I’ve answered the question at SO. This is essentially the same answer as over there.

In single dispatch—what you see in most modern OO languages—a method is dispatched based on the run-time type of a single object. This shows up as the dot operator (in ruby, java, javascript, etc.) or the arrow operator (perl, c++).

# look, ma single dispatch!
# method on obj's run-time type that is called
dentist.work_on(patient)

Double dispatch, then, would be based on the run-time type of two objects. There are a few ways this could look; and on which object should the method live?

# Hmm, this looks weird.
# Is the method in to dentist.class or patient.class?
(dentist, patient).do_dentistry()


# okay, this looks more familiar; the method lives on obj1.class
# This only works in static-typed languages which support double dispatch
# in which you declare the type of the method parameters.
dentist.work_on(patient)

class Dentist
   def work_on(Adult patient); ...; end
   def work_on(Child patient); ...; end
end

Languages like groovy that have multiple dispatch generalize the second example above; they consider the run-time types of all parameters when choosing which method to run. See for example this blog post about groovy and multiple dispatch.

Most modern OO languages only have single dispatch and the Multiple Dispatch Pattern is an attempt to get the benefits of multiple dispatch into the language. It even works for dynamic languages like ruby. It works by doing single dispatch twice in a row. The first method call will call a method on the second object.

class Dentist
    def work_on(param)
       param.dispatch_work(self)
    end
    def work_on_adult(patient)
      drill_as_hard_as_you_can(patient)
    end
    def work_on_child(patient)
      use_bubble_gum_toothpaste(patient)
    end
end

class Adult
    def dispatch_work(dentist)
      dentist.work_on_adult(self)
    end
end

class Child
    def dispatch_work(dentist)
      dentist.work_on_child(self)
    end
end

The double dispatch pattern is what I call a low-level pattern because other patterns are built on it. For example, the Visitor pattern relies heavily on the double dispatch pattern.

Looking at your gists, your first gist doesn’t really doing double dispatch. Sure, you’re dispatching twice, but you’re not changing the behavior in that second dispatch. To change it to double dispatch I’d do something like this.

class Chicken
  def make_dispatch dish
    dish.make_with_chicken self
  end
end

class Beef
  def make_dispatch dish
    dish.make_with_beef self
  end
end


module Dish
  def make meat
    meat.make_dispatch self
  end
end

class Sandwich
  include Dish

  def make_with_chicken chicken
    puts "Grilled Chicken Sandwich"
  end

  def make_with_beef beef
    puts "Roast Beef Sandwich"
  end
end

class Stew
  include Dish

  def make_with_chicken chicken
    puts "Thai curry"
  end

  def make_with_beef beef
    puts "Beef stew"
  end
end

class Casserole
  include Dish

  def make_with_chicken chicken
    puts "Chicken Pot Pie--or something"
  end

  def make_with_beef beef
    puts "Shepard's Pie"
  end
end

Sandwich.new.make(Chicken.new)
Stew.new.make(Chicken.new)
Casserole.new.make(Beef.new)