Ali's Journal

In science, simple solutions favour over more complicated ones. If a model in physics also explains evolution and other topics in other fields then it favours over other theories because it will simplify science.

In the math course I’m working on, it is explained that symmetries organize people’s viewpoints. Psychological phenomena such as confirmation bias are like inertia. They stop people from changing their minds every day. However, when people are encountered by new perspectives, their viewpoints are challenged. That is similar to a sinusoidal wave. Different opinions push one’s viewpoint up and down but psychological phenomena try to pull it back to where it was. This is a wave.

The same is true about evolution. Every new mutation generates a wave. Nature will then be about interacting waves. The subject of the field of evolution will be to discover those basic symmetries that produce those waves.

So the language of waves is not exclusive to the theory of probability. This will be used in many different areas.

UPDATE 1:

last year I submitted an idea to Campbridge’s startup scheme. It was about a programming language. New AI tools have changed programming. In some years programmers won’t write codes line by line at all anymore. It was suggested this new approach required a new programming language.

Very briefly, the programming language is based on common building blocks. To write a code some of those blocks will be linked to produce some functionality. So AI tools will not write codes from scratch every time. They search through a long list of all available blocks and connect them.

The same idea can be used for the wave language. Some months ago I wrote something that there should be some universal format for arguments and any type of expressions. Imagine instead of verbs and nouns, etc. a language consists of objects (as described in OOP). Then since objects are built by common building blocks, different objects may share common building blocks. Those shared elements can interact with each other (augment or diminish one another). However, each object is restricted by a symmetry which limits the amplitude of deviation from the equilibrium state (i.e. the state of no interaction).

Then probability expressions can also be expressed similarly by block-based wave languages.

It was previously said that the wave probability would be constructed by moving waves so that each observation of that wave generates fuzziness. In the example of quantum mechanics different wavelengths produce a wave packet so it can be said that waves are moving in that space. However, things were ambiguous about probability and the concept of moving waves for probability was very imprecise in the previous writing. Today things will be clarified a bit more.

In binary coding, things are denoted by 0 and 1. For example, if someone wants to send a number to another person online, the number will be transmitted as a sequence of zeros and ones. Binary notation is one method for coding. Now let’s imagine one wants to pick an object from a bag containing three such objects. Denote objects A, B and C. If the experiment is repeated for N times, the outcomes might be:

S_1=ABAACBACCBABB…. or S_2=CBCBCBABBCBAAC…. etc. Since the probability is equal for 3 possible outcomes then different sequences of experiments (i.e. S_1, S_2, …S_i) are more or less similar because in all of them, A, B and C occur around N/3 times (assuming N>>1). So S_i sequences can be considered different microstates for the macro state where p(A)=p(B)=p(C)=1/3.

In thermodynamics, it is assumed that microstates continuously turn into other microstates, and after a sufficiently long time, all possible microstates for some macro state will be generated. This idea can be used in wave probability to explain the concept of moving waves. Each experiment in the above probability example is comparable to one constituent element in a thermodynamic system. Then S_1 continuously turns into S_2, …S_i.

However, the construction is still very incomplete. Mainly because S_i sequences are not waves. A simple ternary notation is used to denote a sequence of experiments. It’s obvious that this notation method is not unique. For wave probability, other notations should be used. Before proceeding consider this example:

Each language conveys meanings by concatenating different phrases. Each phrase is comparable to a sequence of binary code for example. Then a message is a concatenation of several such phrases. Now imagine a new language is invented where each phrase is like a wave then different waves interfere with each other. The meaning that is conveyed with a set of waves is not a simple concatenation of phrases (due to wave interference).

So the objective is to invent that language for the wave probability. This language is relevant for probability because S_i outcomes are different mental copies of the same system. They don’t occur in sequence (it’s not that S_2 occurs after S_1, etc). Since all micro-states co-exist at the same time, the wave language is more relevant.

In general, this language is relevant for concurrent processes. For example, in a society, people don’t make up their minds in a sequence, one person after the other. In reality, the viewpoints of people in a society interact with each other and reshape other people’s viewpoints while at the same time forming their own point of view as well. This is a wave language.

In the OOP course, I explained that dimensions could be more complex than axes in R^n for example where points on the x-axis are specified by a real number. For example, in a room that contains several lions and tigers, it can be said that the space of objects is 2 dimensional. Lions and tigers define two distinct axes for this space. The thing is it’s not easy to organise all lions for example in a line (similar to the line of real numbers where all numbers could be placed in a line). The axis defined by lions is more complex. For this purpose, it should be clarified what a lion actually is.

The human brain more or less automatically distinguishes lions from other animals. But if one wants to do the process consciously it becomes a very complicated task. Probably that person should write a list of all the properties of lions. Some properties are not straightforward. For example, behavioural variations cannot easily be notated. Imagine a notation method that identifies all possible such variations. When all properties of lions or tigers are precisely defined (that is all possible variations for all properties could be notated by some notation systems) then it’s possible to construct the dimension defined by lions. However, This “dimension” is a type of space. Every lion then will be a vector in that space.

The same method can be used for memories. There should be some type of tag assignment that organizes memories. Related memories are organized under one tag and so on. Based on the previous discussion, it’s possible to consider memories as entities (similar to lions for example). Then each memory will be a vector in that space. That space is flexible. It means it is reshaped over time. This is true about memories. Not only some details of memories will be lost over time but also they can be reinterpreted once new memories are added.

In R^n axes are always fixed. But in the space of memories, the base vectors can be redefined and so the space will be reshaped over time. As a result, all vectors contained in that space will also be modified. To clarify if lions acquire new traits or some existing traits change over the span of thousands of years, the space that contains lions will also be modified. The same should be true about the space of memories.

The question that arises here is that how consciousness is linked with the formation of this space. I know nothing about consciousness myself, but before working on that topic, the mathematical aspects of the article should be clarified more.