This cocktail was inspired by Dr. Brown's Cel-Ray, a soda from 1868 that was flavored with celery seed.
Bring 1/4 cup water and sugar to a boil in a small saucepan, stirring until sugar is dissolved. Let cool completely, then refrigerate, covered, at least 1 hour and up to 1 month.
Puree celery and 1/2 cup simple syrup in a blender until smooth. Pour mixture through a fine-mesh sieve lined with damp cheesecloth set over a medium bowl.
In a small pitcher, combine celery syrup, lime juice, and gin. Fill tumblers halfway with ice, then pour 3 ounces cocktail base into each. Top off with seltzer, sprinkle with celery seeds, and serve, with celery stalks.