My uncle used to visit us on many occasions when I was young and my father would share a few beers with him. They used to have a competition to see who could crush an empty can of beer into the smallest pulp. Their rough hands would destroy the piece of tin. This machismo impressed me for awhile until I posed the question- could they return the squashed can to its original state? Now the assault course on the Krypton Factor would be a breeze for these guys, this intelligence test part that I’d put to them was more of a challenge.
Lots of unwinding and unrolling of the metal took forth. The two dimensional plane was taking on a 3D shape again. But no matter how hard they squeezed and manipulated the object it could not regain its original form. They put their efforts in front of me. The cans of beer were wrinkled, pock marked and off cylindrical. It was an impossible task for the pair of Herculean brothers.
There’s lots of things that are impossible. Take 1,000 piece jigsaws, for instance. Hard as it is to complete a millennium puzzle, it is not impossible. What is impossible is taking an inside piece out of a completed 1,000 piece jigsaw. An edge strip is easy to snap off, any fool could do that. Taking an inside piece off the board is impossible. You could have the sharpest, finest nails a hand or further down the extremity, a finger has ever seen, you would still be struggling to get into the grooves.
If, by a miracle, I could take a piece out of the map I’d wipe out the gale-lashed shipping region of Malin.
Malin. Need to get Malin. No more Malin. Ooops, got Rockall. Put it back. Get Malin.
Boadicea's Chariot 
I never could manage such a task. Well, neither task. A crushed tin was always a crushed tin. What I would do when trying to take out a middle piece of a puzzle is a very fine pincette.
That’s tweezers to me, Christopher. I’ve spent many a happy hour with tweezers (let me finish, Janus, let me finish) playing the great game of operation.
http://en.wikipedia.org/wiki/Operation_(game)
BZZZTTT.
If it’s any consolation, I pronounce the word pintsette — the German way. It’s always fun to watch our webbed-foot friends squirm when they hear it.
JW, we were so poor (end quote) we ‘ad to play doctors and nurses.
Cans ???
We never had cans, always bottles. Quarts was the bottle of choice (actually 750ml but still affectionately called quarts.) and of course a returnable deposit.
I never drink out of cans if I have a choice, don’t care what the manufacturers say it does taste different!
MM- who would want to? Sounds one hell of a waste of time!
And instead of getting rid of some totally inoffensive piece of water off of Iceland what about getting rid of Pakistan instead? Preferably for good.
Btw, all the pink bits are wrong. Was the map published by a terrorist?
Hi JW. Your beer can crushing adventures reminded of my trip to the Science Museum when I was in London. While I was there I picked up a book on cryptography, called the Code Book by Simon Singh. In it he talks about the key, (excuse the pun) to successful cryptography being something called a one-way function. Many routine tasks we perform are two-way functions. Adding and subtracting. Multiplying and dividing. Opening and closing. Picking up and putting down, etc. But some are one-way functions that cannot be undone as you pointed out to your father, such as breaking an egg and crushing a can. Modular, also known as clock arithmetic, it is an example of one-way function.
2 way function
Way out 10-6 = 4
Knowing that the answer is 4 and given that 6 was one of the starting points, you can find your way back using addition.
Way back 4+6= 10
Same for multiplication and division
Way out 5×6 = 30
Way back 30/6 = 5
In modular arithmetic with a 12 hour clock
8+7 = 3
(8+7=15/12 =1 remaining 3)
Knowing the answer 3 and a starting point 7, does not ensure that 8 was the other starting point.
20+7 = 3
(20+7=27/12 =2 remaining 3)
You can tell that I am neither a mathematician nor a teacher so those who are better qualified and more able, please feel free to improve on the above.
The whole study of cryptography is fascinating.
http://en.wikipedia.org/wiki/Public-key_cryptography
With Christina here – possibly because I can’t crush a can! I can think of a few other places, along with Pakistan, whose removal would improve the planet!
Boadicea, we could start a little list and none of them would be missed, I bet.
TR, what would be the point of uncrumpling cans? Better to get out the ironing board and uncrumple some clothes.
Sheona, anybody can uncrumple clothes, but cans…that’s different.
Morning Sipu:
Fascinating subject and one of the ways I waste my time in retirement.
Code Book is a fine read. One of the lessons of the book is the futility of keeping really useful information secret. The independent discoveries of Whitfield Diffie means that his name is associated more with public key distribution and Rivest, Shamir and Adleman with what became known as RSA rather than James Ellis and Clifford Cocks at GCHQ. The same applies to the rather ridiculous prosecution of Phil Zimmermann for his PGP (pretty good privacy) code distribution.
If you would like to play with modular arithmetic, using large primes take a look at
http://demonstrations.wolfram.com/PrimeFactorizationTable/
If you enjoyed Code Book you should look for “In Code” by Sarah Flannery a remarkable young Irish lady.
Then if you are happy with modular encryption have quick look at Quantum Computing and how it may apply to RSA code breaking, and to bring you right up to date, check this one out.
http://www.theaustralian.com.au/australian-it/government/australian-engineers-write-quantum-computer-qubit-in-global-breakthrough/story-fn4htb9o-1226477592578
Sorry TR nothing to do with jigsaws except in the abstract. I liked the shipping forecast when Finisterre was still in it, I thought it really meant the edge of the World when I was a kid.
Different, but not nearly as useful.
Thanks LW, I am glad that I was not entirely peeing into the wind. I confess that I had not heard of quantum computing before, but I had sometimes wondered if there could not be something more advanced than binary. I frequently ponder about what the effect of such rapid advances in technology will have on humanity which has not evolved to keep pace.
You would be surprised!
Goodness, am I glad that theroyalist here has confirmed the impossibility of taking out a middle piece from the jigsaw.
Sipu:
You’re not alone … 🙂
Sipu, Boadicea: Fortunately for most of us all the encrypting and decrypting we do is done almost transparently, it’s ubiquitous, if you have ever bought on line or checked an account balance the transaction should always be encrypted (the https is a clue)