Its truths are considered to be indipendent of any "real" world. Personally, I see mathematics as a human activity that is very much a part of our physical world. I fear that we may make some metaphysically wrong assumptions if we uncritically allow concepts such as infinity, that these metaphysic concepts will "seep" into our worldview from platonic math. That numbers and cocepts is considered more "real" than reality.
I think you hit the nail on the head. His arguments are all based on the premise that there is some number X that is the limit of what intelligence can conceive and that somehow this fundamental limit to intelligence somehow limits natural numbers themselves.... which is ridiculous.
I think it's simpler than that. He seems to be implying that, in his opinion, when we think of a number we actually enumerate it in our heads e.g. if we think of 8 we have eight discrete "instances" in mind rather than the figure being a symbol for that number.