h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Sorrento, Italy – May 3, 2007

It’s 3 AM. I’ve been standing on the balcony, in the rain, looking at the lights of Naples over the Bay. I listen to the waves crash. We are in a small hotel on the coast about two miles down a steep winding road. You have to drag your suitcases the last 100 yards because there is no road to the hotel. I got up at 1:30 AM. I’ve been unable to sleep, thinking about the number of times you must clink glasses in a toast as you add more people. With two people, you make one clink; with three there are three clinks and with four people six clinks are needed.

You can see the malignant black tower of Vesuvius in the background over the city of 3,000,000. The last eruption was in 1944.

Eventually it works out:
N(N-1)/2 = Clinks, where N is the number of people.
So if you have 1,000 people drinking you must clink 499,500 times.

It doesn’t stop there. I work out how many candles you need for Chanukah ceremonies and how many times “goodnight” must be said as you add people to a bedroom. I start to work out the number 6 billion people in the same bedroom and get up at 1:30 AM in disgust. My mind hasn’t misbehaved this way in a long time. Goodnight Johnboy. Goodnight Sarah.

So now I’m standing in the bathroom with the laptop on a windowsill, plugged into an AC converter, trying not to disturb Mrs. Phred. I don’t worry much about disturbed sleep patterns while traveling. Eventually the body always regains equilibrium. I do worry a little when I begin to make up random math problems and worry at them like a meth-crazed rat in a maze.

The weather has been pleasant, mixed rain and sun. We eat well, of course. Several antipastos, a liter or two of vino bianco, a pasta dish, a meat or fish dish, dessert, coffee, grappa, a lemon alcohol drink...the quality and variety is amazing.

Two days ago we went into the City of Sorrento and took a ferry to the Isle of Capri. We took the chair lift to the top of the island for a view of the surrounding cliffs and azure seas. Yesterday we drove along the rugged Amalfi coast and walked in the hillside city of Positano. Small farmers cultivate lemons and grapes everywhere in terraced small plots. The roads and alleys are insanely twisted and narrow. I think about knocking down the ancient buildings and walls and putting in some four-lanes…but it would be wrong

Today we will drive south to sleep in Tropea and stop along the way to see the ruins of ancient Paestrum, then move on to Sicily.

I wonder how many people in history have looked out over the Bay of Naples at 3 AM in May in the rain?

Here are a few pictures of Sorrento
http://good-times.webshots.com/slideshow/559163497zzNXMm

Oh my god - I do that kind of stuff the whole time! I have a ton of spreadsheets on my laptop that have tried to assist me with the following problems:

* If you are sitting in a car park, waiting for a car to leave (and you know on average how often they leave) what's the longest you should you expect to wait?

* How to construct a digital readout using AND / OR / NOT gates.

* How long it would take for an object to fall out of geostationary orbit and back to Earth.

* How many years it would take Voyager to travel to Gliese 581

* A simple heat transfer model in a two dimensional crystal lattice

* A time-based work out of the Prisoner's Dilemma

* How many times a Pyramid Scheme needs to be repeated before everyone in the world is involved

* A cool looking wave function - don't ask me what for.

* A model of a bottleneck situation using a sine wave function as input

Enjoy Italy!

Oh Crud! I'll be up all night again with those. Gliese 581 is about 20.4 light years. A parsec is 3.258 light-years, 30,860,000,000,000 kilometres, or 19,180,000,000,000 miles. So if voyager 1 is eating up roughly a million miles a day, it will take 120 million days or roughly 350,000 years to make the trip....???

Heat transfer in a two dimensional crystal lattice???

Yep - that's what I got for Gliese.

Actually I've just looked at that again, and it's just a one dimensional strip of interconnected atoms - temperature 1 degree. Apply a 10 degree temperature at both ends and a 4 degree temperature at the other end, and model how the strip warms over time and what the steady state temperature is.

I too was ponering permutations recently but couldn't come up with the maths to find the number equal to each human asking every other human one question that is, approxiamtely 6.7x10^9!

Where ! (factorial) is : 1 x 2 = 2! = 2; 1 x 2 x 3 = 3! = 6; 1 x 2 x 3 x 4 = 4! = 24 &c...

It turned out that the mathematician Sterling knew the answer some time ago.

6.7x10^9! ~ 5 x 10^(10^10)

Still piffling in comparison to Roger Penrose and his "ten to the power ten to the power 123", though. ed.

ponering = pondering

approximately!

The Number of question, I think, might be a variation of the glass clink problem?

N(N-1)
2 people = 2*1=2
3 people = 3*2=6
6.7 billion people = 6,700,000,000 * 6,699,999,999 = a lot

So on the car park problem, don't we need a measure a departure variabilty like a standard deviation or some such, as well as a desired level of confidence, like 99%? Or at least specific departure interval observations so we can calculate our own variability measure?

6.7 billion factorial is approximately equal to 5 x 10 raised to the power (ten raised to the power 10).

Gaussian analysis will also help me with the eta Carinae problem/obsession as well as any car-parking issues: have you included a third (vertical) store in the current car-parking configuration space?

I'm building a spreadsheet of work on what eta Carinae will 'look like' here:: http://eclipse2006.netfirms.com/etacarinae.htm

Cheers again. ed.

Ok...I looked up the meaning joule and got a value of about 8 something for 3.22e...I'm not sure what the tilde sign (~) and the associated 149 means, but I suspect it's a bunch of energy. Right?

The countdown 10..9..8.. looks ominous. I put eta Carinae first on my newsgroup so I can start digging a hole when the time is right.

There seems to be an some thought that the primary danger of a supernova would be a burst of gamma rays that would destroy the ozone layer? However, some seem to think that this would require the poles of eta Carinae to point toward earth like a very improbable cosmic sniper shot.

Those are pretty red pictures. Thanks. Let me know when to dig.

How long (theoretically) would it take you to shake the hands of everyone on planet Earth, if you were allowed 1 second for each person and you were not allowed any rest periods or sleep etc?

205 years.

We assume of course, that everyone has hands. If they don't you can say "hello".

Actually, it's 212 years (I used 6.5 billion as the starting point but a pesky 200 million people seem to have arrived from somewhere in the last couple of years)

That reminds me of the line of Chinese marching 4 abreast. The line never comes to an end because of the birthrate problem...although I think that changed with the population control measures in place...

Yeah - China has a very bumpy population profile - the 2000 census showed a peak at age 14 and another one around age 33. Child numbers below 10 are about half that.