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Laws of Form (Spencer-Brown, 1969, 2011)

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George Spencer-Brown, also known as George Spencer Brown

Niklas Luhmann found this work to be very interesting and it has been said that approaches to understanding Luhmann's work should include reasonable attempts to understand Spencer-Brown. What did Luhmann find interesting here?

By the way, if you want to know what the thought of a genius is like, Spencer-Brown's semi-lucid ramblings (complete with pages of hieroglyph-like "brackets" which follow a logic of their own) are about as close as you are going to get. Readers should note the painstaking care that went into the presentation of the material, which has turned what otherwise would be an incomprehensible cave-painting of figures into a readable mathematics, of form. I last remember going through exercises of this nature in high school Geometry.

Amazingly, Charles Sanders Peirce dabbled in "existential graphs" of similar kind, based on the topology of Listing. Johann Benedict Listing (1802-1882) was the first to use the word topology. Listing's topological ideas were due mainly to Gauss, although Gauss himself chose not to publish any work on topology.

xiv I have aimed to write so that every special term shall be either defined or made clear by its context. I have assumed on the part of the reader no more than a knowledge of the English language, of counting, and of how numbers are commonly represented.

xxi what I am saying has nothing to do with me, or anyone else, at the personal level.

p.1 Once a distinction is drawn, the spaces, states, or contents on each side of the boundary, being distinct, can be indicated.
 There can be no distinction without motive, and there can be no motive unless contents are seen to differ in value
.

p.56 At this point, before we have gone so far as to forget it, we may return to consider what it is we are deliberating.

p.85 Thus we cannot escape the fact that the world we know is constructed in order (and thus in such a way as to be able) to see itself.
 This is indeed amazing.
 Not so much in view of what it sees... but in respect of the fact that it can see at all.
 But in order to do so, evidently it must first cut itself up into at least one state that sees, and at least one other state that is seen.

p.88 Discoveries of any great moment in mathematics and other disciplines, once they are discovered, are seen to be extremely simple and obvious, and make everybody, including their discoverer, appear foolish for not having discovered them before.

p.89 To arrive at the simplest truth, as Newton knew and practised, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behavior of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know.

p.179 I have always maintained that if a theorem can be proved, there will be a proof that a child of six can follow and understand. My simplest proof of the 4CT [JLJ - four-color map theorem] is a case in point.