1. What is this?
This group of lines, this image you see, I ask again, what is this? The answer we are
all taught when we are very young, say 3-4 years old, is “that is the number four” and
since then most people have not questioned that answer. Some of us may have looked
deeper, there are others answers to the question, Wikipedia has lots of very interesting
things to say about it. (http://en.wikipedia.org/wiki/4_(number))
In our “age of information” that answer is not really right, actually it was never really
correct at all. So what is this?
Lets explore ZEN for a moment, that which “does not stand upon word”. There is a story
of Buddha that can help us to understand the answer to this question:
The Buddha sat and held a flower, doing nothing and saying nothing, he sat silently
showing the flower to his follower Mahakasyapa. Mahakasyapa did not know what to say
or do but followed his master’s lead by sitting silently and looking at the flower. As he
gazed at the flower Mahakasyapa broke into a smile. The Budda then knew that his
disciple understood and said
“You possess the true Dharma eye, the mind of Nirvana, the true form of the formless,
that subtle Dharma gate that does not rest on words or letters but is a special transmission
outside of the pysical.”
Mahakasyapa had what we may call a realization, an understanding that cannot be
expressed in words, he had an abstract thought. Abstract thoughts are defined as non-
concrete thinking, thoughts that do not involve physical objects. A concrete thought has a
physical entity it can link to like “tree” or “car” and abstract thought is along the lines of
non-physical space per ideas such as “a kite flies” or “I’m happy”. This leads us to a
more western way of thinking called Logicism or Logic. Logic states that all notions are
reducible to laws of pure thought, or ordered principles.
Where did Logic come from? From many learned men of course, men whose names you
know. A line of students of teachers becoming teachers of students, a process of great
minds that over time winnowed their thoughts to give us Logic, the diagram below shows
the people of this progression.
Pythagoras The Mathematician
Parmenides – Supported his views with abstracts rather than reality
Zeno of Elea – ordered thinking
Protagoras - Sophists justified by reason
Socrates - importance of care and rigor in the use of language
Plato – the distinction between verbs and names
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2. The result of this culmination of what Logic defines, that a noun is a person, place or
thing, “Bob”, “Oklahoma”, “tree”, concrete thought. Also knowing a verb is an action
word, “running”, “holding”, “thinking”, abstract or pure thought.
Laws of pure thought! Now we are ready to answer the question!! Sorry, no, we aren’t,
but we are getting there :)
We translate mathematical notions (pure thought) to a result, 2 + 2 = 4, these
notions/laws help us solve problems with abstract thought applied to concrete objects.
“I need 4 feet of rope.”
“I saw 4 fish swimming”
“If Johnny had 6 apples and you took 2 away, how many apples does Johnny have
left?”
Logic is a path to a result but that is not what this is. We can interpret it as a result
but it is not the result.
The next step in the thought process leads us to Formalism. Formalism describes an
emphasis on form over content, that there is no transcendent meaning in form only in
interpreting the form. Art is formalism, art makes people interpret an image or sound
(pictures, music) for meaning, for information. Therefor form gives information, another
word for form is shape and a shape can be called a symbol.
A Symbol! OK, stick with me, we are there, the final sumation is……
A symbol, in this case, is a mark or shape that represents the pure thought known as four.
Four, in its pure thought interpretation, cannot be sat on or held or eaten. Four is abstract
in this form, a word (word - a grouping of symbols) to narrow the explanation is numeral.
This is four a numeric symbol that can represent the logical expression of a grouping
or counting of concrete objects.
This is a symbol representing a pure thought used to interpret a concrete world.
Hence Mahakasyapas smile
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