Acme

Cool beans. You may have missed the Lucas Numbers appended to my earlier post. This appending automatically joins 2 recent posts into 1, and so such posts are often overlooked. Those who can't count, don't count. PS Maybe add a few more colors for 6,7,8...?

Just to clarify, they are "1-dimensional" cellular automata. This is because the initial-condition set is on a 1-dimensional line. Conway's Game of Life on the other hand is a 2-dimensional cellular automaton because the initial condition set is on a table of rows & columns. Anyway, try this set: {77 119 143 161 209 221 299 323 329 371 377 407 413 437 473 497 527 533 539 551 589 611 623 629 689 707 ...} These are the ordered odd numbers that are not polygonal numbers and not Prime. Or this set: {8 14 20 26 32 38 44 50 56 62 68 74 80 86 92 98 104 110 116 122 128 ...} These are the ordered even numbers that are not polygonal numbers. (All are of form 6x+2) Good times. . Addendum: Try the Lucas Numbers too. {2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843 ...}

I point out again the error in the author's work that you keep quoting on the C14. He says there's more C14 in the plants because of more cosmic rays hitting plants, but this is not what happens. The C14 is created in the upper atmosphere and the plants respire the C14.

Ordinals, cardinals, remainders of primes, I like to find numbers in everyday rhymes. First one then another go how many times, round manifold boundaries too twisted for climbs.

I would call them 1-dimensional cellular automata. The difference part is simply the 'rule' and the Primes the 'initial condition(s)'. Addendum: Try using some other sets for your initial condition, such as Perfect Squares, Fibonacci numbers, Triangular numbers, etcetera.

Hmmm...I see your point. But if we follow otriolet's essay carefully, it may be that trephination will suffice. "...light is a window to the very heart of the atom." Then too, perhaps cardioomentopexy is better called and the resulting increased blood flow to the heart will send electricity to the brain and it will shoot it back like rocks on the furniture. The atoms then of course will light the inside of the skull and we can peer in through the windows to the soul. Then when we see an issue, we can pull it out through trephined openings on both the temporal bones with an electromagnet, weigh it, and then use it to power our time ship to Mars. Yes Endy, I think you have it right.

Just for clarification, what is the mass of 1 issue? I want to calculate the attraction of one issue to another. I just love this kind of work.

Erhmm...no. Earth's magnetic field extends far into space. Moreover, a refrigerator magnet has around 150 times the strength of Earth's field and as everyone knows the astronauts' refrigerators are covered in magnets. source Edit: add space station refrigerator magnet image.

It might be useful to differentiate between 'theory' and 'theorem' in regards to mathematics. theory theorem Often times a 'proposition' is referred to as a conjecture. Once a conjecture is proven, it can properly be referred to as a theorem. In practice, this may vary. Properly speaking, Fermat's-last-theorem was just a conjecture until Wiles proved it, even though it was historically referred to as a theorem. With that out of the way, one 'invents' a proposition or conjecture by making some [unique] observation on mathematics that is true insofar as all examples looked at. If one then can prove it, it becomes a theorem.

The purpose is research into the effects of using radio transmitters of a certain frequency range to modify an area of the upper atmosphere in such a way that that area becomes a reflector of radio signals in a different frequency range. For example RADAR signals are line-of-sight, but if you can bounce them off the high atmosphere then you can see around the curvature of Earth beyond the normal line-of-sight signal. Otherwise to see these areas you would need RADAR transmitters 'out there'. By all means read the Wiki section on the conspiracy signal business.

Whether Fred had Gödel in mind or not, Gödel did not say what hoola said Fred might have said he forgot that some mathematician might have said. What Gödel proved was source I'll have the pork please.

I finished reading the above piece and while I don't pretend to understand every argument or equation I do find that such reading over time allows a goodly amount to seep in. Following the body of the paper, Tao accepts and answers questions from readers. Anyway, this particular response from Tao is telling. First, the question by a reader: Terry's response: Edits for typos and formatting.

... and I think people took this to mean uniformly randomly distributed, which I think we all agree is not right. I added some of what you left out of John's quote Bignose, as it is germane to some of the misunderstanding. And yes, I agree I did not suggest uniformly randomly distributed. Above John says 'could easily be pseudorandom' and earlier Peter liked pseudorandom as well. Let's explore that term. Pseudorandomness Note that counting is an entirely deterministic process. Let's explore 'statistical randomness'. Statistical randomness @ Wiki So we can see patterns within larger otherwise patternless structures. Let's visit the Wiki on 'randomness'. randomness @ Wiki So if random is a philosophical judgment, then my detractors are no less intransigent then I. Ah well, so it goes. I would like to sum up with a quote from Terrence Tao. It comes from some of his lecture notes from 2007 that were linked to from the last article I quoted from on the Yitan Zhang affair. Simons Lecture I: Structure and randomness in Fourier analysis and number theory Random, pseudorandom, hybrid, unpredictable, structured, pseudo-randomly-hybrid-structured, yada, yada, yada; in any case I dare say no one can give me the 9347593714679763402706530846308460346034760th Prime before next Thursday.

From An Outline of Intellectual Rubbish: A Hilarious Catalogue of Organized and Individual Stupidity ...Throughout the last 400 years, during which the growth of science had gradually shown men how to acquire knowledge of the ways of nature and mastery over natural forces, the clergy have fought a losing battle against science, in astronomy and geology, in anatomy and physiology, in biology and psychology and sociology. Ousted from one position, they have taken up another. After being worsted in astronomy, they did their best to prevent the rise of geology; they fought against Darwin in biology, and at the present time they fight against scientific theories of psychology and education. At each stage, they try to make the public forget their earlier obscurantism, in order that their present obscurantism may not be recognized for what it is. Let us note a few instances of irrationality among the clergy since the rise of science, and then inquire whether the rest of mankind are any better. ... source

For you mere mortals, that is. My deepest genuflection in your general direction as I have in the past been compelled to beg to prevail on such demigods and demigoddesses as yourself to exercise your great and splendiferous powers to the benefit of this humble mere mortal servant in seeking to correct egregious errors. May you and yours live long and prosper with the force. Can I get a yo Josiah up in here?

ERASMUS's Praise of FOLLY An oration, of feigned matter, spoken by Folly in her own person.

Phhhh. The Beauty of Bounded Gaps: A huge discovery about prime numbers and what it means for the future of math

Down vote? I can't imagine. Your continued arguing for argument's sake in the face of contrary facts is little more than trolling. Whether you agree about the use of terms is irrelevant to what those terms describe. I dare say nothing you have presented would be taken seriously at any gathering of mathematicians or in any mathematical journal.

Knowing full well that my advisement will go unheeded, I will quote some from the article and add some bolding and commentary. Note I have bolded the reference to Ulam's spiral and that I early on here gave it as an example that showed Primes are randomly distributed. See post #5

In Praise of Idleness By Bertrand Russell [1932]

+1 +50 if it were allowed. Formula for Primes@ Wiki Failing to read the entire article and its supporting links, but continuing to argue against the randomness of Primes is ...erhm...uhhhh... ill advised.

You are babbling. Maybe instead of arguing with me you can quote Bignose or imatfall in their statements that support what I have asserted and then argue with them.

I am saying the random distribution of Primes is referred to as a 'random distribution' because no one in a couple thousand years has shown a way to give the nth Prime even if given the n-1th Prime. It is an hypothesis that Primes are randomly distributed. I gave no proof; I simply characterized the problems. You said you didn't understand after explanations from multiple sources. You have received your due. Again, mathematicians don't care what laypeople think. This is true whether they complain or laude.

That was an implication I meant to allow, yes. It might equally imply just like Orville and Wilbur.

Very good. Focus & critical thinking go together like forums and arguments. The random distribution of Primes is self-evident. Adding the caveat 'no function, yet discovered' only allows us to continue -logically- looking for patterns without giving much thought to the very real possibility of our being on a fool's errand. As Gödel showed, if our math system is consistent it is incomplete and so the question of the distribution of Primes may -logically- be unanswerable. The editing is an impediment to the reader, not an aid. Knowing about primes 'in the large' is not a solution to the problem of knowing in the small. This is the same mistake Peter is making when he challenged the quote I gave from Wolfram by focusing on the military precision' idea -the large- while ignoring growing 'like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout', -the small'. It is the small that is the big problem.