The Cross

Humankind has long been inventive when it comes to the sphere of killing one another; I could probably write a whole other blog solely on the subject of weaponry for the next 50 years before running low on material, and that doesn’t even approach the field of organised execution. Hanging and stoning are two old-as-the-hills methods still, unfortunately, in use in some parts of the world, and countless others have been developed with varying degrees of complexity, pain and success involved. However, one execution method has proved to carry more cultural weight than all others, and mostly thanks to one man; I speak, of course, of crucifixion.

We all think of crucifixion as a Roman punishment, but like so many Roman things it wasn’t their invention (seriously, even their religion was nicked from the Greeks). Crucifixion first started off in Persia in around the 6th century BC, in the area that would later become the Seleucid Empire after Alexander the Great went and conquered all of it. Like so many other things, the practice later spread across the remnants of Alexander’s Empire, including his native Greece, and here it began making its way towards the ‘civilised’ world of the time. The Greeks were, apparently, generally opposed to this horrible method of execution and used it very sparingly, but much of Alexander’s old Empire would later find its way into Roman hands, and so the idea eventually made its way to Rome. Given that this was a culture whose primary form of entertainment (garnering hundreds of thousands of spectators, something even modern sporting culture can’t match) involved various people and animals dressing up to kill one another in as ‘entertaining’ a fashion as possible, it is perhaps not surprising that the Romans thought crucifixion showed potential as an execution method, particularly for those they wanted to make an example of.

This is hardly surprising; of all humanity’s execution methods, few can rival crucifixion when it comes to being horrifying and showy. This is partly helped, slightly bizarrely, by its cheapness; to show them off to the general populace, something like hanging or beheading would require some sort of raised platform, which covers only a small area and takes a decent amount of time and energy to create. The Roman alternative (the arena) was even more expensive, requiring an investment in either animals or an elaborate set of costumes and procedure in order to provide an ‘entertaining’ execution, and given that games were generally free to go and watch (paid for by the emperor or local governor to curry goodwill with the populace) it wasn’t going to pay itself back. By contrast, the sum total of all monetary investment required for crucifixion is two long sticks, some rope or nails, and a bloke to affix the resulting structure to; the crosses were even moved to the required site by the prisoners themselves, and erecting them took a few soldiers almost no time at all. This cheapness made it easy to show off their victims on a vast scale; after the gladiator Spartacus’ slave revolt was crushed in 71BC, the 6,000 captured prisoners were all crucified along the Appian way, a trail of crosses stretching from Rome to Capua. That’s 200 kilometres (125 miles), along both sides of the road. A forceful example indeed.

The very nature of crucifixion itself also helps when it comes to being showy. The crosses used in crucifixion were big old things, three or four metres tall if they’re an inch, just to ensure the unfortunate victim could be seen from great distances away. The mechanics of the execution build on this; it is often assumed that death by crucifixion comes from exhaustion, hunger, pain and blood loss, but in fact crucifixion causes death by suffocation as much as anything. With one’s upper body held only by spread eagled arms, it becomes very tiring to keep it in position, and one’s head and torso tend to fall forwards after time. However, with the arms pinned in position this stretches out one’s joints extremely painfully, offering no respite from the agony, and pulls upwards on the ribcage. This in turn puts extreme stress on the diaphragm, meaning it has to pull one’s entire weight upward every time you attempt to take a breath, and crushes the lungs under one’s own weight, slowly squeezing the air and life out of the victim. If the executors were feeling kind, then the victim would be tied to the cross, resulting in a slower but slightly less agonisingly painful death. However, Jesus was famously attached to his cross by nails through his feet and wrists (some versions say the hands, but the flesh there isn’t strong enough to hold up the weight of a body properly), and whilst this could offer the possibility of blessedly quick unconsciousness and death due to blood loss and the extreme pain, the sheer agony of the experience doesn’t bear thinking about. No matter how devoted to their cause the victim was, their screams must have undoubtedly echoed for miles as they died, just adding to the showiness of their death. Crucifixion was the ultimate tool, for the Romans, for sending out a warning, a very obvious, demonstrative way of discouraging people from following the lead of the victim.

That this approach failed somewhat is like saying the Pope thinks God is a kinda alright guy; crucifixion has guaranteed martyrdom for countless early saints and, of course, Jesus. The concept of ‘he suffered and died on the cross for us’ is, more than anything, the fundamental message of Christianity, embodying the idea of undergoing extreme pain and hardship simply to try and do right by the world and emphasising the pure and unadulterated goodness of Jesus as a person. But this has had an unexpected effect in the long run; since the story is told so often to children, the gory details are often glossed over, or the story simply because so fundamental and oft-told that it becomes very easy to forget just how horrific his agony would have been. Even this post has treated the subject of crucifixion with a decidedly neutral tone, without considering properly just how horrible it is to inflict this level of pain onto a fellow human being. Crucifixion might have been abolished by the Roman Empire 1600 years ago (by Emperor Constatine, if you’re wondering), but it would not do to forget it. Very few things are ever worth forgetting, and torture and murder are most certainly not among them.

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Crypto

Cryptography is a funny business; shady from the beginning, the whole business of codes and ciphers has been specifically designed to hide your intentions and move in the shadows, unnoticed. However, the art of cryptography has been changed almost beyond recognition in the last hundred years thanks to the invention of the computer, and what was once an art limited by the imagination of the nerd responsible has now turned into a question of sheer computing might. But, as always, the best way to start with this story is at the beginning…

There are two different methods of applying cryptography to a message; with a code or with a cipher. A code is a system involving replacing words with other words (‘Unleash a fox’ might mean ‘Send more ammunition’, for example), whilst a cipher involves changing individual letters and their ordering. Use of codes can generally only be limited to a few words that can be easily memorised, and/or requires endless cross-referencing with a book of known ‘translations’, as well as being relatively insecure when it comes to highly secretive information. Therefore, most modern encoding (yes, that word is still used; ‘enciphering’ sounds stupid) takes the form of employing ciphers, and has done for hundreds of years; they rely solely on the application of a simple rule, require far smaller reference manuals, and are more secure.

Early attempts at ciphers were charmingly simple; the ‘Caesar cipher’ is a classic example, famously invented and used by Julius Caesar, where each letter is replaced by the one three along from it in the alphabet (so A becomes D, B becomes E and so on). Augustus Caesar, who succeeded Julius, didn’t set much store by cryptography and used a similar system, although with only a one-place transposition (so A to B and such)- despite the fact that knowledge of the Caesar cipher was widespread, and his messages were hopelessly insecure. These ‘substitution ciphers’ suffered from a common problem; the relative frequency with which certain letters appear in the English language (E being the most common, followed by T) is well-known, so by analysing the frequency of occurring letters in a substitution-enciphered message one can work out fairly accurately what letter corresponds to which, and work out the rest from there. This problem can be partly overcome by careful phrasing of messages and using only short ones, but it’s nonetheless a problem.

Another classic method is to use a transposition cipher, which changes the order of letters- the trick lies in having a suitable ‘key’ with which to do the reordering. A classic example is to write the message in a rectangle of a size known to both encoder and recipient, writing in columns but ‘reading it off’ in rows. The recipient can then reverse the process to read the original message. This is a nice method, and it’s very hard to decipher a single message encoded this way, but if the ‘key’ (e.g. the size of the rectangle) is not changed regularly then one’s adversaries can figure it out after a while. The army of ancient Sparta used a kind of transposition cipher based on a tapered wooden rod called a skytale (pronounced skih-tah-ly), around which a strip of paper was wrapped and the message written down it, one on each turn of paper. The recipient then wrapped the paper around a skytale of identical girth and taper (the tapering prevented letters being evenly spaced, making it harder to decipher), and read the message off- again, a nice idea, but the need to make a new set of skytale’s for everyone every time the key needed changing rendered it impractical. Nonetheless, transposition ciphers are a nice idea, and the Union used them to great effect during the American Civil War.

In the last century, cryptography has developed into even more of an advanced science, and most modern ciphers are based on the concept of transposition ciphers- however, to avoid the problem of using letter frequencies to work out the key, modern ciphers use intricate and elaborate systems to change by how much the ‘value’ of the letter changes each time. The German Lorenz cipher machine used during the Second World War (and whose solving I have discussed in a previous post) involved putting the message through three wheels and electronic pickups to produce another letter; but the wheels moved on one click after each letter was typed, totally changing the internal mechanical arrangement. The only way the British cryptographers working against it could find to solve it was through brute force, designing a computer specifically to test every single possible starting position for the wheels against likely messages. This generally took them several hours to work out- but if they had had a computer as powerful as the one I am typing on, then provided it was set up in the correct manner it would have the raw power to ‘solve’ the day’s starting positions within a few minutes. Such is the power of modern computers, and against such opponents must modern cryptographers pit themselves.

One technique used nowadays presents a computer with a number that is simply too big for it to deal with; they are called ‘trapdoor ciphers’. The principle is relatively simple; it is far easier to find that 17 x 19 = 323 than it is to find the prime factors of 323, even with a computer, so if we upscale this business to start dealing with huge numbers a computer will whimper and hide in the corner just looking at them. If we take two prime numbers, each more than 100 digits long (this is, by the way, the source of the oft-quoted story that the CIA will pay $10,000 to anyone who finds a prime number of over 100 digits due to its intelligence value) and multiply them together, we get a vast number with only two prime factors which we shall, for now, call M. Then, we convert our message into number form (so A=01, B=02, I LIKE TRAINS=0912091105201801091419) and the resulting number is then raised to the power of a third (smaller, three digits will do) prime number. This will yield a number somewhat bigger than M, and successive lots of M are then subtracted from it until it reaches a number less than M (this is known as modulo arithmetic, and can be best visualised by example: so 19+16=35, but 19+16 (mod 24)=11, since 35-24=11). This number is then passed to the intended recipient, who can decode it relatively easily (well, so long as they have a correctly programmed computer) if they know the two prime factors of M (this business is actually known as the RSA problem, and for reasons I cannot hope to understand current mathematical thinking suggests that finding the prime factors of M is the easiest way of solving this; however, this has not yet been proven, and the matter is still open for debate). However, even if someone trying to decode the message knows M and has the most powerful computer on earth, it would take him thousands of years to find out what its prime factors are. To many, trapdoor ciphers have made cryptoanalysis (the art of breaking someone else’s codes), a dead art.

Man, there’s a ton of cool crypto stuff I haven’t even mentioned yet… screw it, this is going to be a two-parter. See you with it on Wednesday…