Going back home

This is basically of theoretical interest, but here goes:

Assume one is dropped somewhere on the vicinity of the Milky way. Could a
consistent and practical Mathematical model for navigating around be found
assuming one has unlimited time to travel?

Making the question more specific: Does there exist a sufficiently accurate
(to be practical) Mathematical model that would allow one to calculate one's
way back to Earth, once one was dropped, say, near a star which sits 6,000
light years away from Earth?

It seems to me that an appropriate (linear(?) because the distances are big)
transformation T: R^3-R^3 could be used to calculate the new star positions
at any location, but how could one utilize such a device to find one's way
back to Earth?

Thanks,
--
Ioannis Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

"Ioannis" wrote in
:

It seems to me that an appropriate (linear(?) because the distances
are big) transformation T: R^3-R^3 could be used to calculate the new
star positions at any location, but how could one utilize such a
device to find one's way back to Earth?

Even if you could, you'd run into the Borg first and then
you'd pretty much be screwed. (And besides, since you're giving
yourself infinite time and the stars move, it's not going to be
a linear transformation.)

I'd just grab my towel and electronic thumb, and hitch a ride.

Oh yeah, and maybe use the "Guide" too.

Ï "Bart Goddard" Ýãñáøå óôï ìÞíõìá
...

"Ioannis" wrote in
:

It seems to me that an appropriate (linear(?) because the distances
are big) transformation T: R^3-R^3 could be used to calculate the new
star positions at any location, but how could one utilize such a
device to find one's way back to Earth?

Even if you could, you'd run into the Borg first and then
you'd pretty much be screwed. (And besides, since you're giving
yourself infinite time and the stars move, it's not going to be
a linear transformation.)

Um, what about if we want to caclulate the path and assume instantaneous
travel instead?

As far as the Borg are concerned, they are us in the distant future. So the
solution to this problem is to find a way to communicate to them effectively
this very fact. If they understand it, they will have no reason to
assimilate us, cause they will understand that eventually we will turn into
them. No need to hurry :*)
--
Ioannis Galidakis
http://users.forthnet.gr/ath/jgal/
------------------------------------------
Eventually, _everything_ is understandable

"Ioannis" wrote in
:

Um, what about if we want to caclulate the path and assume
instantaneous travel instead?

As far as the Borg are concerned, they are us in the distant future.
So the solution to this problem is to find a way to communicate to
them effectively this very fact. If they understand it, they will have
no reason to assimilate us, cause they will understand that eventually
we will turn into them. No need to hurry :*)


Subject has some useful inquisitiveness, we'd better assimilate
him. Let's hurry so as to cut down on the noise.

So I suppose that I know exactly what the Big Dipper looks like
from Earth, and now that I'm at a random spot in the galaxy and
I have a 3-D map of the stars in my computer from my new location,
so I should be able to do something better than have the computer
search all possible locations and test all possible points of view
from those locations to see if it can see the Big Dipper from
there.


The transform might be represented by a 3x3 matrix, but there's
still some assumptions about what the observers knows. If he's
Arthur Dent, and has only a 2-D spherical surface picture of
the stars from earth, (which is what I outlined in the above
paragraph) then it's not a 3x3 matrix we're dealing with. The
original positions of the stars are not known, but we could in
theory, find our way back home since we have lots of extra information.
(More than three stars. And hopefully there's no other Big Dippers
in the Galaxy.)

Even if you decide on the type of map you want, I'm not sure
how you pin it down at even one point, since before you leave
earth, you have no idea where you're going, so you don't know
which of the zillions of maps it's going to be. And once
you get there, you're going to need its inverse, and since you
didn't know which map it was, and you don't know where you are,
you sure can't come up with even a single inverse image point.
(And I'm thinking you need at least 3 no matter what rules you
play by.)

Best case scenerio: You're stuck on an Edenic planet with Seven-of-Nine
for a couple of decades.

Worst case scenerio: She spends the entire time in the astrometrics lab
obsessing about this very problem.

On Thu, 18 Mar 2004, Ioannis wrote:
"Bart Goddard"
"Ioannis" wrote in
It seems to me that an appropriate (linear(?) because the distances
are big) transformation T: R^3-R^3 could be used to calculate the new
star positions at any location, but how could one utilize such a
device to find one's way back to Earth?

(And besides, since you're giving yourself infinite time and the stars
move, it's not going to be a linear transformation.)

Um, what about if we want to calculate the path and assume instantaneous
travel instead?

Then by relativistic effects you'd arrive infinitely in the future long
after good old Sol went supernova and long after the big bang universe
came to it's big crunch, heat death or big rip end, looking for a space
traveling society, which if they didn't self destruct within decades of
your departure, would have much improbability surviving the universal end.

The suggestion to the use the "Hitchhikers' Guide to the Universe" may be
helpful, especially the improbability drive which might let you break the
speed limit. As I recall somebody built a hotel at the end of time for
time traveling tourists to view a very unique event.

No matter how you travel from distance random location, you'll
need time travel to adjust your travels back to the home you know.

Ioannis wrote:
Assume one is dropped somewhere on the vicinity of the Milky way. Could a
consistent and practical Mathematical model for navigating around be found
assuming one has unlimited time to travel?

I have an article that's sort of related, he

http://astro.isi.edu/games/dimension.html

which actually started from a discussion on SAA. The introduction goes
a little into that (although it doesn't mention SAA specifically). It
might answer your question a bit.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

In sci.math, Ioannis

wrote
on Thu, 18 Mar 2004 14:18:23 +0200
:
This is basically of theoretical interest, but here goes:

Assume one is dropped somewhere on the vicinity of the Milky way. Could a
consistent and practical Mathematical model for navigating around be found
assuming one has unlimited time to travel?

Making the question more specific: Does there exist a sufficiently accurate
(to be practical) Mathematical model that would allow one to calculate one's
way back to Earth, once one was dropped, say, near a star which sits 6,000
light years away from Earth?

It seems to me that an appropriate (linear(?) because the distances are big)
transformation T: R^3-R^3 could be used to calculate the new star positions
at any location, but how could one utilize such a device to find one's way
back to Earth?

What information is available to the traveler, and what equipment?

Isaac Asimov, in one of his Foundation series (I think it
was _Second Foundation_) hypothesized a Lens, in which
one can superposition the actual starfield with various
theoretical ones (computed by an on-ship computer unit).
A later story hypothesized a supercomputer which could
automate the Jump sequence. While the Jump[*] has been
discredited (a pity since it sounds like a neat way to
travel :-) ), a variant of the Lens could be used for
navigation purposes, given the conditions you propose.

Failing that, if one has a list of stars dotting the
Galaxy, one might be able to search through thems using
a spectroscope. The main problem with that of course is
finding them, although one might automate the spectroscope.

Also, there are some considerations regarding dimensions.
The Milky Way has an estimated radius of 60,000 light
years, taking the black hole as the center. This is
5.67 * 10^20 m. log2(5.67 * 10^20) = 68.94, which means
standard IEEE-754 precision equipment won't quite cut it,
as it can only handle 52 bits in the mantissa. Of course
one can shift into another coordinate system when one gets
close enough to one's destination; the Earth orbits with a
radius of 1AU = 1.5 * 10^11 meter, which translates into a
galactic radius of about 3.78 * 10^9 AU, with log2(3.78 *
10^9) = 31.8. This is still beyond standard floating-point
metrics, as one has to compute a square root of sum of
squares. Pluto is about 36 AU away on average (with an
eccentric orbit); I'm not sure if 100 AU is close enough,
or not.

Isaac Asimov also write _Star Light_, a very short story which
illustrates might happen were one to automate the process: a
nova definitely bollixes up things. Even without this problem,
stars move.

If one knows the location of a neighboring galaxy when dropped
into the scenario (ideally, the galaxy would be on the
extension of the Milky Way disc), one can set up a coordinate
system using a line from the center of the Milky Way to this
galaxy, the normal to the galactic disc, and the cross-product
of the two -- a fairly standard quasi-Cartesian coordinate system.
(Quasi, because space is warped by the stars and/or the galactic
black hole.)

You might want to clarify your question, but it is an interesting
problem. :-)

[.sigsnip]
[*] The notion was to somehow jump into hyperspace, "die" for
a brief fraction of a second, then emerge back into real
space (and yes, in at least one story in the _I Robot_ anthology,
everyone survives :-); unfortunately I can't find my copy).
Variants of this idea are all over sci-fi, from the relatively
prosaic (unless an unbalanced engine pack generates a wormhole!)
high-speed travel in Star Trek to the power-assisted jumpgates
used in Babylon 5 to the device in Stargate.

--
#191,
It's still legal to go .sigless.

William Elliot wrote in message ...
On Thu, 18 Mar 2004, Ioannis wrote:
"Bart Goddard"
"Ioannis" wrote in
It seems to me that an appropriate (linear(?) because the distances
are big) transformation T: R^3-R^3 could be used to calculate the new
star positions at any location, but how could one utilize such a
device to find one's way back to Earth?

(And besides, since you're giving yourself infinite time and the stars
move, it's not going to be a linear transformation.)

Um, what about if we want to calculate the path and assume instantaneous
travel instead?

Then by relativistic effects you'd arrive infinitely in the future long
after good old Sol went supernova and long after the big bang universe
came to it's big crunch, heat death or big rip end, looking for a space
traveling society, which if they didn't self destruct within decades of
your departure, would have much improbability surviving the universal end.

The suggestion to the use the "Hitchhikers' Guide to the Universe" may be
helpful, especially the improbability drive which might let you break the
speed limit. As I recall somebody built a hotel at the end of time for
time traveling tourists to view a very unique event.

Hilbert?


No matter how you travel from distance random location, you'll
need time travel to adjust your travels back to the home you know.

The Ghost In The Machine wrote in message ...
In sci.math, Ioannis

wrote
on Thu, 18 Mar 2004 14:18:23 +0200
:
This is basically of theoretical interest, but here goes:

Assume one is dropped somewhere on the vicinity of the Milky way. Could a
consistent and practical Mathematical model for navigating around be found
assuming one has unlimited time to travel?

Making the question more specific: Does there exist a sufficiently accurate
(to be practical) Mathematical model that would allow one to calculate one's
way back to Earth, once one was dropped, say, near a star which sits 6,000
light years away from Earth?

It seems to me that an appropriate (linear(?) because the distances are big)
transformation T: R^3-R^3 could be used to calculate the new star positions
at any location, but how could one utilize such a device to find one's way
back to Earth?

What information is available to the traveler, and what equipment?

Isaac Asimov, in one of his Foundation series (I think it
was _Second Foundation_) hypothesized a Lens, in which
one can superposition the actual starfield with various
theoretical ones (computed by an on-ship computer unit).
A later story hypothesized a supercomputer which could
automate the Jump sequence. While the Jump[*] has been
discredited (a pity since it sounds like a neat way to
travel :-) ), a variant of the Lens could be used for
navigation purposes, given the conditions you propose.

Failing that, if one has a list of stars dotting the
Galaxy, one might be able to search through thems using
a spectroscope. The main problem with that of course is
finding them, although one might automate the spectroscope.

Didn't the Pioneer satellite that left the solar system include
some kind of "map" showing the relative position of the sun to
nearby stars based on spectroscopy?


Also, there are some considerations regarding dimensions.
The Milky Way has an estimated radius of 60,000 light
years, taking the black hole as the center. This is
5.67 * 10^20 m. log2(5.67 * 10^20) = 68.94, which means
standard IEEE-754 precision equipment won't quite cut it,
as it can only handle 52 bits in the mantissa. Of course
one can shift into another coordinate system when one gets
close enough to one's destination; the Earth orbits with a
radius of 1AU = 1.5 * 10^11 meter, which translates into a
galactic radius of about 3.78 * 10^9 AU, with log2(3.78 *
10^9) = 31.8. This is still beyond standard floating-point
metrics, as one has to compute a square root of sum of
squares. Pluto is about 36 AU away on average (with an
eccentric orbit); I'm not sure if 100 AU is close enough,
or not.

Isaac Asimov also write _Star Light_, a very short story which
illustrates might happen were one to automate the process: a
nova definitely bollixes up things. Even without this problem,
stars move.

If one knows the location of a neighboring galaxy when dropped
into the scenario (ideally, the galaxy would be on the
extension of the Milky Way disc), one can set up a coordinate
system using a line from the center of the Milky Way to this
galaxy, the normal to the galactic disc, and the cross-product
of the two -- a fairly standard quasi-Cartesian coordinate system.
(Quasi, because space is warped by the stars and/or the galactic
black hole.)

You might want to clarify your question, but it is an interesting
problem. :-)

[.sigsnip]

[*] The notion was to somehow jump into hyperspace, "die" for
a brief fraction of a second, then emerge back into real
space (and yes, in at least one story in the _I Robot_ anthology,
everyone survives :-); unfortunately I can't find my copy).
Variants of this idea are all over sci-fi, from the relatively
prosaic (unless an unbalanced engine pack generates a wormhole!)
high-speed travel in Star Trek to the power-assisted jumpgates
used in Babylon 5 to the device in Stargate.