trouble with basic remote_function usage

I've tried moving the code around in different ways, but so far I haven't
gotten remote_function to work for me (I'm using Rails 2.3.2 on my Mac). I
want to make an AJAX call when I double-click a word on my page, and the
Javascript function is being called when the ondblclick event is fired, but
nothing happens when it gets to my the "new Ajax.Request" part of my
function. The Rails console doesn't even show it as making a call to my
controller.

There is a DIV called "definition_box", so my remote_function call used to
read like this:

<%= remote_function(:update => "definition_box", :url => { :action =>
:lookup } ) %>

Then I read
http://craiccomputing.blogspot.com/2009/02/rails-ajax-and-rjs-issue-seeing.html
this and took that out since supposedly it might be duplicating the
reference to the DIV (here in the view and in the controller), so now it
looks like this:

<%= remote_function(:url => { :action => :lookup } ) %>

As you can see, I'm not even trying to pass the Javascript parameter to
remote_function at the moment. My Javascript function looks like the
following and does show me the alert box:

function lookupWord(t) {

  alert('moving forward');

  <%= remote_function(:update => "definition_box", :url => { :action =>
:lookup } ) %>
  
  }

This is what I currently have in my controller:

class HomeController < ApplicationController
  def index
  end

  def lookup()
    logger.debug('here')
    render :update do |page|
      page.replace_html 'definition_box', 'Done!'
    end
  end
end

There used to be a new line in my routes.rb, but it seems like if I'm going
to the same controller, that doesn't need to be there. I tried adding this
and still my controller action debug statement doesn't show up in the server
console:

map.connect 'lookup', :controller => 'home', :action => 'lookup'

Can you tell me why the text in my definition_box DIV is not changing to
"Done!" ???