{Hawking [(1)][continued (3)]}[19th July 1988]

[Redbook5:212-214][19880719:0000c]{Hawking [(1)][continued (3)]}[19th July 1988]

(19880719. )

[continued]

[…] *’What we think of as “empty” space cannot be completely empty because that would mean that all the fields, such as the gravitational and electromagnetic fields, would have to be exactly zero. However, the value of a field and its rate of change with time are like the position and velocity of a particle: the uncertainty principle implies that the more accurately one knows one of these quantities, the less accurately one can know the other. So in empty space the field cannot be fixed at exactly zero, because then it would have both a precise value (zero) and a precise rate of change (also zero). There must be a certain minimum amount of uncertainty, or quantum fluctuations, in the value of the field. One can think of these fluctuations as pairs of particles of light or gravity that appear together at some time, move apart, and then come together again and annihilate each other. These particles are virtual particles…: unlike real particles, they cannot be observed directly with a particle detector. However, their indirect effects, such as small changes in the energy of electron orbits in atoms, can be measured and agree with the theoretical predictions to a remarkable degree of accuracy.' (He then goes on to show how pairs of matter particles may appear, and while one may fall into the black hole, the other may escape and appear as if emitted from the black hole.)**

This seems to be a classic example of the Scientists' tendency to take limits on observation as limits on possibility, going on from there in this case to build a whole explanation*** of theoretically predicted and/or empirically observed phenomena on this basis. Hawking is honest enough casually to discuss the possibility of a supernatural observer,**** without apparently appreciating its significance; the actual existence of the supernatural observer is not required (Berkeley notwithstanding):# only the possibility of his existence – even the possibility of considering the possibility of his existence, is sufficient. Once you have considered the possibility of observation not affecting the outcome, the potential independence of the outcome irrespective of your observation or inability to observe it is established, and the explanation given for the particles in empty space falls.

*[Stephen Hawking, 'A Brief history of Time', Bantam, 1988] p105[-106] [Chapter 7: Black Holes ain’t so black]

**[– as follows: 'Because energy cannot be created out of nothing, one of the partners in a particle/antiparticle pair will have positive energy, and the other partner negative energy. The one with negative energy is condemned to be a short-lived virtual particle because real particles always have positive energy in normal situations. It must therefore seek out its partner and annihilate with it. However, a real particle close to a massive body has less energy than if it were far away, because it would take energy to lift it far away against the gravitational attraction of the body. Normally, the energy of

the particle is still positive, but the gravitational field inside a black hole is so strong that even a real particle can have negative energy there. It is therefore possible, if a black hole is present, for the virtual particle with negative energy to fall into the black hole and become a real particle or antiparticle. In this case it no longer has to annihilate with its partner. Its forsaken partner may fall into the black hole as well. Or, having positive energy, it might also escape from the vicinity of the black hole as a real particle or antiparticle' (Ibid, [p106] [Chapter 7: Black Holes ain’t so black])]

***(or was the theory the explanation?)

****[See last previous entry]

#[Presumably a reference to the theory of Immaterialism propounded by Bishop George Berkeley (1685-1753), and/or the summary attributed to Ronald Knox (1888-1957):

'There was a young man who said "God

Must find it exceedingly odd

To see that this tree

Still continues to be

When there's no-one about in the quad".

Dear Sir, Your astonishment's odd;

I am always about in the quad;

And that's why the tree

Still continues to be

Since observed by, Yours faithfully, God.'

]

[continues]

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{Hawking [(1)][continued]}[19th July 1988]

[Redbook5:211-212][19880719:0000b]{Hawking [(1)][continued]}[19th July 1988]

(19880719. )

[continued]

On Heisenberg's Uncertainty Principle: *'… The more accurately you try

to measure the position of the particle, the less accurately you can measure its speed, and vice versa. …. This limit does not depend on the way in which one tries to measure the position or velocity of the particle, or on the type of particle: Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.

(But) **'… We could still imagine that there is a set of laws that determine events completely for some supernatural being, who could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as Occam’s razor*** and cut out all the features of the theory that cannot be observed. This approach led ... to ... quantum mechanics […].'

*Ibid, [Stephen Hawking, 'A Brief history of Time', Bantam, 1988] p55 [Chapter 4: ‘The Uncertainty Principle’]

(Having explained how a method of observation disturbs the particle observed....)

[-- as follows: 'The quantum hypothesis explained the observed rate of emission of radiation from hot bodies very well, but its implications for determinism were not realized until 1926, when another German scientist, Werner Heisenberg, formulated his famous uncertainty principle. In order to predict the future position and velocity of a particle, one has to be able to measure its present position and velocity accurately. The obvious way to do this is to shine light on the particle. Some of the waves of light will be scattered by the particle and this will indicate its position. However, one will not be able to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs to use light of a short wavelength in order to measure the position of the particle precisely. Now, by Planck’s quantum hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will disturb the particle and change its velocity in a way that cannot be predicted. moreover, the more accurately one measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single quantum. So the velocity of the particle will be disturbed by a larger amount. In other words... [– continues at * above]']

**Ibid, [Stephen Hawking, 'A Brief history of Time', Bantam, 1988] p55 [Chapter 4: ‘The Uncertainty Principle’]

*** Actually, 'Non sunt multiplicanda entia praeter necessitem' – entitities are not to be multiplied beyond necessity. (E[ncylopaedia ]B[ritannica ]VIII,867.

(On p125 [in Chapter 8: The Origin and Fate of the Universe], also, he seems to be misusing it)

[continues]

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{Hawking [(1)]}[19th July 1988]

[Redbook5:210-216][19880719:0000]{Hawking [(1)]}[19th July 1988]

(19880719. )

I have reached p.105* of Stephen Hawking's 'A Brief history of Time',** and have come up against problems. Hawking is an honest and engaging writer; he is describing in non-mathematical language the results of mathematical consideration, which should make the layman hesitate. But some of his conclusions seem very strange.

For example, ***at the beginning of this chapter**** – in which he starts to describe his own more recent work – describing black holes, defined as the set of events from which it is not possible to escape to a large distance: 'It means that the boundary of the black hole, the event horizon, is formed by the light rays that just fail to escape from the black hole, hovering forever just on the edge.... Suddenly I realized that the paths of these light rays could never approach one another. If they did they must eventually run into one another.... {The colliding rays would both} fall into the black hole. But if these light rays were swallowed up by the black hole, then they could not have been on the boundary of the black hole.# So the paths of light rays in the event horizon had always to be moving parallel to, or away from, each other.... If the rays of light that form the event horizon, the boundary of the black hole, can never approach each other, the area of the event horizon might stay the same or increase with time, but it could never decrease – because that would mean that at least some of the rays of light in the boundary would have to be approaching each other.'#*

I entirely see that if anything within a certain boundary falls into the black hole, that boundary cannot contract – only remain the same, or expand: although the second possibility – expansion – depends upon a non-exclusive meaning of the initial definition,#** contraction depends upon its alteration. What bothers me is Hawking's method of connecting the definition and the conclusion. Is he right to say that 'they could not have been on the boundary'? Or should he say: 'they could not be on the boundary'? A layman would say, if the apparent boundary of something turned out suddenly to be within it, either that he had got the boundary wrong, or that it had moved. And surely, if the decrease of area of the event horizon (and the black hole) would involve formerly parallel (or at least non-mutually-approaching) light rays moving outwards, i.e. away from each other: it is the increase in area which would involve light rays#*** falling into the black hole, either before or after intersecting with each other.#****

*[Ref next entry but one, [Redbook5:210][19880719:0000c]{Hawking [continued (3)]}[19th July 1988]

**([Stephen Hawking, 'A Brief history of Time',] Bantam, 1988)

***Hawking, ibid, 99-100

****[Chapter 7: 'Black Holes Ain’t So Black']

#[My emphasis]

#*BUT [ibid] p107: 'As the black hole loses mass, the area of its event horizon gets smaller....' Have I misunderstood something?

#**[of the black hole, presumably]

#***from the former event horizons

#****Perhaps the boundary alone is meant: i.e. like a 3-d [sic] version of Saturn's rings, its volume expanding or contracting without the volume of the [Black] Hole changing.... But then, why say 'area' not 'volume'?

[continues]

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{Tarot Jokers}[17th July 1988]

[Redbook5:209][19880717:1610d]{Tarot Jokers}[17th July 1988]

19880717.1610

[continued]

Somewhere earlier* – I cannot now find where – I added M~ and G~ to the Tarot Pack as two 'Jokers', making 80 cards in all – noting that this seemed a more satisfactory number than 78.

I now note** that the total number of Christ's Apostles and Disciples, in an accepted variant, is 80: 12 Apostles (the number of the Tribes of Israel) and 72 other Disciples (the traditional number of Gentile nations).

*ref IV/V [[Redbook4:28-33][19870709:2358]{The Invisible Cards}[9^th July 1987]ff,

& esp [Redbook4:31-32][19870710:0855d]{The Invisible Cards [continued(6)]}[10^th July 1987];

& [Redbook4:253][19871221:1955d]{The Tarot Pack [continued (6)]}[21st December 1987]] ?

**ref Luke IX.1; X.1

***per the New Jerusalem Bible Luke X.1.(a)

{& cf VI .[] 270: Christ as an invisible card?}

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{Outer Action and Will}[17th July 1988]

[Redbook5:209][19880717:1610c]{Outer Action and Will}[17th July 1988]

19880717.1610

[continued]

I am more and more inclined to identify the Outer M[~] principle – Outer Action – with Will; perhaps even to rename it so.*

*No; Willed Action? <891010>

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{[O] of the Ascension}[17th July 1988]

[Redbook5:208-209][19880717:1610b]{[O] of the Ascension}[17th July 1988]

19880717.1610

[continued]

As the [O] passes hugely overhead, the Individual on the ground – giving up all thought of escape – looks up and sees within that immense disc the ascending of an extra dimension: the inside of a hollow cone whose base is the circle(s) of the [O] itself and whose infinite apex is that far central point of light* which is also the light at the end of the Tunnel of Death.** This Ascending Dimension is the Ascension.

*[cf [0] as revised; this is mathematically not inconsistent with a partial view of what is seen at the end of [O], just as the original disc is not inconsistent with a partial view of what is seen here.]

[cf e.g. [Redbook5:225-226][19880724:2355]{The Sphere [continued (13)]}[24th July 1988]]

**(& Love, I suppose)

[& cf [Redbook5:230][19880727:1010]{The Sphere [continued (22)] – The [O] in the Sphere}[27th July 1988]]

(cf IV [], end c. [Unclear to what this refers])

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{Forgiveness: What we do and what we are}[17th July 1988]

[Redbook5:208][19880717:1610]{Forgiveness: What we do and what we are}[17th July 1988]

19880717.1610

*On the problem of Forgiveness without Repentance: the Victim can forgive the Wrong-doer for what the latter does to him, but not for what he is. What he does and has done is included in what he is, in one way or another. What he is can only be transformed by his Repentance, which may be the Human end or part of the Transformation of which Divine Forgiveness is God's end or part. Only God can forgive us for what we are.**

*(ref [[Redbook5:81-83][19880317:2010]{Forgiveness and Repentance}[17th March 1988],] 81, etc.

[& see fns on that p for some other refs])

**VI. [] 125

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{Synthesis - Analysis}[8th July 1988]

[Redbook5:208][19880708:1754]{Synthesis - Analysis}[8th July 1988]

19880708.1754

The *C17^th and C18^th Rationalist philosophers' Analysis – Synthesis method** is the opposite of mine, which follows the Inner Circle correctly:

[Text from diagram above:]

		C~
	/ –		←\
G~	SYNTHESIS [↓]	+	[↑] ANALYSIS	M~
	\→		→/
		A~

The comparison does not look so good on circles 1 and 3:*** the implication is that Analysis should not overrule Synthesis, but should guide it within an awareness of Analysis' own limitations.****

*[C = Century]

**ref [[Redbook5:170][19880618:0000]{Analysis and Synthesis}[18^th June 1988],] 170

(& [[Redbook5:191-193][19880620:1040i]{Horizontal Contra-Rotation}[20^th June 1988],] 192)

***ref [[Redbook5:170][19880618:0000]{Analysis and Synthesis}[18^th June 1988],] 170

****That's what I would like it to be [sic], anyway <880717>

#In fact the final circle on [[[Redbook5:170][19880618:0000]{Analysis and Synthesis}[18^th June 1988],] ] p170 is the most useful. <891010>

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{(Extract, & Comment:) The Nature of Mathematics}[7th July 1988]

[Redbook5:207][19880704:0000]{(Extract, & Comment:) The Nature of Mathematics}[7th July 1988]

198807(04)

'The theory of computability prompts many philosophical questions, most of which have so far not been answered satisfactorily. It poses the question, for example, of the extent to which all thinking can be carried out mechanically. Since it quickly turns out that many functions employed in mathematics – including many in elementary number theory – are nonrecursive,* one may wonder whether it follows that a mathematician's mind in thinking of such functions cannot be a mechanism and whether the possibly non-mechanical character of mathematical thinking may have consequences for the problems of determinism and free will. Further work is needed before definitive answers can be given to these important questions.'**

This is probably the most important thing I have read so far – and confirms my tentative feelings about the nature of mathematics***,**** up to a point, anyway (leaving the way open for the rest).

*(Recursive functions are functions ('laws governing numerical or other precise one-to-one or many-to-one relationships') which can be computed: that is, mechanically (which may equal effectively) calculated.)

**E[ncyclopedia ]Britannica ]XXV.720-1[, ]Philosophy of Logic]

cf [[Redbook5:167][19880617:1949f]{Inner Truth: Love [continued (5)]}[17^th June 1988]&ant?,] 167,

[[Redbook5:185-186][19880620:1040b]{Revival?}[20^th June 1988],] 186 [Presumably an incorrect ref?]

[It is possible that this fn refers not to this Vol, Vol V, but to Vol II, ie:

[Redbook2:168-169][19800805:2325]{'[0]'}[5th August 1980], &
[Redbook2:185-186][19810628:2240]{A Tarot Reading}[28th June 1981],ff]

***(& its position on the Circles at ?C~-S~?)

****not to mention the Materialist v Idealist controversy over the nature of Mind

(ref [[Redbook5:178-179][19880619:1707h]{Materialism and Idealism: The Nature of Mind}[19^th June 1988],] 178

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{A Mathematical Experience}[3rd July 1988]

[Redbook5:206][19880703:0145]{A Mathematical Experience}[3rd July 1988]

.0145

Some days ago, on the edge of sleep, having whizzed through elementary mathematics for several days, I felt a re-arrangement (as it seemed) of my rather patchy mathematical knowledge throwing up algebraic formulae before my eyes. There seemed to be some idea that the Circles pattern (or perhaps its square cross structure) could be described in terms of the resolution of one of the simple 'two squares' expressions,

i.e. (a + b)² = a² + 2ab +b²

&/or (a - b)² = A² – 2ab – b²

&/or (a + b) (a – b) = a² – b²

– or something of that sort.*

**

In fact, this confusion may have arisen from equations for maximum and minimum curves, quadratic equations in fact, e.g. y = x² -2x -5

and y = x² +4x -3

– which I noted in passing might lead me one day towards mathematical descriptions for Circles Analysis.*** I think that all this shows is that I have a very long way to go.

- - -

(I did think that the graph of a circle should have a π in it somewhere; and I now find that 'Circular Functions' are dealt with**** under Trigonometry, and seem quite different. Oh dear!)

*In fact it seems that the Circle is described by x² + y² = r² where r = radius

(Pascoe, Teach Yourself Modern Mathematics) <880721>

**But see [[Redbook5:218-229ff][19880722:2307]{The Sphere}[22nd July 1988],] p218-219!

***[See [Redbook5:225][19880724:1443l]{The Sphere [continued (12)]}[24th July 1988], fns]

****Bostock and Chandler, 'Pure Mathematics'

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