James' World 2

Click the link below the picture

.

Ever since the Rubik’s Cube was released, it’s taunted almost a half billion tinkerers who think they can crack its confounding mysteries, only to be stymied by its maddening secrets. Now, it’s time to unpack the puzzle once and for all—using some deep math. The cube’s literal insides are made of plastic, but its real guts are nothing but numbers. Let’s dive in

Breaking Apart the Blocks

Starting with some basics, a 3x3x3 Rubik’s Cube has six faces, each a different color. The center of each face is attached to the core scaffold that holds the cube together, so they don’t move other than rotating in place. As a result, the same colors always end up opposite from each other; on a standard cube, white is opposite yellow, red opposite orange, and blue opposite green.

Bust open a Rubik’s Cube, and you’ll see it’s made of three types of building blocks. First, there’s that central scaffold, connecting the center of each face. Then there are the cubies—the nickname for the little 1x1x1 blocks. The corner cubies have three colored sides, and the edge cubies have two. A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies.

The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (3⁸8!)(2¹²12!)/12. Here’s how that comes together.

The first term, 3⁸, counts every way the eight-corner cubies can be rotated. A corner cubie can fit into its slot, rotated three different ways. That’s a factor of 3 for each of the eight corner cubies, so they multiply to 3⁸.

.

Photo by  Andrew Spencer/Getty Images

.

.

Click the link below for the article:

.

__________________________________________

Click the link below the picture

.

Lawns are a sign of prestige. Once a sign of upper-middle-class British wealth, over the past century, the traditional yard transformed into an element of the “American Dream”—owning a house of surrounded by a mini field of greenery.  It takes a significant amount of water, fertilizer, and labor to maintain a simple grass lawn—and even more resources for keeping sporting arenas, golf courses, and gigantic McMansions in top shape. 

Still, some eco-conscious people and landowners are swapping pristine green grass for a sustainable lawn. Plants still cover the ground and provide beautiful greenery, but take up less water to maintain. Some are even great for local pollinators and utilize different plants and grasses that are often native to an area instead—creating beautiful, unique landscapes that support local wildlife. And in a changing climate, there’s plenty of reasons to ditch the monotonous green grass lawn for something more resilent and resource-savvy. 

Native Grasses and Plants Use Way Less Water Than a Typical Lawn

According to the Natural Resource Defense Council, grass lawns consume nearly 3 trillion gallons of water a year, 200 million gallons of gas (for all that mowing), and 70 million pounds of pesticides. A challenge to maintain in some areas, considering that some rivers out west are facing historically low levels—it means water shortages for residents out in Western states. The U.S. has experienced a “megadrought” this year, and hot dry conditions are also worsening the incidence of forest fires in various states across the West Coast. 

Creeping herbs like thyme and oregano, ornamental grass, evergreen moss or even covering an area with rocks and then surrounding it with perennial native plants require less water and physical maintenance than regular grassy lawns but still make for a beautiful, colorful lawn.  

.

Clover is a great plant to start with for making your lawn more environmentally-friendly. Couleur from Pixabay 

.

.

Click the link below for the article:

.

__________________________________________

Click the link below the picture

.

Plenty of articles about gardening “hacks” assume that everyone has access to truckloads of nutritious soil and enough space for plenty of plants. This will not be one of them. We know these gardening staples aren’t always easy to come by, especially if you live in a city. Thankfully, there are some veggies that can regenerate using water and sunlight alone.

The premise behind regrowing vegetable scraps in water is simple: plants are generally built to harness energy from the sun and nutrients from the earth. A small glass or dish of water won’t provide the same nutrients as hearty soil, but plants can still use it to grow new tasty shoots or soil-ready roots.

Plants that will grow shoots

You can easily regrow the edible stems and leaves of some common kitchen veggies by simply placing their inedible base in water. For best results, position these stumps on a sunny windowsill and change the water frequently.

Lettuce and cabbage

Chances are, you usually discard that tough white chunk at the base of a head of cabbage or lettuce once you’ve torn off all its leaves for your salad. But by placing this part in water, you can coax out some new leaves. Put it in a wide mug or shallow bowl with an inch or two of water, leaf-side up, and check it often to make sure the outside isn’t getting slimy. Within a week or two, new baby leaves should start sprouting from the center of the stump. Your homegrown head won’t return to its full leafy glory, but this can be a great way to grow garnishes or supplement a larger dish.

.

You might not get enough mint to sustain your mojito habit this way, but you can certainly grow some starter plants. DepositVad / Depositphotos

.

.

Click the link below for the article:

.

__________________________________________

Click the link below the picture

.

One of the most frustrating hobbies I ever took up was archery, but not because it’s hard to hit a target on the wall (it is, but I got pretty good at that). My problem was that one of the popular ways to go out and have fun with archery was to do “3D shoots,” where you would have to shoot at a series of statues of animals, each positioned at an unknown distance.

Estimating distance turned out to be my downfall. If you don’t have a good sense of how far away the fake deer is, you’ll end up shooting way over its back or burying your arrow under the ground beneath its feet. At the time, I assumed that estimating distance was less a learnable skill and more a gut feeling. Hence, my surprise when I recently came across a quick eyeball-and-mental-math trick that allows anyone to estimate distance pretty accurately.

The technique involves some gut-level estimation, but a much easier type. Then you just multiply by 10. Here’s how it works:

1. Hold your thumb in front of you (with your arm fully outstretched), and close one eye. Line up your thumb with an object whose size you have some sense of (for example, a car).
2. Without moving your thumb, close your open eye, and open the other one. Your thumb will appear to be in a different place. (see article for next steps)

.Credit: Veranika848 – Shutterstock

.

.

Click the link below for the article:

.

__________________________________________

Click the link below the picture

.

Not long after the James Webb Space Telescope came online in 2022, astronomers’ jaws hit the floor.

“I remember thinking, This just can’t be right!” says Mike Boylan-Kolchin, a University of Texas Austin astronomer.

The observations he’s referring to would, to you and me, seem like little smudgy red blobs among a field of other smudges and blobs. But in his eyes, they represented a potential challenge to the story scientists have painstakingly constructed about the formative years of our universe.

That is, some time after the Big Bang, around 12-plus billion years ago, when the universe went from a dark, diffuse place full of gas to a light-filled universe populated by stars and galaxies. This is the era that laid the foundation for everything to come — including our solar system, and you and me.

Scientists had some theories about what happened during this crucial period, but the new telescope put them to the test by observing regions of space humans have never seen before.

And if the observations were correct, Boylan-Kolchin thought, “everything we know about cosmology is wrong at some level.” Cosmology is the study of how our universe evolved from the earliest times onward. So, the potential to be wrong about it “was pretty unpalatable,” he says.

Boylan-Kolchin was agog, but not alone in his thoughts. “I cannot even get across how mind-boggling the past year has been of looking at JWST [James Webb Space Telescope] data,” says Caitlin Casey, also an astronomer at UT Austin. “We have been seeing all sorts of wild, wild things in the early universe.”

.

The James Webb Space Telescope can produce “deep field” images that reveal the history of the cosmos. NASA, ESA, CSA, I. Labbe (Swinburne University of Technology), and R. Bezanson (University of Pittsburgh). Image processing: Alyssa Pagan (STScI)

.

.

Click the link below for the article:

.

__________________________________________