- Sense of pain is phylogenetically an old sense.
- Nerve fibers for pain exist in all kinds of membranes and tubes (Mf), hence what may be regarded as the tissue level underlying level of organs. (Embryos in their first stages consist mostly of membranes and tubes before a nervous system is developed.)

Pain is a general sense with little specificity, primarily a chemical sense at destruction of cells but may be activated by temperature and pressure as well.
   The function of pain is to preserve the organism as an integrated whole; raggedness and breaks gives pain. It's a witness of the integrating force of an organism, hence at bottom of all differentiations within its body. In terms of the dimension model the sense of pain can be regarded as an expression for the primary binding force from 0-pole at polarization of 5th dimension degree (shortened d-degree).

On the chemical level destruction of a cell membrane leads to outflow of K+-ions. There is a strong connection between quantity of K+ in the intercellular tissue fluid outside the cell and the intensity of pain (LEL p. 170); thus it's a chemical expression for a destroyed membrane. It's mainly the level of K+ inside a cell that decides its rest potential.
   At propagation of all nerve signals there is an outflow of K+, however in very small quantities, followed by an inflow of Na+. It would be possible here to see a connection between nerve signals as such and the sense of pain, where the counter directed, opposite inflow of Na+ is lacking. Pain becomes a one-way direction force outwards. (Cf. mental pain when the "I" doesn't meet confirmation from others.)
   Another similar example that connects pain with direction and position of otherwise usual substances in the nervous system is Acetylcholine, a very old transmitter in the history of evolution. It's found in a multitude of synapses - inside nerve fibers and with a very short life time outside in the synapses. Applied on the skin in a high dose it gives pain. As in the case for K+ the condition is an unusually high concentration and localization outside cells, i.e. outside the regulation in nerves and synapses.

[There are obviously exceptions from the rule that innervation for pain sensations exists in all membranes and tubes. Evidently it's possible to cut and burn in bowels without pain for the patient, while stretching lengthwise gives pain. Could it have an embryological and geometrical explanation? Pain from stress that can hurt their original geometry? Intestines have their origin from archenteron and primary vegetative 0-pole of the embryo, implying the character of outward direction (divergence) in d-degree 4 (0 → when unnaturally reinforced giving pain? While outer skin derives from the animal 00-pole, with circular geometry in d-degree 3, when broken giving pain?]

Other features that point out pain as a fundamental sense of high d-degree in our model:

- Pain is a sense with only free nerve ends, more or less branched. The other general senses have free nerve ends too but have also developed encapsulated ends of specific types.
   It indicates a way from a primordial, more elementary radial structure towards differentiations, in geometrical terms of our model from vectors in d-degree 4 to the polarity circular - radial in d-degree 3.

- Part of the nerve ends react to several kinds of stimuli, both to chemical ones, temperature and pressure, are "polymodal". Others react only to specified stimuli as high temperature or strong pressure (Nf), which indicates a step to differentiation, halfway to the following senses - as a result of "polarizations".

- The nerve ends don't adapt, which seems natural with respect to their function to preserve the organism. In relation to adapting senses it's like a mathematical function relative its derivative.

- Pain has the steepest log-curve of all the senses. (All senses are logarithmic in the relation between intensity of the stimulus and perceived intensity.) Log-curves of the senses ordered after steepness:
   Pain - Heat - Pressure - Cold - Vibration - Hearing - Light (Nf).

Pathways of the pain-conducting nerves are special:
- Most curious - if shown to be a fact - is that the nerve fibers for pain seem to enter also ventrally (Nf p. 461) into vertebra (while all other sensory nerves enter only dorsally). It looks like a reminiscence of the underlying two-way direction of d-degree 4 in our model?

- Pathways for the general pain - and temperature - pass in a special lateral tract in the spinal cord, nearer the ventral horns, the paleospinal tract, phylogenetically older than the dorsal tract in which nerves for other senses pass as for lower pressure, touch, vibration and motions in joints etc.
  The nerves for pain are also more disordered.

- It should be underlined too that this paleospinal tract - via the limbic system and thalamus - spreads out the signals widely to the whole brain - as a radially directed vector field.

C-A-delta fibers:
That the sense of pain include also a half step towards senses "of lower degrees" is evident from the two kinds of nerve fibers for pain: C and A, corresponding to a step from a more general (diffuse) pain to a distinct:
- C-nerves, unmyelinated, propagate the "slow pain". They pass as mentioned in the paleospinal tract and have the general, divergent distribution.
- A-delta nerves for "fast pain" are myelinated and pass through the neospinal tract to special areas in primary sensory cortex with its map of the body.
   C-threads only branches, A-threads form plexa, more complicated structures (Nf p. 466).
   C-threads lie also deeper in the skin than the A-threads.

Pain - Temperature:
A step of polarization seems obvious between pain and temperature. The sense of temperature too has C- and A-types of nerves but here polarized to complementary receptors, with C-threads for warmth and A-threads for cold (TA p. 73). Cf. that strong warmth gives pain and that this sense had the next steepest log-curve:

     Fig Gs-1-127-1

This implies also a d-degree step as from a function to its derivative:
- Pain receptors are tonic, not-adapting, always with a certain activity.
- Thermal receptors are "phase receptors", fast adapting, reacting to changes, the "derivative" type (Aph).

Types of pain and muscle tonus:
- Superficial, shrill, burning, shooting, localized pain raises blood pressure and muscle tonus, effects like those of the sympathetic nervous system.
- Diffuse, dull pain from deeper tissues lowers muscle tonus and blood pressure: effects like those of the parasympathetic system (LEL).
   Hence, it seems as the two reactions can be described in terms of opposite directions:
- Pain from anticenter: 00 —> 0 : Sympathetic nervous system as center-pole activated: —>0.
- Pain from center: 0 —> : Parasympathetic nervous system as anticenter-pole activated: <— 00.

The inhibiting system is of the "antiparallel" type as for the other skin senses, with signals coming from higher centers, mostly centers in the brain stem near the aqueduct between 4th and 3rd ventricles (LEL p.171).
   Lateral inhibition doesn't exist, but activation of other skin senses as touch may have some inhibiting effect.

2. Temperature:

Shapes of receptors and functions:
   As mentioned above the sense of temperature has free nerve ends as those for pain but also, according to older sources (Zf ) specialized, encapsulated end organs. This latter apprehension may have been revised but mentions round capsules (Kruuse's) around branched nerve fibers for cold and more oval or banana-shaped capsules for warmth - around a more horizontally branched nerve fiber (Zf p. 268).
       
          Cold                          Warmth
    Fig Gs-2-128-1

Such a geometrical polarization in shapes resembles those between sacs in the sense of equilibrium and the windows in cochlea, the organ for hearing. It may be apprehended as expression for an angle step outwards in d-degrees, as from 360° towards 180°.
   Cf. temperature as degree of spread in molecular velocity: colder = decreasing spread, warmer = increasing spread. Vertical axis = number of particles, a principal sketch:

      Fig Gs-3-122-1

Higher warmth implies more of motions, of kinetic energy, the direction towards increasing entropy. With this aspect cold comes to represent the 0-pole, warmth a relative 00-pole, ~ lower d-degrees.
   As mentioned about pain the receptors for temperature are of the derivative type, reacting to changes - and even to the the velocity of these changes (Zf).

It should be observed here that they react to the direction of these changes: cold receptors on decreasing temperature (~ convergence), receptors for warmth on increasing temperature (~ divergence).
   Cf. contraction of blood vessels as reaction to cold, dilation of the vessels as reaction to warmth. It confirms the view on the polarity in figure Gs-1 above.

- A-threads, myelinated: convergence from a 00-pole towards cold.
- C-threads: divergence from a 0-pole towards warmth.

 Myelination is also a later development.
   (It has been shown however that C-threads also can relay cold but then as it seems at much lower temperatures than the A-threads (Nf p. 443). Could it be a reminiscence of an older system with only unmyelinated C-threads and their general spread in the brain?)
   Receptors for cold lie deeper in dermis (or subcutaneous layer (Zf p. 268) than the receptors for warmth.

Another information (Nf) may be interesting with the dimension chain in mind: The sensitivity measured as threshold stimulus of receptors are 4 times higher for warmth than for cold (0,001° relative to 0,004°), a relation 4/1 that can illustrate increasing differentiation towards lower d-degrees.

Temperature intervals:
Receptors for cold answer in a temperature interval roughly 15° to 35° C, receptors for warmth roughly between 20° to 45° where they finish answering (Nf p. 442). Hence an overlapping interval 20° - 35°. The latter receptors have maxima around 38° to 43°.
   However, cold receptors get activated above 45° together with specialized pain receptors, which shortly can give what is called "paradoxical cold" sensations from heat objects. In the central nervous system there are also nerve cells that get impulses from both cold and pain neurons that get identified as heat (Mf p. 313 f).

   

Fig Gs-4-129-1

One interpretation could be that the activation of cold receptors occurs through pain as underlying level as shown with dashed arrows in the figure below - in agreement with the dimension model and with interpretation of pain as the general sense polarized in the following ones.

      Fig Gs-5-129-2

Or with a related view: The presumed "pole exchange" in a d-degree step 1 → 0/00 (represented in each step of a dimension chain) should imply that heat as divergence defines a secondary 00'-pole, redefining cold on the thermal scale: cold as direction inwards the 0-pole. (5th d-degree equivalent with 0/00, d-degree of motions.)

        Fig Gs-6

Receptors as a keyboard for temperatures:
The receptor threads registering temperature are differentiated with their maximal burst frequencies at different degrees of temperature (Nf p. 442), reminding of hair cells in response to sound waves. How this differentiation is organized in cochlea is well understood, but how among receptors for temperature? (No information in used references.) Perhaps through a map of positions within different domains in the skin or inner membranes - with a corresponding one in the brain?

3. Pressure, Touch, Vibration - mechanical senses:

The senses for pressure, touch and vibration are mechanical and appear as a further differentiation from the sense of pain. Cf. the differentiation of pain above as a) polymodal, b) for warmth, c) for pressure, and the order of steepness in log-curves: pain →> warmth →> pressure.

- Nerve fibers for pressure are mostly thicker, myelinated threads in opposition to the thin threads for pain and temperature (Mf).
- The pathways for most of these mechanical senses go in another, more distal neospinal tract in the spinal cord than the more lateral, ventral tract for pain and temperature, the paleospinal tract, which also is the one for hard pressure (Aph).

Ends of nerve fibers:
Free nerve ends exist as for instance around roots of the hairs, which are encircled by nerve ends. Mostly however, the nerve ends for mechanical senses are encapsulated in capsules of connective tissue and further differentiated in specialized structures in at least 4 known types.

We can identify 2 polarization steps:
- in slow and fast adapting ones (tonic and phase types), each of which polarized
- in those with small and those with bigger receptive fields.

Fig Gs-7-130

Further, there is the differentiation in function between fine touch and pressure (only a difference of degree) and deep pressure.
   The fast adapting end organs are simultaneously sensitive to vibration and differentiated between low and high frequencies (f.) of vibration.

1. Slow adapting, simpler kind of embedding:
a) Merkel's discs : Receptive fields small (~ center pole)
- Structure: Dendrites disc-shaped, closely ("vertically") attached to special big cells in epithelium.
- Sensitive to fine touch and pressure.
b) Ruffini's corpuscles: Receptive fields bigger, vaguely demarcated (~ anticenter pole).
- Structure: Nerve ends spread in a bundle of "horizontal" collagen fibers.
- Sensitive to pressure and distortion, tension of skin. Note this angle step.

2. Fast adapting, more complex kind of embedding:
a) Meissner's corpuscles: Receptive fields small (~ center pole).
- Structure: doubly embedded, branched and coiled dendrites with ends surrounded by modified Schwann cells and this whole enclosed in a capsule.
- Sensitive to fine touch and low frequency vibration.
b) V. Pacini's corpuscles: Receptive fields big (~ anticenter pole), vaguely demarcated.
- Structure: one single dendrite thread within several layers of concentric collagen fibers (lamellae), rather flat.
- Sensitive to deep pressure and high frequency vibration (~ "overtones").

It's noteworthy that the structures differ more clearly than their functions seem to do.
   If we should try to apply the dimension chain on these separate structures, certain features at least are possible to identify as such:
- The relation between "radially" spread discs of Merkel's type versus the horizontally arrangement of Ruffini's type as poles from step 4 →> 3.
- The big rounded, doubly embedded Meissner's type versus the more flat concentric Pacini's type as a feature relation 3 to 2 (and 2 to 1 with regard to the structure of dendrites within the corpuscles).
   It has been proved that it is the embedding in corpuscles of the nerve ends that makes them fast adapting.

The fast adapting types, sensitive for vibration, could perhaps also be described as derivations from the slow adapting in two steps (?):

   4 -|- 3: Merkel's: radially branched nerve ends: fine touch and pressure.
      ↓→  Meissner's: branched, coiled nerve ends: fine touch and low f. vibration.
  3 -|- 2 - 1 Ruffini's: horizontally nerve end(s) in bundles: pressure and tension.
      ↓→  Pacini's: one single, vertical nerve end: deep pressure and high f. vibration.

Positions in layers of skin:
Pain: - Merkel's — Ruffini's + Meissner's - Pacini's: →> more embedded:

If we may regard the senses from pain to the mechanical senses touch and pressure as differentiations analogous to steps towards lower d-degrees, from free nerve ends to big end receptors and from non-adapting to fast adapting, the direction in positions becomes roughly from outer layer of the skin to inner, underlying layers. Epidermis originates from the animal 00-pole, deeper layer from endoderm of the vegetative 0-pole and mesoderm embryologically.
   The localization of receptors in opposition to the suggested d-degree of their character could perhaps be understood in terms of lacking answers:
   - Pain as outward directed, not answered by adequate response from outside, outer skin.
   - Deep pressure as inward directed, not answered by balancing pressure from inside.

4. About receptors in joints, an addition:

Besides other sensory receptors within the body as e.g. baroreceptors in blood vessels and proprioceptors in muscles and joints etc. there are receptors similar to Pacini's and Ruffini's in joints (Nf p. 440). Those which adapt slowly give information about direction of motion, velocity and position.

- They react to motion in the joint within a certain angle interval, a differentiation of receptors as along angle steps in a dimension chain: change of Direction, ~ d-degree 4.

- Frequency of receptive response is linearly proportional to the velocity of the motion. Velocity has in this dimension model been suggested as the physical quantity of a dimension step, type 1→>0/00 (the very quantum jump between d-degrees.

- Discharge of the receptive response drops to a level that corresponds to the position of the joint, hence a spatial qualifier as out of angled directions; position, d-degree 3.
   The same receptor mediates information of all three properties: direction, velocity and position:

D-degrees in the dimension chain:
   4 —————————————3
Direction       Velocity            Position

5. All senses: dimensional aspects on their mutual relations?

Usually in human biology there is talk about 5 to 6 senses (at least the hitherto identified):
   Equilibrium - Taste - Smell - Sight - Hearing plus
   Kinetic sense from inner muscles and joints.
To these comes the skin senses for pain - temperature - touch/pressure - vibration, plus all inner receptors for blood pressure, chemical milieu etc.
   An interpretation of all these senses in their mutual relation with aspects from a dimension chain becomes probably most natural with a division in kinds of stimuli they respond to, and how these stimuli are related to fundamental physical qualities (or "quantities"). (About how these physical qualities are suggested to be stepwise defined in the dimension chain, see here.)
   Sense of equilibrium is connected with gravitation and outward acceleration, chemical senses with mass and matter in next steps (and charge), sight with electromagnetic waves related to charge etc.:

Fig Gs-8-132-1

* D-degree step 1 →> 0/00 debranched from step 5 →> 4: Temperature as warmth is related to density among particles, partly a matter of their motional energy and velocity (a quality distance/time), partly a matter of imbalances in radiation (EM-waves).
   Step 1→>0/00 debranched from step 4 →> 3: motions of the body registered by the sense of equilibrium and receptors of the kinetic senses.

With the loop version of the dimension model the senses regarded in such a chain becomes also roughly an illustration of steps from inner senses to outer "near senses" as taste and smell to outer "distant senses" as sight and hearing:

Fig Gs-9-132-2

Thus, pressure may be translated into a relation force (4) and distance (1), or to mass (3) and the quantities distance plus time.
   Directions and sense of Equilibrium are expressed in motions of the body and closely related to Sight.
   Mass →> Matter as Chemical senses: body motions governed by Smell and Sight in seeking for food.