# On nuclear fusion reactors and why they will all fail.

To be precise: I am talking about all nuclear fusion reactor designs that use magnetic confinement for the fusion plasma. So these are the standard tokamak reactors that are build in a lot of places but also the stellarator fusion reactor from the Max Planck institute in Germany. Some years ago it came to my attention that the USA based company Lockheed Martin was also going into the fusion reactor thing and they were bragging about new technology and making mobile 100 Mega Watt nuclear fusion reactors. But their talk was a little bit strange, it was some CEO kind of guy that explained how their new technology would outbeat the tokamak design because with the new much stronger magnetic fields they could make, the magnetic field would be much stronger at the place of the fusion vessel wall. According to the Lockheed Martin CEO type of guy, plasma was diamagnetic and as such would stay away from the fusion reactor wall. Needless to say I had to laugh because in my view on physical reality electrons carry magnetic charge and will always make fusion plasma instable. In fusion reactions the protons (or the isotopes of hydrogen to be precise) need to fuse and that cannot be done if electrons constantly get accelerated to relativistic high speeds.

A few years back a lot of folks were bragging that by the year 2019 Lockheed Martin would have those mobile nuclear fusion reactors on large trailors, something like 100 Mega Watt per mobile unit. If they would have pulled that off, Lockheed Martin might be the first company to achieve a market capitalization of 10 trillion US$. That would be gigaenormous because after all 10 trillion = 10 thousand billion… It was supposed to look like this: As you see, the 2013 pipe dream is still not at the scene now in 2019. Why not? Well if plasma theorists keep on using the electron as a magnetic dipole, all of the advanced models they have for plasma behaviour will never depict an accurate picture of physical reality. If in practice electrons come in two varieties, monopole north and south ones, in all of those fusion reactor designs they will move in opposite directions. It is more or less ‘along the magnetic field lines’ because all acceleration caused by the magnetic field makes the electrons accelerate in that direction. And this acceleration in two directions that will grow in a turbulent fashion and make the fusion plasma uncontrolable. In this regard, I mean how turbulence arises, the density of the plasma is an important factor. In a low density plasma the electrons will have plenty of acceleration before they interact with other plasma particles. The denser the plasma is the shorter the length of those interaction free paths, that is obvious. In all present day plasma models, there is nothing that makes electrons accelerate along the magnetic field lines. That means all those models are wrong. Before we go on with wrong mathematical models of plasma behaviour, sometimes the news upon nuclear fusion can be very funny. I just made an intenet search upon ‘Lockheed Martin nuclear fusion’ and I stumbled upon the next hilarious title from Yahoo finance: Lockheed Martin doubles down on cold fusion. Link: https://finance.yahoo.com/news/lockheed-martin-doubles-down-cold-120300203.html As you see in this world there is just never a shortage of idiots; at Lockheed Martin they do not understand why the fusion plasma gets so instable but compared to the total idiots of Yahoo finance the Lockheed people look like pure Einsteinian human material… How stupid and 100% uninformed you must be to think that Lockheed is chasing cold fusion reactors… Ok, a bit more on those math models they use to simulate plasma behaviour. It was in 2016 I came across that weird news from MIT, they simulated very large scale with lots of computer time how plasma should behave. There was actually an electron going round the entire plama vessel. Now my dear reader I was dumbfounded, if the electron is a magnetic dipole, how could it go round? In my world where plasma electrons carry magnetic charge, the only thing the electrons want to do is going round and round… I never found how the model works that was used by the MIT smart asses, but here is a short video of the ‘result’ of the MIT plasma simulation: In the video description there is a link where it even get more hilarious. Let me quote it: A long-standing discrepancy between predictions and observed results in test reactors has been called “the great unsolved problem” in understanding the turbulence that leads to a loss of heat in fusion reactors. Solving this discrepancy is critical for predicting the performance of new fusion reactors such as the huge international collaborative project called ITER, under construction in France. Comment: Don’t worry, ITER will never work if electrons carry magnetic charge. Plus the famous standard model says electrons are magnetic dipoles, so why worry that ITER will fail & fall flat on it’s stupid face? Link where you can find the quote: New finding may explain heat loss in fusion reactors http://news.mit.edu/2016/heat-loss-fusion-reactors-0121 Come on, don’t worry & be happy. # On Benford’s law. Benford’s law is a statistical observation. If I remember the story more or less correct, Benford found at some point in time that those old logarithm tables had pages that were far more worn out compared to others. And it seems that people used those old (but at the time very important) tables much more for numbers starting with small digits like 1 or 2 and much less for high leading digits like 8 or 9. The observation was that the probability of a leading digit of d was given by log(1 + 1/d). I remember that during a train ride to the city of Utrecht about two decades ago I found a very simple distribution that gives the Benford law perfectly for numbers written in the usual base 10. Basically if you use a uniform distribution in the exponent, that more or less always gives rise to some approximation of Benford’s law. A few weeks back for no reason at all, I did a search on the preprint archive on the subject of Benford’s law and a rather strange article popped up. It is written by Kazifumi Ozawa. Title: Continuous Distributions on$(0, \infty)\$ Giving Benford’s Law Exactly.

Yet the way I did the stuff two decades back suggests that it is very hard to make a continuous distribution on such a large interval like 0 to infinity (the positive real line). So I decided to give a bunch of examples that all give Benford’s law perfectly. And I skipped studying the theorem at the end of the article of Kazifumi Ozawa. Yet that theorem of Suihara looks very interesting so may be that is something for a future post although this website is more or less dedicated to higher dimensional complex numbers of course.

The math in this post is more or less as basic as it gets: You need to know what the logarithm with base 10 is and it would be great you need the first course basics of probability theory. So it is handy you know about probability density functions p(x) and if you integrate them you get the probability for a particulat set. I guess all university introductionary courses in probability theory cover that for a lot of studies like math, physics, chemistry, biology and so on. Ok, it is handy if you can integrate such probability densities a bit but I have to admit I skipped all things related to that (so basic is this post). But I skipped a lot of things yet this post is still 10 pictures long. All pictures are of size 550 x 775.

# A dog named Loïs, David Pakman, Sean Carrroll and Harry Potter.

I am sitting on my couch watching Youtube videos while the dog is lying next to me. Is the dog always shaking from fear that I will beat her up? Come on, she is a dog and not a math professor! Anyway to my amazement there is a video from the David Pakman show with Sean Carroll, Sean is one of those television physics professors that you see relatively often on television or other media outlets. I get a warm feeling in my stomach because I can listen to the intelligent words of Sean, he truly is a high shot smart ass. So I play the video and everything looks fine but all of a sudden Harry Potter materializes behind the show presentator David Pakman and why does Harry Potter look so angry? Something to do with Brexit or so?

All of a sudden Harry Potter pulls his magic wand, points to to Sean Carroll and he shouts ‘Imbicilus Totalus!’. A sudden flash of lightning leaves the magic wand and enters the head of Sean. Slowly David Pakman is turning around to see what is behind him but Harry is much faster; out of a bag he pulls a short broom with a big handle and I can read the inscription on the broom. It is a SmartAss3000, fast and with a routine Harry sticks it in his ass and he flies away in the darkness of the night. Wow man that is totally different from what I remember from those Harry Potter movies! How life changes over time… May be those old Harry Potter movies are now in some parallel universe far far away.

I need to calm the dog because the dog understands I am very agitated so I explain to her that not all humans do such weird stuff with a SmartAss3000. Loïs does not seem to understand what I am trying to say but since I am calm again she waggles her tail and soon she calms down again. Finally I started to watch the video while hoping that Harry Potter did not do too much damage with the Imbicilus Totales curse. My hopes were idle, after all Harry is a very good wizard, and after about 8.30 minutes Sean Carroll explains electron spin: “If you measure electron spin, the electron can only spin clockwise or counter clockwise” Sean explains… Oh oh, Harry Potter clearly succeeded with his curse because just a few posts ago we calculated that the electron needed to spin many times the speed of light in order to explain the magnetic properties the electron has. Say it needs to spin about 100 times the speed of light, in that case any electron spinning can account for at most 1% of it’s magnetic behaviour. No problem for Sean Carroll: it is spinning clockwise or counter clockwise and that is enough explanation for him…

Well not for me because I have a long list of problems with electrons being magnetic dipoles (the official version of an electron is that it is a magnetic dipole, of course we have zero experimental proof of that but who bothers?) The clockwise / anti clockwise spinning of an electron is nonsense because if it is a magnetic dipole, that vector can point into any direction. But as far as I see reality, all experiments point much more towards electrons having a magnetic charge. That is electrons are all magnetic monopoles and not magnetic dipoles.

But Sean is not the only to hang on the electron magnetic dipole thing, at CERN there are thousands of physics professors that actually think that electrons are pure point particles, that is they have no volume but are true points. If that were true, if the electron has no size, it would be completely impossible to accelerate electrons with a magnetic field like in the Stern Gerlach experiment. By the way, here is the video:

Ok, after having said that kind of stuff, the next post will be about Benford’s law. If I remember it correctly I worked a short time on that nice law back in the year 1999. One or two weeks back I made a search on the preprint archive and after a bit of thinking I decided to craft a post for this website out of it. It is very easy to find and craft all kinds of probability distributions that fit Benford’s law perfectly. Benford’s law is about numbers as we find them in nature and gives the probability distribution for the leading digit. Do an internet search if you never heard from it. Here is a teaser picture to get started for the next post:

That was it for this post.

# New roots of unity (the 3D complex ones) & The rain theorem.

I just finished brewing the 100-th batch of a beer under the names Dark Matter and Spin 1/2 beer. All in all that is an amazing amount of beer; in the past I brewed 35 liter per batch but now it is 40 liter per batch so all in all an amount of something between 3500 and 4000 liters… So ein prosit my dear reader.

The ‘new’ roots of unity aren’t that new, this post is a re-editing of something I posted on 05 Jan 2014 on the other website. Later that year I started this website. Actually these roots of unity are just over five years old. In mathematical terms that is still very young so in that sense they are still new.

Recall the roots of unity in the complex plane are solutions to z^n = 1 and as such these roots are found on the exponential circle (the complex exponential) in the complex plane. As you have found the exponential circle or exponential curve in some space, from that you can always make new roots of unity. That is hardly a mathematical achievement because it is so simple to do once you have found your exponential circle or curve. But in the diverse spaces these new roots of unity behave very different, for example in this post we will add them all up but unlike in the complex plane they do not add up to zero. That is caused by the fact that in the complex 3D space the number alpha is at the center of the exponential circle, as such if we add n roots of unity in 3D space the result is n times alpha. Last year we studied the space of 4D complex numbers and if you would craft new roots of unity in that space it will behave much more like those in the complex plane because in the 4D complex numbers we have 0 as the center of the exponential curve. (For dimensions above 3 the exponential curve always lies in a hyperplane so it can never be a circle.) It always amazes me that you have all those physics people who study string theory but as far as I know never use exponential curves…

Life is beautiful, because how can you do string theory without math like that? But in physics almost everything is beautiful, for example if they explain the outcome of the Stern-Gerlach experiment always 50% of unpaired electrons align with the applied magnetic field and the other 50% for some mysterious reason do the anti-align thing. And if one hour later the same physics professor explains how a permanent magnet can attract some piece of iron, all of a sudden 100% of the unpaired electrons align and all that talk of 50/50 suddenly is not observed… Life inside the science of physics is wonderful; all you have to do is a bit of blah blah blah and if people complain this is not logical at all you simply say: Quantum physics is such that if you think you understand it, you don’t understand it… How wonderful is the life of physics professors; talk some blah blah blah and if people complain you blame them for ‘not understanding quantum things’. For sure that is a beautiful form of life.

But enough of the talking, somewhere in the next seven pictures I did forget to insert a graph of the determinant. Yet I showed you the structure of the non-invertible numbers so often, I think I post it with that fault included. After all why should life be perfect? If life would be perfect you would have no way of improvement and likely that is the moment you die: no more possibility of improvement. As usual the pictures are 550×775 pixels but I had to make the first one a tiny bit longer. Good luck with digesting it & have a bit of fun in the process.

For myself speaking it was fun to read my own two proof for the rain theorem again after five years. Please do not forget that new roots of unity on other spaces can be very different in behavior, after all they are always part of the exponential circle or curve in that space so they will derive their math properties from that. Till updates.