Happy New Year.
Beginning January 2020, I plan to periodically provide a commentary (Sanskrit ब्राह्मण, Brāhmaṇa) on Quantum Integer Programming (QuIP).
It will consist of short expositions written in everyday vernacular speech (भाष्य, bhāṣya).
As I mentioned in an earlier post, QuIP is Book One of Neo-Quantum Organon (paying homage to Francis Bacon), a technical manuscript that is in preparation, whose content is, not surprisingly, mathematically dense.
So: Śrīdhara (श्रीधर) Brāhmaṇa (ब्राह्मण) is its commentary by its author.
Quantum Integer Programming brings together Integer Programming and Quantum Mechanics. I want to open with two short pieces.
The Origin of Modern Numerals
By Modern Numerals, I mean:
the use of nine distinct figures, along with an additional sign 0 (for zero, śūnya शून्या, literally vacant or empty or nothingness), to write all the numbers one wishes.
In Ancient (Vedic) India, it was not important (for counting, Aṅka अङ्क) what shapes these nine figures had, as long as everyone understood their meaning and how they were manipulated.
Over time, certain set of nine figures were considered more beautiful (than others) by practitioners, and became used more repetitively.
Muslim astronomers (of Persian origin) and other Arabic mathematicians wrote about what they had witnessed while in India; the Europeans (including the Greeks), having read these books, travelogues in current vernacular, mistakenly labeled them as “Arabic Numerals.”🤷🏽♂️
Sanskrit is one of the oldest languages, viewed by the Vedic Indians as the language of the gods. For centuries, it was mainly oral. Around 600 BCE, the Brāhmī script was used to write Sanskrit (for instance, Buddha, that is सिद्धार्थ गौतम, Siddhārtha Gautama, had mastered it in his youth).
The Brāhmī script (known as “mother of Indian writing”) spawned a variety of descendants: Nāgarī (literally “of the city”, urban) being one of them.
Continuous refinement of this Nāgarī script led to something that was considered to be so beautiful, that it became known as the “writing of the (city of) gods”: Devanāgarī (देवनागरी). Sanskrit is संस्कृत.
Modern numerals we use today (1, 2, 3, 4, 5, 6, 7, 8, 9 and 0) are descendants of the beautiful figures from the Brāhmī script. 😌
The Origin of Magnetism
Although magnetism was discovered centuries ago in Greece (name derived from μαγνῆτις λίθος magnētis lithos) and India (Suśrutasaṃhitā सुश्रुतसंहिता), until quantum mechanics (specifically, spin) came to be conceived, it could not be explained.
Quantum theory originated when Max Planck postulated (in desperation!) that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit:
where h is Planck’s constant, and ν is the frequency of the radiation. Why? It was his “Hail Mary” to save Blackbody Radiation analysis from Ultraviolet Catastrophe. It worked (spectacularly).
The concept of spin emerged when Paul Dirac successfully incorporated relativistic considerations (of Einstein, specifically, that space and time co-ordinates have to appear symmetrically) in his study of the electron (discovered by J.J.Thomson) into Schrödinger equation.
What triggered Einstein to conceive of Special Relativity? The (absolutely inexplicable) Null Result of the Michelson-Morley experiment and the remarkable accuracy of the Lorentz Transformation.
What possessed Schrodinger to come up with the eponymous equation? He wanted to retain the Hamiltonian formulation (named after William Rowan Hamilton, also known for quaternions) from classical physics while being able to explain the puzzling results from Double-Slit experiment.
The Dirac equation is considered to be among the most beautiful equations ever.
Another by-product of the Dirac equation is the prediction of anti-particles; the positron (anti-electron) was soon discovered by Carl Anderson.
The Dirac equation originated Quantum Field Theory (QFT). For the purposes of quantum computing, QFT is not needed. Spin is.
Here is an aphorism (सूत्र, sūtra):
QuIP: Optimizing over integers using magnets.