Archive for May, 2016

The Fourfold Self

May 28, 2016

sq_fourfold_selfA recent post by Sandeep Gautam synthesizes several distinctions of the human being as self to come up with a nice fourfold model. These are the Materialistic (or perhaps Substantive), the Experiential or Experienced, the Remembered (or perhaps Visualized), and the Prospective or Anticipatory (or perhaps Envisioned). These can also be neatly labeled as “having”, “doing”, “being”, and “becoming”.

I have talked about Gautam before in my post The Fundamental Four of Sandeep Gautam. The fourfold discussed then was developed from evolutionary problems and drives but reminds me somewhat of this new fourfold, where Food/Foes -> Materialistic Self, Family/Friends -> Experiential Self, Focus/Frame -> Remembered Self, and Flourishing/Fun -> Anticipatory Self.

There are several other fourfold models of the self that are readily found. There is the ancient “Modes of Consciousness” from the Upanishads: Physical, Emotional, Intuitional, and Absolute. There is the anthroposophical model of Rudolf Steiner: Physical, Life/Etheric, Astral/Feeling, and Ego/“I”. There is the one by Friedrich Nietzsche: Deepest, Ego/“I”, Ideal/Higher, and True. And there is the religious or new age model: Body, Mind, Soul, and Spirit.

The problem with most of these older models of the self is the lack of consensus on the meaning and existence of the terms used in their construction, much less a way to know if the set is complete or not. Thus the fourfolds seem to be rather diverse and vague. I favor a more pragmatic and psychological approach in choice of models, plus those that can be easily mapped into Aristotle’s Four Causes, both attributes of which I see in Gautam’s models.

The comparison and contrast of these models to come up with a synthesis might still be a worthwhile future effort. There are also several fourfold models of the brain itself that could be entered in to the mix.

References and Links:

To Have or to Do? To Be or to Become?

https://equivalentexchange.wordpress.com/2015/03/22/the-fundamental-four-of-sandeep-gautam/

https://www.academia.edu/4122124/Nietzsches_Fourfold_Conception_of_the_Self

http://www.universaltheosophy.com/articles/johnston/the-fourfold-selfs-three-vestures/

https://en.wikipedia.org/wiki/Anthroposophical_view_of_the_human_being

http://www.enlightened-spirituality.org/Body-Mind-Soul-Spirit.html

[*9.130, *9.132]

<>

Buy One Get One Free

May 6, 2016

sq_free_group2Speaking of paradoxes, the Banach-Tarski Paradox is an interesting theorem in mathematics that claims that a solid 3-dimensional ball can be decomposed into a finite number of parts, which can then be reassembled in a different way (by using translation and rotation of the parts but no scaling is needed) to create two identical copies of the original structure. The theorem works by allowing the parts of the decomposition to be rather strange.

One of the important ingredients of the theorem’s proof is finding a “paradoxical decomposition” of the free group on two generators. If F is such a free group with generators a and b, and S(a) is the infinite set of all finite strings that start with a but without any adjacency of a and its inverse (a^-1) or similarly b and b^-1, and 1 is the empty (identity) string, then

F = 1 + S(a) + S(b) + S(a^-1) + S(b^-1)

But also note that

F = aS(a^-1) + S(a)

F = bS(b^-1) + S(b)

So F can be paradoxically decomposed into two copies of itself by using just two of the four S()’s for each copy. Both aS(a^-1) and bS(b^-1) contain the empty string, so I’m not sure what happens to the original one. One might think that aS(a^-1) is “bigger” than S(a) but they are actually both countably infinite and so are the same “size”.

The generators a and b are then set to be certain 3-dimensional isometries (distance preserving transformations which include translation and rotation). The rest of the theorem requires further constructions that may be of interest, as well as needing the Axiom of Choice or something like it. It is also curious that the paradox fails to work in dimensions of 1 or 2.

The diagram above tries to list the beginning of each of the sets S(a), S(b), S(a^-1), and S(b^-1). The empty string can be thought to occupy the center of the diagram but it is either not shown because it is empty, or it is shown as being empty. Alternatively one could create a more general fourfold with the aspects of structure, (paradoxical) decomposition, parts, and reassembly.

References:

https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

https://en.wikipedia.org/wiki/Paradoxical_set

https://en.wikipedia.org/wiki/Axiom_of_choice

http://faculty.mccneb.edu/jdlee3/thesisonline.pdf

[*9.124, *9.125]

<>