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Phronesis · working note

Insensible

Rincón, D., with Claude · phronesis · 2026 · a correction

The phrase is "anything warm perspires." Taken as biology it is wrong, and not narrowly — most warm animals have almost no sweat glands, and a bird has none at all. Taken as physics it is right, once one word is moved: any warm and wet surface, in air that is not saturated, is losing water, and that loss is how it stays cool. The correction that matters is what drives it. Not warmth. The vapour-pressure gradient — which is why a hot dry day is survivable and a cooler humid one is not.

The kernel, granted

There is a real process under the phrase, and it has a name older than the physiology that explains it. In 1614 Santorio Santorio published Ars de Statica Medicina, the record of an experiment he ran on himself for more than thirty years: he built a weighing chair — the statera medica, a platform hung from a steelyard balance — and weighed his food, his waste, and his own body. The numbers did not close. Mass left him that appeared in nothing he could collect. He named the gap perspiratio insensibilis, insensible perspiration, and it is generally counted the first quantitative study of human metabolism.

What he had found was not sweating. It is water leaving continuously through intact skin — diffusing up through the stratum corneum and evaporating off the surface, with no gland involved anywhere in the process. Modern dermatology measures it as transepidermal water loss, and unlike sweat it comes out as pure water, carrying no solutes. The figures usually given are roughly 300–500 mL a day through the skin of an adult, with a similar amount leaving on the breath, for something like 600–900 mL a day in total. It is not evenly distributed: hands lose on the order of 80–160 g an hour, feet 50–150, the head and neck 40–75, and the rest of the body 15–60.

So the everyday claim is right in the way that matters most. A resting body is losing water constantly, is cooled by that loss, and does not need to be sweating for any of it to be true. Santorio's word for it is still the good one.

The correction, in two parts

The first part is the biology. Perspiration, in its ordinary sense, means glandular sweating, and that is not a general property of warm animals — it is close to a specialty. Humans are one of the few species that thermoregulate primarily by sweating over most of the body surface; horses are another. A dog has eccrine glands essentially only in its paw pads and sheds heat by panting instead. Birds have no sweat glands at all and rely on panting and gular fluttering. So "anything warm perspires" is not a small over-reach — it is wrong about most of the warm animals there are.

The second part is the physics, and it is the one worth keeping. Warmth is not what drives evaporation. The driver is the difference in water vapour pressure between the wet surface and the air above it. Warmth matters only because it raises the saturation vapour pressure at the surface — the Clausius–Clapeyron relation — and so usually widens that difference. Usually, not always. Put a warm wet object into air already saturated at its own temperature and the gradient is zero: it evaporates nothing, cools by evaporation not at all, and stays exactly as warm as it was. Relative warmth is a good proxy for the gradient across ordinary conditions and stops being one precisely where it counts.

Warmth does not drive it. The gradient does.

The limit, and it came in lower

This is not academic. A human body at rest produces around a hundred watts of metabolic heat and must lose it somewhere. When air is hotter than skin, conduction, convection and radiation all run the wrong way, and evaporation is the only remaining route. Close the vapour-pressure gradient and the last route closes too. That condition has a standard measure: the wet-bulb temperature, the lowest temperature reachable by evaporation alone. It is the temperature a wet thermometer settles at, and therefore the floor beneath a sweating body.

The figure long carried in the climate literature is a 35 °C wet-bulb survivability threshold — the point where a human at rest can no longer shed heat at all. It was a theoretical limit, derived rather than measured, and it assumed an idealised body.

It has since been tested on people. The PSU HEAT project put young, healthy subjects into controlled hot environments and found the point where heat stress became uncompensable. No subject reached 35 °C. Across humid conditions with ambient temperatures of 36–40 °C, the mean critical wet-bulb temperature was 30.55 ± 0.98 °C — several degrees below the theoretical threshold — and it fell further in hotter, drier air. The limit also turned out not to be a single number at all: it moves with ambient vapour pressure, so the same wet-bulb reading means different things in different air. A follow-up analysis argued the practical consequence plainly: the population exposed to genuinely unsurvivable moist heat is larger than the 35 °C figure implied, because the real limit sits lower.

The subjects were young and healthy, which makes these the optimistic numbers. The old, the ill, the medicated and the working are worse off than this.

A proposal, offered as one

The rest of this site treats materials by what they do to a body in contact with them, and the effusivity instrument already carries a vapour axis for exactly this reason: a surface that feels correct on contact can still be wrong if it seals. The claim there is that a material must keep a vapour path open so that heat it stops absorbing can still leave.

Read alongside the wet-bulb result, the two are the same failure at different scales. Saturated air closes the gradient globally; a sealed surface closes it locally, across whatever part of you is touching it. In both cases the body is not too warm — it is unable to spend the water it is producing. That is a proposal about how to read the material work, not a physiological finding, and it is offered to be argued with. What is not a proposal, and is measured, is that the last cooling route a warm body has is evaporative, and that the route can be closed by air or by furniture.

The limits, plainly


Sources. Santorio Santorio, Ars de Statica Medicina (Venice, 1614) — the weighing chair and perspiratio insensibilis; see the US National Library of Medicine and the replica study of the chair. Transepidermal and regional water-loss figures: Taylor & Machado-Moreira, regional variations in TEWL and sweat rates, and Brandis, Fluid Physiology, §3.2. Wet-bulb limits: Vecellio et al., "Evaluating the 35 °C wet-bulb temperature adaptability threshold for young, healthy subjects (PSU HEAT Project)," J. Appl. Physiol. 132(2), 2022, doi:10.1152/japplphysiol.00738.2021record at Penn State, plain-language summary. "Greatly enhanced risk to humans as a consequence of empirically determined lower moist heat stress tolerance," PNAS 120(34), 2023, doi:10.1073/pnas.2305427120. "Is a wet-bulb temperature of 35 °C the correct threshold for human survivability?", Environ. Res. Lett. 18, 2023.

On the links. The two journal DOIs above are given as identifiers rather than hyperlinks: both publishers refuse automated requests, so a link here could not be checked and would be one this site could not stand behind. The DOI is the durable reference either way, and the Penn State record and summary are open.

These get worked out in the open, at whatever length the problem takes. I do the same thing on a problem of yours — one thing diagnosed and written up plainly, no build. what that costs