#logic gate

Beyond Descartes - Part 3
Logic Gates and Switches: Introduction

(continued from here)

It has been often noted throughout this work that mandalic geometry does not view points as fundamental geometrical elements in the manner Descartes and Euclid do. It considers them to be evanescent communions of two or more dimensions.  This  alternative perspective  conveys further the insight  that such conjoint formative interface locations both separate and connect. They are both boundaries and tipping points between all the participating dimensions,  what I have whimsically referred to  previously as dimension interchange lanes.  This is a far cry from the way Descartes regards and handles hispoints.

Descartes’points are locations, pure and simple, defining occupants of a uniform geometrical space. They don’t really doorattempt anything; they simply are.  They do not act,  but are acted upon by the equations of Cartesian geometry.  The  points themselves,  for all the reality Descartes attempts to imbue them with, turn out,  when the curtain is drawn,  to be no more capable of mustering an original thought  than is  the Scarecrow in  L. Frank Baum’s  The Wonderful Wizard of Oz.  Being of feeble mind themselves,  they just sit there awaiting brainy algebra to act upon them. In and of themselves,  beyond determining location,  they are essentially impotent.^[1]

A useful way to apprehendpoint locations of mandalic coordinates is to  interpret them  as  logic gates  which can handle  transition operations in a variety of different ways  depending upon the  dimension amplitudes verged on.  Passage through such locations is potentially bidirectional,  in theory if not always in actuality at a given moment, so they accommodate both  convergent and divergent flows  throughout varied amplitude levels of the mandalic structure.  To wit,  they can promote both  differentiationandpotentialization  phases of an evolving process.  Because these points arise through confluence of dimensions,  they bear within their transitory being information imparted by the participating dimensions.  Contrary to Descartes’ simpleminded points, these points have the capacity to encode an intelligence derived from their parent dimensions.^[2]

In electrical engineering,aswitch is an electrical component that can control an electrical circuit  by initiating or interrupting the current  or by diverting it from one conductor to another.  The most usual configuration consists of  a manually operated electromechanical device  having  one or more sets of electrical contacts.  These contacts are connected to external circuits. Each set of contacts can be in either of two states: either “closed” meaning the contacts are touching and electricity can flow between them, or “open”, meaning the contacts are separated in which case the switch is nonconducting. The mechanism that brings about the transition between these two states - openorclosed - can be either a “toggle”  (flip switch for continuous “on” or “off”)  or  “momentary”  (depress and hold for “on” or “off”) type.

Understand that logic gates don’t apply only to electronic devices nor are they controlled only by such devices. The concepts and methodologies involved go far beyond simple electronics.

• Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic. Wikipedia

For our purposes here and now, we need only mention that scalar numbers and vectors can be implemented in the context of Boolean logic as well.  Indeed, the incessant complex cotillion performed by subatomic particles can likely be subjected to such an analysis or one similar.^[3] And, of course, also digital circuits and computer architecture.

This has been just an introductory teaser to the topic of logic gates in mandalic geometry.  I’m getting my feet wet now myself. This is all still quite new to me so we’ve barely scratched the surface here.  An upcoming post will survey the logic gates and switches identifiable among groups of transliteration Cartesian coordinates and mandalic coordinates. This may take a while to materialize, but I think will be worth the wait.  And in case I forget to bring up the subject of how fractals fit into all this sometime in the next month or two, remind me please that I intended to.

(continuedhere)

Notes

[1] This could be a mathematician’s beautiful dream, but a physicist’s abhorrent nightmare.

[2] Although this statement pertains especially to composite dimension points, it is true, to a degree, of ordinary three-dimensional points as well when viewed in a manner similar to that using trigram tranliterations of Cartesian triads.  This means then that Cartesian coordinates could do the same and to the same degree, if  they were handled in the same manner as trigram coordinates are. The point is they are not and presumably never were.

[3] With that last remark I likely committed quantum mechanical heresy. If I in fact did, so be it. If it doesn’t quite hit the intended mark we can refer to it as steampunk mechanics.

Image (lower): Boolean lattice of subsets. KSmrq. Licensed under CC BY-SA 3.0viaCommons.

© 2015 Martin Hauser

Please note:  The content and/or format of this post may not be in finalized form. Reblog as a TEXT post will contain this caveat alerting readers to refer to the current version in the source blog. A LINK post will itself do the same. :)

Scroll to bottom for links to Previous / Next pages (if existent).  This blog builds on what came before so the best way to follow it is chronologically. Tumblr doesn’t make that easy to do. Since the most recent page is reckoned as Page 1 the number of the actual Page 1 continually changes as new posts are added.  To determine the number currently needed to locate Page 1 go to the most recent post which is here. The current total number of pages in the blog will be found at the bottom. The true Page 1 can be reached by changing the web address mandalicgeometry.tumblr.com to mandalicgeometry.tumblr.com/page/x, exchanging my current page number for x and entering. To find a different true page(p) subtract p from x + 1 to get the number(n) to use. Place n in the URL instead of x (mandalicgeometry.tumblr.com/page/n) where
n = x + 1 - p. :)

-Page 279-

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

Please note:  The content and/or format of this post may not be in finalized form. Reblog as a TEXT post will contain this caveat alerting readers to refer to the current version in the source blog. A LINK post will itself do the same. :)

Scroll to bottom for links to Previous / Next pages (if existent).  This blog builds on what came before so the best way to follow it is chronologically. Tumblr doesn’t make that easy to do. Since the most recent page is reckoned as Page 1 the number of the actual Page 1 continually changes as new posts are added.  To determine the number currently needed to locate Page 1 go to the most recent post which is here. The current total number of pages in the blog will be found at the bottom. The true Page 1 can be reached by changing the web address mandalicgeometry.tumblr.com to mandalicgeometry.tumblr.com/page/x, exchanging my current page number for x and entering.  To find a different true page(p) subtract p from x+1 to get the number(n) to use. Place n in the URL instead of x (mandalicgeometry.tumblr.com/page/n) where
n = x + 1 - p. :)

-Page 304-