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In article <9510917.10781@mulga.cs.mu.OZ.AU>,
bromage@cs.mu.OZ.AU (Andrew Bromage) wrote:
> madhudvisa@krishna.org (Madhudvisa) writes:
>
> > Just suppose [...]
> > Now I'm not saying this is true but just, as an
> > intellectual exercise, lets see if we can establish a plausible
> > description of a flat earth.
>
> An interesting thought-experiment --- just warped enough for
> me to like it. :-)
>
> > So how could this planet be flat and we have not noticed? Sometimes
> > we can find two or more hypothesis to explain a given set of data
> > equally well.
>
> [snip]
>
> > The earth is a flat plate-like affair with the Himalayan mountains
> > in the centre (you might like to sketch this out). Then project all
> > the continents around the centre so the distances we have measured
> > remain the same (I'm sure somebody out there can do this--it's
> > beyond me).
>
> Okay, let's assume that this is correct.
>
> In the globe model, there is a point dismetrically opposite the Himalayas.
> In the plate model, this is a circle (corresponding to the circumference
> of the disc). No matter how you contrive it, you cannot make a finite
> distance (circumference of the disc) into zero-distance (the circumference
> of the point) and make the projection distance-preserving! If we went
> there, I'm sure that we would not find a discontinuity in the geography
> of the area.
I agree there are problems with the Himalayan model... But there is
a better alternative. If you try the exercise using the North Pole
as the central point things look much more promising.
As for diametrically opposite points, remember for this exercise we
are talking about a flat plate not a sphere. For our model to find
the diametrically opposite point you start at the original point
and travel through the centre (which we are now taking as the North
Pole) for the distance of the radius of the circle. If it is midday
at our original point it will be midnight at the opposite point. So
now we have opposite points for everything except the North Pole --
the opposite point is not a point but it is the circumference of
the circle.
This is a lot better because it makes the whole Northern Hemisphere
exactly as we have observed it... Things only get tricky when you
go "down under". We now have a North Pole exactly as we have
observed it and we also have a South Pole -- which is no longer a
point but a rugged icey mountainous region surrounding the whole
planet. If you think about it there hasn't been so much exploration
down there -- there's really no reason to go there. There are some
Antarctic weather and research stations down there but that's about
it.
>
> You see, this problem has plagued cartographers for centuries: How to
> represent a globe on a flat piece of paper. It cannot be done in a way
> which preserves distances. This is because the geometry of a plane (or
> on a disc) is Euclidean, but the geometry on the surface of a sphere is
> not. You have to use some strange approximation such as treating the
> Earth as a cylinder (Mercator) or two cones (Conic). Even then you have
> problems with discontinuities (eg the left- and right- hand sides of a
> Mercator map). There are much more complex projections, but in the end
> they are all approximations.
>
You don't have to represent a globe as a flat piece of paper for
this exercise. We are considering it is flat. Anyway you only have
to flatten out the Northern Hemisphere and just let the Southern
bits stick out over the edges.. ie: South Africa and South America
just stick out as we have observed them and you put Australia out
there somewhere, throw in a few little islands and you've got it.
It does mean there would be rather serious discrepancies in the
distances as you approach what we think to be a point but what, in
actuality, might be the circumference of the earth. But would you
notice? You get in your plane and head South and after the correct
distance you come to some icy coastline where you have your
research station and do your work and go home. How much of the
interior of Antarctica has been explored? It's terribly cold out
there!
> Also, your model does not explain lots of geographic, geophysical and
> meteorological details, such as:
>
> - The Earth's magnetic poles. (They seem to be diametrically
> opposite, based on our globe model.)
>
The North Pole is the North Pole and it also happens (in this
model) to be situated in the centre (horizontally, not vertically)
of the universe so why shouldn't magnets point towards the centre
of the universe?
> - The absence of the coriolis pseudo-force at what we know
> as the equator, but its presence everywhere else.
>
In this (new, revised) model the equator has a special position. It
is the circle situated half way between the North Pole and the
circumference of the planet (the South "Pole"). This will become
more clear later on.
> - Just what is that ozone hole doing over Antarctica? (Why
> isn't it somewhere else?)
>
Well Antarctica now becomes a special place also, it is no longer a
little point on the map, its a mountain range surrounding the whole
planet. Have you wondered what is on the other side of the
mountains?
It is important to understand, for this exercise, the earth is
stationary. The easiest way to describe the universe is to compare
it to one of those oil-pressing machines they use in India. There
is a big circular trench in which a huge grinding wheel runs. There
is a high pole in the center of the circle and from the top of it a
short, pivoted rod is attached, this short rod is then attached, by
another pivot to a much longer one which runs through the grinding
wheel to the outer edge of the trench. The effect of this
arrangement is to slant the grinding wheel towards the center. The
whole thing is then connected to two bullocks yolked together who
walk around and around in circles pulling the big stone wheel which
crushes the seeds to extract the oil. (You have to see it really,
but I hope you get the drift.)
Our position in the universe is stationary, in the center
horizontally but below the center vertically. Directly abobe the
North Pole we see the polestar, that is the point where the small
rod (which is described as a "rope of wind") is attached. That
small "rope of wind" drops down fairly steeply until it is about
half a million miles above the earth. It then joins a long rod
which extends a distance of half the radius of the universe
climbing at quite a steep angle. This rod is the center of the
whole universal structure. It is figuratively described as
"sisumara", meaning a dolphin in the sky.
"This form of sisumara has its head downward and its body coiled. On
the end of its tail is the planet of Dhruva [the pole-star], on the
body of its tail are the planets of the demigods Prajapati, Agni,
Indra and Dharma, and at the base of its tail are the planets of the
demigods Dhata and Vidhata. Where the hips might be on the sisumara
are the seven saintly sages like Vasistha and Angira. The coiled body
of the Sisumara-chakra turns towards its right side, on which the
fourteen constellations from Abhijit to Punarvasu are located. On its
left side are the fourteen stars from Pusya to Uttarasadha. Thus its
body is balanced because its sides are occupied by an equal number of
stars. On the back of the sisumara is the group of stars known as
Ajavithi, and on its abdomen is the Ganges that flows in the sky [the
Milky Way]" (Srimad Bhagavatam 5.23.5)
This whole thing, the (the Sisumara-chakra) turns 360 degrees every
24 hours... so it is the whole universe rotating. We are
stationary, in the center and looking out. The other end of the
axle supporting this gigantic structure rests on a mountain range
half way to the edge of the universe. This mountain range (like our
South "Pole") surrounds the earth but it is much higher. We are
stationary, looking into the tail of this huge, dolphin-like thing
rotating in the sky. Unlike the oil-pressing machine, the
Sisumara-chakra does not rest on the ground, the axle rotates along
the top of the high mountain range half-way out to the edge of the
universe. It's arranged so one rotation of the whole thing takes
twenty-four hours. The whole affair is gradually circumnavigating
the universe and this takes one year.
The "fixed-stars" are fixed on the body of the Sisumara-chakra.
Their relative positions never change but the sun, the moon and
other planets, while moving with the Sisumara chakra, also have
their own independent movement. The analogy is a potters-wheel. If
there are some ants on the potters-wheel, although they move with
the wheel, at different times they are seen in different positions
relative to the stationary objects on the wheel.
> > If you want to put an end to this rumor just go to the southenmost
> > tip of South America, get in your plane and travel to Tasmania (the
> > southernmost tip of Australia in a few hours. But alas, I think it
> > can not be done, so this rumor is here to stay.
>
> Do we have a volunteer? :-)
>
--
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