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...

« 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...

We've bought our first home, and we are so excited to remodel the kitchen! We're keeping our updates simple and on a budget, but the imact will be HUGE!

The post Mini Kitchen Remodel – The “Before” – Virginia Beach, VA appeared first on Joyful Abode.

So this week, we decided to make a pretty Valentine's canvas for their playroom, that can stay up all year. My kids really love looking at art that they've created and declaring, "I'm the artist! I made that!"

The post Valentine Canvas – Easy Art Project for Kids appeared first on Joyful Abode.

How to make folded paper window hearts. This is a step by step tutorial that will have your windows looking full of love in just a few minutes.

The post Paper Window Hearts – DIY Valentine Crafts appeared first on Joyful Abode.

Looking for the simplest Waldorf kite paper star pattern? You’ve found it! Anyone can make a beautiful sun catcher for their window out of translucent paper. This pattern gives young children the delight of creating their own decoration, while practicing fine motor skills. Please note though – it may be a bit tricky for kids […]

The post The Simplest Waldorf Star Pattern – Beautiful and Easy Decoration appeared first on Joyful Abode.

Are you ready to make some kite paper stars? Here’s the tutorial you need – a simple, step-by-step breakdown of this classic craft, so you can follow along with no confusion. At the end of this project, you’ll have a beautiful paper star you can hang in your window as a sun catcher. Try making […]

The post How to Make Kite Paper Stars – Simple Tutorial for a Classic Craft appeared first on Joyful Abode.

Have you ever had a personal word of the year before? Did you choose the word? Or did a word choose you? I don’t choose my word of the year. It comes to me, generally in December or January, and sometimes it surprises me. It’s something that’s been happening for me for the last seven […]

The post My Personal Word of the Year (And How to Find Your Perfect One) appeared first on Joyful Abode.

This post may contain affiliate links. If you make a purchase through an affiliate link, the site author may receive a small commission. The mini kitchen remodel reveal Have you been on the edge of your seat, wondering how my DIY mini kitchen remodel turned out? Well, here we go! We didn’t do a full […]

The post Mini Kitchen Remodel – Bright & Airy AFTER (You’ll love it!) appeared first on Joyful Abode.

Here's your ultimate guide to declutter kids' clothes and keep the clutter from coming back! A whole new way of thinking about kids' wardrobes.

The post How to Declutter and Simplify Kids’ Clothes – The Ultimate Guide appeared first on Joyful Abode.

Getting organized is always one of the most popular New Years resolutions every year – not surprisingly. And you need. To. Do it. This year. Why? It’s not just because being organized for organization’s sake is a good thing (It’s not good or bad – it’s morally neutral). You NEED to stop procrastinating and finally […]

The post 8 Reasons You NEED to Get Organized This Year appeared first on Joyful Abode.

A travel guide for moms who are traveling alone. It can be hard to find time to do things for yourself when you have young kids at home, so why not take advantage of the opportunity to travel without them? Here are some great ideas for your next solo momcation.

The post 9 Tips for Your Best Momcation – How to Maximize your Relaxation appeared first on Joyful Abode.

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 […]

The post The Practice of Examining Our Beliefs appeared first on zen habits.

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.

When your 2020 wrapped congratulates you on all four episodes of content you produced this year, it must be PotterCast!

Welcome to season 16, in which we are, we swear, on the edge of actually producing this thing at a normal clip. See how it's going to start to work in this episode in which we introduce a few new segments — a bit of opening chatter (including an IN-Depp conversation as Frankie puts it) with your gang, then two new segments: POTTER PONDERINGS (in this episode, we wonder what it takes to make a Hufflepuff go dark) and HEY NETFLIX (in which we pitch spinoff shows about the Potter universe — today, what would we want from a show about the Ministry of Magic?). Then join us to chat in the drums as usual!

~*~

Here are ways to support the show!
Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

The internet went crazy today when a rumor seemed to break through about the always-destined Harry Potter television show — specifically that while no series is actually in the works, WB is now officially shopping for writers and pitches for an HBO Max event. We did a quick-and-dirty reaction pod with our three hosts and our good friend Proma Khosla, a longtime LeakyCon staffer and Mashable entertainment reporter, to break down the news, what it means for the franchise, and what the fandom does now. 

Basically, we decided the fandom just needs to get a trillion dollars together and buy the franchise from JKR. 

You can follow Proma on Twitter at @promawhatup  and read her Mashable articles here!

~*~

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

Woo hoo it's PotterCast time and it hasn't even been six months! This week, we are talking about what a TV series starring Arthur and Molly would look like, and pondering what you would or should do if you were to wake up as 11 year-old Harry with all seven books' knowledge in your head. Trippy. 

We are still going through all your amazing emails for guest hosting and will be reaching out to people soon! Please also welcome our new editor, Christine Peruski! It's her first time, y'all, and she did a great job!

~*~

This episode's sponsor is LootCrate! Use THIS LINK (http://multitude.productions/lootcrate) and the code POTTERCAST for a 15% discount on your first box!

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Christine Peruski and Melissa Anelli. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2021.

Welcome back! This week (or, when we recorded this, so awhile ago) we have lots of Potter news to discuss. In Potter Ponderings, we're also getting into what Muggle work the wizards could or should be taking on. And on Hey Netflix... you know what, you're going to have to tell us.

We are still going through all your amazing emails for guest hosting and will be reaching out to people soon!

~*~
Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Christine Peruski and Melissa Anelli. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2021.

Happy 2022 and welcome to season 17! This one was recorded a little bit ago, when we got the title of the next Potter movie, but it's chock full of theories and ideas about what could be coming in the third movie. More soon!

We are still going through your emails for guest hosts! Also, we are still looking for editors so if that's you email us at staff@pottercast.com!

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Christine Peruski. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2021.

We haven't seen it yet, but we've seen all the trailers and we have THOUGHTS. John, Frak, and Melissa discuss the "Fantastic Beasts: Secrets of Dumbledore" revelations — like the fact that it's almost certainly the last one.

~*~

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Melissa Anelli. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2022.

WARNING: Volume. RIP headphone users.