Fire and Forget

By the end of my last post, we’d got as far as the 1950s in terms of the development of air warfare, an interesting period of transition, particularly for fighter technology. With the development of the jet engine and supersonic flight, the potential of these faster, lighter aircraft was beginning to outstrip that of the slow, lumbering bombers they ostensibly served. Lessons were quickly learned during the chaos of the Korean war, the first of the second half of the twentieth century, during which American & Allied forces fought a back-and-forth swinging conflict against the North Koreans and Chinese. Air power proved a key feature of the conflict; the new American jet fighters took apart the North Korean air force, consisting mainly of old propellor-driven aircraft, as they swept north past the 52nd parallel and toward the Chinese border, but when China joined in they brought with them a fleet of Soviet Mig-15 jet fighters, and suddenly the US and her allies were on the retreat. The American-lead UN campaign did embark on a bombing campaign using B-29 bombers, utterly annihilating vast swathes of North Korea and persuading the high command that carpet bombing was still a legitimate strategy, but it was the fast aerial fighter combat that really stole the show.

One of the key innovations that won the Allies the Battle of Britain during WWII proved during the Korean war to be particularly valuable during the realm of air warfare; radar. British radar technology during the war was designed to utilise massive-scale machinery to detect the approximate positions of incoming German raids, but post-war developments had refined it to use far smaller bits of equipment to identify objects more precisely and over a smaller range. This was then combined with the exponentially advancing electronics technology and the deadly, but so far difficult to use accurately, rocketeering technology developed during the two world wars to create a new weapon; the guided missile, based on the technology used on the German V2. The air-to-air missile (AAM) subsequently proved both more accurate & destructive than the machine guns previously used for air combat, whilst air-to-surface missiles (ASM’s) began to offer fighters the ability to take out ground targets in the same way as bombers, but with far superior speed and efficiency; with the development of the guided missile, fighters began to gain a capability in firepower to match their capability in airspeed and agility.

The earliest missiles were ‘beam riders’, using radar equipment attached to either an aircraft or (more typically) ground-based platform to aim at a target and then simply allowing a small bit of electronics, a rocket motor and some fins on the missile to follow the radar beam. These were somewhat tricky to use, especially as quite a lot of early radar sets had to be aimed manually rather than ‘locking on’ to a target, and the beam tended to fade when used over long range, so as technology improved post-Korea these beam riders were largely abandoned; but during the Korean war itself, these weapons proved deadly, accurate alternatives to machine guns capable of attacking from great range and many angles. Most importantly, the technology showed great potential for improvement; as more sensitive radiation-detecting equipment was developed, IR-seeking missiles (aka heat seekers) were developed, and once they were sensitive enough to detect something cooler than the exhaust gases from a jet engine (requiring all missiles to be fired from behind; tricky in a dogfight) these proved tricky customers to deal with. Later developments of the ‘beam riding’ system detected radiation being reflected from the target and tracked with their own inbuilt radar, which did away with the decreasing accuracy of an expanding beam in a system known as semi-active radar homing, and another modern guidance technique to target radar installations or communications hubs is to simply follow the trail of radiation they emit and explode upon hitting something. Most modern missiles however use fully active radar homing (ARH), whereby they carry their own radar system capable of sending out a beam to find a target, identify and lock onto its position ever-changing position, steering itself to follow the reflected radiation and doing the final, destructive deed entirely of its own accord. The greatest advantage to this is what is known as the ‘fire and forget’ capability, whereby one can fire the missile and start doing something else whilst safe in the knowledge that somebody will be exploding in the near future, with no input required from the aircraft.

As missile technology has advanced, so too have the techniques for fighting back against it; dropping reflective material behind an aircraft can confuse some basic radar systems, whilst dropping flares can distract heat seekers. As an ‘if all else fails’ procedure, heavy material can be dropped behind the aircraft for the missile to hit and blow up. However, only one aircraft has ever managed a totally failsafe method of avoiding missiles; the previously mentioned Lockheed SR-71A Blackbird, the fastest aircraft ever, had as its standard missile avoidance procedure to speed up and simply outrun the things. You may have noticed that I think this plane is insanely cool.

But now to drag us back to the correct time period. With the advancement of military technology and shrinking military budgets, it was realised that one highly capable jet fighter could do the work of many more basic design, and many forsaw the day when all fighter combat would concern beyond-visual-range (BVR) missile warfare. To this end, the interceptor began to evolve as a fighter concept; very fast aircraft (such as the ‘two engines and a seat’ design of the British Lightning) with a high ceiling, large missile inventories and powerful radars, they aimed to intercept (hence the name) long-range bombers travelling at high altitudes. To ensure the lower skies were not left empty, the fighter-bomber also began to develop as a design; this aimed to use the natural speed of fighter aircraft to make hit-and-run attacks on ground targets, whilst keeping a smaller arsenal of missiles to engage other fighters and any interceptors that decided to come after them. Korea had made the top brass decide that dogfights were rapidly becoming a thing of the past, and that future air combat would become a war of sneaky delivery of missiles as much as anything; but it hadn’t yet persuaded them that fighter-bombers could ever replace carpet bombing as an acceptable strategy or focus for air warfare. It would take some years for these two fallacies to be challenged, as I shall explore in next post’s, hopefully final, chapter.

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NUMBERS

One of the most endlessly charming parts of the human experience is our capacity to see something we can’t describe and just make something up in order to do so, never mind whether it makes any sense in the long run or not. Countless examples have been demonstrated over the years, but the mother lode of such situations has to be humanity’s invention of counting.

Numbers do not, in and of themselves, exist- they are simply a construct designed by our brains to help us get around the awe-inspiring concept of the relative amounts of things. However, this hasn’t prevented this ‘neat little tool’ spiralling out of control to form the vast field that is mathematics. Once merely a diverting pastime designed to help us get more use out of our counting tools, maths (I’m British, live with the spelling) first tentatively applied itself to shapes and geometry before experimenting with trigonometry, storming onwards to algebra, turning calculus into a total mess about four nanoseconds after its discovery of something useful, before just throwing it all together into a melting point of cross-genre mayhem that eventually ended up as a field that it as close as STEM (science, technology, engineering and mathematics) gets to art, in that it has no discernible purpose other than for the sake of its own existence.

This is not to say that mathematics is not a useful field, far from it. The study of different ways of counting lead to the discovery of binary arithmetic and enabled the birth of modern computing, huge chunks of astronomy and classical scientific experiments were and are reliant on the application of geometric and trigonometric principles, mathematical modelling has allowed us to predict behaviour ranging from economics & statistics to the weather (albeit with varying degrees of accuracy) and just about every aspect of modern science and engineering is grounded in the brute logic that is core mathematics. But… well, perhaps the best way to explain where the modern science of maths has lead over the last century is to study the story of i.

One of the most basic functions we are able to perform to a number is to multiply it by something- a special case, when we multiply it by itself, is ‘squaring’ it (since a number ‘squared’ is equal to the area of a square with side lengths of that number). Naturally, there is a way of reversing this function, known as finding the square root of a number (ie square rooting the square of a number will yield the original number). However, convention dictates that a negative number squared makes a positive one, and hence there is no number squared that makes a negative and there is no such thing as the square root of a negative number, such as -1. So far, all I have done is use a very basic application of logic, something a five-year old could understand, to explain a fact about ‘real’ numbers, but maths decided that it didn’t want to not be able to square root a negative number, so had to find a way round that problem. The solution? Invent an entirely new type of number, based on the quantity i (which equals the square root of -1), with its own totally arbitrary and made up way of fitting  on a number line, and which can in no way exist in real life.

Admittedly, i has turned out to be useful. When considering electromagnetic forces, quantum physicists generally assign the electrical and magnetic components real and imaginary quantities in order to identify said different components, but its main purpose was only ever to satisfy the OCD nature of mathematicians by filling a hole in their theorems. Since then, it has just become another toy in the mathematician’s arsenal, something for them to play with, slip into inappropriate situations to try and solve abstract and largely irrelevant problems, and with which they can push the field of maths in ever more ridiculous directions.

A good example of the way mathematics has started to lose any semblance of its grip on reality concerns the most famous problem in the whole of the mathematical world- Fermat’s last theorem. Pythagoras famously used the fact that, in certain cases, a squared plus b squared equals c squared as a way of solving some basic problems of geometry, but it was never known as to whether a cubed plus b cubed could ever equal c cubed if a, b and c were whole numbers. This was also true for all other powers of a, b and c greater than 2, but in 1637 the brilliant French mathematician Pierre de Fermat claimed, in a scrawled note inside his copy of Diohantus’ Arithmetica, to have a proof for this fact ‘that is too large for this margin to contain’. This statement ensured the immortality of the puzzle, but its eventual solution (not found until 1995, leading most independent observers to conclude that Fermat must have made a mistake somewhere in his ‘marvellous proof’) took one man, Andrew Wiles, around a decade to complete. His proof involved showing that the terms involved in the theorem could be expressed in the form of an incredibly weird equation that doesn’t exist in the real world, and that all equations of this type had a counterpart equation of an equally irrelevant type. However, since the ‘Fermat equation’ was too weird to exist in the other format, it could not logically be true.

To a mathematician, this was the holy grail; not only did it finally lay to rest an ages-old riddle, but it linked two hitherto unrelated branches of algebraic mathematics by way of proving what is (now it’s been solved) known as the Taniyama-Shimura theorem. To anyone interested in the real world, this exercise made no contribution to it whatsoever- apart from satisfying a few nerds, nobody’s life was made easier by the solution, it didn’t solve any real-world problem, and it did not make the world a tangibly better place. In this respect then, it was a total waste of time.

However, despite everything I’ve just said, I’m not going to decide that all modern day mathematics is a waste of time; very few human activities ever are. Mathematics is many things; among them ridiculous, confusing, full of contradictions and potential slip-ups and, in a field whose age of winning a major prize is younger than in any other STEM field, apparently full of those likely to belittle you out of future success should you enter the world of serious academia. But, for some people, maths is just what makes the world makes sense, and at its heart that was all it was ever created to do. And if some people want their life to be all about the little symbols that make the world make sense, then well done to the world for making a place for them.

Oh, and there’s a theory doing the rounds of cosmology nowadays that reality is nothing more than a mathematical construct. Who knows in what obscure branch of reverse logarithmic integrals we’ll find answers about that one…