Some people (humans) are born mages. It's hereditary but not perfectly so. Mages produce mana; in fact they can't stop themselves from producing mana, which is how you can find mage children and train them. All mages can sense mana; a mage-doctor identifies mage children in a routine physical exam at age seven or eight.
When you have mana, you can mentally use it to produce various effects, and this is called magic. However, magic used natively is both very weak and very difficult to direct in a precise fashion. The useful direct applications of magic are all on the order of heating a cup of tea. That is why people through the ages have tried to find ways to make magic more useful. Various traditions arose over time, some of which eventually led to modern sciences, such as alchemy. Implements and spells were developed which interacted with the actual magic to produce useful physical effects. However, while these approaches could create powerful effects, they were still very difficult to make safe and reproducible. The use of magic depends enormously on the exact physical conditions the spell is being cast in; alchemists could boil a lot of water, but they could not catalyze chemical reactions without exploding or melting their apparatus every two weeks.
The first computation orb was invented just a century ago and it revolutionized the field of applied magic. Computation orbs are casting implements in the 'orb and scepter' tradition which, in addition to being orbs, contain mechanical calculators (miniature clockwork) which can perform rapid calculations to adjust the spell being cast. This allows casting enormously complex spells (such as flight) whose formulae would take humans whole minutes to recalculate mentally for each passing moment.
Casting a spell using a computation orb involves manipulating the orb's structure with magic to make it produce the desired physical effect (such as thrust), and learning how to manipulate the flow of magic - in a way that does not always directly map to physical qualities - to achieve the desired results (such as thrust applied to a particular object in a particular direction). And then, practicing with that particular orb and spell until it becomes completely second nature, on the level of muscle reflexes, so that you consciously think not of spells but of flying. And then doing that for another twenty or thirty spells, and learning to cast many of them simultaneously while keeping track of everything around you, on a chaotic aerial battlefield where enemy mages will kill you if you make the slightest error.
Luckily, Sinnah will not be training with the orb today! She will instead practice with the 'scepter' implement, namely, Tanya's rifle. (It is technically a semi-automatic submachine gun but the term persists.) The rifle incorporates a linear casting implement which can apply one of several predetermined effects to a bullet just as it's being fired. Because the effects only need to vary alone one or two dimensions each (for example, a timed fuse) and a rifle's barrel is a fairly static environment, this casting implement does not itself need to perform computations; the mage performs auxiliary computations using the orb to produce just one or two numbers which can be (mentally) fed into the spell being cast via the rifle.
The important part is that these spells are designed to be safe to use on the rifle without a bullet! (You wouldn't want it to break because you didn't notice you ran out of ammunition.) Sinnah can try to feed her mana into it to trigger the fairly simple preset spell and Tanya can tell her what she's doing wrong. And then, hopefully, Sinnah will have the concept of casting through implements to produce much bigger and more complex physical effects, and they can try building from there.
