For eons our ancient ancestors, our forebears of the human race, evolved in the physically tough, uncompromising world totally unforgiving of any errors of judgement required for survival. The individual sensed its existence from a highly subjective platform within the mind, imaging it by eye, and constantly modifying that view by sounds, smells,touch, and of course taste. That almost completes the picture. This multi-million year development of our perfectly honed faculties has served us well over that time during our struggle to survive, but at an incalculable cost to the lives of those who didn't make the grade. The human animal is still effectively the same as it was when it evolved long ago, yet now it lives in modern times. And so an appraisal of how we have changed, if at all, must also be contrived through this updated perspective, gleaned from more life friendly conditions in which we now find ourselves where our basic differences if any manifest themselves in our slightly greater longevity and stature, and of course a more cluttered mind. Though the basic physical world hasn't changed much at all, there is at least one particular aspect of modern human life which has, and I believe that unbounded mathematics and carbon fuels has facilitated this.

As microscopists we are in a slightly advantageous position of being able to understand a little about the scale of things. During the course of practicing our hobby we slowly become accustomed to a random sampling of the earth's variety of tiny artifacts, living or otherwise. After some time we can relate to a narrow bandwidth of this scale which starts at the proverbial 'full stop' where the eye fails, but where the microscope picks up at low power, and proceeds in increasing units of magnification in sequence with each objective of higher power until of course we reach the oil immersion lens and there it ends. Beyond that we are truly flummoxed, having no viewing experience at higher amplification and resolution. When the electron microscope is employed its imaging conveys a clarity that seems unreal, at least that's how its imagery strikes me, and is in part due to the quantum leap in resolution over the light limited views we are used to, and the fact that dust doesn't seem to exist in its lensless system nor at submicroscopic levels.

For individuals who are not familiar with the microscope, it might seem that they have missed out on something which we haven't. But are we so sure that our perception of scale is any different from the uninitiated in microscopy ? Of course we are proficient with the mechanics of handling the necessary apparatus and have had many hours of viewing imagery to our credit, but how much of this is capable of being absorbed in absolute terms into our psyche in the way that it actually is ?

Imagine that we apply a scale of magnification of a 1000, which is about the useful limit of the light microscope's resolving ability, to everyday objects. So at this level of amplification the average adult human being would stand about 1.7 kilometres tall ! The average house would be 10-15 kilometres high and about 20 kilometres long. An average middle aged tree would be as high as Mt Everest, with a trunk about 500 metres wide. Even a cricket stump's diameter would be around 38 metres, with cricket balls of about 88 metres across. Incidentally Mt Everest at x 1000 would be an earthly carbuncle peaking at over 6000 miles into space where about 60% of its upper parts would be snowless, yet sprinkled with the wreckage of low orbit satellites !?

But let's go back to the x 1000 view of the human being with its big toe in view before us. The toe nail's leading edge would be about 20 metres off the ground, and it would be around 2 metres thick ! The whole foot print would span an area of approximately 250m x 100m .. which translates to about 2.5 hectares or about 6-7 acres ! An amplification factor of 1000 is therefore subjectively at least rather more expansive than we might have originally considered, since its implementation through the microscope doesn't reveal the true scale of the diminutive subject under observation.

Of course so far we have only touched upon linear scaling, but there are in fact some surprises in store regarding the change in physical properties of matter when scaling up or down. The most significant and fortunately easiest to understand is an object's change in volume and therefore its mass. Imagine a brick, and another whose dimensions are exactly double its physical size. The latter is twice as long, broad and thick, but it's not double its mass , but in fact 4 times as much as the smaller brick and therefore 4 times its mass. The quickest way to reckon this up is to simply square the ratio of linear difference. Therefore a brick which is 3 times the size of the first will weigh 9 times more than the original. Our giant human is a 1000 times larger so its not a 1000 times heavier but the square of 1000 which works out at a whopping 1 million times heavier ! There are more implications within this realm of the 'mechanical similitude' of matter, but they are not intuitively obvious to simple analysis, being concerned with inertia and stability etc. and not too pertinent therefore in these notes.

Fortunately as it happens when we observe high powered imagery down the eyepiece, the limiting field of view which we are all accustomed to, constrains the imagination from totally realising the magnitude of employing such large magnification powers. So imagine for a moment being able to see an entire house fly at around x 100 which translates into it appearing approximately 1 metre in length ! Few observers would be comfortable with such an idea let alone the realisation of the concept, yet we happily scrutinise its proboscis within the bounded field, where it appears safely constrained and is 'behind' the eyepiece's glass safely at 'arm's length'.

Of course intellectually speaking we realise that imagery on a grand scale through the eyepiece is an artifice of sorts employing the manipulative qualities of lenses on light energy to form an aerial image. We are aware too that our perception of the magnified image is an isolated segment of another world, yet we become accustomed to this as a normal experience.

But before digressing, consider the scaling down of matter that has revelations just as profound as up scaling. So the average human model reduced in size from the 1.7m human form to a thousandth of its normal size, would become 1.7mm high........about the same height as a 'stack' of 10 coverslips ! Not exactly invisible but very easily overlooked. Its mass would be a millionth as normal which would put into the sub 'super flyweight' class at around 0.08 grams ! So it comes as no surprise that microscopic subject matter such as animal cells, diatoms, and bacteria, are so tiny in mass that the arithmetical figures become meaninglessly small and way beyond our life experience. Mathematics therefore, does in one way bring a little sensibility to our awareness of both things large and small. But it's only an indirect awareness as I'm sure you will agree. It comes therefore as no surprise to realise that we cannot be expected to comprehend the extraordinary large or small scale of things around us from so narrow an evolutionary existence on the surface of this planet through the eyes and mindset of perception at a scale of x1. This entrenchment of a single scale is absolute in our psyche ; we cannot undo this nor adapt it, other than to use comparative measures through the tool of mathematics, and of course our earth nurtured imaginations.

Over the relatively short time span of scientific discoveries, our place in the universe has been slowly awakened and in contemporary times we've been subjected to ever more bizarre information relating to the scale of it. How much of this we can comprehend is of course highly debatable and varies from the self effacing views of some to the more confident expansive reflections of those at the sharp end of frontier sciences.

As the human animal hasn't physically changed in any really significant way, are there any examples of scale distortion which are effecting our perception of the world or indeed our surroundings in modern times ?

Our exploratory traits have made significant advances in the all important areas of the survival of our recent ancestors. But surely the most significant of these is the craving for more efficient ways of doing things, presumably in part to compensate for our finite existence, and more lately to improve profits in the world of big business. We know we cannot alter the progression of time, but we like to speed up processes that simulate this. Travelling ever quicker from one location to another is a typical manifestation of this inherent urge. Yet jetting around the world only distorts our primeval perspective of distance, as does journeying in cars to work each day. The Internet itself cushions vast distances between e-mail recipients. In fact I believe that modern western society is less capable of understanding scale than other groups living in far more frugal circumstances, simply because scale is being distorted habitually each day. Only the marathon runner truly understands the scale or magnitude of 26 miles, yet the driver of the car that covers the same distance cannot understand the runner's experience which was a little nearer the norm many years back.

Language has in itself streamlined communications between individuals as well as releasing ideas and notions of many kinds from the imagination : akin to mathematics. We also know that language and mathematics can be misused to distort reality.

Such practises as getting what we want before paying for it, the credit scenario, is I believe a similar distortion of primordial reality, though of course in a different way again. These unnatural 'advances' in our culture have in my humble opinion an undesirable effect on the way we personally percieve our surroundings or how we relate to them. Television has filled the minds of multitudes of the populace with a rather augmented view of the world as it really is, and aiding a slow but nevertheless genuine disenfranchisement of the viewing public from evolutionary reality.

Most recently however the mathematical escalation of sums of money that are transferred in big business may seem in the verbal context to be well within the range of the human psyche, as the utterance of large figures in every day matters seem to suggest. But I believe that these figures have little meaning to many of those who utter them. One of many concepts which is I believe is beyond the ken of mortal souls is personified perfectly in modern times by the word 'Billion'. It's used constantly in economic circles, and reported daily in newsprint throughout the world and spoken of on radio and television. We are certainly used to hearing this figure, but are we aware of its true magnitude ? Indeed are THEY aware of its breath taking significance ? I doubt it. Mathematics has its uses without question, but its many ramifications of scale simply cannot be sensibly comprehended by the human mind.

To have some semblance of the scale of a figure like a billion we can try to imagine one billion seconds in time. As a matter of fact a million seconds translates into just over 11 days, so a billion becomes a thousand times longer. That a billion seconds is in fact over 31 years never ceases to amaze my senses.....nor the fact that my heart's beaten just over 2 billion times in almost a lifetime .......some heart !

No wonder then that our oil driven western society is becoming besotted with large mathematical figures which look amply plump and impressive, and why there is a fervour for the national lottery prizes of ridiculously large sums of money, despite the microscopic odds of winning by a magnitude beyond the senses. My father once let me know he'd worked out the weight of copper coinage a recent lottery entrant had effectively won when he was paid £20 million. In the penny equivalent it makes for a sizable load of 6000 tonnes of copper alloy......that's around 300 articulated lorry loads.............thank goodness for paper money ! Maybe it should be paid in copper coinage......it'd enhance the prospective entrant's awareness of the vast magnitude of such sums of money, and hopefully cool his ardour for it ? The proverbial cheque with its series of mouth watering noughts simply cannot convey the magnitude of its potential in the trembling hand of the recipient !

But what about the magnitude fraternities that abound, exercising their thirst for greater things ? Thus in astronomy for instance the mania to build much larger telescopes overwhelms the senses, as their slick acronym suggests : GOD's : Giant Optical Devices........which include a string of plans to build progressively larger evermore expensive instruments ending with OWL : Overwhelming Large telescope ! .....with a guaranteed OWL price tag for the single purpose of more accurate gauging of the age of the universe : a figure that no one can genuinely absorb into the psyche anyway ? And let's not forget those atom smashers who's incomparable consumption of energy and finance reflects perfectly the crazy world of atomic science where no one really knows what's going on at that fundamental level of atomic physics, but are nevertheless happy for governments to pour truckloads of tax payers money into the bowels of the earth where the humming, energy greedy particle accelerators exist........conveniently out of sight and out of mind of the public ?

So in our magnitude crazed society which extensive misconception of scale wins the 'sublime to the ridiculous' award ? Well in my humble opinion there's one rather unique grouping of figures which I feel deserves the prize.

Thus this mathematical expression gives the total number of sub-atomic particles in entire universe... give or take :-

I apologise if I haven't got the precise number of noughts in place.......or indeed only used one exclamation mark...............but I'm sure you've got the picture :)

That someone can simply subordinate the entire material content of the universe into a scribble has to be the greatest example of magnitude distortion, and the most audacious bit of thinking ever, yet this mathematical 'short hand' was probably conceived in a few seconds and recorded thus onto a scrap of paper with the squiggle of a pencil. It is therefore incomparably unique.

In conclusion I cannot fail to mention one more citation of scale, in this instance of truly ancient human endeavour which is almost mystical, and one which will always raise a special reverence in my thoughts. Near the Olorgesailie settlement in the Great Rift valley of Africa there can be found a small area of land which is littered with stone age shards and axe heads. It was accidentally discovered about 85 years ago, and subsequently researched. The findings are that this area, once beside a lake, was occupied by hominids until about 200,000 years ago, when likely the climate started to change and the lake dried up. But the truly astonishing revelation gleaned from the isotopic analysis of this site was that this occupation lasted for around 800,000 to a 1000,000 years !! ( that deserves 2 exclamation marks )

That such a vast era of occupation by 'peoples' who have left virtually no remains or litter other than their indestructible tool heads over a truly awsome scale of time compared with our post ice age span on earth, begs so many questions about our status as intelligent beings, as by comparison are modern world is littered with the hallmarks of our 'progress' in a tiny fraction of the time the Olorgesailie people occupied their territory.

Having only existed through the post glacial earth for a few thousand years.......or around 1% of the time the Olorgesailie people's reign, we seemingly have more than enough time to get things right. What is in no doubt at all is that we are going to have to utilise our former personal survival systems, and extend our personal exploratory traits again in earnest for survival whether we accept the ramifications of the physical history of the planet or not. The fact is that there are going to be changes of one kind or another if we are to continue in our occupation on earth even for another fraction of the time of the settlement of the Olorgesailie people. The scale of universal change to this planet from our irresponsible endeavours of burning unimaginable quantities of fossil fuels is very real. The problem we face is whether we can devolve in a civilised manner, for the notion that we can carry on at this level of energy gluttony is futile. The embodiment of the need to utilise less than more will be the keystone of success in any surviving civilisation in the future, whilst forgoing the 'tinsel luxuries' of the past.

Fortunately evolution saw to it to provide us with incredibly efficient and reliable body parts, so long as they are nurtured and fed, but the iconic idols of our time will be of no use. Water, food and shelter will eventually sustain the core of distant future commerce, as quickly as the memories of the excesses of scale fade. The lesson learnt about ignoring the obvious whilst exploring the unattainable will also fade into oblivion, but perhaps some of the blunders of our age might remain as an epitaph of how 'excess' brought failure to an animal species that had paid a high price evolving in more austere times, only to be thwarted by its inability to realise its own evolutionary limitations of scale.