DOCS-#2439: Add Documentation for Modin vs. pandas (#2487)

Signed-off-by: Devin Petersohn <devin.petersohn@gmail.com>

Author: devin-petersohn

docs/comparisons/pandas.rst

@@ -1,4 +1,69 @@
-Modin vs. Pandas
+Modin vs. pandas
 ================
 
-Coming Soon...
+Modin exposes the pandas API through ``modin.pandas``, but it does not inherit the same
+pitfalls and design decisions that make it difficult to scale. This page will discuss
+how Modin's dataframe implementation differs from pandas, and how Modin scales pandas.
+
+Scalablity of implementation
+----------------------------
+
+The pandas implementation is inherently single-threaded. This means that only one of
+your CPU cores can be utilized at any given time. In a laptop, it would look something
+like this with pandas:
+
+.. image:: /img/pandas_multicore.png
+   :alt: pandas is single threaded!
+   :align: center
+   :scale: 80%
+
+However, Modin's implementation enables you to use all of the cores on your machine, or
+all of the cores in an entire cluster. On a laptop, it will look something like this:
+
+.. image:: /img/modin_multicore.png
+   :alt: modin uses all of the cores!
+   :align: center
+   :scale: 80%
+
+The additional utilization leads to improved performance, however if you want to scale
+to an entire cluster, Modin suddenly looks something like this:
+
+.. image:: /img/modin_cluster.png
+   :alt: modin works on a cluster too!
+   :align: center
+   :scale: 30%
+
+Modin is able to efficiently make use of all of the hardware available to it!
+
+Memory usage and immutability
+-----------------------------
+
+The pandas API contains many cases of "inplace" updates, which are known to be
+controversial. This is due in part to the way pandas manages memory:  the user may
+think they are saving memory, but pandas is usually copying the data whether an
+operation was inplace or not.
+
+Modin allows for inplace semantics, but the underlying data structures within Modin's
+implementation are immutable, unlike pandas. This immutability gives Modin the ability
+to internally chain operators and better manage memory layouts, because they will not
+be changed. This leads to improvements over pandas in memory usage in many common cases,
+due to the ability to share common memory blocks among all dataframes.
+
+Modin provides the inplace semantics by having a mutable pointer to the immutable
+internal Modin dataframe. This pointer can change, but the underlying data cannot, so
+when an inplace update is triggered, Modin will treat it as if it were not inplace and
+just update the pointer to the resulting Modin dataframe.
+
+API vs implementation
+---------------------
+
+It is well known that the pandas API contains many duplicate ways of performing the same
+operation. Modin instead enforces that any one behavior have one and only one
+implementation internally. This guarantee enables Modin to focus on and optimize a
+smaller code footprint while still guaranteeing that it covers the entire pandas API.
+Modin has an internal algebra, which is roughly 15 operators, narrowed down from the
+original >200 that exist in pandas. The algebra is grounded in both practical and
+theoretical work. Learn more in our `VLDB 2020 paper`_. More information about this
+algebra can be found in the :doc:`../developer/architecture` documentation.
+
+.. _VLDB 2020 paper: https://arxiv.org/abs/2001.00888