# Riemann geometry on-line

Not only will I mess with Riemann’s famous Z-func, today I will straighten out his geometry. To begin with, his correction of Euclid is excellent. I agree with Riemann on that.

Riemannian geometry, also called elliptic geometry, one of the non-Euclidean geometries that completely rejects the validity of Euclid’s fifth postulate and modifies his second postulate. Simply stated, Euclid’s fifth postulate is: through a point not on a given line there is only one line parallel to the given line. In Riemannian geometry, there are no lines parallel to the given line. Euclid’s second postulate is: a straight line of finite length can be extended continuously without bounds. In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same …

In essence; Riemann rejects the idea of linearity. He says all extensions are basically circles. Thank you R, that’s definitely it. All of my space is of circular surfaces extended by pole frequencies. These pol extensions IS what we measure as “space”. Don’t let your mind fool you here, and assume there is:
1. Space
2. Extensions
Wrong Wrong and Wrong!!!

There is: Extensions.
That’s it!

Riemann had it perfectly right in building a geometry out of such extensions, and to have them being circular. They are. The pole extension is circular and of finite area. It is a disc. This is not really a problem if we want to build a 3D reality. We simply stack those surfaces in whatever way we like and, lo and behold, 3D space.

Now, how can we make both being right? It is much related to the problem with making both QM and GR equally correct. It seems they are, but we cannot figure out how that can be since they sort of contradict each other in a disturbing way.

I thought we could approach this academic problem with a little help from one of the academic superstars, Edward Witten of String Theory fame. I’m being a monopole guy, I found a paper on ST and singularities from which I quote:

Here we run into a problem. One can read a textbook recipe for quantization in Dirac’s old book or in more modern texts on quantum ﬁeld theory. But these recipes, applied to the Einstein-Hilbert theory, do not work. Because of the highly nonlinear nature of Riemannian geometry, these methods fail to give a consistent and meaningful result.

So if I read Prof. Witten right, he detects a problem in that quantization seems a fact while Riemann’s geometry also seems true. On one hand, quantization and Riemann agrees on the finiteness of geometry. Unlike Euclid, both say that extension is not infinite in space, but rater in rotation. The closed circle, string, surfce can in priciple spin forever without going anywhere in space. I can draw a 2 km long line on my A4 paper by curling it up in a circle. I can thus “bend” space into a particular Place. Then we ask, is it still a line?
Of course it isn’t, but the energy spent on drawing it can be exactly, has to be exactly, same as if drawing a true line. And please don’t get hung up on the energy expenditure and definitions of “energy”. Try getting the point instead. Thank you.

The problem Witten finds is likely that Dirac’s quantizing recipe will generate a real geometry/space with gaps in it. Reality might ultimately be quantized and dot-like, but it is also true that it acts in accordance with the smootheness of General Relativity, and however discrete Riemann’s infinite dots look like, when put to work they generate a manifold of smooth complexity. Riemann gets there by adding a tensor to his circles. This is the same trick as Einstein used to wrap up spacetime. A metric tensor is a mathematical function that aids in measuring and dimensioning, but it is not a real part of reality.
It simply is not there to look at. I will replace that device with the internal frequency of the geometry since it is pole spin that both extends to a surface and which keeps it in shape. More on that later.

Now I will tell you how to make a continous line from discrete dots that goes on and off like pixles on a screen. This is important, because Dirac’s recipe is a good one, but the “string” he imagined to have it work properly can be replaced with my viscoelastic point of spinning contraction. I reality, the Dirac string is the circular currency of 2 monopole surface extensions spinning in opposite directions. That my friends is what a photon looks like. The string is the photon’s helical twist of transversed waves. It is the 2 poles frequencies that does the twisting extensions, and we get a photon wavelength from that. But that’s off topic.

Looking at the picture makes better sense if you take a look at how my monoples behave. I have a few posts on that so study them before you watch how I get rid of space.

So…how should I phrase this…? Let the extensions be reality because they are reality. Really make a mental effort to let this sink in: Only the extended sufaces are real, as in empirically measurable. It is not because we cannot look close enough to see the poles in their middles. It is because there is only spin frequency there. It is as visible as a black hole. The Riemann geometry of a closed circle prevents outsiders from looking in. It is like having an Euclidian line “bent” around it. That’s excellent, and it should have put an end to ideas of infinite space….I wish.

We see that the Euclidian geometry applied to quantum systems just ends up in infinities. Especially conceptual infinities. However academically rewarding that might be, it won’t take us further around the road. Let’s settle for Riemann’s infinity instead. An infinity that allows a process, like for example universal evolution, to keep going, but prohibits infinities of space. I suggest the arrow of time goes around the clock and not like a hand of time that keeps stretching out the face. If the hands reach out too far, they will lose frequency/momentum and the turning of time will stop. It doesn’t. So if we look at the chart below and realize the monopole itself is a first harmonic string/circle, then it will not have a complete basic unit of space. The minimum circles needed for space to emerge is a pair of monopoles, and that’s a photon. The first harmonic singularity (initial state) is a circular surface of 1 wave. By the way Prof. Witten, that’s the cosmic string soon about to be 2 strings. But in this particular case, it is not a nice and wavy surfers wave, but an instant pulse when the spin of the pole makes it shrink inwards as to press its great circle outwards to extension. The spheroid point flattens out, just like that. Boom.

 Harmonic Pattern # of Loops Length-WavelengthRelationship 1st 1 L = 1 / 2 • λ 2nd 2 L = 2 / 2 • λ

But we still have only half a space, right. No matter how fearful and gigantic we assume this entity to be, with one single loop there’s zero space. It simply cannot achieve “space” on its own. Was it not alone we could assume its existence by looking at what’s external to it, as we do with Black Holes in our already banged up universe. But looking at one single solitaire of a monopole, there is nothing external to prove it existing at all.
It is just frequency/rate of oscillating contraction/extension. We should also be careful with the notion of frequency, because at this point we don’t know the frequency of what. We don’t have a clock to say “It rotates 300 000 000 times in a second”.
Come on guys, “time” is just as not-there as “space”.

So how do we quantize a la Dirac to make a nice wave out of this monster of a dimensionless oscillator? Witten of course wants an electromagnetic wave out of this, and that it should be smoothe, and able to, in multiples, build a Riemann manifold of continous complexities without those crazy quantum gaps in it. I suggest we let the monopole oscillate itself in half. The twist from spin is likely to break it at some point in the sequence, and until further notice, I will set that point at 3. 3 full contractions and extensions and it is suddenly 2 monopoles. By that, we have played the first second harmonic and now we have 1 basic length of space and it took a frequency of 3 times. When you stop laughing at the paradox of having created 1 dimension of space from 3 dimensions of time, you can open your eyes an have yourself a Big Bang of light.

I’m not sure yet how the next breaking plays out so there’s a few options available to this uneducated mind at least. For a pro there may not be so many. Hopefully only one according to what we know of electromagnetism. The important thing to note is that once the monopole singularity is broken in two, we can have a sequence of multiple oscillations. That will bridge the quantized gap so we now face a reality that is no longer black or white, as in on/off quantum flickering, but relatively smooth and continous.
This means we can throw away the tensors and keep the Dirac monopole(s) binary nature intact and build a Riemann manifold. The tensor effect is now inherent in the combined contractions of the multiple spinning poles. It is what gives the space extensions their frequencies and holds them together as “waves” and not Euclidean straight lines.
That we cannot directly measure the quantum jumping with out probes without getting tunnel-vision  should not be a problem if you know how it’s done and what it is. The reality of the many lights being momentarily “off” is shadowed by the many which are always “on”. The pre-reality of what is real will show up in the real measurements however we go about doing them.

We’re swimming in the Dirac Sea as we speak, it’s just that we are the clouds hoovering above it. When we cool down, we fall down into the ocean of insides.
Count to C and we’re up and flying for real again.

Sorry to mess with String Theories, but the opens strings are not neccesary. The math is probably spot on, but I suspect it is way more complex than is actually called for. I believe we can keep the single closed string/surface as it is with wavelength 1, and then we just break it down in as many legos/points we like to fit with the data. I’m sure the flow of currency appearing smooth and continous can be achieved by letting the “off” poles be what they are supposed to be i.e. non interfering with measures of space qualities.
“Flow” is exactly one such quality, and if the silent 1’s are not real is space, they will not affect how space evolves. But they will indeed affect the frequency/timing of space.
The timing is of how that which is linear is curved and folded into complex geometries. Space extension doesn’t do that.
Time does.

# Guten abend Prof. Riemann

Ever since I “got it” 4 years ago, I’ve been looking for a way to express it in various ways. Everyday language is pretty useless, and everyone who “gets it” knows this for sure. In the Zen tradition this pofound inability to express in words what is beyond words is often pictured in short stories. My favourite is this:

Student: What is truth?
Master: Truth is like a river.
Student: How do you mean “like a river”?
Master: Ok, truth is not like a river.

So however you phrase it, it’s not that. You must rely on metaphors and pointers to have the listener find out for herself. There is no other way it seems. But I’m not here to tell you about Zen. I am fool enough to …well, perhaps I am here to tell you about Zen. Zen is whatever happens so there’s no way out of it really.

Chinese Chan master Yiduan (I-tuan, 9th century), a disciple of Nanquan, declared: “Speech is blasphemy! Silence is a lie! Above speech and silence, there is a way out.”

True that, and I’m falling inside out of that door way, so in which direction should I point my finger? Well, ultimately that’s a trick question because there is no door way. There is no way “out” of that which you are always “in”. Forget that and forget the “you” asking all the questions. Let’s go answering instead.
One way of answering is to ask great minds what they don’t know. To know what is not known is probably better than to know a lot. It narrows the search. So let’s ask one of our greatest minds, Bernhard Riemann, what he didn’t know most of all. It turns out he didn’t know for sure if all the zeros of his famous Z-function has the real part 1/2. If you’re not a fan of mathematical enigmas, this is irrelevant. But if you are, you know that proving the Riemann Hypothesis is the Big One in the field. Pro’s has been obsessed by it for decades, but no one seems able to hack it. Bets are on and stakes are high. More than a few insiders believes it is impossible to prove this beast of a function in the way Riemann himself thought of as perhaps possible.

So why would I even bother to look t it? I may be dumb as a rock, but I’m not stupid enough to think I could prove it, because I can’t. Full. Stop. First of all, I hardly know math well enough to count change at the grocery store. Secondly, I know no one who is willing to help me understand it in a formally accepted and correct way. As with physics, I mix it up as I go along and rarely follow the beaten paths of the professionals. I always get lost in complexity when I try. So I stay simple and follow my nose. This doesn’t mean I can’t hack it, because I can. It means no one credible in academia would ever look at my layman doodles. And honestly, who can blame them?

Never the less, here’s my basic message to my dear friend BR: Your hypothesis is definitely on track and all zeros will indeed have real part 1/2. Thing is, I must be rude enough to wreck your complex image to show you why. The reason for this is that the rotation at hand is of a peculiar kind. It is of a monopole, not a known particle or measurable spinor. To throw in a pole in a complex image is sort of how it’s done, so nothing new there. But I’m afraid this one is like an essential singularity with some geometry missing. To picture stuff that has no place in space can be a challange. It messes with the values on X and Y, but what can you do? We’re talking quantum stuff here, and those guys do not behave as expected. Not with any certainty at least. It is also tricky to picture it right when you’re dealing with “time”. Sure time goes around, and the complex rotation goes around, but time is also an arrow of sorts. In this case it means I will throw away what roates a soon as it has made uni verse (one turn). I hope you’ll excuse me for this, but I have thrown a monopole on the table and it just won’t sit still and spin within the image frame. I seems to oscillate, as a light switch going on/off, and to runs off mixing with other values. Most of all, it is never ever alone, so I would need two images to picture something relating to the physical world as we measure it. Then I could show you a photon perhaps.

So Prof. Riemann, there’s a pdf with my monopole/singularity to look at, and below I have copy/pasted a few words from it. Again, this will not make sense without thinking of a physical entity, or half physical perhaps. As a mathematical proof it is of course an obvious failure. But I like to think math has emerged from human mind, and that human mind is the mind of physical reality. Claiming we are the reality that is being pictured in our math and science, one thinks naturally that math is not abstract or un-natural in any way. In reality, everything is equally real, including the complex plane. What I allowed myself to do was to add a little quantum mystery to it. Mystery or not, the blue surface is what eventually builds space and the primes will come from that building. But to do that we would need 3 such surfaces to make an atom, and this is the image of 1. I’d like to show you how the 1 really looks like, but perhaps you already know it has no surface when really being the only 1. My image is of course based on how 1 appears together with 1, but so do all our images don’t they.

There’s a hole  the picture, I know that, and perhaps there has to be. I know you are a religious man Professor, and if you so wish, please insert a Holieness in that hole. I’d love that image. But not to scare away the secular  minds of today, I might choose to regard it “silent frequency” or Father Time to reconcile. I guess Dirac would call it a drop in the ocean. And knowing God as I imagine you do, I assume you know the quantity of 1 better than most. That’s a good thing. Half the seen world and half the unseen always adds up to 1 doesn’t it?

Oh, one more thing. Having XY never go beyond 1+1i  is not only to stay true to the one, but will save some space and keep us on comfortable distance from relativity’s fractions. The big numbers and tedious decimals come later, with the many poles as numerous di-poles. I claim the original complex image should be extraordinarily simple.
A one timer, then….Bang.
Lights On.

RZF_CP

Riemann hypothesis is true in quantum physics.
A real surface is the 2D extension of a spinning monopole. The least real value is 1 since monopoles are not of fractions. All real measurables are of positive values. Negative values are of surface rotation in real quarter. Rotational values must be calculated separately from extensional values. There are 2 zeros relating to the monopoles binary nature. The definite XY Zero is of the monopole as less than real space measurable. The relative .5,.5=1 is the zero in the so called critical strip. Any monopole extension will generate a real quantum of measurable space with the real value 1. All real values 1 of the Z-function will thus show up as having real part .5 in the complex image. The imaginary values are related to the empirically undetectable zero point with definite XY=0. XY=0 is not measurable since it is a point entity which defines the zero limit where the monopole extension does not generate spatial dimensionals. As a real space value 1, the pole frequency of the extended surface wavelength 1 is silent to observation. The silent value relates to uncertainty in measurement and likely to phenomena such as parity, antimatter, flux tube, wormhole and inversion of signs. As the monopoles surface extension is real space, the internal silent zero spin should be understood as real time/frequency. Pi is corrected to be 3 because the extension radius .5 is when including the zero points radius .2. But .2 has no real space value so r.5 is dimensionally r.3 (red dotted circle). When extension is measured as real surface, there is loss of zero point values .2 i.e. the time/frequency values, indicated by red lines. This can be understood as the zero point frequency of any real space that cannot be dimensioned as space itself. Therefore, Pi decimals are added as time, inherent in every basic quantum of space generated by monopoles extensions.