Abide By Reason

SCHRÖDINGER'S ORIGINAL DERIVATION

Currently finishing up the final edit's on the next video, which will be about how Schrödinger originally derived his famous wave equation of Quantum Mechanics. He essentially used just 2 basic ideas: the Hamilton-Jacobi Equation and the Principle of Least Action. You'll find out what these are + how it led him to Quantum Mechanics in the video. Should be out in a couple days! If you want to help shape final edits, you can find the early access rough draft on Patreon: www.patreon.com/AbideByReason. Hope you are having a great week.

Best,
Dan

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3 days ago (edited) | [YT] | 328

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HAMILTON'S ANALOGY BETWEEN OPTICS AND MECHANICS

Hope you enjoyed the latest video on the Legendre Transform! https://youtu.be/P2HZelQm7Lw I'm currently having fun working on the next video which will be about how Schrödinger originally derived his famous wave equation of quantum mechanics. This guy, William Rowan Hamilton, played a key role with his discovery that optics and mechanics can be brought under a single framework, a framework in which Fermat's Principle of Shortest Time (δT = 0) and Maupertuis' Principle of Least Action (δS = 0) are each just specific instances of a more general principle. It was this optico-mechanical analogy that lay the foundation for Schrödinger's thought process in developing Wave Mechanics. Stay tuned for more!

Hope you have a good week ahead.

Best,
Dan

2 weeks ago (edited) | [YT] | 236

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VISUALIZING THE LEGENDRE TRANSFORM

Thanks to everyone who answered last week's poll! Next video will be about the Legendre Transform and its applications in Physics.

1 month ago | [YT] | 168

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Hope you've enjoyed the last 2 videos on Lagrangian and Hamiltonian Mechanics! What would you like to see next? Feel free to comment other ideas below too.

1 month ago | [YT] | 40

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LAGRANGE VS HAMILTON

I just posted a video on Lagrangian vs Hamiltonian Mechanics where you can learn how they are related to one another through the Legendre Transform. Thanks to all who answered my poll a couple weeks ago. If you haven't had a chance to watch it yet, you can find it here: https://youtu.be/tpp1Ahmij_Q

Hope you have a good week,
Dan

1 month ago | [YT] | 162

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Without looking it up, what is the key mathematical tool that relates Lagrangian Mechanics to Hamiltonian Mechanics?

Currently working on the next video where this tool will play a key role. The video will be all about Hamiltonian Mechanics vs Lagrangian Mechanics. Stay tuned!

2 months ago | [YT] | 42

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NEWTON VS LAGRANGE

Isaac Newton was one of the greatest thinkers to ever live. He established the foundations of Classical Mechanics in his highly geometric work "Philosophiae Naturalis Principia Mathematica". Just 100 years after him, Joseph-Louis Lagrange crowned Newton's achievements by codifying and systematizing them into essentially a purely mathematical theory, Lagrangian Mechanics. In his preface to "Mécanique Analytique", Lagrange proudly said "there are no diagrams in this work ... only algebraic operations". In my next video, I aim to help you gain a deep appreciation for the power of Lagrange's approach (will post sometime late next week).

I'd also like to take this moment to announce that I recently created a Patreon. If you'd like to support my work, gain early access, and be a part of the creative process by helping shape final edits, I'd be honored to have you join.

Patreon: patreon.com/abidebyreason

Best,
Dan

3 months ago | [YT] | 113

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THE SCOTTISH BOOK

Thanks to all who answered my poll a few weeks ago. I just posted my video on the Scottish Book, a truly astonishing book created by Stefan Banach and his colleagues in the years between World War 1 and World War 2. The story of Banach's life and the creation of the Scottish Book is absolutely amazing and really deserves to be made into a full film. I hope my short video did it some justice. If you haven't had a chance to watch it yet, you can find it here: https://youtu.be/4K7WVt_qOGg

Best,
Dan

3 months ago | [YT] | 45

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Without googling, have you heard of the mathematical notebook called The Scottish Book?

4 months ago | [YT] | 23

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GUESS WHO?

In 1916 this man "discovered" Stefan Banach during a leisurely walk through a park in Poland. He walked by 2 young men (1 of which was Banach) and overheard the words "Lebesgue Measure". Overcome by curiosity, he immediately introduced himself and they all quickly became friends. This chance occurrence was the pivotal moment that launched Banach's career as a mathematician and the man pictured considered finding Banach to be his most important mathematical discovery. Without googling, can you guess who it is?

4 months ago | [YT] | 48