Some clarifications from Laura

notebooks/Alhazen.ipynb

@@ -685,6 +685,23 @@
     "3. Computation of _feature vectors_ from a set of inputs, which will then be used as input for the decision tree"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Internal and \"Friendly\" Feature Names\n",
+    "\n",
+    "We use two kinds of _names_ for features:\n",
+    "\n",
+    "* _internal_ names have the form `<SYMBOL>@N` and refer to the `N`-th expansion of symbol (starting with 0).\n",
+    "  In `CALC_GRAMMAR`, for instance, `<function>@0` refers to the expansion of `<function>` to `\"sqrt\"`\n",
+    "* _friendly_ names are more user-friendly (hence the name).\n",
+    "  The above feature `<function>@0` has the \"friendly\" name `<function> == \"sqrt\"`.\n",
+    "\n",
+    "We use internal names in all our interaction with the machine learner, as they are unambiguous and do not contain whitespace.\n",
+    "When showing the final results, we switch to \"friendly\" names."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1003,7 +1020,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `friendly` format is a bit more concise and more readable:"
+    "The `friendly` representation is a bit more concise and more readable:"
    ]
   },
   {
@@ -3381,7 +3398,10 @@
     "If the predicate evaluates to `True`, follow the left path; if it evaluates to `False`, follow the right path.\n",
     "A leaf node (no children) will give you the final decision `class = BUG` or `class = NO_BUG`.\n",
     "\n",
-    "So if the predicate states `<function> == 'sqrt' <= 0.5`, this means that if the function is _not_ `sqrt`, follow the left (`True`) path. If it is `sqrt`, follow the right (`False`) path.\n",
+    "So if the predicate states `<function> == 'sqrt' <= 0.5`, this means that\n",
+    "\n",
+    "* If the function is _not_ `sqrt` (the predicate `<function> == 'sqrt'` is negative, see above, and hence less than 0.5), follow the left (`True`) path.\n",
+    "* If the function _is_ `sqrt` (the predicate `<function> == 'sqrt'` is positive), follow the right (`False`) path.\n",
     "\n",
     "The `samples` field shows the number of sample inputs that contributed to this decision.\n",
     "The `gini` field (aka Gini impurity) indicates how many samples fall into the displayed class (`BUG` or `NO_BUG`).\n",