Essay outside of the NMT (No-Me Teaching) series 22

                                                        Logistic Curve with Exponential
Some   Ramana Maharshi quotes:

Of 3 classes of spiritual aspirants, the most advanced realize the Self as soon as they are told about its Real Nature.

Those in the 2^nd class need to reflect on it for some time before Self-awareness becomes firmly established.

Those in the 3^rd category usually need many years of intensive spiritual practice to achieve the goal of Self-realization.

As a metaphor, Combustion describes the 3 levels: Gunpowder ignites with a single spark, Charcoal needs application of heat for a short time, & wet Coal needs to dry out & heat up over a long period of time before it will begin to burn.

For the benefit of those in the top 2 categories it is taught that the Self alone exists & that it can be directly & consciously experienced merely by ceasing to pay attention to the wrong ideas we have about ourselves, These wrong ideas are collectively called the "not-Self‘ since they are an imaginary accretion of wrong notions & misperceptions which effectively veil the true experience of the real Self.

The principal misperception is the idea that the Self is limited to the Body & the Mind. As soon as one ceases to imagine that one is an individual person, inhabiting a particular Body, the of wrong ideas collapse & are replaced by a conscious & permanent awareness of the real Self.

There is no question of effort or practice All that is required is an understanding that the Self is not a goal to be attained, it is merely the awareness that prevails when all the limiting ideas about the not-Self have been discarded.

Perfect Bliss is Brahman.

Perfect Peace is of the Self.

That alone exists & is Consciousness.

Happiness is only the Nature of Self.

Self is not other than perfect Happiness.

Happiness alone exists.

Knowing that & abiding in the state of Self, enjoy Bliss eternally.

The obstacles which hinder Realization the Self are habits of Mind [vasanas].

Overcome the mental habits [vasanas] by realizing the Self.

It is the Ego which raises such difficulties, creating obstacles & then suffering from perplexity of apparent paradoxes.

Find out who makes the Inquiries & Self will be found.

Quantum Reality 4 (beyond the Time issue):

Quantum Reality veers from Classical Physics, apart from other ways, by directly confronting & questioning Materialism (or the new & improved term Physicalism) head-on. As previously mentioned in the Quantum Reality 2 segment, doubting the strongly objective or mind-independent reality, the original (& still officially “standard”) Quantum Mechanics barely fends off the barrage of neo-Materialist counter-attacks & alternative Realism “fixes” to the “troublesome” parts of original Quantum Mechanics. But in that original (Copenhagen II Convention of Consciousness-created Reality) Quantum Mechanics is still only weakly objective at “best” or full-blown Quantum Idealism at “worst” (from the Materialist viewpoint).

As also previously mentioned in the Quantum Reality 2 segment, the statements of Quantum Mechanics remain consistent between Minds discussing its phenomena, but it still stays contained within speculation within the Mind, though predictive of observations, “better” than is Classical Physics in the small-scale & other applicable domains. Realism falls as contradicted by Quantum experiments (such as Double-Slit, Delayed-Choice, Quantum Erasure, Bell’s-Theorem, etc.). Way “back in the day”, Immanuel Kant generally raised good relevant questions & later “copped-out” with some lame concessional answers in his so-called Transcendental Idealism (that happened to be less transcendental than other versions of Idealism), foreshadowing the Madison Avenue Ad-men Newspeak maxim: whatever be the inconvenient truth, deny it with its opposite.

Anyway, Kant asked whether Realism was at all meaningful? He then further asked whether & Classical Physics could be a steadily converging approximation & ultimately “absolutely true” description of the purported “Reality”. The 1^st part holds up pretty good (“approximation” in an ever evolving improvement process) but fails outrageously & totally in the 2^nd part – “absolutely true Reality” (even assuming for the sake of discussion that there “is” such an Objective Reality). Neo-Realism even believes that all its own mental inventions – nuclear particles, electrons, quarks, strings, force fields, etc. are “actually” real entities, beyond convenient mechanisms in their approximate model.

To re-iterate, mind-independent Reality is that which would exist even if conscious beings did not exist. Imagine a mostly “dead” Universe with nothing both alive & conscious to know about it. Why even talk about it? And talk about it to whom, & by whom? Such is an empty speculation in an empty Void. It’s the very similar inverse of the old Philosophical Conundrum: “what if nothing at all existed?” or equivalently, “why does anything exist at all?” Who would we be talking to then & who would we be. That crucial “What am I?” question (Shankara’s version) is not an idle question, its fundamental.

Classical Physics or any other Realist Science has not the slightest plausible explanation of the obvious fact of Consciousness. Overlooking the critical failure, brushing it under some epi-phenomenon rug is sheer madness. Realist Science may furnish Technology income by dint of its approximate fidelity, but that is no–proof of actual Reality. Success is always temporary & can never be proof of the Model that supports somewhat successful strategies. Any Map may get you to your momentary destination, but is never the Territory in itself, nor does your latest “arrival” prove that impossible equation. As a lesser issue, the partial success of a Map does not rule out other & possibly better Maps, even at the analogical level of Maps or Models. Even our Sense Perceptions & mental Conceptions are only Maps & Models, analogies at best (& pure Imagination at “worst”).

Immanuel, later Positivists, the Marburg School neo-Kantians, etc. have only remedied the gap to the weak extent that, while unprovable, Realism need not be “wrong” just because you can never prove it (like the Multi-Verse, for instance, but that is weak comfort). A more sober appraisal must stop at the description of Realist Science as mathematically synthesized relations between observed phenomena.

We have Galileo & Newton to thank for the arbitrary models & inventions that have however resulted in the remarkable empirical success of Science, but that luster has blinded us to the fact that (like the blind men describing an elephant) we are still groping within our own Imagination. On the other hand, Eugene Wigner’s question “as to why Mathematical Physics is as unreasonably successful as it is” provocatively supports the possibility the our so-called Universe or RWOT real-world-out-there is itself a mental creation from the get-go. In other words, mental constructions of Mathematics may fit the Universe so well because the “Universe” is itself a mental construction.

While we exposed the confusing “mess” of alternate theories of Time in a previous segments, the other shoe that Kant questioned, that of Space can be sufficiently dismissed with the following over-short summary from Special Relativity: “absolute void space is nothing & (as declared by the Eleatic Philosophers, ‘nothing is nothing’) Nothing is that which does NOT exist. So-called Space is the term we use to collect all the relationships & distances between postulated Objects, & not an empty “thing” in itself (not even a “container” like Cartesian Coordinate Space). But the very definition of a Material Object (Descartes’ res extensa) require extension in 3-D Space. Space is certainly 4-D (or of more String Theory dimensions) if any “dimensions” really apply at all. An inconceivable “object” that has no dimensions surely resembles a “thought” (ala Sir Arrthur Eddington’s take on Quantum Mechanics) more than anything Material.

One last issue regarding Space concludes this segment, that arising in the 19^th century from the contrasting empirical – theoretical poles of Helmholtz & Riemann, respectively, considering the continuity of an Object when translated or rotated in Space. Does such movement “change” the Object or is the Object, not only mind-independent, but also Space–independent, that is, the same no matter where & how e situate the Object. Such question entail, among other things, the curvature of Space (the General Relativity issue) & the constancy of that curvature which is of course dismissed by Einstein’s theory of Gravity.

The assumption “that Objects exist independently of place” is valid if & only if the properties of Objects remain invariant when moved. That is, if an Object changes place, that is a movement. And if the Object continues to have the same properties in any different place, then its properties are invariant under spatial transformation. Riemann noted that, without this assumption, the units of comparison that are the basis for Space measurements (light rays, rulers, …), the bases of distance measurement, no longer have the invariant properties on which one can base valid measurements.

The idealized alternative, Riemann’s “Axiom of Free Mobility”, finds counter-part in the Helmholtz idea of “rigid motions” that inspired Sophus Lie to formulate Transformation Symmetry groups in terms of Group Theory. Both Helmholtz & Riemann were doubtful regarding that idealized alternative which Einstein’s General Relativity threw out the window, thus casting doubt about our assumptions about both Space & material Objects. 

Calculus for Yogis, part 6
Now just as we call the Integral the inverse of Derivative, will then Derivative is the inverse of Integral.  This reciprocal kind of relationship also applies to functions themselves.  So the inverse of Multiplication is Division as we saw in going from Polymer Derivative to Integral; & the inverse of Addition is Subtraction.
Well the inverse of something more complicated like the Exponential function acquired the name Logarithm.  This was part of its role in making calculation feasible before they were calculating machines.  The qualities of Exponents are such that Multiplication of Terms raised to a Power involves Addition of the Exponents.  And so the Logarithm creates a relationship between Multiplication & Addition. So devices like a slide rule could use Addition distances to effect Multiplication & tables of Logarithms allowed Addition to serve the purpose of Multiplication,
Logarithms, the inverse of the Exponential function happens to be called the Natural Logarithm designated "ln x" whereas "Log x"  with no special base mentioned is assumed to be aligned with the Decimal number system, meaning the inverse of 10^x , that is the Log to the base 10, can often just be called "Log" as the default.
But with computers using Even numbers of what are called "buses" or wires to build on the duality of 0 or 1, of a voltage On /  voltage Off, the Binary number system introduced the usefulness of raising 2 to various powers, or taking the Logarithm to the base 2.

Other Powers of 2 are also useful in computer science, specifically 2 to the 4^th which is 16.  This "Hexadecimal" alternative to the Decimal number system uses 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F instead of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.

In any case, the Logarithm serves another good purpose, besides being the Inverse of Exponential.  It gets us around the difficulty of dividing by 0 when we take the Integral of 1/ x .  There it looks like raising the  –1 power to 1 higher would take us to Zero power, thereby "losing" the Variable since x ⁰  =  1.  Mysteriously, that Integral turns out to be "ln x";  &  d x/ x  =  d ln x.  On occasion we will glance at "Mysterious" coincidences presented to us by Mathematics.  The relationship between   ln x   &  1/x   is only a minor example, only slightly mysterious.  Uncountable others show up in the annals of Mathematics a few small examples here follows:

    9²  =  81                   8 + 1  =  9

  45²  =  2025           20 + 25  =  45

  55²  =  3025           30 + 25  =  55

  99²  =  9807           98 + 01  =  99

297²  =  88209        88 + 209  =  297

703²  =  494209    494 + 209  =  703

999²  =  998001    998 + 001  =  999

1/ 27  =  .0370370370 …      &    1/ 37  =  .0270270270 …

There are no tricks explaining these coincidences, even multiple coincidences in one expression, like there are tricks in some elementary grade school math puzzles.  These truly amazing coincidences, when by accident noticed by mathematicians & scientists, are sometimes referred to in ways like "God winking at you."

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates have been available on:

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[But from now on, they will be different & still usually daily.]

"There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth."  –  the "no creation" school of Gaudapada, Shankara, Ramana, Nome – Ajata Vada