A bouncing ball captured with a stroboscopic f...
A bouncing ball captured with a stroboscopic flash at 25 images per second. (Photo credit: Wikipedia)

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.

FN 57 ballistics 100yd
FN 57 ballistics 100yd (Photo credit: Wikipedia)

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.

English: Diagram of simple gravity pendulum, a...
English: Diagram of simple gravity pendulum, an ideal model of a pendulum. It consists of a massive bob suspended by a weightless rod from a frictionless pivot, without air friction. When given an initial impulse, it oscillates at constant amplitude, forever (Photo credit: Wikipedia)

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.

Cannon Model - Part of my military models coll...
Cannon Model – Part of my military models collection (Photo credit: Wikipedia)

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.

Supply and demand
Supply and demand (Photo credit: Wikipedia)

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!
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!

Model (Photo credit: vpickering)

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)


Assortment of wine from Domaine Chandon in Yar...
Assortment of wine from Domaine Chandon in Yarra Australia showing their sparkling Chardonnay and Pinot noir wine as well as a still pinot noir. (Photo credit: Wikipedia)

Most cultures have some substance that they use to relax inhibitions and induce euphoria. Overindulgence leads to intoxication, the word acknowledging that the substance, whatever it is, damages the body in some way. It is toxic. The most widespread substance that is used is alcohol, and the reason it is so common is probably because it is easy to produce and acquire. Just let some fruit go rotten.

Of course, rotten fruit is pretty nasty, and people are ingenious, and it was soon discovered that fruits and grains and some root vegetables could be made to ferment without first going rotten. In fact it is a yeast that is the agent which facilitates the necessary chemical reaction, which takes in sugars in some form and produces carbon dioxide and alcohol. “Alcohol” when referred to in relation to recreational drinking is ethyl alcohol or ethanol, a substance that has now and then suggested as a fuel for cars.

English: Bai jiu, or Chinese white hard alcoho...
English: Bai jiu, or Chinese white hard alcohol that was made locally in Haikou, Hainan, China, and sold in a dedicated alcohol shop. The signs hanging on the stone bottles show alcohol percentag above, and price in yuan (2009) below. (Photo credit: Wikipedia)

Alcoholic drinks can be made from practically anything and can contain varying levels of alcohol, from relatively low alcohol drinks like beers and ales, through to wines, which represent the strongest drinks that can be made by simple fermentation and on to distilled alcoholic drinks which contain large amounts of alcohol.

English: Elderberries Ripe elderberries growin...
English: Elderberries Ripe elderberries growing by the Roman wall at Calleva Atrebatum. Elderberries can be used in a number of ways, including making elderberry wine. (Photo credit: Wikipedia)

Wine is these days made from grapes, and alcoholic drinks made from other fruits are usually referred to as “fruit wines“. There is an unfair implication that “fruit wines” are not real wines and are inferior to grape wines. While “fruit wines” are generally not as good as grape wines, the reason is probably more to do with the centuries of development and improvements that have gone into modern grape wines than any inherent superiority of grapes as a prime ingredient of wines.

Wines are typically made from the grapes of Vitis vinifera though occasionally other grapes are used, and hybrids of V. vinifera with other species are not uncommon. Wines are classified as either white or red, the colour coming from the colour of the skin of the grapes that were used in the production of the wine. Rosé wines are usually pinkish or pale red and are usually made from red wine grapes. The paler colour results from the removal of the skins at an early stage of production.

Several French rose wines from the Rhone Valle...
Several French rose wines from the Rhone Valley and Provence. (Photo credit: Wikipedia)

There are all sorts of varieties of wine, named after the varieties of grape vines that produce the grapes. I’ve a couple of books on wine which detail the genealogy of grape vines and it is a complicated messy and incestuous family tree. There are stories of skullduggery, stealing, and smuggling. There are stories of cataclysmic crop failures and noble experiments and migrations between countries.

Climate change comes into the picture too. Grapes are grown in areas of southern England where grapes have not been grown since Roman times, when younger and more robust varieties were grown. But the ability to grow grapes commercially in England can’t all be put down to global warming since techniques for protecting vines from frost (the main cause of crop failure in grape vines) have been vastly improved.

Madeleine Angevine growing in England
Madeleine Angevine growing in England (Photo credit: Wikipedia)

Smoke producing machines are used to protect vines from frost and helicopters have been used to good effect too. I’m not sure how these techniques work, but I believe they do. One of the most bizarre protection methods is to spray the vines with water which instantly freezes and cocoons  the buds in an envelope of ice apparently protecting them from freezing.

I find this stuff interesting, but the reason people buy wine is because of the alcohol in it, and the reason that they prefer some wines over others is the taste. I prefer red wines, because white wines seem astringent and too sweet. Which is odd because red wines can also be astringent and sweet! Well, maybe I am exaggerating somewhat, but the beauty of the wine is definitely on the tongue of the taster.

When tasters taste wine, they have a problem. Sweetness or dryness is pretty much describable, as is the tannin level, which gives all wines, red or white, its astringency, but when the subtleties of the flavour have to be described, especially to someone who has not yet tasted the wine, then there are issues.

Vineyard owned by California wine producer Fer...
Vineyard owned by California wine producer Ferrari-Carano in the Dry Creek region of Sonoma county. (Photo credit: Wikipedia)

Wines may be described as “fruity” or “full-bodied”, which gives some impression of the experience of tasting the wine. The taster may have to descend to using analogies for further details. To quote from a bottle label : “This wine is fruit driven with flavours of red berry fruit and black cherries….”.

However, if you actually taste the wine, you won’t taste berries or cherries. What you will taste is firstly the major type, red or white. Secondly you are likely to be able to distinguish the variety, for example Pinot Noir, or at least the style for a blended wine. Then you will get the overall ‘shape’ of the wine (robust maybe, or delicate). You will note different aspects of the wine at different stages of drinking, at first hit, in the mouth and the aftertaste. I find that some wines have distinctive phases of this sort and others don’t.

You certainly don’t want to be analysing every sip of every wine when you drink it, but I do try to taste it like above at least on one mouthful, but I don’t always remember to do so. It does help you when you choose a wine in the store though.

Typical shape and design of a white wine tasti...
Typical shape and design of a white wine tasting glass. New Zealand wine (Photo credit: Wikipedia)

To get back to the red berries and cherries for a moment, you may taste a wine and not be able to detect them in your tasting. That’s because, in my opinion, those tastes are not there as such. So what do the tasting notes mean by these comments? They mean that the taster is reminded by some flavours of the wine of some aspects of the taste of berries. A faint echo of the richly complex flavours of red berry fruit echoes in the mind of the taster, and that is all that he has to work with when trying to describe some of the flavours in the wine.

In terms of familial relationships the flavour being described by the taster is not as close as brother or sister to the flavour mentioned by the taster. It’s more a second cousin twice removed relationship, and the taster is not saying that it is the second cousin twice removed, but that it reminds him or her of the second cousin twice removed. So you may think that there is hint of gooseberry in flavour of the wine and for you there are.

I think that the ability to even register some flavours varies from person to person and not just in wine. One person may taste something complex and say “mint”, while another may say “cloves”.

Wine tasting bar at Ridge/Lytton Springs, Sono...
Wine tasting bar at Ridge/Lytton Springs, Sonoma, California (Photo credit: Wikipedia)

So where does it leave those of us who read wine labels and try to match the description with the label? Well, unless you drink a lot of wine and have an ability to distinguish the flavours that is practised, and have a similar sort of palate to the usually anonymous taster, then the bottle labels or tasting notes don’t mean a great deal. If it says “robust” or “full-bodied” for example, most people would be able to agree, but if it says “hints of gooseberry” you may well not agree that those flavours are there. It might remind you more of apples.

Image of an old Kazakhstan wine bottle.
Image of an old Kazakhstan wine bottle. (Photo credit: Wikipedia)


A Cheezle in a mousetrap
A Cheezle in a mousetrap

In an advert for Cheezles (a cheese flavoured snack) two mice are discussing the risks of trying for a Cheezle. One says “It’s worth a crack, Nigel”. Nigel apparently  tries for the Cheezle, and there is the crack of a mouse trap, and the other mouse says “Nigel? Nigel?”. Now the original ad was, most people would agree, very funny, even if my exposition lacks something. However it deals with something which could be considered tragic, the death of the unfortunate Nigel.

Humour is strange, almost beyond belief. The tragic is often funny. Death is a constant theme in humour. Disfigurement is also a common factor. Other factors are sexuality, criminality, embarrassment. From a different point of view, it’s about surprise and conflict, and a certain discontinuity. But I think that it is impossible to define humour.

English: Young seagull with a sense of humour ...
Juvenile seagull. It obviously doesn’t see the humour in this situation.

It is probably the only human trait which might be totally absent in ‘lower’ animals. I don’t know of any case where a human trait is totally absent in animals, but it may be merely that I haven’t come across humour in animals. It is my contention that no trait in humans is not demonstrated to a lesser extent in ‘lower’ animals. Maybe there is a chimp snatching another chimp’s plaything and then sniggering when his victim can’t find the toy. Maybe. The Internet has anecdotal evidence that animals can demonstrate humour, but nothing too convincing. Or maybe I didn’t search for long enough to come across any in-depth studies.

Animals show joy, a certain self-awareness, disappointment, anger and many other supposedly human traits. They can learn, remember and generally demonstrate that they share our attributes, maybe to a lesser extent (though I feel that for many animals it is not much lesser than humans).

Dogs and Joy
The word for joy is dog.

But animals don’t appear to have the capacity to experience humour (to my knowledge). If this is so, it is significant. It would be the only uniquely human attribute. My dog demonstrates joy, affection, desire, and many other things, but doesn’t demonstrate humour. A dog will never tease you. A dog is direct and forthright. You can’t share a joke with a dog. I’m fairly sure that you can’t share a joke with a chimpanzee or a gorilla, but I’d defer to an expert on that.

If humour is endemic to humans it is at least part of what distinguishes us from other animals. It may be the only thing that distinguishes us from them, as there is nothing else that I can think of that does. All animals have intelligence, at least to a degree, above a certain level of complexity. Some animals show preference for attractive appearance or display (particularly birds) which may be the basis of our aesthetic sense, but no animal, so far as I know shows a sense of humour.


There is a variety of humour that seems somewhat different to the ‘mainstream’ and that is the pun. Puns are plays on words in the majority of cases, but they may be visual. A pun can be based on homonyms, words which sound the same but which have different meanings, and even different spellings. For instance there is a village in Southern England called Brede, so if someone announces that “We are going to Brede” one can understand that a bystander might be somewhat taken aback. Another example is George Carlin‘s statement that “Atheism is a non-prophet institution”.

As I said above, humour often involves some sort of mishap or disaster for someone. In such cases it may act as some sort of tension release mechanism. That’s a fairly obvious, therefore suspect, suggestion, though in practise it seems to work and can be a recommended way to break the tension in difficult situations. Puns don’t give the same sort of release (generally), and mostly involve language so seem to be on a higher intellectual level than mainstream humour. In summary however, I’d say that humour is a facet of human beings, but it still seems mysterious to me. Strangely, infants seem to develop a sense of humour early in life. There’s not many things more infectious than a laughing child.

laughing (Photo credit: ayes)