I am so excited! Here drinking my morning green tea, i have just been visited by an image of St. Peter, who proclaimed to me that all my personal dreams are about to come true, provided i can write them down on this blog in the next half an hour!! Wow. So please excuse any spelling mistakes: I am about to restructure my life, and I need to do it fast, since i can’t type that quickly, but I need be careful, because I am not allowed to revise anything I write!

First of all, I am going to live a healthy life till I’m 100. Unfortunately he said I could only dictate what happens to me, not anyone else, so I can only hope the rest of my family is okay. And why not beyond a hundred? He said I couldn’t actually change my physical characteristics, so I reckon that beyond 100, frailty is too much of an issue. But I’m wasting time explaining these things to you!

Clearly I want a nice house for us, one that we own. Real estate prices are totally ridiculous here in Sydney, what with…oh I don’t need to explain why, it’s too long a story, suffice to say that for only $2 million I can get a beautiful three bedroom house in a good neighbourhood not far from the Uni of NSW. So that’s on the list. A new car, of course, perhaps a luxury vehicle, a Lexus say, since I am very happy with our old Camry. Another $2 million in the bank for a comfortable retirement ahead (not too soon, since I don’t want to get bored) would also be sweet. I can picture it now, a lovely new house, luxury car, money stashed away for retirement travelling and golfing.

Speaking of golf, how about a life membership at one of the nice golf courses close to where I live here. And please St. Peter, throw in a good set of clubs and some nice golf attire. Speaking of clothes, I haven’t redone my wardrobe in a serious fashion for many years: how about a gift voucher for a few thousand bucks at a local department store. I`ll want my theory of Rational Trigonometry to suddenly be understood by the academy, ensuring a promotion at work to full Professor; heh why not one of those Scientia Professorships that pay twice as much with only half the work? That should about wrap it up. But I still have another ten minutes to go. Am I being too modest here? What will my wife think when she finds out I had a blank cheque and came back with only a modest haul. And in a few years that Lexus will be a used car… Shouldn’t I be more ambitious?

And what if some friends come to visit? Let’s upgrade to a 5 bedroom house in Double Bay for $5 million. Let’s add a top of the range BMW, and–you only live once—a spanking new red Ferrari. Actually I don’t care much about cars, but surely I can get interested once these are parked in my triple garage. The rich and famous who live there are probably a bit stand-offish, so I`ll ask that I become an internationally famous mathematician: Rational Trigonometry will be such an educational breakthrough that I will be in hot demand on the lecture circuit, girls will ask for my autograph in the street, and pollies will invite me to their lavish dinner parties. Russell Crowe and James Packer will become my good buddies, and drag me to those tedious football games, where I can sit in the high class enclosures sipping champers. Speaking of, I need a wine cellar, and say 2000 bottles of the good stuff. Probably I want a library too, and a tennis court—let’s make that house a $25 million mansion at Piper’s Point instead.

But then all my new buddies will have holiday weekenders and villas in Tuscany. I want a holiday weekender too, say in Leura (I think I only have about 5 minutes left!!), and a villa in Tuscany. And a helicopter, and a horse riding ranch, say out near wherever James has his. And a private jet. Wait! I will need a lot more dough to pay for all the staff, maintenance and taxes that all this stuff requires. I want $100 million in cash. No, I want $10 billion in stock. Why limit myself? Why should Bill Gates outdo me in my future philanthropy? I want $100 billion in cash, bonds and stock. And–

What? It appears that St. Peter has been timing me, and I just ran over my thirty minutes. [Insert sad face here]. The deal is void. Whoops. Better not tell my wife about this.

But to tell the truth, it was all starting to sound like a major headache, if you know what I mean. Now I am back to the essential mystery of my life, and I better get off to work; I have a 9 am meeting.

Phillip SomervilleRussell BFF violates axiom of choice.

neena joshiVery nice article, goes to prove once again that Mathematicians have a great sense of humor ! !

njwildberger: tangential thoughtsPost authorThanks Neena!

Sharanjit Paddam (@sharanjit)Ahh well, there’s always the Millenium Prizes

Konrad SwartIf I understand you correctly, then there are basically two things you want. Health and wealth, and in that order.

I cannot say anything about health. But I CAN say a thing or two about wealth, because that is somewhat of a specialty of mine, because wealth has to do with money. And I claim to be an expert in understanding money.

As far as activity is concerned, it is not that difficult to become wealthy. It requires some work and a little education. But as far as bringing yourself to DO the things to become wealthy, THIS is the hard part, because it requires a drastic reprogrammation of your emotional structure.

From my insight in money I can see that you do many things that keep you poor. Things, I want to add, which I have been doing also. Only recently I understood, from the basic principle of value from my own book, and from a course I have followed about wealth and how to obtain it, that I had ‘poor making and poor keeping habits’..

According to this money course I have followed, the order is this: THOUGHTS lead to FEELINGS. And FEELINGS lead to ACTION.

That is what I learnt from that course. But that is not all. You also have to ask: where do our thoughts come from? They come from our INNER PROGRAMMING.

For a long time, people believed in the ‘blank slate’ premise, and that THIS made us different from animals. For example from deer, that can walk and run after only a very short time after birth. Recently it has been found that this is not true. Just like deer, we come into the world with an innate programming. In fact, we come into the world with a programming that is more or less identical with the vision of socialism. So we are all born as socialists, because this particular programming has helped us the most when we were still hunters/gatherers. This is because at that time we had the greatest chances of survival when we shared the resources we could obtain through hunting and gathering.

The problem with this programming is that it is ill-adapted to the existence of money. Money is, evolutionally speaking, very recent. The oldest form of real money was the Cowrie shell, which was used for the first time around 1200 BC. Some might disagree, and would say that cattle was the first form of money, because then no distinction between ‘value in use’ and ‘value in exchange’ is made. Therefore I do not consider cattle as proper money, because you must make a distinction between the value of the money itself, and the value of the goods and services exchanged for money.

My own book, by the way, is about money and value. In any case, the transition from a hunter/gatherer into that what followed, a farmer, requires an emotional reprogramming of the innate socialistic programming.

That you, Norman, have the socialistic (keeping yourself poor) programming, can be seen from your activities. You have a lot of VALUE to offer to others. I can even tell you what this value consists of. It consists of a REAL UNDERSTANDING of much of mathematics.

Such a real understanding is RARE, and therefore, just like gold and silver are rare, can be of great value to others, and therefore has the potential to create a money stream into your direction. How rare? Many mathematicians THINK that they understand mathematics, but that is an illusion, caused by the ‘habit’ part of the brain; e.g., you see some formula you do not understand, an are aware of this fact. The next time you see this formula you recognize it as something you do not understand, but as something ‘that works’, although you haven’t a clue why. And the third time you see it, you only recognize it, and from that you conclude that you understand it, which means, it is familiar, you know that you can use it, and it gives you the outcomes you expect, so ‘it works’, and it has become a ‘habit’ to use it. Which means, a thought generating the feeling of recognition, and after that you KNOW it. This habit feeling is then mistaken for understanding which, it is NOT.

Some mathematicians were somewhat aware of this. They expressed it cynically as: ‘you never understand mathematics. You only get used to it’. This was one of the things said in the television series Numbers.

You, Norman, know better. This can be seen from the very clear explanations you gave on youtube beginning with numbers, and then going through all of mathematics, doubting anything you were taught, in particular the infinite. It is from these attempts to reconstruct all of mathematics a real understanding emerged, which makes you a mathematician that is quite different from most mathematicians.

So the VALUE you have to offer is that of GENUINE UNDERSTANDING.

But your socialistic programming causes you to DESTROY the value this canhave TO YOU in such a way, that it does lead to either no, or just a little flow of money in your direction. So what you do that keeps you poor, is GIVING AWAY the value you have. And, of course, if you give the value you have away for nothing, then you must not be surprised to find that you end up with nothing, despite the fact that you work hard, through doing a lot for others.

so, to be precise, the particular activity that makes that the value you offer to others does not lead to an income stream in your direction,and therefore to only a limited value to yourself (fame might be of some value to you) is simply that at this moment you have a lot of value to others, but you do not translate this ability to offer value to others into enough value for yourself. The only thing that leads to SOME value to you, as far as I can see, is the selling of your own book about Rational Trigonometry. And, of course, your position as a professor of mathematics leads to a pay check. But in that latter case you do not create the value for yourself BY yourself, but others do that for you through the structure of the job they have given you.

Web ‘services’ like youtube, facebook, twitter etc might look interesting, but they are, for their participants, ‘value destroying’ institutions. The only thing they are good for, is to become known. So they are ideal for demonstrating that others CAN obtain value for you. But you are destroying value for yourself if you give ALL the value you have away through the kinds of movies you make.

In your case you have caused so much knowledge of your existence, that it would be quite easy for you to ‘change your ways’, and to transform your inner programming in such a way, that you DO generate a stream of income towards yourself.

However, I shall NOT explain all wasy to do this here. I limit myself to just one: it would make far more sense to make such movies, and then sell them as complete courses on DVD’s as some others do.

The reason I just limit myself to this example alone is the exact same as why I explain this for you. If I WOULD explain all of them I know of here, I would do the exact same thing as what I see you doing. I would destroy my own value, and thus would go right against that what I know about value.

So if you, or anybody else, wants to know exactly what I am talking about, there are two things you can do. The first thing is just to send me an e-mail to say that you are interested. If you do, I shall keep you informed about the course I am now preparing about value and money.

The second thing is that in that e-mail you can also place an order of the book I have written, with the title: ‘The Value of Money’. The number of books I now have are quite limited. I have only printed about 20 of them, and only have 14 of them left. I still have these books, because at this moment I have done literally NOTHING to promote them, because they were created as presentation exemplars.

I DO want to warn in advance, however, that the only thing you will find in that book is a clear description of what value is, what money is, and how these two are connected. My book, so I claim, is the very first that is able to explain both what economic value is, AND what we EXACTLY mean when we say: ‘the value of money’. Warn, because the book is not enough to reprogram an inner innate socialistic programming. This requires certain meditation techniques that enable you to become aware of your innate programming, and also certain activities to actually reprogram them so that you can see exactly how you can use your capability to create value to others in such a way that it also creates value to yourself in the form of a stream of income.

This last thing requires my course.

From the few people who have read my book I have heard, that although the theory is almost ridiculously easy to understand, it is hard to ‘go through my book’. There are two reasons for this.

Some of the examples are numerical. Although I have done my best to avoid mathematics in my book, and only use arithmetic so that it can be read by anybody, most of my readers hate arithmetic, and therefore also hate mathematics. Most hate arithmetic even so much, that they hate it even use a calculator!

The second is that my book goes right against the innate socialistic programming. When I wrote the book, I was not aware of that there was such a thing like ‘socialistic programming’. Naively I assumed that most people are like me. When they see an explanation that is better than what they themselves think or believe, so I expected, they would be eager to learn it. So much to my surprise, when I began to give lectures on it, (which were then still free of any charge) there were questions which I failed to recognize as questiONINGS. That is, ATTACKS on my vision. Patiently I explained that and why the assumptions on which their questions were based, only to meet with even more opposition. And that from a group of people I believed to be the most accepting of my ideas: libertarians!

From these encounters, and having followed that course about how become wealthy (which I do not mention here for two reasons: the first is that even mentioning this course is giving away value. The second is that this course, despite the eye – opening techniques it contained to reprogram yourself, its CONTENTS contained many mistakes, therefore I do not recommend it), I saw that this extra capability to reprogram yourself is crucial for the acceptance of the ideas of my book in such a way, that anybody can see how he can create value for both himself and for others.

In any case, let me give an example of the kind of eye-openers contained in my understanding of money and wealth, which seemed to give others such a hard time. Then you can see why an emotional reprogramming is really needed to create wealth for yourself.

What I shall do is state a simple, yes even an extremely simple fact about money which, I think, is completely irrefutable. Nevertheless, its consequences go right against the inner socialistic programming, and therefore right against what almost everybody thinks, and therefore feels about money. (Inner Programming ->Thinking -> Feeling -> Action, remember?)

Suppose you want to earn money. That is, you do not try to obtain it through either welfare or through robbery or through any other form of fraud or violence. What is THE way to do this?

There is only one way: you offer something in return for that money. And to be able to do that you must either offer a good or a service. If you offer a good, you must FIRST make it. That is, goods must exist prior to their sales. This requires work in advance. After all, people do not go to shops that are empty.

The second way is to offer a service. If you do that, then you offer at least your time. Often you offer both your time and your skill, or, better, your skill through your time, so that it is more beneficial for the other to let you do the thing he wants than doing it himself.

In EITHER CASE it is so, that EVERYTHING YOU DO to obtain that money is NOT to create the product or servicing yourself, but for those that are willing and able to pay you. So EVERY ACTIVITY you undertake for the purpose of obtaining money is NOT to benefit you, but is for the sole benefit for somebody else.

Of course, you may LIKE the thing you are doing. If you are a mathematician, you might LIKE it to solve problems for others, or to teach others. But the activity itself, when it is for the purpose of obtaining money, is AIMED SOLELY AT creating some benefit for somebody else.

This makes money to be a very curious phenomenon. The MOTIVE to obtain money is selfish. But the ACTIVITY to obtain money is altruistic. So earning money is both selfish and altruistic. In other words, through earning money we benefit ourselves THROUGH benefiting others.

Now, if this explanation does not ‘land’, and you have difficulties to see what I mean, (especially emotionally), consider this: many politicians say, that taxes and taxation are necessary, because only through paying your taxes you are contributing to society.

And that is a lie, because if we ALL just limit ourselves to working for money, we are all of us working for others. And, through this activity, we CAUSE that we can USE money to obtain goods and services. In other words, I claim that it is not only possible to make a viable society without taxes, but even more. A society totally exempt of taxes and taxation is the most viable society that there can be.

Tax-receivers, whoever they are (social welfare recipients, politicians etc.) do NOT work for money. Therefore they form a DRAIN ON those who do, because they use taxpayers money to obtain goods and services, without having delivered goods and services themselves. And that causes that much lesser amounts of goods and services to be put against money, which manifests itself economically as inflation. So the higher the taxes, the greater the inflation. That, by the way, is the economic reason for the economic collapse of the communist countries. They thought that you could base a social order solely on the principle of ‘working for others without any conscious thinking about your own benefit’.

So this simple fact about how money functions is already able to explain many things. Nevertheless, this simple fact, a simpler form of which can be found in Adam Smith’s ‘Wealth of Nations” (It is not on the benevolence of the butcher and the baker I count on to obtain my food, but on his self-interest) is something that I have found to be very surprising to many people. And it is absolutely obnoxious for any socialist to hear, especially if he believes in the benevolence of taxes and taxation.

This is just a small sample of the kinds of understanding I can deliver. Test yourself to see, whether you have an emotional aversion against this simple fact about money. And if you find you have, you understand the need for a reprogramming of your innate programmings to change your feelings. And therefore you can also understand the need for a reprogramming for yourself for the creation of an ability to become wealthy.

So, to conclude, to become wealthy is, as far as activities is concerned, not too difficult. But as far as emotions is concerned it requires some major paradigm shifts, the biggest of which is the emotional transition from a hunter/gatherer to that of a farmer.

Mark FullertonWhy did Rome provide people with bread? Hint: it had nothing to do with either kindness or justice. It had to do only with the consequences of not providing people with bread.

njwildberger: tangential thoughtsPost authorDear Konrad, I have reread your remarkable post after these years, and am starting to better appreciate your important insights. Is your book still available, and where to get it?

elsimi01Dear Norman.

Sorry, that I did not answer sooner.

To be honest, I was shocked by your e-mail. I had the impression that nothing I said âlandedâ by you. But your e-mail shows I was mistaken!

I do not know what book you are referring to.

I also did not answered sooner, because I am in the process of putting the finishing touch on my book about value and money. I have finished its content and editing, and now I am busy making it ready for publication on Kindle. I hope to do that within the next couple of weeks. It will then be published on Amazon Kindle, and on Barnes and Noble.

Is that the book you are talking about?

In any case, as soon as I have published it, I shall let you know.

I am also working on a book about space and time, in which I explain where the 3 + 1 dimensional structure of spacetime comes from. That book begins with an explanation of what time is.

I am also in a dialogue with Dennis Morris about this. He has also developed a theory that aims to explain where the 3 + 1 dimensional nature of spacetime comes from. His approach is totally different from that of me. But I am interested in his work, because I became stuck in my theory. Mainly because I had not yet found a form of mathematics with which I could develop my theory further. But when I saw the videos of Dennis Morris about how he rewrote the Dirac equation, and his totally unique approach to complex numbers, I started to study his work, and also am now in a dialogue with him.

That dialogue does not go that well, though. My approach is so different from that of his, that he probably thinks I am totally wrong, is too polite to say me that much, and therefore he just ignores what I have sent him.

If you are interested, I can send you what I now have about my own theory of spacetime. It is still in development, though. And I do not know when it will be finished.

Dennis Morris does response to what I do with his multi-dimensional complex numbers, because I have spent some time trying to make Mathematica visualize some of his four kinds of 3D complex numbers. Dennis Morris himself is more interested in his 24 different 4D complex numbers.

Just for fun I connect some of the pictures and their formulas to this e-mail, since you often have shown to have an interest in non-mainstream mathematics.

A short explanation.

You can write a 2D complex number in matrix form

Dennis Morris does it like this.

[[a, b],

[-b, a]]

(Stretch + clockwise rotation)

All other mathematicians do it like this:

[[a, -b],

[b, a]]

(Stretch + counterclockwise rotation)

And the other 2D complex number, the hyperbolic complex number he writes like this:

[[a, b], [b, a]]

And its complex conjugate as [[a, -b], [-b, a]]

Dennis Morris writes his four 3D complex numbers as:

[[a, b, c],

[c, a, b],

[b, c, a]]

[[a, b, c],

[c, a, -b],

[b, -c, a]]

[[a, b, c],

[-c, a, b]

[-b, -c, a]]

[[a, b, c],

[-c, a, -b]

[-b, c, a]]

These four complex numbers are the 3D equivalents of the 2D ordinary complex numbers and the 2D hyperbolic complex numbers.

The equation

x3 + y3 + z3 â 3 x y z = 1

is the three-dimensional equivalent of the equation of the circle x2 + y2 = 1, and the three functions

x(b, c} = Cos3X[b, c], y(b, c) = Cos3Y[b, c], z(b, c) = Cos3Z[b, c] are the three-dimensional equivalents of the functions

x(b) = sin(b),

y(b) = cos(b)

The first four attached pictures show how these three-dimensional trigonometric functions look like. I find it amazing, that their angles are two-dimensional vectors! And the âvortexâ picture arises, when these three functions are used as parametrizations on the three 3D axis.

Just like

(cos(b), sin(b)

Leads to a circle,

(Cos3X[b, c], Cos3Y[b, c], Cos3Z[b, c])

Leads to this fourth (5, 6, 7) picture, this funnel-like structure, which is then the 3D equivalent of a circle.

Dennis Morris uses the notation Va(b, c), Vb(b, c) and Vc(b, c) for these three 3-d trigonometric functions he has discovered. I have tried to make clear to him, that that is a bad idea, because such a notation does not show that we are dealing here with a new kind of trigonometry.

In any case, that is what I have been doing in the last month or so.

At present I try to do the same with the 4D complex numbers of Dennis Morris, of which there are eight. One of these 4D complex numbers is the quaternion. Another one is what he calls the anti-quaternion. And then there are 6 others.

The problem is that you cannot just make a parametrization x, y, z, w and then let Mathematica draw them.

I am working on this. I already have made the 4D circle of a quaternion, which is just a âdouble sphereâ. That is, two concentric spheres. And the other 6 are all hyperboloids. As such this looks much like the 2D case, where you have either a circle or a hyperbola as a â2D circleâ.

By fusing his insights with that of mine, I think that 6 of these 8 4D complex numbers can be used to describe spacetime, and the two quaternions can be used to describe matter.

Dennis Morris is, philosophically speaking, a Platonist. He thinks that mathematics is itself a form of reality.

I am a Popperian. I think that mathematics is a tool with which you can get a grip on reality. You know my vision. There are two ways to understand, which I call analytically, or bottom up, or synthetically, top down. Both correspond to the psychological phenomenon of âexperienceâ and âconsciousnessâ. Therefore, there are two ways to âunderstandâ. You can understand through being able to imagine something. And you can understand through being able to become conscious of something. And my opinion of you is, that your point is, that you cannot understand âthe infiniteâ through imaginative understanding. But, and that is my point, you can understand âthe infiniteâ through understanding based on consciousness. But then the infinite is always a form of incompleteness, because in mathematics you always prove that some structure is infinite, through an indirect proof. That is, you assume the existence of something, imagine it, and then this leads to a contradiction, which then leads to the conclusion, you see that this imagination cannot exist.

For example: the set of positive prime integers is proved to be infinite through assuming that there is a largest positive prime. Then you deduce a contradiction, from which you now become conscious of the fact, that this imagination of a largest positive prime does not exist. Therefore the set of positive prime number lacks the property of having a largest member. And that is equivalent to the statement, that the set of positive prime numbers is infinite. Therefore if something is infinite, it cannot be imagined, because as an imagination it is not complete.

It is through watching your videos, and thinking about this, I came to this conclusion. I think this is an important breakthrough, because this analysis can put the discussion between Brouwer and Hilbert about the foundations of mathematics to rest. But, of course, I should work it out more precisely in a book.

I hope to find the time to describe these two approaches to mathematics, and how they both complement each other.

In any case, maybe we can have a more direct exchange about these matters? After all, it were your videos that made me start about such matters in the first place. Maybe we can have a dialogue, leading to a book we both publish?

I was very pleasantly surprised by your request!

Till next time, Norman.

Again. If you want me to send you what I have written about spacetime, let me know! I will then send you a pdf which shows at least how far I got without Dennis Morris.

Greetings,

Konrad.

COCHello / njwildberger

Professor

Possible question

I love Euclidean geometry and trigonometry I would like to study MA and Ph.D. in Arts (Geometry) or similar Belize Where can I find a university or college ؟

Belize:)