*“Any sufficiently advanced technology would be indistinguishable from magic”*Third Law, Arthur C Clarke

We had set out to write about man’s perception about the universe in the
context of space-time, and the contribution of Sir Arthur Clarke to this
understanding, unfortunately we failed to quit the shores of Sri Lanka. So..

CASE OF THE MISSING LADY |

We were arguing about the mythical Time-machine with Dad in our salad days,
when he expostulated against any possibility of its existence, saying it will
lead to logical (not legal he, he, he) complications. If the user travels back
in time and assassinates one of her direct ancestors, the time-traveller will
cease to exist as her lineage itself will be poof…!!! c

*hole gache!!!*.. A classical ‘bootstrapping’ paradox. Alas you are a Newtonian Dad we said, but in the Einsteinian scheme of things, the progression of a human being’s life can be construed as a graph in a 5-dimensional continuum and in bumping off her ancestor, she is removing the equivalent of a snap in a Euclidean 2x2 graph, leaving all the other 5-dimensional images intact, which to the blinkered senses of a human, will again look like the life lived by the ancestor, the fatal moment perhaps looking like a TV blip caused by a passing electrical disturbance. I don’t understand this at all said Dad in despair. Daddd...we teased...the classic crime query " what murder can a man be never accused of?" ...killing his own widow" comes off the hinges here...". Of course Dad once had eminent comrades, esp the Aetherists. Till Sir Eddington measured the starlight deflection during the solar eclipse of 1919 at Primcipe island off the African coast, many thought of Relativity as a passing fad...
Sir Arthur Clarke was one of the leading writers who strived to drill the
brand new Einsteinian sense into old Newtonian jugheads, brilliant though they
may have been in their days. Sir Bertrand Russell (

*ABC of Relativity*), Sir Clarke (see*Collected Short Stories*), Max Born (*Einstein’s Theory of Relativity*), later George Gamov (*1,2,3…Infinity*) and Isaac Asimov (*Essays*) were some of the evangelists of the new creed.
The theme of the blogpost really is Sir Arthur C Clarke’s contribution
towards helping humanity comprehend a >3 dimensional universe. His
contributions in the shape of geosynchronous satellites, online commerce etc.
have already been highlighted in the previous despatch.

Stephen Hawking in his Brief History of Time illustrates the shenanigans
by asking the reader to map the two dimensional world to three dimensions and
three to four, so as to enable her to imagine 4 dimensions as a successor to 3.
The three dimensions are represented by a 3-D picture drawn on the 2-D plane of
the book, and the fourth, the corkscrew progression of the 3-D image...- a dry
way to explain the theory to dummies. Clarke employed fiction to open
multi-dimensional vistas before the reader, and to give her a flavour of ‘real’
reality. For example in the short story Wall of Darkness, he employs the
concept involved in the making of a
Moebius Strip, which is a single dimensional plane - that is a plane with only
one side, and its 2-3 dimensional equivalent , the Klein Bottle, which looks as
if it is enclosing something, but the inside and outside are one and same.

MOEBIUS STRIP |

KLEIN BOTTLE |

the protagonist of Wall of...approaches the ‘edge’ of the imaginary
universe comprising one star and one planet, he runs into himself! Thence to
stories about back-to-back universes with topological zippers...Of course his
stories invited criticism from friends and non-friends alike, one from among
the former species being none else than Sir Isaac Asimov. One non-friend critic
for instance says about Wall of…: “But it fails me to recognise how exactly the
"wall situation" works with a universe in such a shape”. The short
answer to such nit-picking is that

*chyaayla*Maaaan..! you are critiquing the story without recognising that it is a call from another World. Had comprehension of the underlying world been so straight-forward as to be amenable to our language and our concepts, there would be no*raison d etre*for this genre of fiction…!
Another World-view was attempted thus by a writer, (Clarke or Asimov?),
again inducing the reader to mentally extend to 4-dimensions, a scenario easily
recognisable in a 3-dimensional world.

Imagine a two dimensional creature crawling on the surface of Earth. It
starts drawing an ever expanding spiral, starting point being the North Pole.
The process goes on and on, at the end of which, the 2-D chap finds find itself
hemmed in by its own circle- at the South Pole. The 3-D version will of course
be like this: a human being starts applying layer after layer of thick paste on
a cricket ball, which solidifies quickly. If she survives for aeons, she will
find herself boxed in (‘hemmed in' applies to a plane and ‘boxed’, to 3-D
space) in the sphere of her own making. Instead of the
sphere being in an expansion mode, it closes upon her...

2-D CREATURE IS THE TRIANGLE |

HEMMED IN |

An interesting corollary stemming from the Wall of Darkness was
proposed by Sir Clarke: an infinite but bounded universe, the hypothesis equipped
with the mathematics of it:

Draw a circle on this paper, centre ‘o’ and radius ‘r’.. The mass ‘m’ of
an object located in the circle, which is our Universe is governed by a
Lorentz-lookalike transformation:

m= f {k/√( r^2-d^2)} where k is a constant and d the distance of the
object from the centre, the mass--->∞ as d--->r.

Thus, as the object approaches the circumference, its mass increases,
approaching infinity, and therefore the object cannot go beyond the
circumference. The universe is infinite, but bounded by the circumference... something
like the Xeno’s Paradox:

ACHILLES LOSES TO TORTOISE |

Xeno (5

^{th}c BC), the Greek philosopher formulated this paradox. The mythical Greek sprinter Achilles can’t beat the tortoise which has a significant head-start, for by the time Achilles catches up with the tortoise, the reptile has moved a bit ahead, and so on...
The idea of Relativity perhaps pre-dates Albert Einstein, but the
significance was brought out by him. He developed
it as an all-enveloping philosophical concept and applied it to all walks of
life. Unquestionably the greatest human born, to YT...This blog’s

*rajkavi*, the virile, hard hitting poet who wrought iron words with a feather quill William Blake wrote:*To see a World in a Grain of Sand, And a Heaven in a Wild Flower,*

*Hold Infinity in the Palm of your Hand, And Eternity in an Hour....*

After Einstein, add another line to make the
experience complete: Behold the Nature of the Universe in a Mathematical
Equation!

Finally, where does Schrödinger’s Cat cross Sir Clarke’s path? The word
‘indistinguishable’ in the opening quotation has been construed by some as
referring to this cat phenomenon which is an interesting sidelight of Quantum
Mechanics. It refers to the uncertainty that haunts an observer of a fundamental
particle like the electron. The particle’s state and position change in the
very act of imaginary measurement. In Schrödinger’s ‘Thought Experiments’,
he proposed this model which came to be known as his cat experiment. It’s at
best an amusing idea:...goes like this: if the cat’s life and death is contingent upon the state
of a particle, the cat must be both dead and alive at the same time. Given the
eminence of its formulator, there is hardly any sci-fi writer or physicists who
has not delved into the

*afsana-e-cat...*

CAT IN BOX |

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