What is exciting for me is not mathematics per se, but the possibilities that this opens up.
When we learn at school what a coordinate system and a straight line in it looks like, we only understand that there is a stroke on paper that cuts two other strokes that we call axes.And that’s what we do, because that’s what the teacher wants. boring!
Suddenly, we don’t learn what that means, what we’ve learned.We just look at it from above, see the drawing, read it and do well. I didn’t learn this in high school, even in high school. In computer science, I learned this in my studies, but not so much because a professor came across it, but because I became aware of it.
In fact, the thinking possibilities explode in this Cartesian coordinate system.We can put two things that previously existed independently in their own dimension into a logical relationship. Often way and time. But we can use anything. Money and love, trust and friendship, we can relate everything that can be connected in some way.
Something works together here, we have a function.First, the functions are quite simple, just linear, a straight line, and then the possibilities increase with square functions that represent accelerated processes or cubic functions that represent the acceleration of accelerations. Complex processes such as accelerated acceleration suddenly become a very simple number.
A two-axis coordinate system is two-dimensional.
I recently wrote something about politics: there is not only left and right here, but also pro-business or pro-worker.We can now locate politics in a very different way than with the usual left/right scheme.
But we are not limited to that, we can insert more axes.In politics, for example, environmental protection or acceptance of waste of resources could be at the front/back. This gives us a three-dimensional space where we can look at parties like blobs, which sometimes overlap and merge into each other or even sharply distinguish themselves from each other. Some blobs are round, like balls, others may be squeezed together on one axis, pulled apart on the other.
At this point, mathematically, we already have everything we need for artificial intelligence.
In mathematics, we are not limited to the fact that there are left/right, top/bottom and front/back.We can insert a fourth dimension, for example, Constructive or Destructive. While “Die Linke” works reasonably constructively, other parties gather somewhere in the midfield, left-wing extremists and right-wing extremists are working destructively. We thus have a dimension where left-wing extremists and right-wing extremists are in the same place, namely where they accept violence and destruction as a means. Suddenly, left-wing extremists and right-wing extremists are no longer as far apart as possible, but stand together as violent perpetrators against those who reject violence, whether progressive or conservative. There is therefore a dimension on which the political fabric presents itself in a completely different way than in the classical left/right.
In this way, we can insert dimension after dimension to obtain an ever finer image of the world, to describe movements, accelerations or even accelerations of accelerations.Mathematics shows us how we expect multidimensional functions, computer science even how to process functions with complex data types.
With matrices, we can make connections between the individual dimensions visible.
Mathematics provides us with logical tools to understand, estimate, calculate, evaluate and predict the world in many dimensions.The gaze no longer only goes into the past and the present, one no longer lives only in the present, but at the same time in several futures with different probabilities. You can prepare for different paths that could happen in the future.
You don’t necessarily have to study mathematics, many just have to bother to put into words what they call gut feeling.Mathematics provides the language and language we need to understand these things in words. Understanding his gut feeling means estimating how far you can trust him.
One can predict processes that are so complex that it doesn’t really fit into our everyday experience.Mathematics can be a way to think beyond our everyday experience. We can enter a room larger than left/right, top/bottom, front/back.
When I was around 23, I went in search of the function for artificial consciousness and artificial creativity – not artificial intelligence.Along the way, I’ve derived functions for language. The exciting thing was that I could suddenly think language beyond the spoken language. I could think of language for which I had no vocabulary. Instead of thinking of something in a vocabulary, I could think of things that I could then name with a vocabulary. You could name white spots on a language map. Meanings that no one has yet given a name to.
I was able to step out of what I could explain with words and think of things that I cannot explain in words.It is exciting to be able to think thoughts that describe relationships for which one has no word, but only function modelled on a mathematical function that connects different dimensions.
One understands the world anew, but not with one’s hands or by looking at it with eyes or ears, but with one’s head, which corresponds in a way to a mathematically defined sensory organ.
Language names defined states for a multidimensional Turing machine.If one can define language generically, one can describe more states of the Turing machine. You can insert a new state between two words, so the thoughts can become sharper. If a vocabulary is an integer, but you have a ratio of 3/2, i.e. a fraction, then you can think further the ratio between two dimensions instead of rounding it down to an inaccurate vocabulary. You don’t have a word for it, but you can think of it. Just as there is no integer for 3/2, but you can still count on it.
I see and understand people and their personality differently ever since.Thinking about artificial self-confidence meant that I needed new dimensions to understand consciousness and personality.
Not that I could fully understand people, but a few years ago a friend wrote to me that he finds it incredible how well I know him.I understand a lot of his personality. I can understand it. I do not need to know everything in his life to understand the fundamental principles of his thinking.
And over the years, it turned out that I knew repeatedly better what he was going to do and what the consequences were than he did himself and that before he even talked to me about it.I told him my assessment and he later wrote to me that this was exactly his plan and it was just unbelievable how well I know him.
I have spent about 6 months getting to the point of understanding language.Then, in a journal, Brain and Mind, I read that scientists spent 10 years experimenting and researching how they imagined language in the brain. And we came to the same result. Science through experiments, I conclude by using mathematical rules and the consistent application of what I have learned math lessons in secondary school.
Mathematics suggests that there are dimensions that you don’t see yourself.There are things that my personality doesn’t notice, where I’m probably behaving silly without even realizing it. I can’t see these things, but I can derive them in part. I can identify weaknesses and consider how to eliminate them, eliminate them, or how to turn the lack of dependence into a strength.
Mathematics is actually quite simple.In fact, everything repeats itself, is set one after the other and nested. Mathematics describes recurring patterns, mathematics itself is a recurring pattern. Like DNS. DNS can occupy four states and yet describes what a person is and how it works.
You find mathematics in motion.Be it in dance or the movement of water or pressure waves like music. Mathematics is music. Mathematics are colors. Man sees red, green and blue. The color spectrum that humans see is incredibly small in relation to the real existing colors, i.e. in comparison to the wavelengths we don’t see. With mathematics we can immerse ourselves in this world. We can create washing powder, which is even whiter, create radios and Wi-Fi. We can photograph black holes. And we know beforehand that there is a black hole, what we are photographing, because we have calculated that it has to be there.
Mathematics is the DNA of thought.
I find this incredibly exciting, even though I am far from good at mathematics and can hardly do more than the basic arithmetic.
I often wonder what I might think if I were really good at maths.
That, too, is exciting.
In addition to life, there are many topics on which a mathematical examination entails spanning clues.Death. Time. God. The universe. The multiverse. The micro-cosmos… all topics for which mathematics has tools to derive insights from.
And if you are not interested in all this, you can also draw up a Bundesliga table.;)