Shopping – Me on the net

Celebration of Cavewoman

My daughter and I were discussing innovation and inventiveness. Well, actually we weren’t but the subject got mentioned in the context of “what if….”. What if our caveman ancestor had not banged together two rocks and invented fire starting? My opinion was that it was probably our cavewoman ancestor who did it. Our caveman ancestor would probably have banged his thumbs together between the two rocks.

This started me thinking. Inventors are usually man. Rarely, in recent times anyway, is a great inventor a woman. Why is this? Is there really a gender gap in inventiveness?

Thinking back to the caveman and cavewoman days, it is likely that the woman was responsible for the invention of clothing. The caveman was probably happy to chase pigs through the scrub with his dangly bits flopping in the wind, while the cavewoman would be inventing the loin cloth, which the caveman would likely adopt with glee, as it prevented his said dangly bits coming in contact with the gorse and other spiky plants. For the cavewoman there was an advantage that it hid the dangly bits from her view.

Then when the woman in the next cave over, the blonde one with the big … assets, starting wearing that fitting badger skin outfit, cavewomen had invented fashion. Hmm. The charcoal from the newly invented fire really enhanced the under eyes, and the lighter ash really made the cheekbones stand out. Your move, blondie!

And cooking too. Caveman probably dropped his slice of bear loin in the fire and discovered that it tasted great, after you brushed the burnt bits and the ash off. Cavewoman then got a stone, put it on the fire and sizzled her steak on that. With a few grilled veges on the side, for the healthy touch.

Of course when caveman was unsuccessful in bringing home any meat, the family had to subsist on berries and seeds. Crushing the seeds between two rocks probably made them easier to eat and that a short step from grinding them up, which is a small step from mixing them with water and then dropping them on the hot stone. Somehow I don’t imagine the caveman doing that. He’d be too busy describing the ones that got away.

Then when the caveman invited next door over for tea, then something special was required. So wrap the grilled meat pieces in the flat bread, add a few herbs and spices, and hey presto! Instant cuisine. I bet blondie couldn’t even boil an egg. Oh, wait a minute, we haven’t invented boiling things yet.

What if we take that coconut shell and fill it with water and balance it on the fire? Add a few leaves from that bush over there, and we’ve invented tea. A few ground beans from that other bush and we have coffee. Hmm, let’s domesticate a goat, so that we have an assured source of meat, and hey, we can put some of the goat’s milk in the tea.

My semi-serious point is that all these things that were developed in the dim and distant past were likely invented by the women. While the men were out chasing pigs, goats, and badgers and developing weapons and warfare, and all those men things, women stayed in or around the cave inventing, well, home.

When the men came home with pig-on-a-stick, the woman would break down the animal, with a stone knife probably invented by a woman to make it easier, remove the tubes and other gruesome bits, and set it on the fire to cook. She probably accidentally domesticated the dog by feeding it the bits she didn’t want. The cat was always there.

Of course, when you spend your days, sitting on the ground, keeping the fire going, accidentally inventing smoking of meat by hanging it over the fire, the ground begins to get a bit, well, hard. Animals skins help somewhat, but animal skins with dried grass under them were even better! But to keep the grass from leaking out from under the skins, woman had to invent sewing.

Of course, sewing helped the skins look a lot better. Take that blonde girl. What? You bought yours! You invented shopping? Go, girl!!

I’d bet it was a woman who invented agriculture. While man was out chasing deer and tripping over rocks, while he was gathering a paleo diet on the side from bushes and shrubs, woman was at home noticing that some of the seeds gathered last year were sprouting. What if she were to scratch some shallow lines in the ground and plant those sprouting seeds? What is she were to water and weed them and, well, let’s invent a word, cultivate them? Then they wouldn’t have to go so far to find seeds when that idiot man couldn’t find any prey! And if they did grow, she’d save some seed for next year rather than just eat it all.

Then when the cave gets too small for a growing family, it’s the woman who looks around, finds a bigger, better cave, and pays the occupants half an antelope for it. It’s the woman who invents real estate.

It’s the woman who sticks a few palm fronds in cracks in the rock to give them shade from the sun in summer, and who piles up some rocks to block the wind in winter, it’s the woman who diverts the stream away from the living area. Yes, this cave has running water! No need to go down to the stream to drink! It’s the woman who invents home improvement.

Of course, my hypothesis above, that from fire to home improvement, these things were invented by women. The women were, in general, left behind while the men went hunting. The men didn’t have time to invent things, but the women were able to put their minds to work on improving things around the cave, but people give them little credit for it. But when push comes to shove it seems to me that civilisation is the greatest achievement of womankind.

Models

Mathematical models are supposedly descriptions of a real phenomenon. The descriptive and predictive power of a model depends on how well the model represents the real phenomenon. Extreme precision is not necessary for a good models, so long as it doesn’t vary wildly or deviate from the real phenomenon. If the accuracy of the measurements or observations of the phenomenon are less than the deviation of the model from the real phenomenon, then the model suffices for the purposes.

For instance, a stone thrown upwards or a ballistic round fired from a cannon roughly follow a parabolic trajectory and the model (in this case a simple algebraic equation) is often accurate enough. However other effects, such a the resistance of the air to the passing of the object and the curve of the earth have to be accounted for in the model if the accuracy of the measurements is such that deviations from the model caused by these effects can noticed.

I’m going to draw a slightly artificial distinction here between ‘mathematical effects’ and ‘physical effects’. By mathematical effects I mean effects like the curvature of the earth (and also, the distance to the centre of the earth), both of which affect the geometry of the model. By physical effects I mean things like air resistance, and the roughness of the missile, which can’t be directly deduced from the physical situation and have to be assessed by experiment. Of course in many cases others have studied the effect of things like air resistance and their results can be plugged into our model to enhance its accuracy.

Mathematical effects are ultimately based on physical ones. For instance Newton’s Law of attraction between two masses is a physical effect represented by a mathematical equation – the product of the two masses and the gravitational constant divided by the square of the distance between them gives a measure of the gravitational attraction between them. On the surface of the earth, where the vertical movement of a thrown stone is negligible compared to the distance between the centre of the earth and the stone, this means that we can ignore the variation of the trajectory due to this effect since it is so small and use the mathematical model of a parabola for the projectile’s trajectory.

It turns out that simple parabola is useful as a model only for simple cases where the velocity is low and the distances are small, and the accuracy of measurement is low. For artillery purposes a model based on a simple parabola is not accurate enough. To drop a shell on someone’s head, where you know the distance, you need to factor in not only wind resistance and the curve of the earth, but also such factors as wind direction and strength and even then a sudden gust of wind could put your aim off. The model that artillery men used is contained in a set of tables which were built up over years of experience.

It is clear, I think, from the above discussion that models are pragmatic constructs. If a model doesn’t work you merely change it or replace it with one that suits your purposes better. That doesn’t mean that the old model is totally abandoned. After all, the artillery man doesn’t need his complicated tables when all he wants to do is shoot a basketball through a hoop.

Some models are purely descriptive and non-quantitative, such as the economic ‘supply and demand’ model. This is usually depicted by a graph showing one line sloping down from left to right crossing another line sloping up from left to right. The upwards sloping curve is the ‘supply’ curve and the downwards sloping curve is the downwards sloping one. The vertical axis is marked ‘Price’ or similar and the horizontal axis is marked ‘Quantity’ or similar. Rarely are there any tick marks or values on either of the axes.

The trouble this model is that it is, to my mind, too vague and woefully incomplete to be really useful. Firstly, the lack of any quantitative units means that any usage of the model must be qualitative and prevents it from being useful in any real situation. Secondly, while the trends of the supply and demand curves may be generally in the directions usually shown, this is not generally true, especially if the demand or the price moves far from the current ‘equilibrium’ point. Thirdly price changes are usually discussed in terms of change in demand, whereas the opposite is probably more usually true, and demand is driven by price. Fourthly, the shape of the curves does not stay static and they change with time, often unpredictably. Fifthly, there are many more external influences that are likely to have a bigger effect on price than simply supply and demand. Monopolies and monopsonies have huge effect on prices, and supply and demand can have little or no effect in these situations. The validity, if any, of the model is limited to a very restricted domain of situations.

The biggest criticism of this economic is that it doesn’t lead to quantitative models. It doesn’t direct strategies and few people, I’d suspect, actually use the curves for anything, except economics lecturers. It is not alone in the economics field, though, as there appear to be no models which are quantitative, valid in more than a small domain, and generally accepted in general use. It’s possible that there never will be.

And Again? Throw the Ball! (Photo credit: wharman)

I’ll close off by mentioning two other usages of the word ‘model’. There are many more usages, but I’ll leave those for now.

Firstly there is the catwalk model – young ladies and some men who acts clothes horses for fashion and ‘haute couture’. I’ve no problem with that except the usual one, that the models are thin to the point of anorexia, and sometimes the clothes stray to the bizarre side of the street. These young people, should they catch the eye of the fashion industry, may make many millions of dollars. The people who pay them these dollars must feel that they get some benefit from the payment, which brings us back to economics, supply and demand!

Secondly there is the constructional meaning of the word – where people construct sometimes exquisite copies of objects at a much smaller scale and of different materials to the original. Often these models are placed in context in models of the usual surrounding of the original – a model train may run on a complex layout with stations, signals, bridges and so on. Often as much care is lavished on the model’s surroundings as on the model itself. Many of these are true works of art.

"Carlton J. Dearborn, S2c [cements a stri... — “Carlton J. Dearborn, S2c [cements a stringer on the fuselage of balsam model of Stuka Dive Bomber at Camp Smalls, U.S. Naval Training Station, Great Lakes, IL. Dearborn teaches sailors to identify enemy and Allied aircraft].”, 03/13/1943 (Photo credit: The U.S. National Archives)

Counting.

If you want to count sheep, count the legs and divide by four. This piece of faux folk-wisdom has, as is usual in such cases, a grain of truth. The human eye finds it easier to distinguish elongated objects if the axes of the object are separated and perpendicular (or so I believe). It is easier to count the candles mounted on a cake than the same candles arranged in a line. This – | | | | | | | – is easier to count than this – _ _ _ _ _ _ _ , I feel. (I’ve used Google to see if I can find evidence and came across this, which seems to align with what I am saying, though I’ve not accessed the paper).

If I am correct it is easier to, say, count the horns on a herd of cattle and divide by two than count their backs. It occurs to me that an optical-electrical counting device might have issues in this regard too, since a leg might stand out from the background, and produce a short pulse in the sensor, but a whole cow might take a while and its colours would blend into the next cow. Of course, one could always use higher technology to resolve the issue with respect to cow counting, (RFIDs in ear tags would be an obvious solution), but it doesn’t solve the wider issue.

Maybe the reason that the counting device and the eye/brain find it easier to distinguish objects orientated (roughly) perpendicular to their (roughly) linear arrangement is similar. If they are (roughly) aligned in the same direction as their linear arrangement they may, possibly, overlap, and this can confuse sensor and/or eye. Was that one, two, or three objects that passed the sensor? It’s easy if they are perpendicular, but harder if they are aligned.

English: Geometrical-optical illusions: horizo... — English: Geometrical-optical illusions: horizontal/vertical anisotropy (Photo credit: Wikipedia)

I’m pretty much reduced to saying the same thing in different words, but I hope that what I am trying to get at is clear. It may or may not be relevant that humans and higher primates tend to stand more or less vertically, so one individual is more easily distinguished from others than an individual cow is from the herd.