Different islands may be at different technology levels. Some may suddenly experience a flowering of new technologies as merchants come in from elsewhere; others may be protected by deities who want the locals to evolve at their own pace, and woe betide anyone who attempts to get a major advantage out of improved technology.
If you’re designing an island, you should consider just where your cultures are, technologically.
Check out Jason’s Web Site on Ancient Greek Science, a Multicultural History of Science, the Art of Renaissance Science, the Ancient World Web, and Ancient History at the Mining Company.
There are a number of barriers to the development of science on this world. The only reliable phenomena in the heavens are the sun and moon, and even the observations of those are problematic because islands can easily cover twenty miles in a day. There is no pole star to steer by, no universal magnetic field for orienting with compasses. This makes it quite difficult to study the heavens and impairs the development of mathematics as there are fewer evident applications.
Bear in mind that the fundamental nature of physics and chemistry is open to change as people travel between islands and over chaos. Some islands work based on a periodic table that would not surprise Mendeleev, while others have atoms of earth, air, fire, and water as Demokritos predicted. (Read Richard Garfinkel’s Celestial Matters for a delightful tale of hard science fiction, where the science is classical.) Still other locations may have no fundamental, indivisible building blocks of matter. Travel over chaos is especially risky, because complex devices may not “translate” properly. (Life and the Stable Elements always translate, leading to many speculations among academicians.) Exotic materials from one location may become quite common matter in another— unobtainium may be the wonder metal of one island, but it may become aluminum on another. (There appears to be some “memory” in matter, because unobtainium will turn back into unobtainium when it returns to its point of origin, but aluminum from a land where unobtainium becomes aluminum does not necessarily do so.)
Navigation between islands is a perilous art. Airships, fortunately, can get a decent view into the distance from their flight at one or two miles altitude; this, and the gentle curvature of the planet’s chaotic surface make it possible to actually spot an island at a good distance. Many islands set out lighthouses to signal airships passing in the night that there is a safe place to land— either as individual beacons for landing spots, or as a perimeter to make the border of the island visible from above. The former tend to be a healthy distance inland, away from the chaos that washes up on shore; the latter tend to be dense stone structure occupied by grim, strong-willed individuals, or maintained remotely by coming in regularly and fuelling the beacon with magic every so often.
Other than PC races with the Eat Anything schtick, people need to do some degree of work to get their food.
Cattle have been domesticated for 9000 years, and goat-herding is likely responsible for the existence of the Sahara Desert. Dogs go back to 11000 BCE, cats 7000–6000 BCE, pigs, sheep, ...
Highly magical cultures can use fertility magics to make fruit trees produce larger quantities than usual, year-round, in conjunction with supplying them with plenty of fertilizer.
Baskets can be made watertight with appropriate coatings...
Burnt mud is your friend. Pottery allows for storage vessels that can be well-sealed, and gives greater control over fire: it’s easier to cook with a pottery vessel than a treated basket. The same technology also gives you better bricks— sun-dried mud is a good start, but fired mud is harder.
Humans and animals can pull plows and grind grain. Paddleboats go back at least a thousand years.
Water flowing downhill can turn wheels and save a lot of effort.
Sails can power boats, carts, iceriggers, and skyships. Windmills can do work where the available water may be unable to do so. Sailboats go back at least three thousand years, sail cars to at least the 6th century CE.
Sufficiently powerful magicians can bind spirits to menial tasks. This may be perfectly normal, or tend to make them angry with you; in places where the latter is true, spirits are bribed into the activity when they are needed. (In most places, elementals fall into this category; nature spirits cannot generally be bound in this manner, as few can leave their domains and none wish to forsake them for other activities.)
Skeletons and zombies qualify under this category; the usual bargain with animating such undead is that a crude spirit animates the body and follows order in exchange for tormenting the spirit of the original owner in the afterlife. Animated bodies (or even parts of bodies) can function quite well for turning cranks and treadmills. Of course, this does create “necromantic pollution,” a tendency for manifestations from the world of unlife to appear in the vicinity of high concentrations of necromantic activity, but losing the occasional neighbor to demonic possession, transformation into a hideous creature, or death by poltergeist is a small price to pay for progress!
Steam engines require fairly advanced metallurgy to handle the pressures, and lots of goodies to burn, but they do go back to Hero of Alexandria, though it would have taken a great deal more improvement to make it efficient enough for practical use. Check out the Steam Engine Library.
Check out Archaeometallurgy.com and the Historical Metallurgy Society.
Ceramics are often a prequisite for many other technologies. Learning to fire ceramics gives a control over fire that allows other feats, such as smelting metals that would otherwise not be available.
Occurs freely in nuggets; one of the first metals cultures discover. Its rarity and resistance to corrosion help make it a valuable medium of exchange. Gold is not always pure: impurities of copper and antimony can give it a greenish cast.
Burning pretty green, blue, and purple rocks at kiln heat gives you copper, if the nuggets you can find aren’t enough. Check out Copper: the Red Metal for a good history of copper.
Smelting copper and tin— in about a 9:1 ratio— gives you a harder metal, suitable for beating up on your neighbors. Bronze easily dates back to 2500BCE. Copper and bronze have both been used as historical coinage.
Smelting copper and zinc gives you brass, which dates back to 600BCE.
Lead has been used in plumbing since the days of the Roman Empire (hence its chemical symbol, Pb, for plumbum). Some historians think that water delivered in lead pipes was why the Roman Empire fell— lead poisoning.
Alloys with gold to form electrum, and lead to form pewter.
Burning pretty red rocks gives you iron.
Glass goes back at least to 2500 BCE (see Wondrous Glass and Glass Finds from Sepphoris. Burning glasses were common enough in classical Greece to make it into plays.
Laen (“long thread”) is a magical glass with a very long crystalline structure. It becomes harder as it gets hotter, and can only be worked by application of extreme cold. It is normally cloudy, but proper treatment can make it transparent or give it any color of the rainbow.
Advanced applications of Earth and Fire magic allow the shaping of jewels.
The gem that diamonds want to be when they grow up, nearly indestructible.
A magical alloy of adamant and mithril.
The basic point of weapons is inflicting damage on other people. Fists and feet are quite effective at this, but harder substances transmit more impact to the opponent, levers will increase the force of blows, and sharp edges do a lot of damage.
The earliest melee weapons were likely long bones used as clubs. These have been elaborated all the way up to quarterstaves and tonfa, but the principle remains the same.
The next step up from thrown rocks is applying a little leverage.
Atlatls
Once metallurgy gets good enough to make bronze, swords become practical as weapons.
Bows are easy to invent; the English longbow was extremely effective...
Crossbows require more maintenance to keep operational, and can take more time to crank. Ballistas (the siege version) firing thirteen-foot-long bolts existed in the 4th century BCE, and hand-held crossbows (at least in China) go back to a similar time; they’re mentioned in Sun Tzu.
Catapults, ballistas, arcoballistas, trebuchets... Third century BCE catapults could hurl 173-pound stones up to 200 yards. Around 200 BCE, Philo of Byzantium wrote that a wall had to be at least 15 feet thick to withstand catapult stones weighing up to 350 pounds, and deep ditches were needed 500 feet away from the walls to keep the artillery from advancing close enough to hit.
It looks like the terms ballista and catapult can be confused— I have one page that says the Roman term “ballista” was for rock throwers and “catapulta” for spear throwers, and another one that says a ballista is a giant crossbow. It look like another name for the classic catapult is mangonel, though the Roman term was onager.
Another technology not essential to a fantasy role-playing game is flamethrowers. However, Greek Fire did exist, and was a devastating weapon.
Pottery containers filled with flammables like Greek Fire were effective hand grenades...
Gunpowder permits the creation of projectile weapons such as arquebuses, cannon, muskets, matchlocks, flintlocks, wheellocks, pistols, and rifles, not to mention the occasional land mine.
Gunpowder usualy simply doesn’t work on most islands. While this does deal with projectile weapons and other such upsets to the flow of history, it also causes fireworks to fail, which would be a bummer.
If you want a more subtle way to block such things, adjusting physics slightly so the metallurgy required to make weapons that can stand up to the explosive force of gunpowder or the pressure of steam engines will block those technologies, though not basic bombs made with lots of gunpowder. Blocking those requires establishing that gunpowder will spontaneously combust when brought together in sufficient quantities to make a serious bomb; at some point, though, if you want fireworks, you have to accept a certain degree of explosions.
It may be that the only way to control such explosions is with a healthy amount of fire magics, leading to Gandalf-style pyrotechnic exhibitions that are limited by the availability of your wizards. This keeps explosives safely out of the range of mass production and armies. Inventor-wizards might even take the vast quantities of effort required to create incredibly rare and expensive enchanted muskets— for which Lightning Reload should not be available!
Only a small range of temperatures are comfortable for humans wandering around naked or nearly naked.
Boiled leather hardens; the Chinese had suits of lacquered leather plates by 433 BCE.
Cotton, wool, silk, hemp, flax...
Weaving methods: Linen, ...
Looms.
Clothing of the Ancient Greeks.
The Aztecs had thick cotton clothing that served as armor— quilted, tight-fitting suits of layerd cotton about two fingers in thickness; they apparently got the idea from the Mayans.
Paper can be made from wood pulp, hemp, silk, mulberry bark...
The Chinese had some of the most advanced paper creations— windows, clothing, umbrellas, raincoats, even pleated paper body armor that stopped arrows (though not crossbow bolts).
A find at Dendra, near Mycenae, suggests that Homer’s “bronze-shirted” heroes were likely wearing overlappings plates of bronze: a round neckpiece, vertical plates to protect the shoulders, and three horizonal plates encircling the body down to the thighs. Scale armors with bronze plates over leather clothing dates back to 1400 BCE in China, and bronze scale armor was in use in Egypt at the same time. The Assyrians had iron scale armor in the mid-ninth centure BCE, and even chain mail dates back to the late third century BCE in China, seen on terra-cotta models of warriors guarding the tomb of the First Emperor, Shih Huang Ti.
Life magic (as well as advanced elementalist magic) is capable of shaping living wood within certain tolerances, allowing dwellings to be constructed out of living trees. Broad-leafed trees with large degrees of overlap between leaves can do a good job of keeping rain and cold winds out; this does require trees on the order of a mallorn, which keeps its leaves though the winter.
Roman plumbing was fairly sophisticated, with pipes, pumps, valves, and fittings, but flush toilets existed in the palace on Crete over a millennium before that. Jerusalem and Babylon also had serious plumbing. Check out the History of Plumbing.
Trained memory is always a classic. Some types of priests or bards may be forbidden to learn to read and write, in order to help them preserve their abilities of memorization; they would be important to leaders to keep track of genealogies and other forms of recordkeeping.
Cuneiform, hieroglyphics, kanji. Cuneiform is well-suited to incising into clay tablets. Hieroglyphics and kanji are more inviting when you have access to bark, leaves, papyrus, paper (probably invented in 105 CE in China), leather, or parchment; wax tablets are a good short-term notepad. Longer-duration storage can be achieved by painting onto silk, chiselling into stone, burning on wood, or creating a relief in metal. (This allows duplication using similar techniques to brass rubbings.) Two different languages using the same ideographic symbol system can be mutually comprehensible to readers who could not understand each other’s spoken language.
Relation of phonemes (as in Western usage) or syllables (as in katakana and hiragana) to characters. Alphabets require far fewer characters than ideographic systems, and are easier to develop a shorthand for.
Magical recording of sounds or thoughts. Enchanted crystals usually serve such a purpose. Necromancers sometimes enchant skulls or preserved heads as recording media and secretaries, enhancing their abilities of memorization.
Skis go back eight thousand years; ice skates three thousand. The usual skill for using them is Martial Arts or Melee, which double as general athletic skills.
Bits, saddles, and stirrups need to be invented to get to serious chivalry going.
Wheels aren’t always the best thing for dragging your gear around— they’re mostly helpful on roads. A sled, sledge, or travois can be much better for other environments.
Railways go back to the Diolkos of Corinth in the 6th century BCE; the usual problem is powering the carriages.
Hot air balloons go back to the pre-Inca Peruvians who made the Nazca lines. (Some people think the lines evidence of ancient astronauts, but it has been demonstrated that the ancient Peruvians could have made hot air balloons.)
More advanced dirigibles are the most popular way of travelling between islands; they usually fly well above the chaos, and can even dump cargo and vent nebula ultima to protect themselves from high-altitude chaos storms.
The Chinese and Japanese had big box kites that could carry a passenger.
Historical medicine was not as crude as many people believe. Everything from amputation to brain surgery was practiced before the days of the Roman Empire, and even then they had opium-based anæsthesia. China had toothbrushes and inoculations for smallpox in the 10th century CE, false teeth go back at least to 700 BCE, and prosthetic limbs at least to 300 BCE. Galen’s work on anatomy in the 2nd century CE was only surprassed after the Renaissance. Specialties of surgery, dentistry, and prosthetics should be available to chirurgeons from the more advanced islands.
Medicine is quite a tricky practice on some islands. Depending on the location, illness can be caused by an imbalance of humors, by miniscule creatures (bacteria and viruses), or evil spirits. Some islands are plagued by all three.
Soap goes back at least 4000 years in the Western world, and literally grows on trees in China...
Computers existed long before Babbage came along. The Greeks had an astronomical calculator 2,000 years ago; see also Gears from the Ancient Greeks. Water clocks from Greece and China could be quite sophisticated.
Woodblock printing started out in India in the 7th century CE and moved to China from there, leading to the first complete printed book in the 9th century. (Books as bound volumes go back to the Roman codex, with folded sheets of parchment stitched together with leather thongs. Movable type came into use in China in the 11th century, but was made of earthenware and too fragile for mass production; metal cast type turned up in Korea in the 14th century.
The Assyrians in Iraq and the Egyptians had efficient postal services by 2000 BCE, for those who could afford them— merchants could even entrust money to the couriers. Egypt had a system of relay stations by 1900 BCE, and by the 15th century BCE couriers were running between Egypt, Syria, Palestine, Mesopotamia, and Anatolia. The Persians had a horse-riding version of the Pony Express in the 6th century BCE; the stations of horses and riders could get a message from Sardis to Susa— 1600 miles— in nine days; the Roman one organized by Augustus was almost as good, and lasted from the 1st to 4th centuries CE. The Mongols had an excellent one of a similar nature by the 13th century CE. Homing pigeons were used in Sumer in around 2000 BCE, in Greece by the 5th century BCE, and Rome by the 1st century BCE.