While surfing the Internet last week, I found this torrent: 2,650 year-old math problem solved by James McCanney (a.k.a. Jim McCanney). In this two hour audio file, James McCanney is interviewed by Brad Walton (of the WCCO radio station in Minneapolis, Minnesota, USA) about his book Calculate Primes. It was recorded on March 17, 2007 (they wished each other a happy Saint Patrick's Day) and Walton also blogged about the interview on the same day.

Several of the following references that I link to are surely not reliable sources, but there are not too many references to be found, so be sure to make your own conclusion instead of just blindly believing mine.

Before I talk about the Calculate Primes, let me share what I found about McCanney himself. In the interview, Walton continually refers to McCanney as a professor, but this title misleading. McCanney's website provides a long bio highlighting his past. The first part is about his education history, including the fact that he used be a "introductory instructor" at Cornell University (in Ithaca, New York, USA) for the physics department and then the math department. However, he was fired from both positions for his radical theories in physics (at least according to McCanney's own bio, which I believe). In this forum post, McCanney claims that he has also taught at other schools and "earned" the title of professor. My guess is that he is referring to schools in South America that were mentioned in his bio, which does not count in my book. So as far as mainstream academics is concerned, McCanney only reached the level of introductory instructor before being fired, twice.

McCanney has many theories in phyiscs which are not accepted by the rest of the academic community. The website Bad Astronomy has a page dedicated to McCanney and his more "popular" theories.

Most of the hits on Google for "James McCanney" are related to his work in physics. It seems that everyone disagrees with almost all of his work. However, it is possible that his work with prime numbers is valid, so I will give McCanney's results a chance to convince me.

I was very excited to listen to the interview but also wondered why I had not heard about this before. I listened to the whole interview, but McCanney only discussed specific details about his findings a few times. From what I gathered, McCanny created some sort of function that is repeatedly applied to a set of numbers. He said that the initial set is {0, 1}. I think that the numbers in this set are added and subtracted from what McCanney called "magic numbers." Eventually McCanney said that "magic numbers" were his simplified term for sequential prime products, which are also known as primorials. McCanney also said that this process will produce some "false primes" (some composite numbers). However, I thought he said that in the next iteration of this process, they would no longer be in the set.

In this forum post, an owner of the book said:

"McCanney has to be the worst speller I have ever encountered. McCanney apparently does not believe in proofreading. His books have many typos and incomplete or ungrammatical sentences. Publishing material in this state is almost an insult to the reader."

The obvious lack of proofreading led me to find out who published this book. Both McCanney's website and Amazon had this information. Calculate Primes is self-published by "jmccanneyscience.com press."

The three hour DVD that comes with the book appears to be of the same quality. In this forum, the eleventh poster says:

"I've looked at the DVD a bit. It's not exactly Hollywood. It appears to be essentially a home video. ...I would mention that it seems to be a low budget production."

In this forum post, another owner of the book said:

"...Mr. McCanney changes the names of sets during the book, and sometimes uses different names for the same thing even in the same equation."

This same person goes on to say:

"The (infinite) union of repetition groups, each with an infinite number of members is effectively a sieve of Eratosthenes as far as I can see."

In agreement with this last person, the people on this forum provided some math from McCanney's function and concluded that McCanney's work was probably a reinvention of the Sieve of Eratosthenes. I also agree with this conclusion. Look at the numbers on the left hand side when using the "magic number" 2. They are all numbers that are not multiples of 2. When the "magic number" is 6 (= 2 x 3), the numbers on the left hand side are not multiples of 2 or 3. Finally, when the "magic number" is 30 (= 2 x 3 x 5), the numbers on the left hand side are not muliples of 2, 3, or 5.

Given the limited information that I could find on the Internet, I have concluded that McCanney's book Calculate Primes does not contain a new, revoultionary way to calculate prime numbers. In order to learn more, I would have to buy the book, but I believe that this would only cause me to be more convinced that McCanney did indeed reinvent the Sieve of Eratosthenes.

## Friday, January 16, 2009

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IT DOES SOUND LIKE A SIEVE (WHICH IS NOT VERY EXCITING TO A MATHEMATICIAN).

ReplyDeleteIts like youve just listened to others whove not read the book and base your conclusion on these opinions. I got the book, its very understandably written. If i were studying in university, i would deffy try to use the lessons in that book and internalize the maths contained in it. Its a pretty cool book, yeah!

ReplyDeleteThat is correct, I have not purchased or read his book.

ReplyDeleteWould you care to share with us more details about James McCanney's book, specifically the formula to generates primes?

I've picked up a copy for next to nothing. I'd be happy to send it to you if you'd like to read it (probably take about 8 weeks from UK)

DeleteThis blog contributes nothing to the debate. Just how valuable would be a prime number calculator? Chances are (pun intended) it would be the most valuable and suppressed formula in existence, considering the fact that all military and banking security is dependent on prime number encryption.

ReplyDeleteGiven the level of security in these fields, any such formula would be given the highest classification. Only the highest compartmented clearance would allow one access to the data, either for offensive or defensive purposes.

These are just some of the most general possibilities of the formula.

By making this book available to the public, James has done the noble, rather than greedy thing.

As to McCanney, the lack of compositional polish is a two-edged sword. It leaves him open to detractors who haven't a clue that those skills have no bearing on a person's math or physics aptitude. This is why these skills are measured independently. It seems patently obvious yet the criticisms overlook, often intentionally, these leaps of logic.

On the positive side, errors are evidence of independent concept-to-product process. If you want a perfect picture, get the latest digital camera for x-hundred dollars, and sell your work for a few quid and see how perfect it is. then try and buy a Monet or Degas and see what their pictures sell for.

McCanney works alone on innumerable projects to develop applications to his theories and rectify many errors in mainstream science. the errors are institutionalized because profit is placed above moral code, and a large quantity of university profs stake their reputation on discoveries of dubious merit from which they have secured large grants for their institutions and perks way beyond tenure. One can no more function with integrity in a university than can one in the corporate world, for more than a brief time.

My experience is that universities are little more than collections of specialized bullshit clubs, where "I respect your bullshit sociology , because I bullshit biology too."

I have followed McCanney with interest for several years. I have no doubt the man is sincere, though I disagree with his religious views and consider them to be limiting factors in his understanding of history, but I would never question his math or physics, and I have not seen any attempts by PHDs to critique the work, let alone any valid criticism.

Computer security depends on factoring being hard, not deterministically producing primes being hard. There are some non-trivial corollaries given a polynomial time, deterministic, prime generating algorithm, but I cannot remember any of them at the moment.

ReplyDeleteWhether or not universities should be the model of research, I hope that we can agree that true research will publish results openly. McCanney published his findings but did not do so openly. His greed has compelled him to require people to pay to see his work.

I am not doubting that McCanney's sincerity. He may honestly believe that he has something. With the knowledge that I have about his book that I was able to obtain for free, I have concluded that he rediscovered the Sieve of Eratosthenes.

I bought his book. His method has a "Generator" function that generates prime candidates, then later a "reaper" (my words) process will eliminate some composite numbers. In one part of the book he says something to the effect, "Number X is still in the set, and won't be eliminated until 17 is in the reaper [my words] set".

ReplyDeleteMy conclusion is that he developed a very convoluted method that is essentially the Sieve of Eratosthenes, but harder.

But you should buy the book. Think about it - how often do such nutty books come around? You want to have one on your self, so you can grab it and tell someone, "Hey! Look at this!" It's a collector's item.

You should post the pseudocode of those algorithms here.

ReplyDeleteFactoring large composite numbers quickly would indeed be a world-shaking achievement. But there seems to be a persistent belief, on the fringes of science, that factoring is slow because finding prime numbers is slow; hence, conversely, that finding primes fast would give fast factoring. McCanney is not the first; google for "arnold arnold" and "prime numbers" to find another, who I think started around 1986 but is still going. Both of them are wrong, because modern factoring methods do not need to find lots of large prime numbers, or indeed any large prime numbers at all.

ReplyDeleteBut we can determine if a number is prime efficiently. See PRIMES is in P and Wikipedia's article about it.

ReplyDeleteYes, "PRIMES" is indeed now known to be in P; but what the Wikipedia article inexplicably omits is the approximate size of primes up to which the older exponential methods are still faster than the AKS polynomial method, i.e. the crossover point. It turns out to be absolutely enormous; way, way beyond the size of any primes used in cryptography. So, for the present, this AKS discovery is only academic.

ReplyDeleteBert Hutchings (no URL)

Sure, but efficient and practical do not mean the same thing.

ReplyDeleteAlso, there is a trivial reduction from factoring to splitting (finding two non-trivial factors), so primes, as you said, are not that related to factoring at this stage of things.

"Mccanny's greed"? This guy and his "radical" ideas have been shut out of every portion of the Science and Math Centers Liars Club because he is usually on to something! How hypocritical that so called centers of higher learning, who constantly tell the rest of us that everyone should have the right to make a decent living, are always trying to close him out of HIS chosen field, causing him to make a living the correct way, by earning it. We all now know, A: Comets are NOT frozen snowballs, B) the Universe IS Electric and Mccanny is usually somewhat correct. Stop whining, he did. He has opened more scientific eyes than they care to admit. Excuse my writing, I'm just a layman, I'm going to buy his book. We thank you James.

ReplyDeleteHe hasn't opened my eyes about prime numbers because he put his work behind a pay wall. After you buy his book, you should help him open my eyes by proving to us that he didn't just rediscover the Sieve of Eratosthenes.

ReplyDeleteMcCanney raves about his generator function, perhaps recursive, which gets its start on the set {0,1}. The operation is addition and so, how could this not be the Sieve of Eratosthenes the hard way? If McCanney is really onto something, then let him "calculate" the 50th Mersenne prime (should it exist) or prove that GIMPS is out of business. I'm not holding my breath...

ReplyDeleteI think one aspect getting lost in the discussion so far is that Jim's method of generating primes shows how all prime numbers are related to one another. The process starts with {0,1} and proceeds to identify new primes using addition and subtraction. All succeeding primes are then found by using the previously discovered primes. Using primes to find new primes is a first in mathematics. Dismissing his process because it resembles a sieve is missing the point. Primes are related to one another via repeating and symmetric patterns anchored around the primorials (magic numbers). He re-defines what a prime number is. Truly this is a significant achievement.

ReplyDelete