The Growing Importance of Mathematics
For speaking at this year’s Enterprise Data World conference, I received a copy of Stephen Baker’s amazing book The Numerati, which was inspired by his Jan 23, 2006 BusinessWeek article Math Will Rock Your World (one of my all time favorites!).
“When it comes to producing data,” explains Baker, “we’re prolific. The very air we breathe is teeming with motes of information. People with the right smarts can summon meaning from the nearly bottomless sea of data. The key to this process is to find similarities and patterns. We humans do this instinctively.”
Humans Teach, Machines Learn
Advancements in machine learning technology using sophisticated mathematical algorithms are providing the capability to make better data-driven decisions.
“Learning machines swim in numbers,” explains Baker. “The learning process starts with humans…the annotators. Their work is…to teach the machine what we humans know at a glance.”
Therefore, these advancements are not an attempt to replace human knowledge workers. The number crunching capabilities of these advancements will allow us to “gradually evolve from data serfs into data masters.”
Advanced Geometry
There are many mathematical disciplines involved in machine learning. However, perhaps one of more surprising is advanced geometry.
“Scientists often describe the world of data as a domain of sharp angles, colliding planes, and vectors shooting along endless paths,” explains Baker. “Imagine a vast multidimensional space [with] dozens of markers…each marker occupies its own patch of real estate.”
Imagine each marker representing an individual character within a string of text. Machine learning using bipartite graphs to allow data to “produce a line – or vector – that intersects with each and every one of its own markers…it’s a little like those grade-school exercises where a child follows a series of numbers or letters with her pencil and ends up with a picture of a puppy or a Christmas tree,” explains Baker.
However, the picture that bipartite graphs are drawing are too complex for the three-dimensional world of the human imagination.
“The computer has no trouble depicting [data] as vectors,” continues Baker. “They all run neatly from one dimension through countless others and, more important, through every one of their distinguishing markers. [Data] that resemble each other, naturally enough, are neighbors in this vector space. [Data] that have a lot in common tend to point at similar angles. Each link shared is a line connecting them, a so-called edge. The next step is to calculate the importance of each edge…[edges] given a higher score…those lines on the graph are thicker.”
A New Era of Applied Mathematics
“The information age that we’re in is going to be an emerging new era of what would be called applied mathematics,” concludes Baker. “Mathematicians are going to dip into the sea of data to form…the mathematical modeling of humanity.”
From the beginning of civilization mathematics has been central to our advancement. It is after all the language of science. But our relatively new found ability to collect digital data has ushered in a new era for leveraging and benefiting from mathematics.
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