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.
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.
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.
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 "2nd 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 1st Derivative equal to itself, or proportional to itself if other constants were involved. But fir SHM, it is the 2nd 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 = 90o]
To take the 1st Derivative we use the above mentioned Chain Rule for
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 2nd 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 ωo 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 ωo. 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 2nd
Derivative, for Friction which depends
on Velocity, we add a 1st Derivative with a frictional Damping Coefficient b.
– k x – b d x/ d t = m d2 x/ d t2
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for very succinct summary of the teaching & practice, see: www.ajatavada.com/