The thing about Ruby is that it has uniform syntax — a.b for any a+b mean "send a message :b to a." So `self.foo` (and `self.foo = bar`, too!) are possible to write, but these are always interpreted as message sends (to the :foo and :foo= methods, respectively), not as direct field accesses. The "syntax-ness" of @ and @@ show are that you're specifically breaking out of† the paradigm of "everything is a message send", to instead "just" access a field. It's what makes this make sense:

    def foo # define a getter method
      @foo # in terms of a field access
    end

How would you write that, if the field access was spelled `self.foo`? The language wouldn't be able to tell that you're not just recursively calling the getter!

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† Though, technically, you're not breaking out of the paradigm; @foo is short for self.instance_variable_get(:@foo). It's message-sends all the way down, until you hit natively-implemented methods.