User blog:Edwin Shade/My Hierarchy Of Mathematical Understanding

Throughout the yesteryears there have been attempts to bring about the continuous lexicographical stratification of the numbers we've come to know and love in the study of fast-growing functions; some examples of which of are PsiCubed2's "Psi Levels" and his "latter Letter Notation". Although well-developed, these attempts at making a universal scale for large numbers will inevitably fail to carry out their purpose fully due to the plain fact that there are numbers whose proportions are inaccessible to our finite resources of mathematical ingenuity, as Saibian himself has brought out. Seeing however, as we can only construct a universal hierarchy for that which has clearly defined limits, why not make a hierarchy for knowledge itself ? Yes, that is exactly what I have decided to do in this blog post, which sets out a ranking system for mathematical knowledge and all matters numerical.

My System
My hierarchy of mathematical knowledge is not contained in just one number, but instead consists of a string of values, each of which represents a different aspect of knowledge. These values will be separated by dashes like so: "v-v-v-v-v-v".

Self-Awareness
The first and foremost measure of knowledge appears to be self-awareness, so thus the first number will be a measure of how self-aware a being is of itself. Without broaching the tricky issues of consciousness, I still feel confident it will be easy to ascertain where a given being should fall in this hierarchy.

Level 0: Level 0 self-awareness is no self-awareness at all. A being who falls into this category may be able to carry out complex mathematical arguments, (like a computer), but it will not have the notion that it exists, or even have any notion of what it means to exist. Level 0 encompasses the realm of inanimate thinking objects like computers, pocket calculators, and all forms of current technology known to human civilization. It most likely also includes biological organisms whose "brains" are too small to allow them any ability to self-reflect, like ants, amoebas, and the vast majority of the insect kingdom. Though computers and insects fall into the same class in my system of self-awareness it should be stressed that the smallest denizens of the insect kingdom are far more sophisticated than the most advanced supercomputer, and that therefore this level does not necessarily arbitrate between the living and the inanimate.

Level 1: The next level in self-awareness is realizing you exist, and is a quality I would suspect most rodents along with the larger mammals possess. It has been shown by scientists in fact, that when certain animals are confronted with a mirror they eventually realize it's just them, and go about their business normally. So level 1 would easily include creatures like dogs, cats, elephants, and monkeys, and most likely aquatic lifeforms like the octopus or dolphin.

Level 2: Level 2 self-awareness consists of seeing yourself in relation to the world, and realizing you affect the world around you.

Level 3: If you have Level 3 self-awareness that means you not only have an internal picture of the world around you, but that the internal picture is more or less aligned with the reality of matters. Surprisingly, many humans fail to supersede even this level of self-awareness, and manage to convince themselves they are above others when they are not, or conversely, think of themselves less than they actually should. Balance is the key to having a level 3 self-awareness, as you must see yourself the way others see you, untainted by false beliefs about yourself, (i.e. those of inferiority or grandiosity).

Level 4: Level 4 self-awareness is knowing the exact extent of your power and knowing how to exercise that power to achieve your means. Many either over-estimate or under-estimate their abilities, and therefore are disappointed when they apply themselves to a matter, for they either do not find joy in what they're doing, or they get into water too deep for them.

Level 5: Level 5 self-awareness is accepting that everyone else's life is just as complex and sophisticated as your own, and represents a shift of focus from considering yourself at the center of existence to contemplating you are just one of billions of individuals. Many consider this an abysmal thought because it makes them feel small and worthless in the grand scheme of things, but on the contrary it should give you an incentive to strive for greatness in an area no one has yet touched, and rise above the masses in whatever you excel at. You may have noted this level of self-awareness is not strictly about yourself, but rather about others. This is intentional - for by self-awareness I was really referring to one's knowledge of the world, and that includes everything.

Level 6::

[PROGRESS PENDING]

Clearly this is in progress, if you have any recommendations, comments, or questions please leave them below and I will keep them in mind when continuing this hierarchy.

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