Bukalov on the dimensionality of functions

[krieger]

(a,b,c,d) are extremely general scalar quantities measuring any linear complexity the function might have. What does this linear complexity represent in terms of psychology? Well, it probably represents any extraneous alterations to the function, or any complexity it might have not directly stemming from its vector composition. Hence, it could represent the process of educating the function or any number of other building-up activities. Setting a,b,c,d = 1 gives a representation of the psyche upon it's first entry to the world, prior to any experience. We needn't specify anymore except to say that these skew the original value of the function's output in proportion to the numerical value of a,b,c,d.

putting everything together yields: Y= aI^4 - bL^3 + cF^2 - dR

Thanks. What gather from this is the following:

- Bukhalov assigns "dimensionality numbers" to each of the functions in the model A
- Bukhalov claims there is a factor multiplying the performance of each function (we can speculate it is affected by training, education)
- the dimensionality determines the power to which this factor is raised

A particular thing to notice: training the base function leads to growth of a factor to the power of 4, whereas training of the PoLR function leads to growth of a factor to the power of 1. As such, the effect of training the PoLR is in comparison negligible.

Further, we have the performance of + functions counteracting that of the - functions in the determination of how large a resulting value is.

All this as claimed by Bukhalov, with little to no given justification.

Something that is still hazy to me: if functions themselves (I, L, F, R) are said to be values, what is the use of the factors (a, b, c, d) multiplying them? Appearently a,b,c,d signify training, but what do I, L, F, R say about a function?

-The input-
The formulas don't even bother answering that question. The input is defined by the four different vectors - whether it's input about the situation, or input about norms or whatever. The above equation only provides the most general/barebones formulation of this by setting the dimensionality of the functions. Do you see why I said that the math was almost trivial?

-The output-
Y = the output = the psyche, and it is merely the sum of each individual function added together. Again, it doesn't take a genius to figure out that the psyche is the sum of its parts.

Ah, so using this we can calculate the volume of the psyche. Finally! Millions of lives will be saved.

On a serious note, thanks for the clarification.

[krieger]

-The output-
Y = the output = the psyche, and it is merely the sum of each individual function added together. Again, it doesn't take a genius to figure out that the psyche is the sum of its parts.

I think an alternative interpretation is needed here, by the way. The resulting value signifies the extent to which the + functions overpower the - functions.

A potential weakness of the model: when the variables a,b,c,d and the values of the functions themselves amount to less than 1, the higher dimensionality functions end up weakening their accompanied function as opposed to strengthening it. So one needs to be clear about the fact that 1 is the lowest value the model can handle, unless one thinks it acceptable that in situations where experience is very low, the PoLR function has an advantage over the base function.