This is just for fun, and you can interpret my question any way you
want... my only request is that the Researcher be someone who loves
science and technology.

After a global catastrophe, what are the five most important things
the survivors should know to have the greatest chance of rebuilding
Western civilization?  Let's assume they can feed and clothe
themselves, practice basic first aid, etc.  What ideas, concepts,
equations, etc. should they know to maximize their chances of
recreating a technologically advanced civilization?  The periodic
table?  The laws of thermodynamics?

Here's another way of looking at it: if you had to write a short
booklet for the survivors to memorize and pass down to their
descendants, what would you put in it, assuming your main interest was
to preserve scientific and technological know-how?

Thanks for playing!

Carl

I will dwell on this a while and see if I come up with worthwhile insight.

At first glance, I begin with this observation.  One advantage people
in this situation would have, even if they did not know the details of
a particular technology, would be the simple knowledge that something
is possible.

In other words, one of the hurdles to discovery and progress is the
doubt of the things that have never been done before.

For example, they would know that it is possible to build airplanes,
even if they did not know exactly how.  They would know that computers
are possible, even if they did not have an immediate means to
fabricate them.  Knowing that something is possible, puts one on a
different footing than someone shooting in the dark not knowing if
what they are attempting can be done.

Another factor I am considering is, some of our most recent advances
have not yet fully been adopted by society... so, one wouldn't need
them to rebuild civilization per se, but, it would be an incredible
loss to human knowledge.

For example, mapping the human genome is a tremendous discovery, but
many of the benefits will occur in the future and have not yet
impacted civilization.

Still, it is an interesting question.

Greetings Carlhollywood:

Two things come immediately to my mind: communication and transportation.

Some type of distance communication would be vital whether it is the
natural fire/smoke signals or a simple pony express mail service. 
Some type of united communication service -- people produce more and
better ideas when working together and exchanging information. That
brings us to transportation.  In your scenario, have an abundance of
pack animals survived?  I'm assuming that petrol-powered vehicles are
out along with electric-powered ones.
Other things to consider are:
1. Disease prevention
a. Through the creation/maintenance of sanitary systems (clean
drinking water and waste control)
b. Creation of simple antibiotic
2. How to start a fire without matches or lighters
2. How to build a simple steam engine and/or water wheel - the former
uses natural elements of fire and water in a most productive manner
3. Safe/clean childbirthing methods/practices 
4. Educational system - if the libraries are intact, then finding an
accessible one would solve a lot of problems.  I'm assuming the
survivors can read and will teach their descendants.
4. How/where to find/make chocolate treats and/or wine - must haves
for crowd control...and barter.  ;)

I love questions like this!  Thanks for asking it - I'll be checking
in frequently to see what other GA members have to say and thinking
more about your Top 5 tips.

Best regards,
journalist-ga

Just prior to the global catastrophe, people would be filling land
fills with usable and repairable devices. These items should be
removed from recent land fills and protected from the elements until,
and if, someone with skill to repair/reproduce and/or modify for other
use. The protector could trade dupicates for useful items or items not
in his collection. Each such repository would be somewhat like a
museum and would be of interest to the next generation in helping them
understand the civilization before the catastrophe.
 Even if only 60,000 humans survived, some manufacturing facilities
would be more or less intact. They should be kept intact if possible
with the intent that production may resume at some time in the future.
 With a population reduction of 100,000 times, there would be an
abundance of some kinds of things for about a year. By the 2nd year
most of the pre-catastrophe batteries, food, medication etc would be
approaching (if not past) unusable. There would be a temptation to not
plan for possible substitutes until after the usable stuff was mostly
gone.     Neil

The survivors with technical and science knowledge should teach as
many of the next generation as are interested. Even proceedures and
processes that likely will not resume for centuries can be spring
boards to new inventions that are with in grasp of the survivers.
 It is likely impractical to restart a coal fired electric plant or
even a big gas turbine, but a nuclear power plant might produce
elctricity of decades, if enough survivors are available to operate
and repair the many sub-systems.   Neil

Carl,

You might want to have a look at Jules Verne's novel, The Mysterious
Island, which is available online (among other places) at:

http://emotionalliteracyeducation.com/classic_books_online/milnd10.htm

In it, some Civil War era adverturers are stranded on an island and
essentially recreate modern (for them) civilization there, relying on
found quantities of coal, iron ore, sulfur, etc.

When you think about it, it would be far easier and more plausible for
survivors of a catastrophe to recreate 19th century technologies than
it would to recreate our modern technologies, with their incredible
complexities upon complexities.

Survivors with a solid knowledge of basic industrial techniques and
chemistry (circa 1850's) might be of far greater value than, say, a
computer engineer...the former could actually create things, while the
latter would have nothing to work with.  So too with farming --
knowing 19th century techniques of production would probably have more
value than a familiarity with 21st century techniques.

I would also add in some good, early medical knowledge -- how to grow
penicillin mold, synthesize ether, etc.

And as Verne himself would say....Voila.  Civilization!

Ecclesiastes 12;13, from the Bible, " The conclusion of the matter,
everything having been heard, is. Fear the true God and keep his
commandments. For this is the whole obligation of man".
John 15;12..[ Jesus speaking]..."This is my commandment, that you love
one another, just as I have loved you"
John 8;42...Jesus said to them,"if God were your father, you would
love me, for from God I came forth and am here. NEITHER HAVE I COME OF
MY OWN INITIATIVE AT ALL, but that one [ god] sent me forth.
John 8;28..then you will know I am he, and that I do nothing OF MY OWN
INITIATIVE , but just as the Father [God] taught me I speak these
things.

Above is the behaviour expected of all of us, even following a global
catastrophe. but will there be one?.
Psalm 37;29...the righteous themselves will possess the EARTH, AND
THEY WILL RESIDE FOREVER UPON IT. This is a promise from God that the
earth will not be destroyed, either by man`s actions [ nuclear bombs]
or by meteor strike.
The God that created untold millions of thermonuclear powered objects
in space [ all the suns] surely has the power to prevent us setting
off too many, and destroying ourselves.
Revelation 11;17 & 18...But the nations became wrathful, and your own
wrath came, and the appointed time [ armageddon] to bring to ruin
those ruining the earth!.

Thanks, everyone, for all the great feedback!

Journalist, please assume anything you want to regarding the survival
of pack animals.  I'm only assuming a "Boy Scout Handbook" level of
knowledge to start with.  Thanks again.

Carl

These would need further development, but, here are some to consider.

1.  Energy.  Harnessing electricity, AC/DC, batteries.  Harnessing the
atom.  From there, one could examine specific forms of energy,
preferably avoiding fossil fuels.

2.  Mechanization and interchangeable parts.  How to build machines
that do work (motors and engines) using interchangeable parts that
make assembly lines possible.

3.  Communication.  Radio wave, satellite, printing press, telephone,
video, photographic.

4.  Antibiotics, Penicillin, Pasteurization, Vaccines, Sterilized
Insturments.  One better have a handle on avoiding plagues, otherwise,
this could be over before it begins.

5.  Microprocessors, Integrated Circuits.

(Others to think about).
Refrigeration (providing food storage and air conditioning)
Water and Waste Management (Acqueducts and Sewers)
Flight (though knowing this is possible is half the battle)
Metallurgy and Plastics

Or, you could boil it all down into including a text on the scientific method.