Homemade Ginger Beer

I found this on a NYTimes blog.  It is part of a recipe for a mixed drink called the Dark 'n' Stormy

Ingredients

2 ounces freshly grated ginger
4 ounces lemon juice
6 ounces simple syrup
1/8 teaspoon commercial bakerís, brewerís or Red Star Pasteur Champagne yeast
20 ounces non-chlorinated water (filtered, distilled or spring)
1 to 4 grams cream of tartar (not necessary, but traditional, to help the yeast and bacteria thrive).

1. Take a 1.5-liter plastic bottle of spring water and empty it into a clean pitcher. Use some of it to make simple syrup by stirring 1/2 pound sugar into 1 cup hot water until fully dissolved.
2. In a large measuring cup, mix all ingredients and stir well. Funnel back into the plastic bottle and cap tightly. Store in a warm, dark place for 24 to 48 hours. (I put mine inside a box, to contain it if it should blow.) The top of the bottle will expand and become tight. Check it and very slowly release the pressure if itís looking groaningly tight. Some people ferment it with no top, or with the top on loosely, to allow gas to escape. I suppose if you wanted to get fancy you could spend $1.50 on a fermentation lock and stop worrying about it. If the temperature is quite warm, above 80F, a single day may be sufficient. The longer you let it ferment, the drier the final mix will be.
3. After 48 hours, refrigerate it to stop the fermentation. Once chilled, you can strain out the pulp and dead yeast, which will have made a sediment on the bottom. Makes 1 liter and will keep up to a week in the refrigerator.