Butter a 21x18-inch piece of heavy foil and set aside.
In a heavy 3-quart saucepan, combine the sugar, corn syrup, water, and butter. Cook mixture over medium-high heat, stirring constantly with a wooden spoon to dissolve sugar (avoid splashing mixture onto side of the pan).
Boil candy mixture for 3 minutes. Reduce heat to medium. If using a candy thermometer, carefully clip to the side of the pan, making sure the bulb is immersed, but not touching the bottom of the pan.
Cook, stirring frequently, to 240 degree F on candy thermometer (soft-ball stage, 30 to 35 minutes). Or use this cold-water test: With a spoon, drop a small amount of hot candy mixture into very cold, but not icy, water. It should form a soft ball that immediately flattens between your fingers when removed from the water.
Stir in walnuts. Cook over medium heat, stirring frequently, to 295 degree F on candy thermometer (hard-crack stage, 20 to 25 minutes). For cold-water test: Using a spoon, drop a small amount of hot candy mixture into very cold, but not icy, water. It should separate into hard, brittle threads that snap easily. Watch closely so mixture doesn't burn.
Remove the saucepan from the heat and remove the thermometer from the pan. Immediately stir vanilla and baking soda into the hot candy, stirring constantly till the mixture is light and foamy. Quickly pour and spread candy into a rectangle on prepared foil sheet.
Cool brittle completely; break into pieces. To store, cover brittle tightly. Makes about 2 pounds (100 pieces).