Archive for July, 2010

Rational Mysticism

July 21, 2010

Rational Mysticism

By John Horgan (2003)

I read this book a few years back and had prepared a set of quotes from this book. Having read and reflected on these quotes several times, I thought of sharing the same with my friends through this blog.

1. If you say you are advancing towards God or the Absolute, and (you) are not growing in love and charity towards your fellow persons, you are just deluding yourself. – by Huston Smith, Ph.D., University of Chicago.

2. Religious institutions have caused a great deal of harm, particularly when they insist that “believers are superior and non-believers are inferior or evil”. That is where religion becomes a damaging force. – by Michael Persinger, Psychologists, Laurentian University, Sudbury, Canada (1999)

3. God is unnecessary for my living or loving or being comfortable. I am amazed by the marvels of nature surrounding me, but I feel no need to attribute them to a divine creator. We can decide that this is God-inspired. Or, we can decide that this is some kind of happening that is ‘beyond belief’. – by James Austin, Neurologist, University of Colorado, Health Sciences Centre. Denver (1998).

4. Why should I be afraid of dying? I was not afraid of being born – by James Austin (1998)

5. You have this divine source that has the propensity to create and project itself out. Then when you end up here as a separate unit, there is trouble, suffering and so on. All these propel us back towards the source. These two opposite forces are called ‘hylotropic and ‘holotropic’, (i.e.) centrifugal and centripetal. – by Stanislov Grof, Psychiatrist, John Hopkins University.

(LVN’s Comment: It is like a man-made fountain, where the same water circulates from the tank to the fountain and back to the tank.)

6. Many psychological problems are ‘spiritual emergencies’ that stem from a deep rooted yearning for spiritual meaning and consolation. Properly treated, these spiritual crises offer a tremendous opportunity for growth. – by Mrs Christina Grof, Patient, student and wife of Stanislov Grof (referred above).

(LVN’s comment: Can we call the Tamil Poet, Subramania Bharati, as a classic example)

7. Ancient Hindu texts, the Upanishads, claim that the only reality is the formless, infinite and eternal void, from which all things emerge and to which they return. All else, including your mortal self is unreal. We cannot die because we do not exist in the first place. The Upanishads promise us that when we really know this fundamental truth, we will achieve Nirvana, Bliss or Heaven. To ordinary men like me, seeing the world and myself as unreal, itself, felt more like hell. Those who are enlightened, blissfully enlightened, must somehow sidestep or push past this dreadful state. BUT HOW? – by John Horgan, Author of Rational Mysticism.

8. The ‘mysterium tremendum’ (the inner sanctum of reality) is not a thing we can possibly identify with, let alone become. It is not a deity, nor a force, principle, spirit nor a ground of being – it is not a thing at all. It is ‘wholly other’, ‘nothingness’ and the opposite of ‘everything that is and can be’. It is absence not presence. Our encounter with ‘mysterium tremendum’ can strike us chill and numb and fill us with an utmost grisly horror and shuddering. (the state that could be called ‘mysterium tremens’ ) Religions do not reveal the ‘mysterium tremendum’ so much, as they shield us from direct confrontation with it. – By Rudolf Otto, German theologian.

9 You may call it infinite or call it God, Allah, Brahman, Void or ’mysterium tremendum’. It is the nothingness from which we came and to which we must return. You may feel compelled to ‘guess the riddle’, to explain how a ‘finite human something’ emerged from ‘infinite inhuman nothing’. You may respond to such a vision with joy, madness, terror, love, gratitude, hilarity – or all the above at once. You may delight in the world’s astonishing beauty or despair at its fragility and insignificance. – by John Horgan, Author of Rational Mysticism.

10. If a miracle is defined as an infinitely improbable phenomenon, then our existence is a miracle, which no theory natural or supernatural will explain. Science can never answer the ultimate question: How did something came from nothing? Neither theologies can. Honest physicist will admit that they have no idea why there is something rather than nothing? – by John Horgan.

11. You know there is no reason for you to exist. The odds seem over-whelming, our miniscule human hubbub will be swallowed up by the emptiness whence we came. But the flip side of this mystical terror is joy. We should not be here. Yet we are here. How lucky we can get? – by John Horgan.

12. In my kitchen, we put garbage in bag that come in boxes of twenty. After I yank the last bag from the box, the box becomes garbage and goes inside the last garbage bag. There is a paradox lurking within this ritual.- by John Horgan.

13. FREE WILL – Our belief in free will has a social value. It provides us with metaphysical justification for ethics and morality. It forces us to take responsibility for ourselves rather than entrusting our fate to Jehova, Allah or Tao. We must accept that things will get better and better, only as a result of our efforts, not because we are fulfilling some pre-ordained supernatural plan. If ‘free will’ is an illusion, it is the one I need – that I need, even more than God. I have no choice but to choose free will. – by John Horgan, Author of Rational Mysticism

Please read and reflect.

“Reactive Power – A Strange Concept”

July 10, 2010

L V Nagarajan 

It was very interesting to read a paper by R.Fetea and A. Petroianu (of University of Cape Town), on the above subject. (refer: http://www.el.angstrom.uu.se/kurser/water05/Reactive_Power.pdf).

Reactive Power as a concept is really strange, but is very necessary for power system management. So we have to live with it. But we need some kind of reconciliation with many valid points raised by the authors of the above paper. Let me try the same in the following paragraphs. 

Let us start from their first two equations:

v = Vmax Cos(ωt)

 i = Imax Cos(ωt – θ)

Actual Instantaneous power = vi = Vmax Cos(ωt) Imax Cos(ωt – θ)

Let us now take the expression for current:

 I = Imax Cos(ωt – θ)

    = {Imax cos θ cos ωt + Imax sin θ sin ωt}

    = {Imax cos θ cos ωt – Imax sin θ cos (ωt – π/2)}  

We may now recognize the two terms in the above expression as:  in-phase and 90-deg-lagging components of current, I.

We say,

Active component:      Ia = Imax cos θ cos ωt

Reactive component: Ir = Imax sin θ cos (ωt – π/2)

Let,

Root Mean Square value of v, V= (Vmax/√2)

Root Mean Square value of  i,  I = (Imax /√2)

Then,

(instantaneous) Active power, p = v Ia

 i.e.,    p =  Vmax cos(ωt) Imax cos θ cos ωt

                 = (Vmax/√2) (Imax/√2) cos θ (2cos2 ωt)

                 = VI cos θ (2cos2 ωt)

                 = P (1 + cos 2ωt),        where P = VI cos θ

This is a positive sinusoidal function with an average value of P, the active power, transferred through the circuit.

(instantaneous) Reactive Power, q = v Ir

i.e.,  q = Vmax cos(ωt) Imax sin θ sin ωt

              = (Vmax/√2) (Imax/√2) sin θ (2 sin ωt cos ωt)

              = VI sin θ (sin 2ωt)                                        

              = Q (sin 2ωt), where Q = VI sin θ

This is a sinusoidal function with an average value of zero. But still we say a reactive power of value Q is transferred through the circuit!! Why at all?

Assume a power source and a load connected as below

If the load R is purely resistive,

            V —————————- R

there will be only active power flow through the circuit, as voltage and current will be in phase.

Suppose we add an inductive load XL. Now the current will lag the voltage by an angle, and hence there will be some reactive power flow also.  

            V —————————- R+ XL

Though average of this reactive power will be zero, the source will still have to ‘supply’ this reactive power flow also.

Suppose we now add a capacitative load Xc, to exactly compensate this inductance.

            V —————————- R + XL +  Xc

Then the source need not ‘supply’ any reactive power, as the same is ‘compensated’ by the capacitance. (i.e, the lag by inductance is nullified by the lead created by capacitance). However there will be reactive power flow between XL and Xc. Sometimes it is said, Xc ‘produces’ lagging reactive power to ‘supply’ XL

It is exactly in this way, we handle the reactive power Q, even though its average is always zero.

Actual instantaneous Power

                          = Active power p + Reactive power q

                          = P (1 + cos 2ωt) + Q (sin 2ωt)

                          = P + P (cos 2ωt) + Q (sin 2ωt)

The average values of both second and third terms above are zeros over a voltage cycle. Hence P become actual average power transmitted over the circuit.

As phase angle θ varies from 0 to 90, the value of ‘active’ power P reduces from maximum value of VI to zero and ‘reactive power’, Q increases from zero to VI. However all through, the magnitudes of AC voltage and AC current remain the same and hence the value of VI. For this reason VI is known as apparent power, S.

 S2 = VI2(cos2 θ + sin2 θ)

       = (VI cosθ) 2 +  (VI sinθ) 2  = P2 +  Q2  

S = √ (P^2 + Q^2) = VI, is an important parameter known as VA which is widely used for specifying power ratings of electrical devices such as generators, transformers and even major loads. Now, in phase component of S, S cosθ is same as active power P. The cross phase component of S, S sinθ is called reactive power, Q, which does not appear very strange now.

Now we may use complex algebra to revisit the same concepts as above. 

Phasor Representation

By using Euler’s Formula, any sinusoidal function can be expressed as
V = Vmax cos(ωt- θ) = Real Part of [Vmax ej(ωt- θ)]

                                           = Re[Vmax e-jθ  ej(ωt) ]

[Vmax e-jθ] is known as V’, the phasor representation of V(ωt), represented as V∟-θ

Now, V = Re [V’ ej(ωt) ]

The time-dependency has been effectively factored out, in the phasor representation as it deals with only the static quantities of amplitude and phase angle.

By phasor representation as above, we may write,

V’ = V∟0 and I’ = I∟-θ

Apparent Power S’= V.I* = V.{I e-jθ }* = VI∟θ

Alternately, if V’ = V∟-θ1 and I’=∟-θ2

Apparent Power S’= V.I* = V e-jθ1.{I e-jθ2 }*

                                      = VI∟(θ2- θ1) = VI∟θ,

where θ = (θ2- θ1), the actual phase difference.

 (i.e)    S’ = VI e-jθ   = VI (cos θ + j sin θ)

                  = VI cos θ + j VI sin θ

                   = P + j Q

As we see the real part of S’ is ‘Active Power’, VI cos θ; and imaginary part of S’ is Reactive Power, VI sin θ. In this representation the Reactive Power does not seem as strange as earlier. 

Let us again consider only a resistive load, R. As in this case current will be in phase with voltage, θ = 0. Hence,

 S’ = V’. I’* = V∟0 . I∟0 = VI cos 0 + j VI sin 0

(i.e)      S∟0 = P + j0, where P = VI

Impedance Z’ = V∟0 / I∟0  = V/I cos 0 + j V/I sin 0

                             = R + j0

Now consider only an inductive load of XL   In this case the current will lag voltage by an angle of 90 degrees, i.e., π/2. Now,

S’ = V’ I’* = V∟0. I∟π/2  = VI cos π/2 + j VI sin π/2

(i.e)      S∟π/2 = 0 + jQ, where Q = VI

Impedance Z’ = V∟0 /  I∟-π/2  = V/I cos π/2 + j V/I sin π/2

                              = 0 + j XL

Now consider an combined load of R and XL . In this case there will be a phase difference of, say, θ, lagging. Hence,

S’ = V’ I’* = V∟0. {I∟- θ}*  = VI cos θ + j VI sin θ

(i.e)       S∟θ = P + j Q, where P = VI cos θ and Q = VI sin θ

Impedance = Z’ = V∟0 /  I∟- θ  = V/I cos θ + j V/I sin θ

                                 = R + j XL

               We recognize R = V/I cos θ and XL = V/I sin θ    

When a capacitor is added to the load, we have

                Impedance Z’ = R + j XL – j Xc

Here also we observe the mutually nullifying effect of XL and Xc. Hence we are able to represent combined resistive and ‘reactive’ loads conveniently as a phasor or a complex number, known as impedence, Z.

It appears that Reactive Power concept, though somewhat strange, is very useful. By this concept, complicated trigonometric functions have been reduced to simple(!) complex algebra.

Yet another set of strange things about reactive power is its direction of flow and sign. If you still have appetite for further confusion you may refer to my blog:

 https://lvnaga.wordpress.com/2010/02/19/electrical-power-and-power-factor/   and

https://lvnaga.files.wordpress.com/2010/02/direction-of-flow-of-active-and-reactive-power.doc

We may meet again later.

L V Nagarajan