Actually, the neglect of Arbor Day is a double shame, because too many people have attempted to assuage their guilt over human environmental assaults by engaging in the bankrupt practice of purchasing carbon "offsets," one of the most popular types being to have trees planted, somewhere, by someone. Of course, there are the nagging questions of how much good that could possibly do, if in fact such actions are taking place (and how can you even verify that), for basic questions, as where should such trees be planted--in your local area, over part of the area you fly over, in a deforested nation overseas--are just the beginning of the carbon offset tree planting dilemmas.
Great ways to celebrate Arbor Day, seems to me, include either planting tree(s), or, at the least, appreciating the ones already planted in your area. Today's sunny weather was perfect for Arbor day, as the Washington area is thick with fluffy blooms from the next tier of cherry, and other, trees.
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Less direct, but no less important, ways of celebrating Arbor Day include using resources that don't require more trees be cut to provide products. If your community is considering converting residential recycling to a single stream recycling system, more power to you! Single stream recycling is an easy way to get more participation in a recycling program, as the only separation is of garbage (wet or greasy stuff, which is to be composted) from trash.
Of course, if you recycle, it's best to complete the process by purchasing recycled products or tree-free paper products, whenever possible. Their prices have come down, and the quality has gone up, a win-win situation. My favorite 100% recycled writing pad is the Riverside Paper Ecology Premium legal pad, as its paper is high quality; it's much better than other recycled writing pads, but I haven't seen it in brick-and-mortar stores in a while. The easiest to find almost-tree-free paper is the Staples eco-friendly writing pad, which is 80 percent sugarcane content, which is also high quality at reasonable cost (and is also available at Giant Food, oddly enough).
I like to think of Arbor Day as a day to kick back, to walk around, and in all other ways, simply appreciate the beauty remaining in the world.