# Geometry

The best Gehennese maths is geometry. In the Archaic Period people make use of the fact that a triangle with sides in the ratio 3:4:5 contains a right angle, and use the properties of similar triangles to estimate heights and distances that cannot be measured directly.

Classical Period geometry is familiar with the equivalent of Euclid's postulates and Pythagoras's theorem, and is doing some fine work with solid geometry, and calculating areas and volumes. The existence of irrational numbers is known.

By the Decadent Period, Gehennese mathematicians have estimated the value of pi using the method of exhaustion, and are working on determining the shapes of the orbits of the planets. Surveyors are using triangulation, and but for lacking a convenient notation for equations, would be on the verge of inventing trigonometric functions.

# Astronomy & navigation

The Gehennese know that their world is a globe. If it were not obvious from the appearance of the horizon and the variable altitude of Indarian, they would know because the daimons of the Sun, Moon, planets, and Indarian have told them so. As early as the Archaic Period they have correctly estimated the circumference of the globe as 250 000 stadiums.

By the Classical Period the heliocentric theory is well established (having been asserted originally by priests of the Sun), and the correct explanation of the retrograde motion of the planets is known. Small moons have been observed circling the outer planets. By the Decadent Period is is known that the orbits of the World of Isles and other planets are not circles, and geometricians are working on determining what shapes they are. The discovery of Kepler's laws can not be long off.

On that face of the World of Isles from which Indarian can be seen, navigation is comparatively simple. Since Indarian is fixed in the sky above Elusium, it is easy to determine the direction to Elusium, and with a compass (or careful observation of the fixed stars) determine one's bearing from Elusium. With an astrolabe or (in the later periods) a sextant it is easy to determine the altitude of Indarian above the horizon. Simple arithmetic gives the angle between Indarian and the zenith, and this is proportional to the observer's distance from Elusium. Thus it is possible to determine your distance and bearing from Elusium by a few simple observations of a single heavenly body: this uniquely identifies your position.

On the World of Isles (or one face of it), positions are given as a bearing and an altitude of Indarian, rather than as latitude and longitude.

Gehennum is on the the Equator, east of Elusium, and consequently Indarian is seen pretty much due west. From the westernmost tip of Eumoria Indarian is about 18 degrees above the horizon. From the eastern part of Bethany it is only about 7 degrees above the horizon.

# Physics

In the Archaic Period Gehennese engineers and savants have a quantitative understanding of the mechanical advantage of the lever, inclined plane, and pulleys, and (as this requires) are aware of the notion of force. They also understand Archimedes's Principle, and work confidently with the notion of the specific gravity (density) of a material. However, they are unfamiliar with the concept of inertia, and believe vaguely that heavy objects fall faster than light ones.

In the Classical Period the artist and engineer Lykomorphus performs experiments equivalent to those made on Earth by Galileo Galilei. Inertia proportional to mass is established, and the uniform acceleration due to gravity is well-known among engineers and the more empirically-minded natural philosophers. Working from Lykomorphus's observation of the constant period of oscillation of a pendulum, mechanics have built pendulum clocks.

Further progress in physics is hampered because the Gehennese do not have Cartesian geometry or the calculus, nor, for that matter, a convenient notation for equations.

# Biology

Gehennese biology is almost entirely descriptive. At no point do the Gehennese discover genetic inheritance, hormones, or enzymes. Natural philosophers teach spontaneous generation in the Archaic Period, and the belief is not quite extinct in the Classical Period. But by the Decadent Period several purported instances of supposed spontaneous generation have been debunked, and it is generally known that organisms result from reproduction, and resemble their parents.

Several Gehennese natural philosophers have speculated about the possibility that the various species have evolved, but none ever puts together inheritance, mutation, competition to survive and reproduce, and natural selection to construct a workable theory of evolution.

In the Archaic Period the leading speculations organise animals and plants separately into 'sequences' of increasingly sophisticated organisms, and suggest that the more complex categories arose from the simpler in order. Later the theory that the development of different types resembled more a bush of branching lines is more popular, and it is recognised that simple organisms can be highly adapted to their niches.

Gehennese herbals and bestiaries are on the whole much better-observed than their Greek or European equivalents. They are certainly much less infested by non-existent beasts with allegorical significances, and do not report ridiculous rumours about the behaviour and life cycles of animals, even of distant parts.

# Medicine

In Gehennum the science of medicine is accelerated and retarded by turns by mystic disciplines, especially yoga and healing.

Practitioners of yoga provide a useful source of information, because they can sense or feel a lot of the things that are going on in their bodies. Partly for this reason Gehennese medical scientists have a good idea of what the various organs do, and some idea of the aetiology of many diseases. From the Classical Period at least its is clearly established that the germ theory holds for some diseases, while others are caused by deficits, excesses, or imbalances of internal substances of some sort. Even some dietary deficiency diseases are recognised.

On the other hand, mystic healers are available to relieve the rich of their injuries and other ailments. The financial incentive to develop a systematic knowledge of anatomy and physiology is greatly vitiated: physicians (or, rather, apothecaries) and surgeons in Gehennum treat the poor and domestic animals, not nobles, rulers, and the wealthy. Medicine and surgery have about the same status as midwifery: they are not dignified professions, and rarely attract the interest of great minds.

Copyright © 1988-2004 Brett Evill. All rights reserved.

Copyright © 1991 by Brett Evill. All rights reserved.