Essay outside of the NMT (No-Me Teaching) series 27

Some   Ramana Maharshi quotes:

Even the knowledge sense-perceived of the world without has for its ground the Self above. To search for knowledge somewhere else apart from That is but to grasp the shadow, not the substance.

Whatever notion may arise, never to let it live or grow, but to turn it that very instant, firm &stern, back to its source &merge it there, this is robust, intense detachment.

The knowledge that ignores the Self, the knower, &  holds as true the field perceived, is but illusive folly. No matter how much one has learned, true knowledge is the merging of all indicative knowledge in awareness of the Self.

The one true light there is, is pure Awareness. Other kinds of knowledge clinging to it &  claiming to be real are ego-born conceptual clouds. To trust them is sheer folly.

All other kinds of knowledge are base, trivial. The only true &  perfect knowledge is the stillness of pure awareness. The many differences perceived in the Self whose nature is awareness are wrong attributions & not real at all.

What sort of knowledge is this wretched bodily–mental knowledge of objects ? Would those who long for pure awareness hanker after this ?  To know pure awareness is true wisdom. All other knowledge is mere folly.

What if one knows the subtle secret of manifold inscrutable mysteries ?  Until one knows the awareness which reveals all other knowledge, does one know the Truth ?

Based on the Teachings of a great Sage:

Consciousness is the kernel of every experience.  There is no experience, whether in the form of a Thought, Feeling, or Perception, or without form as in Deep Dreamless Sleep or between 2 thoughts, that is not of the nature of Consciousness.

It is from the Mind level that we talk of thoughts or their absence.  We have seen that Consciousness is always present; it is beyond Name & Form & thus from its own level, Consciousness alone exists.

Any observation itself requires, a fixed "Seer" to observe the changing object or "Seen", & also a "Memory" in which to record the observation.  The flow of events recorded as "Memory" also requires that "I" be a fixed or changeless reference state.

From the experience of Memory as a reference, Non-Dual betrays the underlying position of Consciousness more directly perhaps than from any other common experience in form. 

We remember our previous thoughts & feelings, we remember as well the thinker who had them.  f we remember our Bodies & Minds along with the things we observed & the thoughts we had, our Bodies & Minds must also have been witnessed by us in the same way.

The Mind becomes one with whatever it has as its object.  If the Truth or Consciousness becomes the object of thought, thought merges into Consciousness.  Consciousness can never be the object of our thought, since it is in or by Consciousness that our Minds functions.  We can never look at Consciousness. It can be understood by itself alone.  Every experience is a moment of pure Consciousness.

   

Calculus for Yogis, part 13:

When casting the image of a Point, the point of intersection of the Radius line & the Circumference of the unit Circle, the image of that Point revolving CCW counter-clock-wise from the right-most place that would be East on a compass, or Angle 0 on the positive X-axis, we mentioned that the shadows, sideways or vertically, would exhibit Simple Harmonic Motion, SHM.  We want to use the partial introduction of Cosines & Sines, Derivatives & Integrals, to look at this SHM, Simple Harmonic Motion.

Newton's 2^nd Law for Force. F, can be put in terms of Acceleration, a which the Time Derivative of Velocity, v:

F  =  m  a  =  m  d v/ d t  

whereas Velocity, v is itself the Time Derivative of Distance, Displacement:

v  =  d v/ d t  =  d x/ d t

so that putting Force. F, in terms of Displacement, which is the "2^nd order" Time Derivative of Displacement [Derivative of the Derivative]:

F  =  m  a  =  m  d v/ d t   =   =  m  d² x/ d t²

The Spring with stiffness or Constant k, characteristically has a (negative) restoring Force. F given by:

– k x   =   F  =  m  a  =  m  d² x/ d t²

– k / m  x  =   d² x/ d t²

The Exponential Function had a 1^st Derivative equal to itself, or proportional to itself if other constants were involved. But fir SHM, it is the 2^nd Derivative of x that is proportional to  x .  This SHM characteristic is fulfilled then, not by the Exponential, but by a trigonometric function, Sine or Cosine.  So making this substitution for F we get:

x (t)   =  A cos (ω t  +  φ)  ,  for  A – amplitude, ω  –  angular frequency,  φ  – phase shift

[This could be put in terms of Sine, with appropriate  phase shift φ  since  Cos  &  Sin  have a phase shift of  π /2  =  90^o]

To take the 1^st Derivative we use the above mentioned Chain Rule for Cos of a function. that function being,

d y/ d t   =   (d y/ d x) ( d x/ d t)   = [ – A sin (ω t  +  φ)]  [d x (ω t + φ) / d t ]

since:   d cos / d t  =  – sin   &   for constant ω  &  φ,   d x (ω t + φ) / d t   =   ω

d cos (ω t  +  φ) / d t   =  – A sin (ω t  +  φ)  d (ω t  +  φ) / d t   =  – A ω sin (ω t  +  φ)

Taking the 2^nd Derivative, with:   d sin / d t  =  cos

d² x/ d t²   =   d² [A cos (ω t + φ)] / d t²   =   d [– A ω sin (ω t + φ)] / d t

                  =  – A ω² cos (ω t  +  φ)   =  – ω²  x (t)

[Incidentally, comparing to the above:   – k / m  x  =  – ω² x    &   k  =  m  ω² ,  which describes ω_o the "natural resonance" frequency of whatever be the "harmonic oscillator", Driven by Force (a shove or tug of a spring instead of a stretch & just letting go) another transient frequency would settle back to ω_o. The forgoing describes a frictionless system. With Friction, the system slows down & stops.]

For short swings of a weight on a nearly "massless" String, a Pendulum, the same SHM equations apply with the substitution for the above (k / m) being (g / l) for g the acceleration of Earth-surface Gravity & l the length of the String.  For a twisting Torsional Pendulum, the parallel is even closer with Spring Constant k becoming the Torsion Constant; & mass m becoming a Moment of Inertia I.  The exact same terms extend the description to a Pendulum whose String has mass, or object suspended from a point, floating, or otherwise "rocking" object. Hence the some of the Physics of "vibes".

If we go back to:  – k / m  x  =   d² x/ d t²      describing SHM Acceleration, the 2^nd

                                                                        Derivative, for Friction which depends

                   on Velocity, we add a 1^st Derivative with a frictional Damping Coefficient b.

– k x   – b  d x/ d t   =  m  d² x/ d t²

The transient frequency would settle back to ω_o. The forgoing describes a frictionless system. With Friction, the system slows down & stops.

[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:  

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"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

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/