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Homeostasis is the maintenance of usable internal conditions despite disturbances. It concerns selected regulated physiological variables, rather than keeping every part of an organism unchanged: core body temperature may remain near its usual range while skin temperature, sweating and blood pressure change. Regulation makes a relatively dependable environment for biological cells out of a changing external world. ^[ref]

A useful causal description separates a physiological sensor, a physiological integrator and a physiological effector. The return from the physiological effector's action to the sensed regulated physiological variable closes a feedback control loop. In negative feedback, that return opposes the disturbance. The insulin and glucagon articles already trace the blood glucose example; synaptic integration explains how several inputs can jointly influence a neuron. These are implementations and ingredients, not a requirement that every regulatory loop use one anatomical control center. ^[ref]

Homeostasis is useful precisely because internal activity can change: a nearly steady temperature can conceal a large increase in heat transfer. Conversely, observing a flat trace alone does not identify a regulatory mechanism. The environment might simply be constant, or the measuring instrument too insensitive; a perturbation and an independent response readout provide stronger evidence. The skin-temperature perturbation experiment below makes that distinction tangible.

The historical motivation was the puzzle of stability in changing living material. In his 1932 The Wisdom of the Body, Walter Bradford Cannon emphasized that an organism exchanges material with its surroundings and continually replaces its own structure, yet maintains relatively steady internal conditions. This authored excerpt presents homeostasis as active compensation for external and internal disturbances, rather than a static body. ^[ref]

Here is an explicitly synthetic mathematical model of a warming disturbance and its compensatory cooling. It is a teaching analogy for thermoregulation, not a measured human heat budget. Write $x=(T-T_r)/\Delta T$, where $T$ is a lumped internal temperature, $T_r$ is a fixed reference and $\Delta T>0$ is a chosen temperature scale. Let $d$ be an additional heating rate and $u$ an additional cooling rate, both scaled to the same reference rate. All three are dimensionless variables, while $\tau >0$ is a time constant in the chosen time units. The ordinary differential equation isThe term $-x$ idealizes increased passive heat transfer with increased internal temperature, around the baseline. The term $-u$ opposes warming through proportional control with feedback gain $k$. This local signed model does not treat a negative $u$ as negative sweating: it would represent decreased cooling relative to baseline. Changes of the environment and multiple body compartments are omitted.

For a constant disturbance $d=D$ and initial condition $x(0)=0$, the exponential function solution isSubstitution checks the ordinary differential equation directly. Increasing $k$ reduces the lasting offset and, in this instantaneous model, shortens the response time constant to $\tau /(1+k)$. It does not make $x_{\ast }$ zero for a nonzero disturbance and finite $k$: a persistent cooling command requires a persistent displacement under proportional control. At the equilibrium point, the extra heating is balanced by passive loss $x_{\ast }$ plus active cooling $u_{\ast }$. Zero change of temperature means balanced rates, rather than zero rates, consistent with conservation of energy.

The first diagram uses $D=1$, $\tau =4$, and a pulse from $t=2$ to $t=10$, comparing $k=0$ with $k=3$. The latter approaches $x_{\ast }=1/4$ during the pulse, compared with $1$ without active feedback control. After the pulse ends, each displacement decays as $x(10)e^{-(1+k)(t-10)/\tau }$. These are computed curves, not physiological measurements. The $k=0$ curve still has passive loss; it is not a claim that an unregulated body warms without limit.

Real physiological effectors take time to respond. To isolate that issue, set $\tau =1$ and replace the instantaneous command by another ordinary differential equation:Here the disturbance remains $1$ from $t=0$ onward and the effector time constant is also $1$. The equilibrium point is still $(x_{\ast },u_{\ast })=(1/5,4/5)$, but the characteristic polynomial is $(\lambda +1{)}^2+4$. Its eigenvalues $-1\pm 2i$ give decaying oscillations and asymptotic stability. The exact response isIn particular, $\dot{x}=e^{-t}\cos (2t)$, so the first maximum occurs at $t=\pi /4$, with $x=1/5+(2/5)e^{-\pi /4}\simeq 0.3824$. The response exceeds its eventual displacement while remaining above its baseline. The return has the same negative sign as before; the extra state changes the timing. A finite effector time constant is distinct from the fixed time lag in the delayed negative feedback model.

The nervous system regulates visceral movement, glandular secretion, blood flow and coordinated bodily responses, while also influencing nutrition indirectly through those functions. Organic or vegetative life here means activities maintaining the body, such as blood circulation, digestion, pulmonary ventilation, secretion and excretion. It does not designate an independent form of living substance.

One influence is directly motor. Autonomic nerves alter the rate and force of the heart, contract or relax smooth muscle in the intestine, urinary bladder, airways and blood vessels, and coordinate movement with the opening and closure of sphincters. Their effect need not be excitatory: an active vagus nerve can slow the heart, while other pathways accelerate it. In the modern account, sympathetic and parasympathetic effects depend on the target and its receptors; they are not respectively universal accelerator and brake systems. Some organs receive both divisions, while others do not have a simple balanced double supply.^[ref]

A second influence is secretomotor. Activity in appropriate nerves can increase salivary secretion, alter gastric acid secretion and promote sweating. This is distinguishable from moving a duct or changing its calibre. A convincing experiment collects a secretion from a cannulated duct while a nerve is stimulated, rather than inferring secretion from a change of colour or organ size. For example, stimulation of the chorda tympani can evoke fluid from the submandibular gland. The response depends on functioning secretory biological cells; the nerve communicates a command rather than supplying the material constituents of saliva.

A third influence is vasomotor. Changing the calibre of arterioles changes local vascular resistance and perfusion. The classic comparison of an ear before and after interruption of its cervical sympathetic supply illustrates loss of vasoconstrictor tone: the vessels dilate and the ear becomes warmer because more warm blood reaches it. Stimulation of the peripheral cut pathway can produce the converse vascular effect. Warmth therefore need not mean that the local nerves themselves generate more heat. Vascular control also changes the delivery of oxygen and nutrients to a gland or tissue, so it can modify function indirectly.

These outputs are organized by sensory feedback and reflexes. Distension of the intestine can evoke coordinated movement; changes in blood pressure or blood-gas composition influence heart rate and breathing. Local circuits in the enteric nervous system permit some digestive activity without an intact connection to the brain, while longer reflexes involve the spinal cord or brainstem. Central states also matter: the sight or expectation of food can initiate preparatory digestive responses, and fear can alter heart rate, sweating and visceral movement.^[ref]

Somatic motor activity also supports vegetative functions. Breathing uses the respiratory diaphragm and other skeletal muscles; swallowing and continence use coordinated skeletal muscle as well as smooth muscle. Thus organic function cannot be identified solely with the anatomical distribution of the sympathetic nervous system.

The historical idea of a direct trophic influence requires discrimination. A denervation region may change through loss of movement, altered perfusion, loss of protective sensation or changed secretion. Those observations alone do not establish a special nutritive fluid flowing down the nerve. Modern biology recognizes molecular signalling between nerves and their targets, as well as neuroendocrine signalling pathways: the hypothalamus can influence hormone release, and sympathetic input can evoke adrenal medulla secretion. These are mechanisms added to, rather than evidence for an undefined historical nutritive force. A useful experimental design measures the motor, vascular and secretory consequences separately before assigning a residual effect to direct trophic action.

Translation. For rapidly developing, or acute diseases, also resolve of their own accord, sometimes through favourable chance and sometimes through nature's favour. Consequently, ignorant people, carried away by this, often avoid physicians and attribute these favourable outcomes to new incantations and amulets, or to chance; for these rapidly developing diseases are driven out either by a flow of sweat, by blood discharged through the nose, or by a discharge from the intestines. But chronic diseases, or diseases of slow development, which have already gained possession of the body with a kind of prior claim, call for the skill of the physician alone, since they are resolved neither by nature nor by chance.

Interpretation. Caelius Aurelianus contrasts spontaneous resolution in acute disease with the entrenched course of chronic disease. Here passiones means affections or diseases, not emotions; ligamenta means protective bindings or amulets, not anatomical ligaments; proventus means favourable outcomes. The metaphor praejudicio quodam gives the established disease something like a prior claim on the body. The final assertion is the author's defence of professional medicine, not a present-day law that every chronic disease requires effective medical treatment or that none can remit spontaneously. The account of sweating, nosebleeds and intestine discharge describes his historical explanation, not evidence that deliberately producing these discharges cures acute disease. ^[ref]

The electrical conductance of skin, often measured between two recording electrodes. Sweating changes the conductive properties of the skin. Baseline, movement and recording conditions must be considered before interpreting an event-related response as evidence about emotion.

Sweating supports thermoregulation through evaporation of water, which carries away latent heat.

Thermoregulation regulates body temperature. Skin signals can anticipate a change of core body temperature, so a response need not wait for an internal error. ^[ref]

These responses have costs and environmental limits. Shivering consumes metabolic resources; cooling through sweating removes water that must eventually be replaced. High humidity restricts evaporation, so secreted sweat and successful cooling are not interchangeable. Maintaining core body temperature also depends on maintaining circulation: depleted blood volume can compromise skin blood flow and heat transfer. Seeking shade or reducing work changes the disturbance itself, whereas a larger regulatory command merely attempts to counter it. ^[ref]