Re: Primes: Randomness and Prime Twin Proof

i might make myself unpopular bye saying this but
i do have a little more confidence in martin then most do on this forum here.
I do believe in an important relation between statistics and primes !! actually i have some "martin like" conjectures about primes , based on traditional statistics.

how else should a short proof of a complicated number theory look like ? you cant use geometry or basic algebra
or even integrals
you would need group theory topology and math above the "riemann" level.

i did not say Winer proved anything (yet) but he's got my attention.
ive seen worse (crankpots ? ) on forums(like yesterday's discussion about distrubitivity and f(0)=f'(0)=0 blah blah blah , most here will know who i mean , i send a nasty response to him solving the case bye differential equations to make him shut up ). he doesnt seem like an idiot to me !
further more i have some arguments to defend his theory and his posts
namely
your all taking about

1) the 2 different coins.
well like he said that is splitting up randomness ; so not random!
and even worse thats a finite set !! although you compute and talk about the tosses wich are infinite , the group to pick from is finite and remains finite ; just 4 elements and afterwards 2 ( identical or not)
there are many wrong ideas about statistics and groups
it looks like a good counterexample but it doesnt
its equivalent to saying:

let the probability that there exists a prime between a and b be 100/(b-a)^n ( = smaller than 1 )

where n is the number of samples a and b and therefore denote the group.

now notice its a nonzero probability
and its probability sum for infinite tries (or samples , tosses ,...) can be 1 or even 2 or 5 or infinity

but to make an equivalent of the coins , the group must be finite .
we always pick between the same a and b, and if we pick then it doenst matter what probility we have.
the probability depends on being a prime there or not and not on the number of tries , so even if the picking is random or group sample is random,
statistics does not apply here.(in that sence of counter-example)

simply put the cardinality is not equal to the integers. so its not a counter-example !!
its a totally different thing
and im glad martin brought it up here
but for some reason everybody missed that concept of cardinality

cardinality is very important in statistics !!
simply put you will get lucky bye picking if there is a non zero probability and the cardinality of the probability sum matches the cardinality of set or equivalently its "countability"

cardinality is even more important than total randomness !! (wich does not really exist anyways and dont start about cellular automaton rules e.g. rule 30 plz)


2) 1/3 0.3333333333 seems good but another bad argument!
this time the cardinality of the field is the highest!
so the cardinality/set is uncountable and statistics to countable infinity is of course wrong in an uncountable set! logically because the possibilities are higher than countable infinity.

however you could remove the cardinaly (bye function or whatever) to a countable one that would be unrandom , very ! unrandom

i write very because i believe statistics does apply to more or less random sets. but of course not to very unrandom ones.

( you might have noticed that i have a slightly different set theory (of my own )then cantor's one .
But it is still consistent with statistics , combinatorics ,analysis , countability and probability so it is a correct one. For the ones who are curious , i have more classes of cardinality / countability but that does not interfear with the correctness of what i say since finite sets are countable in every set theory of course)

and as far as i can see thats about it for the good counterexamples

however i must admit that probability 1 does not imply certainty!

however consider the following probability sums
(yes i take sums of probability since there is almost independance (to put it more complicated the cardinality of the independance is smaller than the cardinality of the set or the probability so it is allowed)

if the sum turns out to be 1.01 probability , the picking is random , and the cardinality is countable, you will have a hard time disproving its uncertainty !!!!
even if he picks unlucky ; consider the probability of unlucky picking (forever !! wich is even very unlikly ( probability 0 ) as a decreasing function of the normal probability f(x) = x-0.004 than the probability = 1.01 -0.004 = (still!) 1.006
and even worse ; for probabilities above 1 it remove a bit of the neccesarity of the randomness!
e.g. if ya have probability 100 ( as sum ) and you have a sample that is pseudorandom ( very close to random )
you will still get lucky
(note unlucky is mathematical equivalent to not totally random ( but almost ) )
a hard time to disproof the uncertainty im telling ya !!
if possible to disproof!
wich is not possible in general because in general it is true !!
it will be hard en veryyy unlikely to disproof also because the probability that you cant prove the uncertainty is at least 1 now.

it might be new for most of you to read about probabilities above 1
its a little abstract but it simply means certainty.
under certain restrictions of course ( mentioned above )
so you see he aint so wrong after all

many will probably disagree
if ya do plz read again with an open mind
i dont mind critics but dont insult me

and btw martin you should thank me on your site :-)

for my support and
since i explained it better than you :p

well at least probability , dont wanna steal any honor of your work.

although i did some of that stuff myself im convinced you did not steal any of my work ( since you dont know me and i never put many details on it on the net , else i might have gotten suspicous :p )

greetz
tommy

my favorite selfmade constant
tommyzeta[1]= 2^((3/2)^((4/3)^((5/4)^...)
=3.503809972
second constant-> lim n-> inf [5^(2^n)] "written backwards" so -> 0.5260.. (=algebraic ??)
.

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