Absolute and Potential Values of Unifiables

[The Voice of Time]

As I was enjoying some evening air walking back and forth from the shop (and yes, this thread is gonna be complex and lengthy), I started thinking about the relationship between the mathematics I'm currently learning and the mathematical nature of unifiables, which I also call Objects of Need (the course is first year high school, I'm redoing it because I failed the first time when I was in the momentum-gathering of my teenage revolt. I need the course to take software engineering courses in college and university).

Especially, this time I was interested in properties of "unifiables in time" (the appearance in a moment of time of a unifiable), and how these can be calculated. To do this, I needed a couple of definitions. First, unifiables are either actual or potential. That is, either all of the functions exist in time (not mathematical functions per se, but functions as in "the functions that make this "x" be that specific "x"), or, some or none of the functions exist in time.

You could say actuality means "being in time", and so all functions of a unifiable (an object of need) are actuals if the unifiable itself is actual, and vice versa. If only a few of them are actuals, then the unifiable, the object of need, does not exist in time, but, given that the remaining ones are filled, it has a value as a potentiality.

However, more definitions follow, because actual and potential are very boring values. The calculation in both instances is either "n above, i = 1/n or 0/n below, sigma sum", where actual unifiables always has "i = 1/n".

For an actual unifiable with 3 functions, the expression is "sigma sum 1/3 + 1/3 + 1/3" or "actual value = 1/3 + 1/3 + 1/3", or more textually you divide 1 by the number of functions in the unifiable and then summarize all the functions. For a potential unifiable, you would first input algebraic unknowns instead of 1 for a generic formula, and then as you figure out the unknowns you input their respective value as either 1 or 0. The sum of an actual unifiable of 3 functions is 3/3, or 1, which is unity. The sum of a potential unifiable is a+b+c/3. The output value of an actual is extremely boring, and although its appearance varies, its sum is a constant 1 value (3/3 = 1), for the potential unifiable, it is less boring but still very boring, because the variable you get just tells you how much is unfulfilled, nothing less, it gives no aids to actually "doing something" with it.

For this reason I was thinking of two other properties, namely the "security" and the "expanse" properties. And how to calculate them? Well if we start with "security", we'll see that actual unifiables will have an actual security, whereas potential unifiables have a potential security value. Meaning that potential unifiables aren't actually secure before they are first realized, before they become actuals, before that they only have a potential to be secure, as security means how well they are supplied in the event of some function being stricken, that is:

A function may have several sets of conditions that all make the function possible. For instance, in a recipe for food or making anything or even if you are hiring people for a job, there may be many people or things that can fill that particular function, and as long as they are available, they are securities for that function being fulfilled, they are all sets of conditions that can complete the specific function and so actualize it.

The way in which we calculate the security of an actual or potential unifiable would depend on whether the properties of the mathematical expression equates the properties of the functions and the unifiable itself and their relationship with security. For the security of actual unifiables, we just add to the numerator in each part of the expression the number of alternatives available to replace that function in case it is stricken, so if we have 6 different alternatives, we have 1+6/3, giving 7/3. However, because actual unifiables cannot have a zero value in its numerators, we could change the terms to factors by exchanging the additions signs with multiplications signs, and we would also reduce all denominators to one shared, because this way, the new product value would be "1*7*1/3 = 7/3". We can see that this can never have a zero numerator, because "0*7*1/3 = 0/3", and actual unifiables can never have a zero value as then they wouldn't be actuals. However, despite what we may have achieved, the security value of actual unifiables is absolute, that is, it's not relative. It presumes that there's an equal chance the second function will be stricken 6 times as any of the others being stricken just once. But for the actual unifiable to fail, just one of them have to be stricken, and therefore we are more concerned how big a chance there is of an "overall penetration" of the unifiable, the object of need, than any specific function... what exactly is the dependability of the unifiable?

We can answer this question by looking at the relationship between the factors. If we expect the risk to increase as the distribution becomes more and more unequal, we should expect a relationship between numbers that gives a result which increases as the inequality increases. There happens to be just such a relationship, namely if we change again and turn the factors into divisors we'll see that as any number of functions gains more and more sets of conditions able to be the function, the overall dependability will decrease. For instance, 6 and 3 and 2 is more dependable than 12 and 2 and 2, as 6/3/2 is 1 whereas 12/2/2 is 3, the first one, despite having 3 less total conditions, have a more dependable set-up, because it is assumed that any one of them can be stricken at any time instead of us being able to choose which one is stricken, we measure dependability and not brute strength as we did the first time. In a universe where they are totally stricken 30 times and you permute the strike targeting set-up you'll see that statistically speaking, there will be more set-ups in which the unifiable is penetrated and unactualized with 12 and 2 and 2 than 6 and 3 and 2, because there will be an equal amount of different set-ups possible for striking each function in a maximum 30 number of times, and because of that, the number of times that 2 and 2 fail will exceed the number of times the 12 will repel.

The number of possible set-ups for strikes is 205891132094649 times (or 3 raised to the power of 30). If you want to know how many set-ups will result in a loss in the second function of the 12 and 2 and 2, you divide 205891132094649 by 3, and get 68630377364883, if you want to how big a chance it'll strike there again, you divide 68630377364883 by 3 again, and you get 22876792454961, or a 1/9 chance. At this stage, the second function is lost and the unifiable unactualizes. Because the 3rd function has the same value as the second, it has the same chance that this will happen to it, and so its value is also 1/9. Combined, the chance that any of them will fail is 2/9. The chance that the first one will fail is much lower, in fact it's 1/531441, however, the second and the third have already raised the overall chance hugely. Compare this with the other example of a unifiable with three functions, the one of 6 and 3 and 2. There is 1/9 for the third function, then 1/27 for the second and 1/729 for the first. While 729 is nowhere near the tiny chance of 531441, the value of 1/9+1/27+1/729 is smaller than 1/9+1/9+1/531441, meaning that there is a bigger chance of penetrating the pool of the later rather than the former unifiable. If you need further convincing of this, consider that 1/9 is 22876792454961 possible set-ups whereas 1/27 is 7625597484987, if you notice that lack of a digit going from the first number to the second, you'll know that 2 of the former would require more than two of second in order to be of the same or greater value, and that since the next function in line (the third) is a fraction of the former in turn, you'll know that there aren't enough functions in the unifiable with the right value to attain the level of penetrating set-ups created by 1/9 + 1/9 alone in the second unifiable.

Going back to the head topics, we can see that we now have a way of outputting the value of the security of an actual unifiable. Any circumstantial variables may be added to the formulae in order to get even more useful information, and information we can use in our everyday life. For instance, any function of the unifiable may be dependent on environmental input through some mathematical function (now we're talking about mathematical functions, like f(x) functions, and not about unifiable functions) that will result in variable security levels. Consider you have a car and you know the likelihood of every piece of it breaking down. The car is the unifiable, and the pieces are the functions of the unifiable, and the number of sets of conditions that can fill in whenever any function is stricken, is the amount of extra car parts corresponding to the pieces of the car. If you know the chance that x car piece will break down and need a part replacement, you'll have deterministic information (in a practical statistical sense) about where the car is gonna be stricken. This means there's no longer an equal chance that all pieces of the car are gonna be hit. This means that the security of that piece is gonna be altered to be more or less than the basic equal naïve presumption (which is that they all have an equal chance of being hit in each round of striking). As it increases, the pool left for the others decreases, and the sum of total times they are gonna be stricken is lessened, as that piece is decreased however, the pool left for the others increases, and the risk of being stricken for each one of them is going to increase, at least as long as the total pool, including the function you have extra information about, stays at the same volume. You could say that for a function you are informed about and two functions you are naïve about, the values are as such: 6/(3*(informed value modifier)), (3*((informed value modifier)/a))/3 and (2*((informed value modifier)/a))/3.

Whatever you multiply the denominator of the first fraction with (the first function of the unifiable) you have to somehow add to the remaining functions. This is because, for instance, if you find out that there's a bigger chance that the first function is gonna be struck in proportion to the others than was the case (like when you were naïve about all the functions), the value of its 6 possible sets of conditions have to be proportionally less capable at mitigating an overall penetration per set than the other functions, and this is achieved by a bigger denominator, inflating the value of each unit in the numerator of this fraction (the 6 possible sets of conditions). However, if you summarize all the functions now, the overall value would've been decreased, and this is not intentional, so we have to increase the relative value of the other functions to make up for the decreasing value in the first function. Here we multiply the second and third function by that value after first dividing by the number of functions (the number being "a", in this case a=2) we are distributing the surplus value to.

This exemplifies the way in which we manipulate the function values of a unifiable in order to get its dependable security value relative to a deterministic environment. Now to the "expanse" property, we can calculate the expanse of a unifiable by first finding an environment in which it is to have an expansion upon, that is, another unifiable which is said to be an "environment" and which has shared functions or shared sets of conditions for functions with the expanded unifiable, and then simply easy peasy divide those shared sets of conditions by the total shared sets of conditions in the environment unifiable. If they share functions, then all sets of conditions within that function are part of the division including any other shared functions and other shared sets of conditions. If only individual sets of conditions then those go independently into the pool of shared sets of conditions from the expanded unifiable divided by the pool of all sets of conditions in the environmental unifiable, or more simply said for the environmental unifiable: we divide by its absolute security value, which is the total of sets of conditions.