Symmetry and Balance

COMING SOON - an expanded version of this article  in our  Extras section!

(This post is meant to point out just a few ways a parent or teacher can utilize the concept of symmetry to illustrate all kinds of learning at different age and ability levels. We hope you find it useful and that it generates ideas of your own for its use. More detailed suggestions will be added in our EXTRAS for different age groups, including an Open Letter to High School Students.)

Reflected landscape, photo by J.J.

In its simplest form, symmetry means having parts that exactly match each other. This can mean the reflection of a scene in clear, calm water, the wings of a butterfly, or a square bandanna folded into two triangles. But it can also mean much more. Just look at some of the words used in definitions of it: similarity, balance, harmony, proportion, rhythm, equality, order, agreement, equilibrium. Can you see opportunities to use the idea in art, music, mathematics, writing, science, human relationships and comparisons of almost anything?

Everybody has two knees

It is possible to start teaching about symmetry to children as soon as they understand the number 2. You can get the idea of 2 hands and 2 feet across and proceed from there. This can be done one-on-one, but is faster and more entertaining for the child if it is done with two or more children. Make it a game like "I Spy". I also use a song with a pattern like "'Old MacDonald Had a Farm". [Ital] Hold your hands up, palms together and have the child do the same. Establish that we have 2 hands. Say (or sing) "Everybody has 2 hands, eieio". Get the child to clap hands and say or sing the phrase with you. Point to your feet and stamp them, followed by "Everybody has 2 feet". Every few days introduce a new body part: ears, elbows knees, lips, etc. Repetition builds remembrance.

Motorcycle vs. bicycle

Working with symmetry leads directly to comparing and contrasting things: objects, living things, words, conditions, events, even ideas. This is one of the most useful skills you can teach. Constantly ask:  "How are these alike? How are they different?" This promotes observation, comparison, and consideration about how the likenesses and differences may matter in the long run. Don't be surprised if a child comes up with a difference that you haven't even considered. Praise them for correct observations, and gently correct misconceptions. Be prepared to answer "Why?" questions. If you don't know the answer, say so and discuss how you and they might find out what the correct answer is. (Introduce children to a library as soon as this is possible.) The more adept children become at sorting out similarities and differences, the better they will be at organizing their thinking and solving problems — in school and out.

Butterfly, photo by J.J.

Symmetry in Nature can be an interesting way to begin learning about Science. Studying pictures of butterflies and moths or making a leaf collection can can give children a hands-on experience with wings or leaves that are or aren't symmetrical.  Observing the growth habits of shrubs and trees can also be useful. For more about trees, see our posts for April 18 and May14, 2020. Emphasize that such characteristics are what scientists use to classify living things and establish how they are related to each other.

Pushme - pullyou?  (Photo by J.J.)

Navajo storyteller statuette

Symmetry is very important in the visual arts. I always tried to discuss symmetry when we were talking about cultures,  Both symmetrical and asymmetrical features are important when looking at the art of Native Americans. For example, in understanding why certain techniques developed in the Arctic and different ones in the desert Southwest, even though the tribes who now live in both places are closely related.  Recent studies have traced the people who are commonly called Navajo have strong genetic and artistic connections to tribes in Canada. Their art has made it possible to trace migrations made centuries ago and to reunite people who share an ancient heritage.

Original pastel sketch in center, "mirror" sketches on sides

As babies, our faces are very symmetrical, but as we grow older, the sides of the face become less alike.  If students have one of their class pictures, have them use a small mirror or aluminum foil to double one half of their faces. *We used to do this when school pictures were delivered.) Repeat this by doubling the other half. Students may already begin to see differences in their "two faces".  Have some photographs of mature and older people that they can experiment with. Exercises like this will make your students more discerning. Ask them to draw "self-portraits", either as they really are today or as they think they will look in the future. To illustrate the process let me show you a sketch of a lady who let me sketch her years ago in Panama. I thought her face was very interesting and made the other two sketches, one with the left half of her face doubled and one with the right half.

Symmetry is vitally important in any study of either history or current events. There is a great deal of truth in the idea expressed by the statement that "History is written by the conquerors." Unfortunately, textbooks tend to give only one side of an event or series of events, when there are always at least two sides involved — and often many of them.  I have been distressed to hear and read that the latest generations of our young people are not familiar with the Great Depression, World War II, the Holocaust, the Korean War or the Cold War (which is sill going on) and, consequently, are not in any position to put these events and their subsequent effects in perspective.

Guitar picker and audience, photo by J.J.

Most of those events have a great deal written about them and even old newsreels from the times which students, particularly, should be made aware of.  I lived through most of them. I encourage students to interview and perhaps record conversations with "senior citizens" while we are still around, as well as consulting the resources mentioned above.  The same thing is true for understanding the contentious issues of the present, many of which have very long roots. Debate is a great activity to practice that kind of symmetry. Not only must a team produce a compelling argument to support their proposition, but they must understand and anticipate the arguments that will be put forth by their opponents.

"Balance" and "rhythm" are terms associated with symmetry. To be successful in any sport, there are positions and movements that must be practiced over and over to train the body to react and respond correctly without having to stop and think about it. This is true whether you are making a free throw, swimming the backstroke, heading a soccer ball, or sticking a landing.  Gymnastics offers a good example in which not only is body position vital in performing different exercises, but it must look good while doing so.  Almost any kind of dancing requires that two or more people must coordinate their movements with great accuracy.

Square dancers (public domain photo)

When was in college, I belonged to a square dance group. In addition to following all the calls, each eight-person "square" was supposed to figure out a special finale for their performance. I was the smallest girl in our square and weighed the least. My partner was the tallest fellow in the group and very strong. For our finale the other three pairs danced backwards to give us plenty of room while we answered the call for "Swing your partner". We started with a standard "swing", but my partner kept turning and lifting me off the dance floor. We turned until my body was horizontal and parallel to the floor, level with his shoulder at the end of his extended arm. A couple more turns put my feet back on the floor and we danced backward to complete our "square".

Haiku by Basho

In a writing class you can introduce older students to the symmetrical "shaped poem" (also called diamante).  This kind of poem does not rhyme; nevertheless, it has very strict rules for its construction. Prepare a number of examples beforehand so that the students can figure out those rules. Be sure students know what participles are and how to break a word into syllables before they undertake the assignment. For the rules and a couple of examples of shaped poems, see our post from September 25, 2020. Another good activity is creating a haiku. There also is more information about haiku in this post.

When teaching or learning a second language, it is imperative that students realize that just because a word is paired with an English word in the vocabulary list, that doesn't mean it necessarily has that meaning in a conversation.  All languages contain many colloquialisms, in which a word may not convey anything like its dictionary meaning.  Pronunciation is also important. When we were stationed in Germany, my soldier husband went to a store selling car parts to buy an exhaust pipe for our old car. He had read the word for exhaust pipe in a parts catalog and asked for one at the counter.  He was angrily thrown out of the store. It seems his pronunciation was a little off and instead of requesting an exhaust pipe, he had requested, shall we say, a "woman of ill repute".

Now I'm going to turn this discussion over to J.D. to tell you about some other areas of his expertise...

J.D.: In music, it is very easy to find examples of symmetry, from the simplest exact repetition of phrases in "Frere Jaques" to the call-and-response of early Christian religious music to the inverted melodies used as base lines in things like Pachelbel's "Canon". It is easy to see these symmetries in the pitches of musical notes (melodies and harmonies) in written music notation, but nearly all elements of music — rhythm, volume (loudness), timbre, and many more — can demonstrate various symmetries. But one thing can never be symmetrical: because music, like dance or films, always changes from one moment to the next it must have a beginning and and end. Even if you make a piece of music where the second half is an exact mirror of the first, there is a point in time when no-sound becomes music and a point where music becomes silence.

 

 

Of course, particle and quantum physics tells us that it doesn't have to be that way, that the 'arrow of time' can go the other direction, but they have yet to find a way to demonstrate this in any practical way. And that is why the 'time travel' in our previous post was just an intellectual exercise.

Particle physics interactions

Physics, especially the exotic realms of particle and quantum physics, and those disciplines that try to reconcile Einstein's General and Special Theories of Relativity with them, thrive on symmetries. Particles have antiparticles with opposite charges; quarks (a staple of quantum physics) have properties like color and charm — which are not at all what they sound like they should be — which can be mirrored; and ... that is why Annake asks me to write about subjects like these which make her eyes glaze over when she hears me going on about them.

Physicists depend heavily on some pretty esoteric mathematics for their work, but even the simplest math — things we use every day — are based on symmetry. Not really a surprise: math is basically measuring things, and the word "symmetry" is derived from ancient Greek for "same measure"! And the first thing any one learns in mathematics (beyond simple counting) is the equation:

1 + 2 = 3 ;  "The sum of the squares of the sides equals the square of the hypotenuse"; x + y =  7

And even though the expressions on either side of "equals" don't look the same, they must be for the equation to be true.

The term "symmetry" takes on additional meanings in mathematics and the sciences as students get into more technical work. Be sure that they are aware of these. This occurs even in literature and the arts.   But once your students are accustomed to looking for symmetries, they can use this principle to increase their understanding of art. mathematics, science, music, current events — even culture.  But they need to have developed a skill for determining a sensitivity to how things are the same and how they are different. You can help them do that.

Good luck. Stay safe and well.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

How Light Became Sight: All About Color, Part V

Logo for our hypothetical time travelers

Imagine with me for a few moments that mankind has mastered time travel, and that we are members of a scientific expedition to a time 700 million years in the past. We stand in our heavily protected spacesuits on a small sandy beach along a strip of rocky coastline beside a shallow arm of a much larger sea. A plume of smoke rises from a volcano on the far horizon. We need the spacesuits because the atmosphere is thin and doesn't give much protection from the planet's sun. We cannot breathe the air of this planet, because it is mostly nitrogen and carbon dioxide. Despite the light reflected from the coarse sand, our thermometers show an uncomfortably chilly temperature. We will have to work fast, because the days are considerably shorter than we are used to. We have come to study the alien life on a planet far stranger than Mars.

Welcome to the Earth.

Underwater ROV

After a short session of directions from the team leader, including that all specimens must be enclosed and sealed immediately and that their surfaces as well as our suits will go through a decontamination process before returning to our own time. Scientists scatter to locate promising collection spots. They march across the narrow, orange-tinted beach toward low, darker orange rocks. You and I remind the scientist who is preparing a probe to the top of the atmosphere that we will need a copy of her data, and walk to the place where a robot submersible is being deployed.

Depth of penetration for colors

The operator describes how the machine will first make a circle 2 kilometers wide on the surface and then descend in concentric circles at 10 meter intervals until it reaches the bottom, where it will take samples. It will collect live specimens as we direct as it makes its circuits. We explain that we need measurements of the light entering the water at each level, both in intensity and color. This is set up for automatic measurements and we settle down in front of our monitors, told to "sing out" when we see an organism to be collected. We advise him to watch for "cloudy" or colored patches which indicate concentrations of microscopic life.

Cyanobacteria (field sketch)

The water is surprisingly clear, with a distinctly green color.  We have already heard an excited scientist reporting a pool with blue-green algae (actually bacteria) on our intercoms, so they were certainly in the water as well. Moments later the submersible secured a specimen of the "blue-greens" for us. We could later compare it with the specimens from the pool as well as with ones from our own time.  As the hours pass, we direct collection of thin films of red and green organisms, hoping the green might be an early plant, and anything unusual in the water. We know that we are dealing with organisms far too small to see even with the magnifying lenses on the submersible's probes, plus the ones on our monitors.

Sponges

As we descend,  the colors fade and the light grows dimmer. We are excited to encounter a colony of small sponges — the first multi-cellular creatures we have seen. We gather both the organisms that move toward us and the ones that move away. One group about the size of marshmallows appears red, a color that would not show up against the darkness of the water below 200 meters. They move away from our lights, quickly, followed with a flash of blue luminescence. A probe swings out to collect some of them.

Lichen

A warning from the submersible indicates that it is approaching the sea bottom. Additional floodlights come on and the submersible hovers close to a vertical wall of rock. A number of samples of the sea bottom are taken, separating the levels of sediment. We get a call warning that we should return to base and have our specimen boxes ready for decontamination within the next half hour. The submersible rises at an angle to take it increasingly closer to its launch point. We secure our monitors, sorry to bring our adventure to an end. We dock to find other scientists ready to help us get our specimen boxes decontaminated and secured and then line up for the decontamination of our suits.  People are chatting about their finds. "There 's a lot more oxygen in the atmosphere than we expected," the atmospheric specialist tells us. "The ozone layer may already be forming." The man who found the blue-green bacteria is disappointed that he didn't find lichens. We tell him that the ultraviolet light is probably still too strong.

Well, that was fun, but what does it have to do with light, color, and sight?
 

Some squid are benthic night feeders

First of all, let's look at the chart above showing how colors of light disappear as they penetrate water. This phenomenon holds true in deep, relatively still water anywhere on the planet. You can see that the color red disappears very quickly. Up to that depth everything looks pretty much like it does above the surface. Only a few meters further and a red or orange fish would look almost black. (Sediment, algae, debris or turbulence would reduce visibility still further.)  Eventually, you would need powerful lights to see anything at all.  Even those would not penetrate the darkness to a very great distance. Yet organisms live at great depths.  Don't you wonder how? Many benthic (deep water)  animals come to the surface at night to feed or spawn. Some of them have eyes and some do not.

Algal bloom on Lake Erie

The team member's finding of blue-green bacteria was significant. Very soon after the oceans formed on young Earth, these bacteria developed the ability to use sunlight to make food using carbon dioxide (photosynthesis), releasing oxygen as a by-product. For a long time, the oxygen was absorbed by different kinds of rock, but eventually it began to replace some of the carbon dioxide in the Earth's atmosphere. It still does. Now we could observe the process and see how, or even if, it had changed.  These cyanobacteria live in most lakes and are part of a lake's normal ecosystem. Unfortunately, high nutrient concentrations can cause "population explosions" and a "bloom", especially in warm weather.

Our Sun

The information from the atmospheric scientist was also quite important. It meant that the atmosphere was soon going to be able to support many more kinds of organisms. It also hinted that an ozone layer might already be forming at the top of the atmosphere. The sun delivers three kinds of light: visible light, infrared light (heat), and ultraviolet light. Too much ultraviolet tends to damage or kill cells, as you know if you have ever had a bad sunburn. The ozone layer would stop a large portion of the ultraviolet from reaching Earth's surface. This favored many multi-cellular organisms, while it caused other species to become extinct. Today these "blooms" are altering water quality in bodies of water like the Great Lakes, fouling the water and air.

Electron microscope

Now let's look at those specimens we collected.  These sketches represent fossils of known microscopic organisms or modern species which are believed to have an ancient ancestor, which they resemble.) Each specimen is shown as it would look under high magnification. The fossil record of such organisms has been greatly expanded and improved in the past few years with the use of electron microscopes.

"Red tide"

I try to keep up with science news as much as possible. Recently I saw a sentence that really caught my attention. It said:"The dinoflagellates are not happy." No, they're not. And that means trouble in two different environments worldwide. Just as the cyanobacteria are smothering the Great Lakes with their "blooms" and contributing to already polluted air, the "red tide" is fouling coastal areas and killing large numbers of fish and sea mammals. Florida has been hit especially hard this year, as you can see from this recent photograph. (Not all of these blooms are red, nor are all of them made by dinoflagellates.)

Dinoflagellate (field drawing)

Dinoflagellates are many kinds of one-celled protists that come in a multitude of diverse forms.  Actually, there are probably more dinoflagellates than there are other kinds of protists.  Protists are neither plants nor animals, but may display characteristics of both. Some are as large as 2 millimeters in diameter, meaning that they can be seen with the naked eye. The one shown here is capable of photosynthesis because eons ago they began to take in organisms like cyanobacteria that could make food by photosynthesis. Instead of consuming these organisms, they just kept them. They went on consuming other small organisms and digesting them. Over a long period of time, the "inclusions" became "organelles" — little almost-organs that provided a specific function for their host. (You can see many blue and brown ones as dots and little blobs inside the organism. The red area is the nucleus and is capable of responding to light.)  As it grows larger, the host divides into two identical organisms by splitting in half, each half taking its organelles with it.  Dinoflagellates got their name because they are propelled by two whip-like flagella. The ones on this species seem extremely short.

Bad as the "red tides" are, there is a much more pressing problem with dinoflagellates. Long ago some of them formed partnerships with corals. Bear in mind that they are protists, while corals are animals. A partnership between the two might last for thousands of years. Then conditions in the environment changed and the dinoflagellates "were not happy". They pulled out of the corals, turned into small hard bodies called "cysts" and sank to the bottom. We don't know how long they can stay as cysts — maybe indefinitely. The corals, on the other hand, weaken, bleach, and die — something that is happening all around the globe today. When the situation improves, the cyst can produce another dinoflagellate, which will find another kind of coral and start the whole cycle over again.

Mature, healthy coral reef

 

Jellyfish (field sketch)

Finally, we come to our "catch of the day".  The red organisms that fled from our lights and showed some bioluminescence. These were jellyfish, animals belonging to the same group as sea anemones and corals. They are probably the first animals to actually swim, rather than just drifting with the current. They are deceptively simple, little "umbrellas"with an outer layer of cells covered with a net of nerves, an inner layer that handles digestion, and muscle tissue between the two which enables them to swim. Their long tentacles have stinging cells that stun or kill prey. They often have light-sensitive cells around the edge of the "umbrella" that tell them whether it is day or night, the angle of the light, and how bright it is. Dimming of the light indicates other organisms and gives some indication of whether they are small enough to be eaten or big enough to be predators.

Box jellyfish eyes

Today, the deadly box jellyfish, named for their shape, live in shallow waters where there are obstacles like mangrove roots. They have 24 "eyes" arranged in clusters around the bottom of their bodies. There are 4 different kinds of eyes. These are arranged in sets of 6 organs. One kind is very simple and probably just separates light from dark. Another is more complex and possibly can detect different degrees of light intensity and direction and may give some idea of shapes.  But each cluster has a pair of organs that each have a cornea, a lens, an iris, and a retina. In other words, they are eyes (without the quotation marks)! This little animal does not have a brain, but it has functional eyes that allow it to form images, avoid obstacles, change its swimming speed, and always return to its "home base". It can even see above the surface of the water and may actually hunt prey, rather than just waiting for it to swim past. It appears that "simple" animals are not so simple after all. It also may be the earliest animal to sleep at night. I guess it needs to rest its eyes.

And that, my fellow time-travelers, is how Light from the Sun penetrated Earth's waters and, bit-by-bit, the "simple" organisms developed the power of Sight.

Have fun. Stay safe.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Fun With Felt

Felt butterfly picture by Annake

Felt is a versatile fabric with many uses. Because it does not need to be hemmed, it takes less time and work to make something from it. It comes in a wide variety of colors and a number of patterns like zebra or tiger skin,  "psychedelic" colors, and small repeated motifs.  Most of the felt pictures you will see today are done with fabric glue, but there is no reason you cannot stitch them down by hand or machine if you prefer. They will probably be more durable done that way, but if you are going to frame the design. sewing is probably not necessary.

Fancy felt assortment

 

Projects like this, whether backed, framed or hung with a fancy hanger, are good to fill narrow or awkward wall spaces, like beside or above a door, above or below a window, down the wall beside a staircase, or beside a set of shelves.

Simple pattern idea, adaptable to felt

They are great for children's rooms, unframed or framed without glass, because they are unbreakable. I make my own patterns, but you may not feel comfortable doing that. However, pictures for small children should be simple. Too much detail is confusing and makes it harder for them to identify and name things. There are patterns available online. Some of them are free; others have a fee. But you can use children's coloring books or trace pictures from children's picture books. Here is a design I adapted from one of my puppets.

 

Shopping bag with felt applique

 

Tools and materials

You will need;
     a felt rectangle for each color of your design
     fabric glue
     sharp scissors for the felt*
     another pair of scissors for paper patterns
       a pencil or marker
     paper for the pattern parts

* Please don't use your fabric scissors for anything but fabric. You would be amazed how much paper will blunt a blade edge. We have a gentleman who sharpens scissors here in our little town, but that sort of help can be hard to find and you can end up spending quite a bit for another good pair of scissors or shears.

Because shopping is so difficult this year, I am not going to recommend any brand names for materials. The felt pieces can usually be found at the big chains like Walmart or Target, fabric stores, or craft shops. Read the directions on the fabric glue carefully and follow the directions closely. If you are using a spray glue, which I don't recommend, try to use it outdoors or in a large space like a garage and wear a mask while dealing with it. Elmer's white glue will work for a piece that is meant to be temporary, but it is messier and may seep through.

Simple Iris pattern

When you are making a pattern for a felt picture, keep it as simple as possible. Once your sketch is finished, make a clean copy of it. Use paper about the weight of computer paper. I like to go around the outlines of the pattern pieces with a colored marker. That makes a thicker line than a pencil or a pen, so that I can more easily cut right down the center of the marker line. I find this gives me a better fit with adjacent pieces which share a common borderline.

Saved pattern pieces

Choose your background color. As each piece of the picture is cut out, remove that part of the pattern. write the name of that particular piece (for example "long leaf, upper right") and store the pattern piece in a business-sized envelope for future reference. Label the front of the envelope with an appropriate title and file it in a shoebox or similar container.

Finished felt iris picture

Arrange the pattern pieces on the background exactly where you want them to be in the finished composition. Carefully lift the pieces one at a time and apply the fabric glue as directed on the container. Carefully put each section in place and let the pieces dry completely. If you decide you need to press the piece, use a pressing cloth over the felt and a moderate temperature for the iron.

Easy hanger method

The finished composition can then be backed, framed without glass, framed under glass, or whatever you wish. If you want it to be a small wall hanging, stitch or glue a folded piece of another color of felt at the top of the picture so that it becomes a tube that will hold the hanger. Slide the rod of the hanger through the tube, close and fasten it.

 

 

Are you taking the advice I have seen and heard for having a candy "treasure hunt" around your house or apartment for your children, instead of the traditional "Trick or Treat" activity this year?  Here is an idea for something a little special for the dinner table before the treasure hunt. Make a special Halloween placemat for each child and cover it with clear plastic wrap or slip it into a clear plastic bag to prevent food spills. Then the child can have it for a keepsake, room decoration, or whatever they choose. I think everything we can do to make this very different celebration special for the children is worthwhile. (We are talking about felt today, but of course you can do this activity with colored papers; however, the mats will not last long and won't make very good keepsakes.) If you want another activity, make a draw-string bag for the collection of the candy. The child can use the bag for other purposes after the holiday.

 

You can do quite a bit with a simple design like this. For example, you can make any kind of jack-o'-lantern design on the pumpkin that you like — friendly or scary or silly.  You don't have to have a black cat coming out of the pumpkin. It could be a bat, a ghost, an owl, a pirate — anything you want.

Finished leopard "portrait"

For "portraits" of animals or storybook characters, just the head is necessary. I enlarge the heads of my puppets for such pictures. We have published several articles about puppets with color photographs and the occasional pattern. You can find those by using the "Search My Blog" feature at the side of this article. Just type in the word "puppet".  Incidentally, all the dog and cat puppets I do are outfitted with a collar and tag to remind people to do that for their pets. There is also an article about teaching with puppets in our EXTRAS section, listed at the top of this article.

An easy way to display a picture is to "frame" it with a wooden or plastic embroidery hoop. Plastic hoops come in a variety of colors. A wooden hoop can be left as it is, varnished, or painted. Choose a hoop that will display the amount of background that you want. Place the felt picture over the bottom part of the hoop. Adjust the upper part of the hoop so that the tension screw is directly above the center of the picture. Push the top part of the hoop gently down over the felt. Tighten the screw a little at a time, pulling the felt taut as you do so. When the picture is completely flat, turn it over and trim away the extra felt. The small space left under the screw is usually large enough for you to slip the screw over a "headless" nail for hanging.

Stuffed toy from puppet pattern

 

 

 

 

I stuff the heads of my puppets with fiberfill (you can use cotton), leaving just enough room for one or two fingers of the puppeteer. You can make a soft doll by stuffing the whole body and sewing the bottom edge securely closed.

Puppet used as treat bag

Or you can prepare it as a working puppet but fill the body with cellophane-wrapped hard candies, miniature candy bars, small trinkets, etc. Sew the bottom shut with easy to remove stitches so the child can pull them out to open the seam. Then he or she can enjoy the treats in the gift bag and still have the puppet to play with.

Felt scraps

Save your felt scraps in a bag or a large mailing envelope for use in future projects.  For, as my Grandma used to say:

"Use it up,
Wear it out,
Make it do,
Or do without."

I hope you have gotten some ideas from this article. I put the emphasis on fun because that is something we all need to get us through these challenging times.

Stay safe. Be well. Our best wishes go to all of you.

 This post by Annake's Garden is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.