General:
Duality was born and raised in Canterlot, where she remains to this day. She lives a few blocks away from her old family home, where her parents, Photon Particle and Electra M. Wave - although not her middle-aged younger brother, who works as a taxicab driver in Manehattan -, still reside, in a medium-class neighbourhood in the lower South Quarter of Canterlot, although nowhere near the stunning vistas off the rim of the mountain city that aristocrats pay millions of bits to catch a glimpse of out their window. Her cosy urban cottage is uninhabited save for her and two large and affectionate male cats of rather dubious heritage, Spotspot and Britches, although Dot Dash, her much-removed cousin and closest friend, lives in an adjoining flat. She visits her parents regularly (every other Saturday and once or twice in between), and has a colourful and good-natured clique of friends from variegated walks of life whom she visits the local coffee shop with on a monthly basis - not that she drinks coffee herself, of course.
Duality was educated in her local public school, and managed to pay her way through a doctorate in applied mathematics with the financial support of her parents and the help of several part-time tutoring jobs she picked up along the way. Her casual employment teaching academically challenged ponies caused her to realise how much she enjoyed facilitating the learning of others, and guided her into seeking a job as lecturer at Celestia's School. She began as an assistant professor of mathematical metamagic, working under the then-dean of the Department of Arcane Mathematics, but was promoted within a respectable timespan when the elderly dean retired and recommended her to fill his position as primary lecturer in his field (although not the full position of departmental dean, of course, that title was given to another professor with a far longer period of tenure at the School).
Cutie Mark:
Ever since a very young age Duality Wave-Particle had wanted more than anything else to be a unicorn (as opposed to a slightly scrawny not-yet-grown-into-her-height pegasus), so as to pursue a star-studded career working with magic. She alternately moped around the house and feverishly plotted ways to gain a horn and its corresponding thaumaturgic powers. After one particularly unpleasant day, involving concerted mockery at school for her obsession with magic and a 'gentle' - but rather patronising, even her youthful self thought - lecture by one of her peers' parents along the lines of 'your aspirations are unattainable, child, so give up on them before you're disappointed any further', she tearily sought refuge under the wing of her father, Photon Particle. He willingly provided her soothing sanctuary, but knew that his daughter needed more than just a shoulder to cry on; she needed a hoof on her own shoulder guiding her away from the source of her pain.
As she finished sniffling an explanation of what had upset her into his newly-starched work shirt, he began to describe what he was working on: a scientific paper on the subject of wave-particle duality. The physical concept that Duality's name was inspired by, he revealed, was a revolutionary scientific discovery of the last few decades, proving that particles could behave like waves under certain characteristic situations. This, her father went on in a softer voice, was why he named her for it - particles, once held as set entities that could be entirely described with a few simple numbers, were now known to be intrinsically indescribable and transcendent of anything ever suspected of them. And if particles could do it, what possible reason was there for her not to do the same? She could defy the mathematical model that others attempted to constrain her to, she could reflect and refract around life's obstacles as if she was made of light itself, she could transcend anything she had ever dreamed of becoming, and, in so doing, become the pony she was truly intended to be all along.
Being just scarcely past foalhood, Duality only understood about half of this, but she still absorbed enough to realise that trying to become something she wasn't was neither productive nor possible, and she should instead accept what she was and work from there. This sent her into something of an existential tailspin, however, as she had no idea how to work from being a skinny juvenile pegasus to being a brilliant mage renowned throughout Equestria. After some time (about three hours, since she wasn't a dumb adult who spends their whole life figuring out easy existential enquiries like that), she came to the realisation that she didn't have to do magic to be a mage, as a mage, strictly speaking, is one who studies magic. She could study magic and be a nerd like her dad! Of course! So simple! This must be her destiny!
And, the next month, as she gave an intensively researched presentation to her class on the topic of the cutie mark she thought she might have in the future ("with detailed description of possible talent, justification of possible talent based on real-world evidence thereof, and demonstration of possible talent through a step-by-step explanation of the reasoning and experimental evidence behind Poni's Exclusion Principle", to quote the teacher's notes), her cutie mark materialised, so she was obviously right. Happily ever after. And an automatic A+ for getting her cutie mark while accurately predicting what it would be.
Duality is introverted in that she gains energy from time spent alone, but her carefully-cultivated social skills, honed by many years of teaching large university-level classes at Celestia's School for Gifted Unicorns and interacting with colleagues in regular meetings, allow her to be at ease in highly-crowded environments and when forced to converse for many minutes with effective strangers for the sake of civility, although such interactions leave her drained after long work-days. She is agreeable in temperament almost to a fault, courtesy of her parents' strict insistence on constant practice of good manners and empathetic behaviour, but has an irreverent, wry sense of humour that she never fails to bring to bear on a situation that she finds amusing or ironic (although she has become quite skilled at restricting the more sardonic of these quips to her notoriously haphazard stream of thought when voicing them may prove malapropos). Similarly, due to her parents' influence, she finds it extremely difficult to deny ponies when they ask her for assistance, especially when her friends are the ponies in question; fortunately, she takes great enjoyment from helping ponies out and often actively looks for ways to benefit those who seem to be struggling, especially students (in her lectures or another's) who just can't seem to wrap their minds around a particular concept or how it may be applied to a given situation.
Duality has an unusual affinity for liquid water, notably exhibited through her nigh-exclusive drinking of pure spring water - vehemently claiming it tastes far better than any other beverage and is more healthy for good measure - and the spending of much of her relaxation time gazing at scenic pools, rivers, or lakes. She needs a lot of relaxation time to keep herself refreshed and in good spirits, however, as her job demands intensive investment both in terms of her intellectual energy and her solitude-fuelled emotional energy. Fortunately, her job only involves four days a week of class-contact time, so she is usually able to obtain the rest she needs (even taking into consideration the marking, note-writing, and other such academic administration that is often required of her as a senior lecturer).
Duality is a venerable tan pegasus mare with a beige-and-aqua perpetually mussed mane and tail, faded with age. She is an inch or so taller and slightly heftier-built than most ponies, due to her earth pony lineage on her mother's side, and has a mild short-sighted squint - owing in no small part to the amount of close-quarters paperwork examination that her job entails - that persists, out of obstinate habit, even when she dons her corrective reading glasses. She wears a watch slung around her left front hoof constantly, unusual among ponies, which, although she keeps it generally hushed, is not primarily purposed towards keeping her schedule running in good time. Rather, the strap of the watch is a subtly runewoven periapt-bracelet, enchanted to deflect local magical fluctuations of middling power that might otherwise affect her and bought early on in her lecturing career (at ludicrous expense) to protect herself from the random student-sourced bursts of uncontrolled unicorn magic and spagyric sorcery that prove such a common job hazard in her line of work - as she is not a unicorn, after all, she has no natural ability to protect herself against such arcane energies.
Duality's cutie mark is a visual representation of the concept of wave-particle duality, using the analogy of a water droplet plopping into a pool. The individual droplets rebounding from the surface of the water illustrate the 'particle' nature of matter, and the ripples spreading out from the point of impact are a metaphor for the simultaneous 'wave' nature of matter. Her talent, as symbolically implied by the mark, is that of academic proficiency in quantum physics, specifically as applied to mathematical metamagic (that is, the analytical treatment of magical concepts as merely exotic cases of common biophysical principles).
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