The Riemann Hypothesis

[ProKeymaster]

The Riemann Hypothesis

Pro ‘Re: The Riemann Hypothesis’

So in my opinion all we have to do to solve RH is realise that there are three potentials within all numbers including the primes and act accordingly. If we can realise that numbers repeat themselves infinitely then we’re on track I feel.

All numbers start with these three amounts and end with these three amounts. Zero is neutral and so is real point one half and so this is the answer to RH. If we wanted to say definitely whether or not, or rather how likely it is, that RH is true then all we need to do is explore how likely neutrality is in this form.

Zero always has a neutral potential in theory and if the critical line of non-trivial zeros is both comprised of zeros and also in the neutral point between 1 and not 1 then we can reasonably suggest that RH is true.

This has been demonstrated by me in terms of numbers repeating themselves and also by me with the images I posted above showing the visual representation of RH. It all adds up to neutral, middle, in between or whatever you wish to name it as but the result is the same no matter how large or small the prime.Understanding the primes as repeating sets of three potentials is a bit like building a road so large that it defies observation.

You can build a road of any size but the fact remains that you can still drive on either the left, right or middle of the road. Numbers in all their forms are the same in principle.This is why I call Pro theory a theory of everything and also why I use the same kind of explanation for all these problems.

This simple opposites and neutral idea is not only the answer to RH it is the answer to everything :thumbup:

Pro ‘Re: The Riemann Hypothesis’

My first ever exposure to the RH was in a New Scientist article entitled (I think) “Does nature dance to music from the primes?” I read this article back in about 2001 or so and this got me into this problem and the nature and relationship of the primes to the sequences of nature and the universe.

I realised that if I could explain the primes and why they exist fully I could by default also explain the RH as the whole problem is simply about whether or not prime numbers follow a certain unchanging pattern.

Namely do all Riemann zeta function ‘zeros’ lie on the critical line ad infinitum?Let’s begin by saying that prime numbers as I understand them are numbers that may be evenly divided only by themselves and 1.

So this is the basic definition of our building blocks, I say this because the primes are said to be the building blocks of all other numbers.So on the building theme let us imagine that the RH is like a house built of bricks. We have discovered a completely built house made of bricks but we cannot work out its exact construction yet (ie solve the problem).

All we know is that the house seems to be constructed in a certain straight forward way but we’re not sure whether the whole house is made using this same method or not as the house is so enormous as the defy a physical exploration of it.The house is the RH, and the method of construction is the zeta function and critical line.

As I’ve said, the ‘house’ which equates, mathematically speaking, to the sum total of all possible primes, is so enormous that we may never be able to define its size finitely. The size of the group of all possible prime numbers is debatably infinite so using super computers to check all primes may not work no matter how fast our calculations become.

So we’ve got a possibly infinitely sized house with a possibly infinitely adhered to construction method (critical line) so what do we do? Well, it just so happens that when we look at the house we can see that it is made up of many many bricks (primes) which regardless of size or amount all follow the same pattern of formation (i.e. all are bricks).

All bricks are identical in one important aspect, they are all prime. This gives us an important inroad to studying the house (RH) as we can disregard the relative “size” of the house (which is almost impossible to comprehend accurately) and its construction method as we now know that it is built of infinitely repeating identical pieces (prime numbers).So now we’ve removed the basic stumbling block to our solution.

We already knew we had an extremely complex and possibly infinite idea to solve but now we know that this idea (RH) can be split up into repeating pieces that always follow the same pattern, otherwise they wouldn’t be called “prime” would they, if they were not evenly divisible by themselves and 1.

So now we’ve got the idea that understanding primes as separate from RH may help us with solving the problem.In my answer to this problem in this thread I’ve explained the origin of numbers and if you read my original answer to this problem you’ll see that Pro theory takes a completely different approach to most other theories as it attacks the notion of ‘singularity’ at its core.

By this I mean that even if somebody provided a solution to the Riemann Hypothesis the opposite and neutral potentials to their solution would still have to be accounted for to be totally accurate according to Pro theory.Solve one prime and solve them all.We just need to explain the notion of a single “prime” number to explain them all, they are all identical in their (prime) nature of construction, only the size differs and the idea of ‘size’ is relative at best.

The RH is just exhibiting neutrality simply speaking, the critical line with real part 1/2 is in a neutral position when seen visually.I honestly see the Riemann hypothesis as simple and dare I say it, easy to understand in principle. It’s just a mathematical problem that hasn’t yet been “proven” to have a singular answer.Pro theory suggests three simultaneous potentials at all possible moments.

As I’ve said before any singular solution would still be subject to opposite and neutral potentials in turn ad infinitum.The critical line is exactly that in visual terms, a line. Just a line. All we need to know is if this line continues unchangingly. Looking at this request for a singular answer critically we see that the three potentials still occur and so we completely and totally undermine the concept of “singularity” in the first place.

Pro – ‘Re: The Riemann Hypothesis’

I’m not for a moment saying that singularity doesn’t exist, I’m just trying to show my views on things here. The critical line is neutral as it occurs between the two axes when we look at a graph like representation of the RH.

My suggestion is that as the Riemann ‘zeros’ have real part 1/2 (as I understand it anyway) that 1/2 is the neutral point between zero and one.Therefore real part potential 1/2 will exhibit neutral distributional characteristics when studied in forward sequence such as the RH.

Come to think of it we could look at the Riemann zeta function in reverse or look at negative primes as well.All things (everything) work in both forwards and backwards directions and the point at which they are not definably either potential we get zero.

Incidentally, zero as a symbol is a loop, could be coincidence but it makes for an interesting aside I think.My reason for mentioning the loop is Pro theory and its looping properties, the zero(s) are the key to understanding this problem as after all it’s the zeros that seem to lie on the critical line subject to a contrary (opposite) instance.I think that it is simple to understand the RH.

All it says is that all of certain zeros lie on the critical line with real part 1/2. It is a singular statement isn’t it and according to Pro theory we know that in theory there are likely to also be opposite and neutral potentials within all singular statements such as the one made by Riemann.I can’t help but see it as simple like this. It’s real part 1/2 which is not real or non real it is half, neutrality in example.

I think it is because zero is a neutral potential in the first place, itself symbolising the point between numbers 1 or not 1, that zeros will appear to be distributed neutrally when studied in forward sequence like Riemann chose to do.Numbers have three possible potentials of formation I think and the key to “solving” the Riemann Hypothesis is simply to realise that zero is neutral and so is the critical line.

It couldn’t really be any more simple than that I don’t think.Riemann made a conjecture about an equation being either true or false and wasn’t aware that in literal theoretical potential three simultaneous answers are equally possible.

Pro – ‘Re: The Hypothesis’

So there’s a few things I could say now about numbers and the RH which after all is simply the observation of a pattern and a request for an unchanging “proof” of this pattern (ie the critical line).

If we look at what makes a number “prime” we see that it can only be evenly divided by itself and 1. There should be an opposite to the prime numbers as well according to Pro theory. So we now have prime numbers, an opposite to prime numbers, and neutral (between primes in this context).

Primes are simply repeating combinations of the same three fundamental amounts (1, not 1, and zero) as is the same with all other numbers in my view. Numbers are added together, multiplied etc but in reality they still contain only repeats of the same potentials, no matter how relatively “large” or “infinite” they may seem to be.

The RH is often cited as being able to provide an explanation of all numbers isn’t it. I think that if we understand numbers in the way that I stated above we can solve and understand the RH. Solving the RH involves accepting or realising that zero is neutral, the critical line is therefore neutral, and that there are no unchanging singularities ultimately.

By this I mean the fundamental idea of Pro theory and its opposite and neutral suggestions.So the RH predicts and manifests neutrality, as zero is neutral.

If you wanted to say “is zero always neutral?” I’d also suggest three potentials but having said that it’s reasonable to assume that in this specific context of the RH exposing neutrality within numbers that neutrality will always be present in the form of the critical (neutral) line.

This is about as accurate as we can possibly get with a “proof” of the RH. The RH IS the critical line in effect, the absolute crux of Riemann’s original statement was the critical line continuing forever.If indeed we assume that these numbers are transcendental then we can gain an inroad to studying the problem. Again we can see that for every even number there is an opposite.

In this case the opposite would be an odd number. Let’s keep things simple and just say that we have even and odd numbers. Pro theory adds neutral to the mix to complete the loop of three potentials simultaneously and then we have odd, even and neutral (zero) to deal with.To be honest it doesn’t surprise me that people associate the RH with QM and DNA sequencing as my whole point with Pro theory is that everything shares a common pattern of structure and formation.

If you look at DNA for example you see that there are two interwoven strands and nothing in the middle. There are not 10 or 50 million strands there are simply two opposite strands with neutrality in the middle. If we look deep into Quantum Mechanics we see that all atomic structure is based on protons, neutrons, and electrons. The same three potentials again.

If we sink into sub-atomic level we notice that sub-atomic particles are fractional versions of the same original charge. In other words no matter how small we go with particle physics we still see only the three fundamental potentials manifest. Anti-matter for example is the opposite of matter, the point between the two would be not quite matter or anti-matter wouldn’t it.

All anti-particles are opposites of actual particles.The RH asks us “Is this conjecture unchangingly true?”To which I provide three possibilities equally matched in potential.

The SDC asks us “Do these equations have a solution?”To which I provide the same argument.L and zeta functions are simply filters through which we pass values in the same way as every other mathematical function, at least this is how I see them.Perhaps my view is too simple to be properly translated into mathematics as I use a visual method exclusively for my study of RH and I don’t really refer to larger amounts than 1 (singular) More than 1 (not 1) and zero (neutral).

By saying this I only mean that it doesn’t seem to be worth my time to study other higher amounts of create my own commutative groups as in my view this would seem to complicate what is essentially a very simple problem (RH). Although I say this I don’t mean that I’m not interested in the work of others though, I just have my ideas and stick to them personally.

I often think about the “point” at which all number problems converge If there is to be such a point anywhere within the primes it will be the neutral potential of the prime zeros used as a base from which to study RH et al.

Zeros are neutral and the critical line is neutral in relation to the two axes when plotted on a simple graph and this translates into computer generated pictures of RH patterns in action. Zeros will always be neutral won’t they, pretty much anyway, so if zeros are (to quote Riemann) “very probably” neutral forever and the RH zeros lie “very probably” on the critical line we’ve got a proof or as near as we can get in my opinion.

We have to take the looping and infinite nature of all numbers into account here obviously but this is still the correct answer or at least I think it’s the most “correct” answer or “point” in the universally unchanging sense of what we know as “proof.”

So to sum up I’m offering my own version of a “proof” of RH, namely that all non-trivial zeros lie continuously on the critical line ad infinitum literally because zero is the point between a number and not a number. I think this makes sense.

Pro – ‘Re: The Riemann Hypothesis’

I’m editing this text as I go but I thought I’d post the majority of what I’ve said before so that eventually it will be able to be turned into a coherent document :thumbup:

Pro – ‘Re: The Riemann Hypothesis’

All I’m trying to say is:

1. All numbers are based on repeating combinations of three amounts or potentials.

2. All number problems are in turn based around these three repeating potentials.

3. If we can understand and accept the three pronged nature of all things we can see that zero is neutral and so is real part one half.

4. The critical line of Riemann zeros is essentially a neutral manifestation as it’s composed of neutral amounts (zeros).5. This is why when viewed visually the RH zeros seem to lie on a line between axes, at the point in-between real and non real, i.e. real part one half.

[IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Riemann_zeta_function_absolute_value.png/600px-Riemann_zeta_function_absolute_value.png[/IMG][IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Zeta_polar.svg/600px-Zeta_polar.svg.png[/IMG][IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/1/14/Criticalline.png/600px-Criticalline.png[/IMG][URL=”http://en.wikipedia.org/wiki/Riemann_hypothesis”%5DPhoto Source Article[/URL]’,

Pro – ‘Re: The Riemann Hypothesis’

I’ve been thinking a lot about Riemann and the primes etc lately, trying to come to some sort of semi-coherent conclusions. I find it difficult to write clearly without constant reference to opposites and the like which makes for less than easy reading at times I’m sure.

I’ve said before that if we can solve and/or understand a single prime number we can understand them all and by default we can also solve the Riemann hypothesis too.

It’s a lot more simple than currently allowed for. Let me explain.The point of RH is to find out in terms of both abstract theory (patterns etc) and actual calculations whether or not the prime numbers have a definite and unchanging structure or not. It really is as simple as that.

RH asks us a question and expects a singular answer as at the time it was first postulated (around 1859) singularities were taken for granted.So why are prime numbers so important? And why is it often said that solving the Riemann hypothesis will also fundamentally change physics?

The answer is again a simple one. Physics and mathematics are siblings, some might even say of the Siamese type. You cannot study one discipline without an inevitable cross over between the two. It works both ways, mathematics compliments physics and physics compliments mathematics.

So now we know that physics and maths are interchangeable disciplines with at least a fair amount of overlap. The easiest way to look at this relationship is probably to think of using mathematics to study and quantify physics and using the patterns and movements of physics (atomic structure et al) to visualise flows and changing patterns within mathematics.I think it’s worth noting that deciding which of the two disciplines came first in history is a bit like the Chicken And The Egg Paradox, singularly unsolvable.

Humankind has always wondered and measured and calculated since time immemorial and no doubt will continue to do so.Back to RH and the primes then and we’re left wondering just why the primes are considered more important than other numbers. The answer is that primes are said to be the building blocks of all other numbers.

Take this statement as literally as you like, the more so the better, prime numbers are the key to understanding all other numbers in current mathematical thinking.This comes back to my house analogy above, if primes are the bricks of which our house is built, and natural numbers are the cement, all we have to do is understand a single brick as the house is made of many repeated bricks.

Prime numbers create all other numbers because they repeat their same pattern over and over and over again. It is from this process of studying the primes in the positive (forward) sense that we derive all larger combinations. This is true regardless of the relative size or dimension of whatever number we happen to be studying.So if we accept that primes are repeated throughout the structure of all numbers no matter how large or small, no matter whether negative or positive numbers, we can finally see why we can understand a prime of any size because it always has the prime characteristic no matter what.

It shouldn’t necessarily take a load of complicated equations to come to this conclusion, all it takes is an understanding of potential as defined or at least suggested by Pro theory. Simply put this means that we need to look closely at what makes a number prime, and also what characteristics (if any) all numbers share between themselves.

A starting point for this could be a statement as simple as saying that all numbers share the same name of ‘number.’ Or all numbers share the same property of allowing themselves to be manipulated in certain ways, added to others for example.Continued below…

Pro – ‘Re: The Riemann Hypothesis’

All we need to do is to understand numbers, and therefore prime numbers also, from their very beginning. Their absolute fundamental and most simple forms need to be understood first. We cannot hope to truthfully understand RH without a good grounding in basic number theory first.

This is where Pro theory comes into play. We know that the theory suggests three simultaneously possible potentials within all things/everything.

Now without getting too far off topic here if we accept this changing potentials argument or at least apply it to our number studies some interesting conclusions arise. Let me explain.

Riemann was expecting a singular answer that didn’t change, he wanted a definite yes or no answer to his original problem. This has been attempted ever since his paper was published but as yet nobody has been able to prove this singularly. This is the important bit, the singularity.

It’s this single structure that we’re looking for here but in reality we have three potentials for everything, from maths to physics, to algebra, to the meaning of life to quantum physics. We need only note the common structure of electrons, protons and neutrons to see this at its most fundamental level.I’m not going into a rambling diatribe on Pro theory, opposites etc here but suffice it to say that this is the way all things work.

So numbers must surely follow this three pronged pattern of formation, named commonly by me as negative, positive and neutral for want of a better description.

Now we know that all things have both opposite potentials we can clearly see that numbers are repeating amounts. All numbers can run in the positive (forward) sense or in the negative (opposite or backward) sense. Numbers work both ways, this is why we have positive temperature scales for heat and negative (minus) measurements for cold temperatures.

Translated into numbers we see that numbers should follow some sort of three pronged pattern somehow. So if we look at numbers we have the commodities of 1 (singular) and the opposite to 1 (not 1 or more than 1) and we also have a third seemingly unimportant option of 0 (zero).

Zero seems unimportant because it is neutral, it’s neither completely 1 nor completely the opposite to 1, it’s in-between the two opposites, in just the same way that the middle is the point between left and right.No matter how large we make any given set of numbers it still comprises of these three repeating amounts or potentials. No matter how large any number is, it still debatably has both opposite and neutral potentials within it.

Numbers work in the same way that all other things within the universe do, in three ways.Now we look at primes. What I’ve just explained implies that primes must also possess an opposite and neutral potential.

When we think about it we see that there is indeed an opposite to the primes and that the primes also contain the neutral quality of zero. The position of zero within numbers studied or visualised in sequence becomes particularly important when we re-examine the Riemann hypothesis armed with this idea.Continued below…

Pro – ‘Re: The Riemann Hypothesis’

So we’re looking for a neutral potential within the primes and specifically within the Riemann hypothesis. Why are we looking for neutrality? The reason is because zeros are neutral and so is real part 1 half.

If we look at the following photographs we can clearly see that the numbers converge at the point exactly between real part 1 and real part nothing.

For the sake of clarity I’m referring to the middle of the crossed axes.

The absolute centre of the RH as defined here:[IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/3/30/Riemann_zeta_function_absolute_value.png/600px-Riemann_zeta_function_absolute_value.png[/IMG][IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Zeta_polar.svg/600px-Zeta_polar.svg.png[/IMG][IMG]http://upload.wikimedia.org/wikipedia/commons/thumb/1/14/Criticalline.png/600px-Criticalline.png[/IMG]

And this is why I’m constantly referring to the neutrality exhibited by Riemann’s idea, all the RH does is define neutrality within prime numbers simply speaking. I would ask you to note the importance of what I’m saying here as this is the key to not only visualising the RH but also to proving it.

Back to Pro theory then. My theory suggests that everything, whether number, flesh and blood, atom, tree or force has three potentials at all times no matter what. Armed with this knowledge and also knowing that RH is predicting a neutral pattern of formation within the primes we can begin to look at solving the problem.

donaldjeo12 – ‘Re: The Riemann Hypothesis’

FLORENCE, Colorado (AFJ) — American mathematician Theodore Kaczynski, who specializes in boundary functions, geometric function theory, and killing people, won the Clay Math Foundation’s $1 million prize for disproving the Riemann hypothesis.

The Riemann hypothesis involves the location of the complex zeros of the Riemann zeta function. While some mathematicians tried to prove it, others used powerful computers to search for counterexamples. Over a trillion zeros had been looked at, but Kaczynski noticed that they all had positive imaginary values.

He started looking at negative imaginary values, and almost immediately found a counter example, a complex zero that wasn’t on the critical line.

The Clay Math Foundation confirmed that he will be collecting the$1 million prize. Kaczynski said that he had little use for money, and will be donating the full proceeds to his favourite charity, a foundation that teaches underprivileged youngsters how to build letterbombs. Kaczynski had previously won the Clay Math award for other of their seven millennium math problems:

Finding a closed-form solution to the Navier-Stokes Equations. These equations are extremely useful for describing the flow of air or water around airplanes, ships,submarines, missiles, and, most importantly to Kaczynski, bombs.

He had also attempted to also win the RSA Challenge, which consists of factoring a large composite number that is the product of two primefactors. However, he was only able to find one of the two primefactors, so he did not win that prize.His future plans include proving the Birch and Swinnerton-Dyerconjecture, solving P = NP, and digging an escape tunnel with a stolen spoon.

[Author]

Posts