Yogananda is credited for further evangelizing yoga and meditation in the West. His famous book Autobiography of a Yogi chronicles his long and arduous path to Self-Realization.
A boy is discovered on the beach one day and made to be a Messiah. After 20 years of preparation, he dissolves his religion of tens of thousands.
Rumored to have been murdered by the CIA, Itzhak Bentov was known for his simple way of explaining consciousness through physics. His core belief being that consciousness is not merely a byproduct of the brain but may be a fundamental property of reality. The universe can be understood as an evolving field of consciousness learning about itself.
Andrew Carnegie adopts a revolutionary, emerging technology in steel production: the Bessemer Method. He builds his steel empire from this new method — see how.
Seldom do people walk so long & hard that their shoes wear out. Calloused and bloody, Kit Carson’s journey racked up thousands of miles across the rugged North American terrain — an odyssey that captured the American spirit of Manifest Destiny. John C. Fremont hired Carson to guide his men during their four year expedition across the uncharted terrain of the “Wild West,” a directive by the expansionist President James K. Polk. This specific leg of the journey led Carson right back to Polk where on September 15, 1848, he informed the President that gold was discovered at Sutter’s Mill in California.
J.P. Morgan had not asked for the role, but it was bestowed upon him. At a Friday service on October 18 at the Triennial Episcopal Convention in Richmond, Virginia, news of the impending crisis reached him. He contemplated what it was he needed to do; his role in America’s financial markets is unique in that his every move inspired confidence or panic in the economy, a self-fulfilling prophecy by a market that placed so much stock on his word. Aware of this constant surveillance, he waited before rushing back in order to avoid spooking the markets. He was in New York by the next night, walked into his library, and began doing what no government institution could do; because no government institution existed to do it. Only he could save the US economy, but would he succeed?
To effectively establish a worldview, one needs to apply the Italian Renaissance painting technique of sfumato: where you soften transitions between colors and tones, creating a smoky, blurred effect without visible lines or borders. I argue that every strongly adopted belief begins constraining the interpretations available afterward. If I commit prematurely, subsequent ideas get filtered through an already hardened worldview. The happy medium is a balanced approach to “shading” across n-dimensional domains.
A critique on the exhaustive set of essays written by psychotherapist and leading Jungian scholar, Marie-Louise Von Franz.
Analyzing key takeaways from Plutarch’s The Lives of the Noble Grecians and Romans. Plutarch already does an incredible job of comparing various profiles, but here we will repeat the exercise at a higher altitude.
An elegant alternative to calculating a cumbersome binomial distribution — the efforts of Gauss, De Moivre, and LaPlace leverages an alternate approach that makes life easier.
When researching content and storing useful information, you need to know what framework/structure your book will take. We should consider two axes — the relationship between the data points (cohesive or fragmented) and the method to convey the idea (prescriptive or descriptive). Below are some writing patterns you can adopt for non-fiction content.
“It’s all relative.” If you could have a Google search for the term relative back in 1905, you’d say without a doubt that we can thank Albert Einstein for that. From it, you may have heard that space informs time, while time informs space, a unified form of spacetime. Let’s dive into what this means and how it works.
This post is a followup to the post on Vector Spaces & Linear Mappings. We’ve explored the use of matrices, their various operations, the linear combinations and linear transformations that arise from their mappings. We’ll dig in deeper around these operations and uncover the beauty behind the geometry that arises from these higher-dimensional mathematical objects.
Bayesian probabilities grant us higher confidence in making predictions when we have some certainty in the past and general uncertainty in the future. As humans we naturally use Bayesian methods to navigate in the world — using Bayesian mathematics can help machine learning models “learn” as well as give traders an edge as they enter high probability trade positions.
Breaking down the essentials of matrix decompositions, explaining how they are used in machine learning and why determinants, traces, eigenvalues, and eigenvectors enable us to draw better decision boundaries when designing our machine learning models.
The use of vectors is commonplace in machine learning, with the use of functions and linear transformations that result in vectors and/or probability distributions. Below we will dive into the mechanics of vector spaces and subspaces that encompass these linear transformations. We won’t cover specifically how they are applied in machine learning here, but will in our other posts pertaining to matrix decompositions and analytic geometry.
One of the more esoteric and mystical explanations of prime numbers is an unproven hypothesis called the Riemann Hypothesis. It involves the use of prime numbers and the zeta function, which when taken to an “imaginary” and “complex” realm, expose a deeper meaning to the foundation of number theory. Before we dive in, we’ll pay our due diligence covering what primes are and work our way up through the millennia of mathematical work that laid the groundwork for Riemann to hypothesize the placement of prime numbers along a unique line, across an even more unique graph.
When we think of things in nature having symmetry, we often think of a reflection – but in mathematics a symmetry has a more durable meaning: when an object remains invariant under any form of transformation. An object has symmetry when you can do something to it and it still retains its shape and position. When you observe a snowflake and its symmetry, we think of symmetry as a passive quality – that an object merely possesses this quality. Very much like our popular conception of beauty, that one has it if they possess symmetric features.
Meetings should not be held to give updates — this can be done asynchronously. Instead, meetings should have a shared agenda of decisions that need to be made, collectively acquired prior to the meeting, so that there is a clear success metric for whether the meeting is done or needs to be extended. There is an inverse relationship between the number of people in a meeting and the effectiveness of the outcome.
The Poincare conjecture is another great math problem that had yet to be proven for over 100 years. Conjectured by the French mathematician Henri Poincare in 1904, he asked “If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere?”
Much of burnout originates in the perception of threat. When work is experienced as a continuous threat to status, livelihood, or belonging, then our thinking narrows. The nervous system shifts into survival mode: fight, flight, or freeze. Each response reduces cognitive flexibility; creativity, nuance, and long-term reasoning disappear. Our world begins to feel like it’s closing in on us.
I provide critique and commentary on the aphorisms of Balthasar Gracián’s book The Art of Worldly Wisdom — but from a modern day lens.
I’ve recently acquired over 20 different Schaum’s workbooks, covering a variety of subjects. My daily routine has been to crack these open and begin working through problems in the morning. Not too many problems, but enough to give my brain a good morning stretch before it runs through the day. This is the fastest way I’ve come to realize I don’t really know what I think I know. The same applies to everyone else, including you.
Rose Blumkin, known to Omaha as Mrs. B, was patrolling the store in her golf cart. She motored down the aisle, haranguing an employee and gesturing with her arms with the vigor of a woman half her eighty-nine years. Her cheeks were flushed, and her auburn hair, done up in a bouffant, showed gray only at the temples. Buffett reckoned that he would "rather wrestle grizzlies" than compete against Mrs. B, and that was why he had come.
Single one pagers have been touted as the only documentation needed to kickstart product development teams at Facebook. The rationale is that this forces the team to engage in continual dialogue as the feature is being built. My belief is that this is erroneous and lazy, that any project should start with a succinct TLDR of the goals and objectives of the feature, followed by the continual documentation of the PRD until completion. The exercise of writing a thorough PRD exposes holes in logic & reasoning that are caught and addressed early on.
Distilling the work of Friedrich Nietzsche. Here we unpack Human, All Too Human.
The Monte Carlo Method was created by mathematicians John von Neumann and Stanislaw Ulam during World War II as a way to improve decision making under uncertain conditions. The premise of their idea is that solutions to mathematical problems, mainly those modeling complex systems or processes, can be derived through the random evolution of sampling. Said differently, most problems are solved with formulas & equations using precision and exact mathematics — while these complex problems are solved using averages of stochastic (random) simulations over a large number of iterations — based off the law of large numbers and the central limit theorem.
A good Product Manager acts more like a GM than just a product owner. Accounting for the bottom line metrics of the business, they should keep an active pulse on the state of the business as well as monitor any signals of interest. The coffee dashboard has been the most effective resource in any company I’ve worked at.
What conversations do we have with our customers? From the moment the user accesses our product, how do we speak to them and what UX elements do we employ in speaking with them? We have a wide range of users that come in at different stages in their self employed career, all needing different levels of assistance. The idea here is that we need a consistent medium to interact with our customer, capitalizing on a relationship we can have as an advisor throughout their freelance career.
I recently purchased an HP SmartInk printer, not realizing I am now tied, ball & chain, to a subscription service just to use the product.
Runway is a measure for the health of a company — public or private, and this can be done through Altman’s Z-Score. This score calculates the probability that a company will file for bankruptcy within the next 2 years using five important variables, factored into a single linear combination.
Covering the basics of generating, circulating, and delivering a Product Roadmap.
Dr. Shigeo Shingo was a Japanese industrial engineer and quality control expert, specifically on Japan’s Toyota Production System and manufacturing processes.
Principles of good writing broken down by: long form, advertising, and story-telling.
A good writing routine is a well-written program you can safely submit to. A writing routine is outsourcing your uncertainties. It allows you to compartmentalize your worries and gives you space to unravel your thoughts in written form. It's a safe space of sorts.
Thinking long term is a luxury with startups. If you have anyone who specializes in “strategy”, a government relations arm, an obscure consultant, or anyone who is thinking too far into the future -- you are doomed. You’re focusing on the wrong altitude.
If one is to express by imitating, then one understands how nature uses networks to synchronize; inherently. Fireflies do this by having a leading node in their network initiate a flash of light, which in effect is followed by another node, etc. The speed in which this is done is so fast that it seems as thought they are doing so as one.
There will be those who have a touch of nostalgia who will wish for the times when humans weren't lost in their smart phones. A lost era of the past where people swear society wasn't attention hungry nor reliant upon the likes and gratitude of mere acquaintances or strangers. I'm here to argue that we can't go back in the past and we need to operate within the current domain we live in. Smart phones are here and frankly the internet is a basic human right.
Life is a series of connections. Life does not exist in isolation. Life is context. Life is relative. Nothing about life is general or objective. It morphs, it is ever-changing, and it continually builds upon itself.
I noticed when I was in college that, although I was a Philosophy major, any of the other pre-requisite classes I was required to take (California History, Psychology, Anthropology) all seemed to overlap with each other. There was always a core theme behind the education of one subject that philosophically aligned with that of another. Whenever I saw this overlap, I was able to piggyback off of the information I acquired from one to benefit the other. It was like I was studying twice as much.
Looking back at the pandemic, we’d fall into another fallacy that Taleb claims history continues to fall victim to: the narrative fallacy. This is when we look at the past, assess and explain what happened and why it led up to that black swan event using broad brush strokes and oversimplifying these causal events. It’s dangerous because it convinces people that this was an inevitable outcome, which is contrary to the black swan nature since it’s an unknown unknown.
Graph machine learning is a method in which distance and geometry of nodes play an important role in filling in the information gap with machine learning. Also known as dot product, this is an essential way for understanding the geometric spaces the vectors inhabit.
Leonardo da Vinci was famous for his astute observation of the smallest intricacies of nature. His observations were drawn in his infamous notebooks and one in particular, that of water being poured into a river, leads us to another problem: fluid dynamics.
Emergence is the phenomenon where seemingly simple, dumb bits manage to coalesce in a way where they work in tandem with many parts. The simpler way to phrase it is: the whole is greater than the sum of its parts. These are my definitions of course and how I interpret them, so please do not attack me with any formal definitions that may undercut the central message I wish to get across: that when in large numbers, novel properties emerge from a lower order of complexity, thereby creating a concept of a sentient whole.
Rather than simply using a word processor, the way in which I wrote was radically transformed from the start, by using metadata and attributions for my work, I was able to both write more efficiently but also embed credit in a way you can’t easily do on a word processor. To apply decentralized science to the mix— I would have been able to publish my book in a manner that would have eased my fears around plagiarism.
Analyzing key takeaways from Homer’s The Iliad.
Analyzing key takeaways from Plato’s The Republic.
Analyzing key takeaways from Sun Tzu’s The Art of War.
Analyzing key takeaways from Giovanni Boccaccio’s 14th-century The Decameron.
Analyzing the underlying timeless lessons bestowed on us by the Roman poet Virgil. Written in the style of Homer’s The Iliad and The Odyssey, Virgil establishes Rome’s first heroic myth in epic form, through Aeneas and the burdens he carries to establish the future generations of rulers that manifest into the Roman Empire.
Critiquing the work of Dante Alighieri’s The Divine Comedy, which contains three books as he transcends from hell to purgatory, to heaven.
Analyzing key takeaways from Carl Jung’s essay on Synchronicity.
I’ve ushered in a new era of reading, one that takes more time to metabolize the wisdom I carefully choose to accept or reject into my worldview.
I created a Python script that pulls realtime market pricing data from AlphaVantage and uses specific entry and exit position signals off of my custom superposition bands indicator I’ve created.
As I continue to build out my algorithmic trading models, here is an ongoing list of features I find would be helpful in elucidating high probability trade setups. These may or may not be correct — but these are the features I am experimenting with.
In the current AI bubble, we need to hedge our bets.
A physics engine describes a software program that is used to simulate physical phenomena. The first physics engines were used in military simulations, predicting where artillery shells would land. These engines factored in the shells' weights, forces, and trajectories to simulate the result.
A primer on what a diffusion model is and how it’s used.
Transformers let AI models track relationships between chunks of data and derive meaning. It is an architecture of neural networks that takes a text sequence as input and produces another text sequence as output.
The basis of any machine learning model follows the structure shown below (in its simplest form), using the syntax as defined in scikit-learn.
Using the right-handed rule, we can see the orientation of three perpendicular vectors in a 3-dimensional space. However what these vectors actually mean has been more of a mystery to me, until I learned about torque.
Parkinson’s Law is the observation that a person operates within the constraints they are set. If you tell someone to complete a task in 16 hours, they will take the full 16 hours but if you double it to 32 hours, they will take the full 32 hours. The same can be said for the reverse where reducing the constraint to 8 hours will result in a person using those full 8 hours.
Writing out some of my favorite authors in no particular order.
A summary of the key points from the How I Write Podcasts’s episode: 10 Lessons from the Best Writer in Tech by Paul Graham
A summary of the key points from the podcast How I Write: I Spent 50 Hours With 20 Master Writers
Summary of the key points from the podcast How I Write: How To Master Storytelling with Shaan Puri.
A ranking of my favorite workouts for each body part, including some unconventional exercise and those I created myself.