Martin C. Winer

http://www.martincwiner.com/wp-content/uploads/2009/11/primeconstellations.pdf

A longstanding hobby of mine is the pursuit of the twin prime conjecture. That is: are there infinitely many primes which are two apart? My main work can be found at:

http://rankyouragent.com/primes/primes.htm

An summary can be found at:

http://www.rankyouragent.com/primes/primes_simple.htm

And a nice summary of the counting functions for prime constellations (twins, triplets, quadruplets, etc) between a given prime and its square can be found at:

http://www.rankyouragent.com/primes/constellations.txt

http://www.nationalpost.com/news/story.html?id=394892

Louis de Branges has made a critical error… he has tried to solve the Riemann hypothesis.  The problem is not so much that the Riemann hypothesis has remained unsolved since it was proposed in 1859 but more a human problem.  When a problem of this grandeur survives for such a long time it takes on a life of its own.  It is almost like Hank Aaron beating Babe Ruth’s record;  he was more hated for his accomplishment than admired.  The Riemann hypothesis is something like this… attempts to prove it are met with more derision and hatred than curiosity and exploration.

It’s no wonder than that de Branges titles his paper:  “Apology for the Proof of the Riemann Hypothesis“.  Admittedly, he has claimed to have solved the hypothesis before and has been proven wrong.  Just the same, he has successfully proven the Bieberbach Conjecture some 20 years ago winning him much accolade.  I think as such, he’s earned the tenure to make a few flubs without being dismissed as the mathematician who cried wolf.

This points to the basic human problem in the maths which isn’t getting much press.  A proof is offered by an individual, it is accepted or shot down, the end.  I see little evidence of teamwork.  In many failed proofs, there are parts which can be reused as building blocks for other proofs.  The maths are too much, in my mind, an individualistic science with people seeking too much fame and too little truth.  I speak from experience as I myself have published several proofs of the related Twin Prime Conjecture.

Here they are:

Prime Constellations
http://members.tele2.nl/galien8/twins/twins.html
http://www.rankyouragent.com/primes/primes_simple.htm
http://www.rankyouragent.com/primes/primes.htm

The proofs were met with such skepticism that I was never able to get a valid criticism as to the merits or failings.  I was dismissed out of hand as a neophyte know nothing who couldn’t possibly be right.  So much of perception is based on vantage point.  Because the Riemann Hypothesis perceived as unsolvable, it becomes actually unsolvable due to human error of parallax.

My mistake was slightly different than de Brange’s  I made an error in offering too simple a solution.  I didn’t say that my solution was incorrect mind you, just too simple.  When a grand problem survives this long, it’s answer must be 200 pages long.  This is the case with Andrew Wiles’ solution of the epic ‘Fermat’s Final Theorem’ which most experts agree couldn’t possibly be what Fermat himself had in mind when he scribbled ‘remarkable proof’ in the margins of his notebook.  I think it is likely that even though Fermat’s Final Theorem has been proved to the satisfaction of all mathematicians, the nugget of simple beauty that Fermat had in mind is likely yet to be filled in by some future mathematician on a few short sheets of paper.

This brings me to the final point regarding math and proofs of grandeous problems.  No one will be looking for the golden nugget of simplicity in Fermat’s Final Theorem or any others.  Seeking of fame rather than truth has corrupted mathematics.  The Riemann Hypothesis is intimately tied in with Quantum Physics.  If we only seek to prove it true or false, I fear we’ll miss crucial nuggets of beauty which could elucidate our understanding of the universe.

Here is my latest mathematical work including a proof of the twin prime conjecture and interesting elucidating the mysteries of prime constellation distributions.

primeconstellations

primeconstellations_doc_Mar0509

updated Mar 5, 2009

I found a very useful tool for creating nicely formatted equations. I find MS-Word’s equation editor a little lacking when it comes to some math functions. I came across this site:
http://rogercortesi.com/eqn/index.php
which will allow you to enter a LaTeX equation and it will return the properly formatted equivalent in several convenient formats.

For example if you wanted to enter the equation for the prime twin counting function (the number of prime twins between P(n) and P(n)^2) the LaTeX would be:

\#twins[P(n)\to P(n)^2] =
[\frac{(P(1)-1)*(P(2)-1)*...*(P(n-1)-1)}{2*P(1)*P(2)*...*P(n-1)} *(P(n)^2-P(n))]- n*\log_{10}(n)*0.058652

the output would be:

Many thanks to Roger Cortesi for making this tool available.

http://www.reuters.com/article/newsOne/idUSN1632944820080416?rpc=64

Edward Lorenz, the father of chaos theory passed away at 90 years of age.  His theory is colloquially known as “The Butterfly Effect” but is more properly referred to as: ‘deterministic chaos’.  Basically put, it’s the idea that if you take simple building blocks and allow them to self complicate, you get behaviour that is essentially random.

I had heard of Lorenz but never researched his work.  The similarities to my own research in prime numbers are encouraging.  I also speak of a notion of determinism cross recursive self complication as being random. 

Lorenz’s work has a good summation here:

http://en.wikipedia.org/wiki/Chaos_theory

My work has good summaries here:

Prime Constellations
http://members.tele2.nl/galien8/twins/twins.html
http://www.rankyouragent.com/primes/primes_simple.htm
http://www.rankyouragent.com/primes/primes.htm

My latest math work links prime numbers to the Pareto distribution.  This function is linked to many phenomena in nature.  Primes also have a link to quantum phenomena via the Riemann Zeta function.  My latest work hopes to unify these phenomena, in the very least, provide a better understanding for them.

The PDF can be found here:  Prime Constellations.

Over the years I’ve tried a few tools for converting from various file formats to PDF.  Fortunately, I chanced upon this one:
http://www.download.com/PrimoPDF/3000-10743_4-10264577.html?tag=lst-0-1

What a great tool!  All you need do is install it and it shows up as a printer that you can print to.  Simply print from any application and a popup dialog box will ask you where to save your PDF file.  You needn’t worry about spyware or malware either.  It’s certified spyware free by CNET.

Take a look at the terrific job it did on my Math paper about Prime Constellation Counting Functions.

Number of Prime Constellations

Video of the Program: http://www.tvo.org/cfmx/tvoorg/tvoutils/globalfiles/VideoPop.cfm?spot_id=5566&sitefolder=theagenda

I watched a program on TVO last night about overpopulation. I usually steer clear of this issue because I find it depressing. Just the same, it’s always in the back of my mind. With last night’s program, I posted a comment on their blog which I’ve included here:

A great program on an issue few are willing to discuss. However, it touched on, but didn’t flesh out the issue of exponential (or compounding) growth which lies at the core of the issue. A common math problem given to students in this regard is called the Lily Pad Problem.

Suppose a pond has one lily pad. The lily pad doubles each day. That is 1 lily pad turns into 2 lily pads each day. Given that at the end of one month (30 days) the pond is covered in lily pads: When is the pond 1/2 covered? When is the pond 1/4 covered?

Human psychology is not geared towards thinking in exponential terms. When you push a certain amount on the gas pedal, the car goes a certain speed. When you push a bit more, the car goes a bit more faster. The gas pedal is a linear system and it’s how humans think.

So let’s answer the lily pad problem and comment on the ‘poor record’ of the ‘population alarmists’ in one felled swoop. Suppose someone on day 27 shouted: “my heavens, the pond is almost full!” Casual observers may be perplexed because the pond would be 7/8ths or 88% empty. On the next day, day 28, the pond would be 3/4rs or 75% empty. Even the next day, day 29, the pond would be 1/2 or 50% empty. The alarmist would likely be dismissed out of hand. However only one short day later, day 30, the pond would be completely covered and the naysayers would be proved wrong, only too late.

“Compound interest is the most powerful force in the universe” wrote Albert Einstein. Powerful yes, but counter intuitive for humans and the guests on last night’s program. They pointed to the advents in technology and agriculture which have staved off any population crisis. Going back to our lily pond: doubling the size of our pond gives us how many more days before the pond is covered again? One. Quadrupling the size of the pond gives us how many extra days? Two. Not to mention, that the agricultural revolution the guests mentioned was largely brought about by petroleum based fertilizers. Petroleum in turn is undergoing and exponential growth in consumption and in price.

As a parting parable about the power of compounding: Suppose your child asks you, in lieu of a raise in his/her allowance, to give them a penny a day, doubling it every day. Sounds like a good deal, but with our new found understanding of exponential growth, we need to be cautious. After two weeks, we’d owe our child some $163 which is a hefty allowance but no big disaster financially. However, two short weeks later (30 days from the start) we’d owe them nearly $11 million dollars. Clever kid. Can the human race be this clever? Can we afford not to be?

Further reading:
http://www.ciesd.org/influence/LilyPad.shtml http://mathforum.org/dr.math/faq/faq.doubling.pennies.html
http://youtube.com/watch?v=F-QA2rkpBSY