published: 2021.06.08.09.22

I find that in theory the weird Speed Boost of the interstellar object ‘Oumuamua should be 0.217 mm/s above the prediction and that ‘Oumuamua should slow down less than prediction, in proportion of which the difference is 4.28×10-8 near the Sun. For Pioneer anomaly I have computed the gap between real and predicted acceleration and...

I have been playing with some iterated function systems again. These images were built using two affine transformations, one being a rotation through 20 degree composed a scaling of 90% and the second is a general affine transformation chosen at random. Some of the best of these results I have attached here. I have added...

Above is an image of “dry ice spiders” on Mars. Every spring the Sun warms up the Martian south polar icecap and causes jets of carbon-dioxide gas to erupt through the icecap. These jets carrying dark sand into the air and spraying it for hundreds of feet around each jet forming these wonderful spider-like structures....

In a recent preprint Riemannian Structures on ℤ₂ⁿ-manifolds, Janusz Grabowski and I initiated the study of Riemannian geometry in the setting of ‘higher graded’ supermanifolds. ℤ₂ⁿ-manifolds are, very loosely, manifolds that have coordinates with a ℤ₂ⁿ-degree (ℤ₂ⁿ := ℤ₂ x ℤ₂ x … x ℤ₂, n-times) and are commutative up to a sign factor that...

Orbit equation and orbital precession General Relativity explains gravity as Space-Time curvature and orbits of planets as geodesics of curved Space-Time. However, this concept is extremely hard to understand and geodesics hard to compute. If we can find an analytical orbit equation for planets like Newtonian orbit equation, relativistic gravity will become intuitive and straightforward...

In this article, we derive the gravitational time dilation factor in a new manner, which allows us to identify the mathematical cause of Schwarzschild radius, to give a theoretical way to avoid it and to compute properties of black hole. General relativity effects are computed as simple as in special relativity. Observability of black hole...

The rotation curves of disc galaxies are flat and dark matter is speculated as explanation. Alternatively, the gravity of material disk could explain the flat curves. Using the gravitational force that a disk exerts on a body in the disk, we have computed the the rotation curves of disc galaxies and the curve of their...

Special relativity does not deal with acceleration, general relativity does not deal with non gravitational acceleration, which leave the theory of relativity imperfect. We will demonstrate some relativistic dynamical laws that specify relativistic acceleration, force and kinetic energy. Also, based on equivalence principle does gravitational mass vary with inertial mass? Newtonian kinematics defines motions of...

The orientation of body in space is defined 3 by angles. The step by step rotation process and chain of three-dots multiplication give an easy way to compute pile of rotations in 3D and high dimensional space and give a general orientation system. A visualization of quaternion is proposed. The orientation of a rigid body...

Multidimensional complex systems with 3, 4 or more dimensions are constructed. They possess algebraic operations which have geometrical meanings. Multidimensional complex numbers can be written in Cartesian, trigonometric and exponential form and can be converted from one form to another. Each complex numbers has a conjugate. Multidimensional complex systems are extensions of the classical complex...

Today’s methods for computing orientation are quaternion and rotation matrix. However, their efficiencies are tarnished by the complexity of the rotation matrix and the counterintuitivity of quaternion. A better method is presented here. It uses complex multiplication for rotating vectors in 3D space and can compute orientation without angle and trigonometric functions, which is simple,...

For Newtonian mechanics The Schwarzschild radius is the radius of the event horizon of a black hole. Amazingly, we can compute it with Newtonian mechanics, which is explained below. Consider a big mass M which creates the gravitational acceleration a for a small mass m at the distance r from M, see figure 1 and...

I do a detailed analysis of Cantor’s theory of uncountable sets. The logic of his proofs has some weaknesses. I propose an axiom and a solution to continuum hypothesis. The main idea is: Assumption of Cantor’s proofs: All real numbers (set R) are in a list (list L). This assumption means R=L, considering L as...

An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption assumes R belongs to L. This makes the claim “a real number is constructed...

Cantor’s diagonal argument claims that ℝ is uncountable. When we see real numbers as points on the number line, we can put a name on each point and put the names into a list without contravening Cantor’s diagonal argument because we cannot create a diagonal from a list of names. However, we do not need...

The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex number to compute them which makes the computation easier and more intuitive. Roll, pitch and yaw are angles of orientation of an object in space and the conversion of these angles among different reference frames is...

Polarization of American Politics Ah politics… fun fun fun ‘til Daddy takes the T-Bird away, the polarization of America is getting out of hand. Everyone can buy a gun? State religion? No taxes? Unbridled Capitalism? Socialism? Libertarianism? Communism? Extremism! Oh My! Has everyone lost their collective minds? We live in a society, supposedly a free...

The apparent non‑gravitational acceleration the extra-solar-system ‘Oumuamua exhibits is puzzling. We find that when the position and velocity of the Sun is correctly set in computing the predicted orbit, ‘Oumuamua’s trajectory can be explained with gravity and we have reproduced the unexpected gap by computation. We also propose to search for new extra-solar-system high speed...

This is one of those portraits generated by Midjourney, not that of a real person.Like many people I’m impressed with the facility of Midjourney to create portraits of photogenic people. But how attractive or engaging would a person Iike this seem to be to you if you are someone, as I am, who struggled to...

Hilbert’s Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true. Let us illustrate Hilbert’s Grand Hotel in Figure 1 where each square is a room and is occupied. Suppose that the rooms of the hotel are numbered 1, 2,...

Abstract: The Lorentz force law is fundamental for electromagnetism. However, it is known long ago that the Lorentz forces between two current elements do not respect the Newton’s third law. This seemingly harmless flaw had never been corrected. In physical sciences a discrepancy often hides in it new understanding or unexpected breakthrough. For solving this...

Abstract: The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes the plasma to the wall. We have theoretically discovered this force and named it extra-force. This force appears only on single charges but not on current carrying wire, which is why the Lorentz force law does not contain...

Cindy was appalled at what she witnessed in the next few weeks, “Master” had been back and forth to the apartments as his libido demanded meanwhile Patty and Sally continued their obsession with being being “good girls” for Master. Cindy, much to her chagrin, had to pretend to be in Masters thrall and being patted...

On the ride to John and Bev’s hotel they both began to run their hands all over Cindy, kissing her, sucking and fondling her nipples, her kitty… in the dark the tears welling up in Cindy’s eyes couldn’t be seen but John and Bev’s only thoughts were on how they could enjoy the night using...

« N-complex number, N-dimensional polar coordinate and 4D Klein bottle with 4-complex number» “A concrete representation of a 4D Klein bottle has been desired by many but has never been presented. So, I decided to dive into the Klein bottle. Working with the Klein bottle was my first opportunity to practice with this system. To...

Fantasy Date! I met her in a petshop while buying buying fish food, not quite 5', her short stature was perfect for her chubby busty body. She had a halo of soft light strawberry blond hair, her bright hazel eyes and sweet round baby face hid her real age. She had piercings in her full...

By Leo Babauta Something that has long been a struggle for me is when people complain a lot — I really don’t love the negative energy, and I tend to turn away from people who are complaining. So I’ve been examining this in recent years … and I’ve been learning a lot about myself. The […]

The post Transforming Our Complaints into Something Generative appeared first on zen habits.

By Leo Babauta I talk to dozens of people every month — Zen Habits readers, coaching clients and Fearless Living Academy members — who struggle with a feeling of overwhelm from all of the things on their plates. Overwhelm from tasks, messages, and more is completely normal. It’s based on a fear that we can’t […]

The post Transforming Overwhelm into a Creative, Productive Energy appeared first on zen habits.

By Leo Babauta Let’s imagine that there’s a big task you’ve been avoiding for weeks (or maybe a bunch of them!) … it just becomes this ball of dread that you don’t want to think about, but that you feel really bad that you’ve been putting off. Sound familiar? Everyone has something like this, whether […]

The post Turning Towards a Task You’ve Been Avoiding for Weeks appeared first on zen habits.

By Leo Babauta Most of our stresses and frustrations come from our unwillingness to let go. Hear me out: think about something you’re stressing about, or someone you’re frustrated about. What thought do you have about that person or situation that causes the frustration? It’s often an invisible thought, that we don’t realize we have, […]

The post The Practice of Letting Go appeared first on zen habits.

By Leo Babauta When we’re looking to grow, what we’re really trying to do is step into a new, expanded view of ourselves. For example, if you want to be more mindful, or live more simply, or be more compassionate with yourself or others, or be more disciplined about your meaningful work … these are […]

The post Expanding Beyond Our Old Self-View appeared first on zen habits.

By Leo Babauta There’s a practice that I find to be really valuable, and I call it “Examining Beliefs.” If you regularly engage with this, it will transform you. Let’s say there’s something you want to do but you feel stuck — maybe you’re procrastinating a lot, maybe you’re stuck in an old habit. The […]

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By Leo Babauta Each day, I try to get outside for a walk or run (or other sport like cycling or basketball), and my debate with myself is often whether to bring my phone and earbuds to listen to music, a podcast, an audiobook … or to go tech-free. Tech-free is my favorite option — and […]

The post What Happens When You Walk or Run Daily, Without Tech appeared first on zen habits.

By Leo Babauta Sometimes we decide not to do something because it feels like there’s not enough time to do the task — it will take me 2 hours to work on that task, and I only have 20 minutes, so why bother starting? We do this kind of thing more than we realize — […]

The post There’s Not Enough Time appeared first on zen habits.

By Leo Babauta Last year, I turned 50 years old … and I found myself thinking about aging more than I ever had before. To be clear, 50 years old is still pretty young, but there’s something about the number that had me realizing that my 60s and 70s aren’t very far away, and it […]

The post Overcoming the Fear of Aging appeared first on zen habits.

By Leo Babauta I believe in finding powerful practices for transformation wherever we can find them. And the Stoic philosophers Epictetus, Marcus Aurelius, Seneca are huge inspirations for me. I’ve found there to be a huge overlap between Stoicism and Zen Buddhism, even if there are also some key differences. The overlap between Zen & […]

The post 5 Stoic & Zen Practices That I Believe In appeared first on zen habits.

Osedax worms, or the ‘bone eating’ worms are little soft sacks resembling snotty little flowers. The “bone devourer” is not quite accurate as the worms…

The post Introducing a New Species: My Namesake, a New Bone-Eating Worm first appeared on Deep Sea News.

Guest post by Dr. Melissa Betters Are you afraid of the deep, dark ocean? If so, you’re not alone. Thalassophobia (fear of deep water) seems…

The post  The Cost of Fear: How Perceptions of the Deep Sea Hurt Conservation first appeared on Deep Sea News.

Guest post by Dr. Melissa Betters “They got it!” echoed shouts down the hallways of the Research Vessel Atlantis in Fall 2018. The whole science…

The post The Carpet Dragon Takes Flight first appeared on Deep Sea News.

Between 1948 and 1961, barges laden with industrial waste, including high concentrations of once-ubiquitous agricultural insecticide, Dichlorodiphenyltrichloroethane (DDT), were indiscriminately discharged into the Pacific Ocean.…

The post DDT is a Deep-Sea Toxic Time Capsule first appeared on Deep Sea News.

The ROV Global Explorer reaches bottom at around 9:01 am, nearly 3.5 kilometers deep  in the Gulf of Mexico.  The 1.5-ton machine flies nimbly through…

The post Surviving Toxic Havens first appeared on Deep Sea News.

I have only seen a hydrothermal vent once, during Dive 73 aboard the Monterey Bay Aquarium Research Institute’s Doc Ricketts. Unlike many deep-sea biologists, I…

The post A Journey to the Hottest Place on Earth: Hydrothermal Vents and the Resilient Pompeii Worm first appeared on Deep Sea News.

Tiger sharks are sort of generalist feeders. And by generalist, I mean they will pretty much eat anything. And by everything, I mean everything. On…

The post Tiger Sharks Will Nom Nom Anything first appeared on Deep Sea News.

Like most deep-sea biologists, I have a large collection of decorated Styrofoam cups. A couple dozen line the bookshelf of my office, each displaying a…

The post How Life Thrives Under the Ocean’s Crushing Pressure first appeared on Deep Sea News.

In our fast-paced, modern world, time is our most precious commodity. We’re constantly juggling responsibilities, chasing dreams, and trying to make the most of every moment. But have you ever felt like your days are slipping away, consumed by activities that don’t truly enrich your life? It’s a common struggle, and the culprit is often ... Read more

The post Reclaim Your Time: Conquer the 4 Major Time Wasters appeared first on LifeHack.

A few years back, I found myself in a rut with goal-setting. I had all these grand ambitions, but making actual progress always felt like an uphill battle. I’d set huge goals like “become a famous entrepreneur” or “get shredded,” but within months, my motivation would fizzle and I’d be back where I started. Even ... Read more

The post Reimagining Goal Setting: The Power of Northstar Goals appeared first on LifeHack.

Have you ever felt totally uninspired by those vague corporate mission statements? The ones that say things like “To be the world’s most trusted provider of integrated solutions”? Or by those vague New Year’s resolutions? The ones that say things like “Get in shape” or “Be a better person”? Blah blah blah. What does that ... Read more

The post Discovering Your North Star: Crafting an Inspiring and Authentic Mission appeared first on LifeHack.