#boolean operators
Neo-Boolean - II: Logic Gates
Thinking Inside the Lines
(continued from here)
We have already looked briefly at three of the more important Boolean operators or logic gates: AND, OR,andXOR.NOT just toggles any two Boolean truth values (true/false; on/off; yes/no). Here we introduce two new logic gates which do not occur in Boolean algebra. Both play an important role in mandalic geometry though.
We’ll refer to the first of these new operators or logic gates as INV standing for inversionorinvert. This is similar to Boole’s NOT except that it produces toggling betweeen yang/+ and yin/- instead of 1 and 0. Because it is based on binary arithmetic, Boole’s NOT has been thought of as referring to inversion also (as in ONorOFF). Although both ANDandINV act as toggling logic gates they have very different results in the greater scheme of things, since nature has created a prepotent disparity between a -/+ toggle and a 0/1 toggle in basic parameters of geometry, spacetime, and being itself. This makes Boole’s AND just a statement of logical opposition, notinversion.
Recognition of this important difference is built into mandalic geometry structurally and functionally, as it is also into Cartesian coordinate dynamics and the logic of the I Ching, but lacking in Boole’s symbolic logic. This is necessarily so, as there is no true negative domain in Boolean algebra. The OFF state of electronics and computers, though it may sometimes be thought of in terms of a negative state, is in fact not. It relates to the Western zero (0), not the minus one of the number line. Where Boolean algebra speaks of NOT 1 it refers specifically to zero and only to zero. When mandalic geometry asserts INV 1 it refers specifically to -1 and only to -1 . The inversion of yang then is yin and the inversion of yinisyang.[1] In the I Ching, Taoist thought, and mandalic geometry the two are not opposites but complements and, as such, interdependent.
The second added logic gate that will be introduced now is the REV operator standing for reversionorrevert. This operator produces no change in what it acts upon. It is the multiplicative identity element (also called the neutral elementorunit element), as INV is the inverse element. In ordinary algebra the inverse element is -1, while the identity element is 1. In mandalic geometry and the I Ching the counterparts are yinandyang, respectively. If Boolean algebra lacks a dedicated identity operator, it nonetheless has its Laws of Identity which accomplish much the same in a different way:
- A = A
- NOT A = NOT A
Again, Boolean algebra has no true correlate to the INV operator. There can be no sign inversion formulation as it lacks negatives entirely. Although Boolean algebra may have served analog and digital electronics and digital computers quite well for decades now, it is incapable of doing the same for any quantum logic applications in the future, if only because it lacks a negative domain.[2] It offers up bits readily but qubits only with extreme difficulty and those it does are like tears shed by crocodiles while feeding.
(to be continued)
Image: Boolean Search Operators. [Source]
Notes
[1] Leibniz’s binary number system, on which Boole based his logic, escapes this criticism, as Leibniz uses 0 and 1 simply as notational symbols in a modular arithmetic and not as contrasting functional elements in an algebraic context of either the Boolean or ordinary kind.
In the field of computers and electronics, Boolean refers to a data type that has two possible values representing true and false. It is generally used in context to a deductive logical system known as Boolean Algebra. Binary in mathematics and computers, refers to a base 2 numerical notation. It consists of two values 0 and 1. The digits are combined using a place value structure to generate equivalent numerical values. Thus, both are based on the same underlying concept but used in context to different systems. [Source]
[2] Moreover, I expect physics will soon enough discover that what it now calls antimatter is in some sense and to some degree a necessary constituent of ordinary matter. I can already hear the loudly objecting voices declaring matter and antimatter in contact necessarily annihilate one another, but that need not invalidate the thesis just proposed. My supposition revolves around the meaning of “contact” at Planck scale and the light speed velocity at which subatomic particles are born, interact and decay only to be revived again in an eternal dance of creation and re-creation. Material particles exist in some kind of structural and functional homeostasis, not all that unlike the anabolic and catabolic mechanisms that by means of negative feedback maintain all entities of the biological persuasion in the steady state we understand as life. Physics has yet to get a full grip on this aspect of reality, though moving ever closer with introduction of quarks and gluons to its menagerie of performing particles.
© 2016 Martin Hauser
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