A primary meanings

We humans, as members of specie Homo sapiens, are basically African mammals. One of the very many, well adapted at roaming savannah, and interacting more or less friendly with the many other animals there present, as lions, zebras, rhinoceros, antelopes, elephants, rats, whatever.

Sure we spread all over the world quickly. So quickly, in fact, that our bodies have adapted only in part to the climates of our new lands.

We carry our part of Africa in public parks (have you noticed? they are artificial savannah, with trees standing isolated in grassland), and upon of us, as vests and dresses shielding from weather extremes.

Sure, seeing dresses from a physicist’s perspective may not be what Giorgio Armani or Krizia would imagine, in their tending more to the other dimension, of dressing as a status mark and / or seduction tool.

But dresses, no question, have also the function of protecting us from extremes of cold and warm, and they devise some consideration, in my opinion, to this sometimes understated, yet very interesting, aspect.

What Pantyhose Could Really Meant To Be

I begin with one part of stocking which, on a first glance, may seem to be justified only by the desire to seem more attractive.

Here comes the official story.

People of European ancestry (the initial clients of pantyhose) have light-colored skin, because their agriculture-bound diet does not allow a direct supply of D vitamin, so they need to photosynthesize it by means of radiation in UV band (and our Sun provides quite a lot of it).

But for more or less the same reason, wearing a milk-white skin is not a very good indicator of sun exposition, that is, D vitamin supply. A tanned aspect is surely more interesting.

In addition, what is names “white” skin is really "transparent" skin. The “white” you see is the fat cells below the skin, which you see through it. The actual color is not really white, of course, but light pink: a combination of the white from fat cells and the red of blood capillaries.

Translation: you can see through the skin down to the minimum defect.

Hence the “need” of socks and pantyhoses.

The common explain takes into consideration complicate things like sexual selection and sociobiology. I feel a bit perplexed, as surely the invention of nylon (or even silk) post-dates of some ten-thousands years the time scale in which sexual selection may have operated (provided it did at all - an interesting subject in itself, on which here is not the case to enter).

So, I offer an alternative solution. Maybe a bit crazy.

Let’s return to pantyhose, and the fact they are really worn independently of skin color (which maybe suggests the best color, but not wearing pantyhose per se).

In addition, they are used both visibly, under a skirt or short pants, or invisibly, under longer clothing. This suggests me their use as a seduction tool may be not their primary function, at least in many cases.

And, let’s take into account another thing, this time cultural: it is considered socially acceptable (read: mandatory) to get rid as much as possible of body hair. (Once again, sociobiologists may try informing us this is a trick, to declare the production of androgen is small and "hence" that of estrogen high, a good indicator of fertility - neglecting the fact that no androgen production means a pathological state) (I don't know if it's so clear, but I am not in love with sociobiology - maybe because of the way it has been applied in popular science literature).

Body hair is really a bit mystery in its own: as primates, we humans look naked if compared to our thick-furred evolutionary cousins. Apparently, we owe all our thermal regulation to sweating / radiating, and on a thick layer of body fat. Yet, we have many body hairs. Some visible and colored, and most very small. Their role in thermal regulation is unknown: they are too scant to have some big effect (apart functioning as natural anemometers, and augmenting the skin's aerodynamic roughness length of some tenths of millimeter).

But overall, body hairs interpose between our body and dresses, so under natural condition the skin is not in direct contact with clothes. The separation acts preventing skin wear-out and friction wounds, so may be beneficial.

Clothes were invented as our ancestors left the climate they were adapted to, and so, quite long ago. Does body hair evolved in the process, as an adaptation to wearing hard and heavy clothes?

If ("if!") this has happened, then our social habit of getting rid of it may have consequences - but this time cultural, in the way we manufacture clothes.

Sure, a well shaved leg, or arm, “feel different” that with body hair. For example: - You notice clothes in contact immediately, with a tactile response orders of magnitude larger than with body hair - Skin is subject to wear out, in case of an active life - You hardly realize entering the bathtub, if water temperature is same as body surface - Incidentally, your hydrodynamic resistance decreases a lot - You also feel immediately any air current directly on skin (then, my idea of body hair as natural anemometers may fall short).

Definitely, the world appear quite different with or without body hair (and imagination can only let us figure out what might it happen to furred animals).

Are pantyhose and nylon socks an answer? A (very recent) adaptation to wearing clothes on a shaved skin?

In fact, their texture matches more or less body hair spacing, size and orientation. From a physical standpoint, a pantyhose- or body hair-covered skin behaves more or less the same way, thermally (that is, with minimal effect) and with respect to friction.

And, if nylon can be colored and/or stamped with attracting drawings, why not doing?

Aesthetics and practical consideration may well co-exist!

Topological Type

Topology is a branch of pure mathematics studying high-order connections among figures.

And clothes are a nice topological object.

In topology, two objects (feel free to imagine them as figures in three-dimensional space) are equivalent, if one can be transformed in the other by a continuous deformation.

(Sorry so sloppy.)

Now, this definition of equivalence seems a bit crazy at beginning. But with a bit of imagination, it soon becomes intuitive, even "obvious".

Get two very different objects, for example: a teapot, and a skirt. To a topologist, they are equivalent (and bet you may imagine their morphing). (To a real topologist, a friend of mine once told, they are the same thing, inducing the topologist to attempt wearing the teapot - something demanding a considerable effort, I imagine).

In this case, things are quite simple after all: both objects have two openings, although placed differently.

But this is the key to topological equivalence. Roughly speaking, in fact, the number of openings, handles and connected components turns out to be what really matters: if two objects have the same number of openings, then it is granted (and a bit obvious, once you enter the mechanism) they can be reciprocally deformed, and hence equivalent.

Counting openings (and leaving handles apart, as their function is to date unknown) provides a handy way of sorting out clothes by their topological order.

(This may be a bit crazy way to sort a wardrobe. But if the doctor questions you, you may begin using very difficult and impressive words - however, would things turn to be really too difficult, or the doctor exhibit a strange, alarmed expression, don't hesitate to make my name!)

Beginning with order 1 (that is, clothes with one opening only) we have pantyhose, single socks, gloves, hats.

At order 2 we find skirts, mantles, ponchos.

At 3, we get pants and trousers.

We have to get at 4 to reach T-shirts, blouses, shirts, sweaters, coats, jackets, and alikes.

At 5 we find hard-work suits.

There even are order 0 "clothes", although a bit unusual: space and diving suits, moonsuits, and the like (where having no opening is, I realize, a Big Must).

Humans attach to the topological order of their clothing a value which goes well beyond the need of having hands, head and feet free. In large part the preference is cultural.

Take for example below-waist clothing. Western society has today a preference for order 3 (pants and trousers), apparently. This is just accidental, order 2 (skirts, simpler to manufacture) being the norm in many other cultures.

The main reason traces back to the late Roman Empire. During the Roman republic, skirts and their analogous (not topologically equivalent) order four clothes (togas and long dresses in general) were the norm, with variation for men and women not interfering with topological order.

The discovery of pants is recent, as Romans went in (not always friendly) contact with iron-age populations in central Europe. Those “barbarian” men worn bracae, allowing them some better protection from cold. As modern Europe formed by melting those people in an already diversified Roman Empire, trousers found their way and still are with us, now spreading from their original place (military suits of auxiliary border forces during the Roman Empire) to mainstream women and men fashion.

Why insistence on below-waist clothes? One my reason is, the upper part of body imposes much more constraints, forcing towards order 4 to have free hands and head. The lower part allows much more freedom (from a topological point of view).

Another reason may come from biophysics.

If you are like me (and chances are quite good, this configuration being typical of a slight majority of humans), then your muscular mass is concentrated in the lower part of body, towards thighs and legs. It is not that massive, sure. But, sufficient to carry moderate loads without breaking - and, to walk efficiently. We humans are bipeds, and our overall structure has progressively adapted to long-range walk at moderate to bright pace.

Today we may use this heritage to carry water from afar (and wish that not be the norm!!).

In the past, it may have been used to follow prey herds walking continuously, and disturbing animals (mostly ruminants, who need to stop continuously to feed) maybe literally to death.

Whatever the reason, as we produce our heat in muscles, thighs and legs are the most important energy sources in my body, and any other alike me biophysically. Unfortunately, legs have a very large surface, too, leading to quick dissipation of heat.

Just as a remind: our basal living temperature is somewhere around 36 °C (with wide variations due to monthly cycle, health, recovery, emotional state, amount of sleep, …). The “optimal” air temperature for us is something like 22 °C: the 14 °C difference is maintained actively by our bodies, even at rest, by an immense metabolic activity (as any mammal). Now, the places in our planet where external temperature is 22 °C are quite uncommon, including the highs in the area of Afar, where the human kind is thought to have originated some thousand hundreds years ago. In all other place, there is an imbalance which may be very high, in some places / seasons.

Ideally, clothes should maintain an Afar-style climate around our bodies, either holding heat and preventing its dispersion, or by shielding our body surface from excessive radiation / heat.

From what I’ve said previously, I “deduce” (hopefully!) the lower-body-part clothes to have a comparatively more important role in thermal regulation for me and alike people.

To be more precise: in upper part of body, the muscular mass is low and little heat is produced: you just can disperse it, and if temperature is below 22 °C you can only stay covered there, to prevent excessive heat dispersion (with potentially lethal consequences).

With the lower part of body, and its larger energy production rate, you may play as you want. At least, to some extent.

Now, let’s go back to lower-part clothes.

Order 3, trousers, are surely very convenient, as they allow forming a tight airspace around the lower part of body. This warm, humid airspace at around 22 °C is all what we need to get our part of Africa around of us. That’s fine in a cool climate, as the volume to warm air to maintain is really minimal.

In warm climates, this arrangement becomes less attractive, and the common adaptation is in shortening pants until, in the most extreme case, legs and thighs are completely uncovered.

Order 2 clothes, in case of bit-cool to warm climates, may be of advantage, allowing some degree of protection while in the same time making possible quite an easy warm air dispersion.

Two other factors play a (physical) role, by the way: freedom of movement, and protection against spines, insects, and other tiny threats.

Trousers are considered to allow a considerable freedom of movement (second only to a wide skirt up knees; think to the one worn by Roman legionaries, to whom extreme freedom of movement in walk and run was a life-saver).

A very long, or tight tube-like skirt, on the other side, is just the opposite of freedom of movement, as it constraints step stride considerably. It may be fashionable and seductive, but from the biomechanical standpoint is seems not very comfortable.

Where pants win over skirts by orders of magnitude, is in protecting against snake bites, insects, spines, little hard shrubs, cutting leaves and the like - that is, the kind of things you are likely to find in a temperate, quite humid and not too warm place as Central Europe was during the Roman Empire era, with her many swamps, and thick woodlands.

But in the Europe of following ages, in large part cultivated, the advantage of trousers over skirts is not completely clear (aesthetically, maybe, trousers are more forgiving however). It’s only a matter of social conventions, combined with randomness.

A similar phenomenon has occurred with computer keyboards: today, we’re accustomed to the “QWERTY” key arrangement. But this was just one of the many invented, and sure is not optimal in terms of typing speed and accuracy. Alternative designs, although “optimal”, became extinct after IBM introduced their first model of typing machine, which was a dramatic success. The diffusion of IBM typing machines was so widespread, that soon all other manufacturers adopted the same key arrangement. An accidental design then become the golden standard.

Same with order 2 and 3 lower body clothes. Order 3 gained a lot of success.

Gender Differences, and Never-Occurred Consequences

In our Western culture, skirts are worn almost exclusively by women (Scottish kilts being a remarkable exception), and trousers by both men and women (since recently: not so far away, trousers were intended to be “only” for men, and law prevented any kind of unconventional dressing - think to Joan d’Arc, for a then revolutionary example).

Does this make “physical” sense?

If you compare the “average man” to the “average woman”, you see their body frames are not that identical, and their muscular masses are distributed in a slightly different way.

Overall, females tend to have most of their mass concentrated towards the lower part of body, under waist. Men have a more even distribution, with much larger arms and upper part of body. There are exceptions, and an ample overlap zone of course, but more or less this seems to be the norm.

You can distinguish males and females just measuring their hand temperature with an IR thermometer. I’ve done playing with my colleagues and Therm (the company's IR band light remote surface thermometer), and got a 100% accuracy in that case. Male hands are warmer. Much warmer in fact, even 7 to 10 °C, with an external temperature of 18 °C.

Sophisticated instrumentation is sometimes no more than a way to make the obvious unquestionable. And this is one of these cases.

The “obvious” side is the typical Winter Heating War, in which the company splits exactly in two. On one side (most typically led by me) there are the Ones, willing to squeeze any possible Watt out of the odd-functioning heater, in the desperate attempt to make temperature acceptably not-too-cool.

On the opposite front, the Others find the cold air we have been able to get from the heater excessively warm, then trying to convince the Ones to calm the heater a bit down.

Typically, we arrive at an equilibrium point (skewed towards the need of the Ones).

The reason, anyway, is the different rate of production and dissipation of heat. The Others have just much more available.

I mentioned the distribution of heat production is not casual. And in fact, a huge difference exists as the Ones produce most energy down their waist, while the Others produce it on both sides.

Apart the amusing signs (like placing, in turn, one hand between my tightly packed thighs and the other on the computer keyboard, in an attempt to recuperate heat when at 17-18 °C of external temperature), I feel it is not impossible this difference in amount and location of heat production helps to explain things so widespread as average posture.

Quite obviously, males maintain a position occupying more space, while females use much less. This has been attributed to moral characteristics like domineering attitude in the firsts, opposed to natural modesty of the seconds.

But: couldn’t it (just!?) be a thermal effect? Looking at the Ones and the Others in my company, it’s true their posture match with the expected ones. But, can assure, this bear no relation to domination or modesty. The Ones just try to preserve heat, while the Others do their best to dissipate it.

The only documented exception to standard, gender-divergent postures is when the Ones (especially the two producing less heat, that is myself and a friend in the Administration office) place in Leopard-skin-carpet way directly over the radiator to get a bit of warmth out of it (we take turns: the radiator surface is not large enough for two together).

This all has made me think hard on why, apparently, women clothes are (or seem) “lighter” than men’s. Just the opposite of what is needed!

(My company, thanks to the under-dimensioned heating system, is an exception to this rule. It is the Ones who, in winter, are covered one or two layers more than the Others. But, this is a social exception!)

Are social norms dictating physically (and physiologically) insane dressing habits?

Or more simply, women are not expected to stay out of home or other closed, overheated spaces most of the day, while men are imagined more outside a house-like place.

Maybe, the “most logical” way is something similar to my company typical winter setting, imposed by an unusually low temperature. Habits change immediately, as I've seen, if survival is at stake!

Let’s be quantitative!

As the Math Support Gals, we bear the sacred responsibility to be as quantitative as possible.

In the specific case of clothing, there is a lot of numerical data. The most interesting, and intuitive, is “clothing conductance”.

This is a property of a piece of clothing, with respect to transmission of heat. It is expressed in units of N m / (m2 °C), and gives a precise indication on how quickly a garment loses heat to the external environment. The larger the number, the “less effective” the garment is at protecting from cold (and the “more effective” it is to shield from warmth).

Some figures towards top protection:

Heavy dress (women): 9.5 Heavy jacket (men): 13 Heavy slacks (women): 15 Heavy sweater (women & men): 17 Heavy jacket (women): 17

Some numbers around the middle:

Light trousers (men): 25 Heavy skirt (women): 29 Light jacket (women): 38 Light, short sleeve shirt (men): 46 Light skirt (women): 65

And finally, the highest conductance (minimal cold protection) records:

Sleeveless T-shirt (men): 110 Socks, ankle length (men): 161 Pantyhose (women): 640 Stockings, any length (women): 640

These are averages. And the more “technical” clothes, like the ones we use on high mountains and the like, are not included.

(I confess I spent the full winter in Milan wearing a mountaineering jacket worth the Himalaya, with envy by all the Ones, and perplexed glances by the Others - they can’t say too much however: I’m a V.P.!)

But some figures are baffling, and maybe revealing. What are pantyhose useful for? Apparently not as a protection against cold. So, maybe my theory about mechanical isolation of skin from clothes, or the mainstream idea on them as seduction tools, or both, and maybe something else, are true.

Another point is, clothes are arranged in layers. The amount and degree of protection of all layers is all what counts - and many people prefer wearing more lighter layers than few heavy ones (me included - with the not-so-remarkable exception of my spacesuit-like high altitude jacket).

Still another point (in random order) is that men’s light trousers offer more thermal protection than women heavy skirts. This may explain why skirts are on a possible verge to extinction (and I guess they would already have been vanished, would women not be influenced in their clothing choices by men).

A “logical” fashion.

When a child, I remember of a TV series (Star Trek) in which inhabitants from many planets interacted in many ways. One of the planets was inhabited by purely “logical” creatures (or, they claimed to be).

How fashion might have been, in such a place?

(This is not to say that the whole fashion industry is “illogical”. But…)

First: Would fashion be gendered, as it is now on Earth? Maybe, yes and no. They “might” be, using colors - and maybe a different distribution of underwear layers to account of individual differences in where heat is mostly produced. But the gross shape might be the same (cutting production costs, incidentally). This, assuming gender is considered “important” - maybe, for very logical creatures it wouldn’t.

Second: What clothes, actually? Assuming a temperate climate with four seasons as in Italy, the optimal winter cover might include trousers, thick jackets, and an external cover. The summer clothing might reduce to a light skirt and T-shirt. (This, “logically”, for the whole population, male and female). In other words, I imagine a dressing style which is “thermally optimal” under the whole climatic variation range.

This would give the immense advantage of allowing to pass clothes from the first to last child, regardless of gender: on average, a 50% saving on children dress expenses; apparently the industry isn’t mine opinion: as it turned out on this Christmas, finding a genderless children suit which can be easily passed is really difficult.

Third: very logical people might prefer free, comfortable clothes to constricting, movement-limiting or painful dresses. Not very sexy, possibly. (But not necessarily).

Just a provocation :)

And, is time to close. Hope you now share some of my high consideration of mathematics and physics, when dealing with fashion.

And this might be just the beginning. Actual faschion firms are big industries, in which mathematics and physics are used extensively - from deciding the optimal use of tissue in large production, to cutting and sewing together different textures and fabrics. Numerical control machines are routinely used, on a large scale, in actual clothing manufacturing. And the process is backed by agriculture, for fiber and textile production, chemistry, for colors and some kinds of fabrics, and many more.

I invite anyone who knows, to post comments or articles. The application part of the sister site is waiting to be filled!


Comment on this Post


To me it is very appealing to think how to dress perfectly, mathematically. I once took a sewing class, and making sense of how to draw a dress in paper was harder for me than solving an equation with three unknown quantities!

But then again, when I found the similarity between drawing a dress and calculating proportions, it made sense quite easily.

You are going beyond fashion my friend. You are tricky. You are trying to convince me make overs are not needed. I will not fall for this, though. Get your hands to begin working in your new fashionable outfits, and stop making your brain get in the way of fashion! :)

Take a look at Milan´s newest trends, and make them work for you. And as I once told you, tell me when you see those lovely italian shoes that I am dreaming of...

Love and smiles,


Jacqueline Patiño FundActiva Tarija - Bolivia South America www.jap21.wordpress.com