# The Gravity of Mathematics: Summary of Tech Field Day at SDC 2017

Fair warning – this will likely be one of the least technical posts I write. On September 14, I gave a presentation at Tech Field Day that wasn’t actually storage related, but rather a call to rekindle the relationship between pure math and industry. Here I’ll post the slides from that talk and summarize some of the discussion that carried on around this topic.

## Introduction

I purposely titled this talk “The Gravity of Mathematics”^{1}because mathematics is that force that we generally don’t see, but can’t really live without. Every development in engineering, computer science, chemistry, medical imaging, manufacturing, finance, and so forth can trace its roots back to a necessary topic or concept in pure mathematics. Obviously I sound a bit biased here, but really consider it.^{2} The talk (and this post) will dive into some examples of contributions from mathematicians in industry, some other topics in mathematics that have played huge roles in developing our modern life, and why this is still worth investing in from a research perspective.

## Mathematicians in Industry

Pure mathematicians have traditionally been thought of as needing to be cloistered away behind old brick and stately trees on a university campus, or perhaps a secret government lab or agency. However, mathematicians have made a huge mark on both technology and their field by working in industry.

- William Gosset developed the Student’s t-distribution while working for Guinness .
^{3}So much in statistical inference, especially small-sample inference, relies on this development. - Richard Hamming working at Bell Laboratories developed the error correction codes that are critical to modern data transfer and storage.
- Genichi Taguchi developed the Taguchi array, noted for its ability in the design of experiments to handle otherwise uncontrollable factors.
- Walter Shrewhart at Bell Laboratories developed statistical process control, the underpinnings of what would become Lean Six Sigma.
- Claude Shannon developed the mathematical basis of information theory. Storage companies wouldn’t exist without these developments in mathematics.
- Agner Erlang was the father of queuing theory, invented while working at a Danish offshoot of Bell Telephone company. Queuing theory and traffic modeling allows for efficient resource scheduling in shipping, grocery stores, telecommunications, and computer networks.

These fundamental mathematical developments were all created in industry, funded by executives who saw the value of pure research. Bell Laboratories was famous for the plethora of inventions it created while it was still operational.

## Mathematical contributions industry uses

Obviously, it wasn’t only industry mathematicians contributing essential developments the private sector now uses and loves.

- Experimental design allowed for rigor in manufacturing testing, and optimization under cost constraints when all possible factor-level combinations couldn’t be tested.
- Reliability theory designs product warranties, maintenance schedules, and system design for almost every consumer product we buy today.
- Boolean algebra allows all of your computers to function.
- Group Theory has been discussed on our site as well, with huge implications across many different areas, including coding theory and chemistry.
- Fluid dynamics describes the flow of fluids, including air and water. These help engineers design boats, planes, and hydraulics.

## What happened and why should we care again?

This portion of the talk generated the most discussion. We don’t hear much about Bell Labs anymore. What happened? From Wikipedia:

“On 28 August 2008, Alcatel-Lucent announced it was pulling out of basic science, material physics, and semiconductor research, and it will instead focus on more immediately marketable areas, including networking, high-speed electronics, wireless networks, nanotechnology and software.”

In general, most companies that do “research” today only focus on marketable areas. I realize people say Google and Facebook and other big Silicon Valley companies are into research, but how many of them are into pure research the way the private sector was in the 1940s? Exploration isn’t really valued, marketability is. Research is put on a production cycle, which devolves into advanced development, with incremental improvements rather than the major leaps forward it used to provide.^{4} With the explosion of data science, some attention has been called to mathematics, but it also turned some concepts into buzzwords (I wrote about this topic as a guest post on the blog Quirky Insights). In the beginning, you did need those mathematicians. Now we have black boxes, neural networks, easy visualization tools, and massive GPU computing, so data scientists can develop flashy (and sometimes effective) solutions on that quick development-cycle.

Mathematicians do work slower, seeking analytical solutions. You can’t develop theorems every two weeks, or even hope to have proofs done close to that fast. I won’t have a new paper before your quarterly report. I understand that this is a terrible business argument for funding. Here I’m appealing to something less tangible and longer term than a quarterly spreadsheet. True industry-changing (or creating) developments come from exploration and pure research. The nice thing about mathematicians is that we need very little to do great work. No huge labs, a decent computer, lots of whiteboards, a ton of paper, and some freedom and space.

What followed after a lively discussion with the delegates was some examples of the work I’ve done. Since it’s all published here, I’ll just link most of it.

## Project Risky Business

This project was presented at the Storage Developer’s Conference in September 2017. This project aimed to take a known problem (hard drive failure), and approach it in a simpler, different way. Using only an absorbing Markov chain on medium errors, we were able to give a cumulative risk of drive failure in a customizable range, and then build it into an entirely granular risk model for RAID groups, whole systems, and multiple-asset customers.

The math wasn’t new, the problem was just approached a little differently.

## The surprise star of the show

To be honest, I intended to blaze through this, not expecting technology delegates to be interested in the most theoretical work we do here. (The posts on this work are here, here, and here.). This, to me, was a delightful surprise in how much interest and imagination I saw when I gave the overview of the need for a formal notion of dependence^{5}.

## Theory motivated by application

This one received quite a bit of great dialogue when presented at SDC. My goal was to present the theory and receive some engineering feedback on whether or not the models mirror reality, how to implement the model in specific situations, etc. The work from my dissertation was motivated by applied problems: the need to generalize a reliability model for more complicated server environments. The rest then came from asking “what if I relax this assumption?” or “under what conditions does this property still hold?” The so-called “practical problems” have served as wonderful motivation (necessity is the mother of invention and all that), but the leaps of “what if” yield the most interesting discoveries.^{6}

## Mathematics: Worth the Investment

I concluded the talk successfully (I think) making the case for a renewed interest in even small investment in exploratory research, particularly in mathematics where the cost/benefit ratio is extremely small^{7}. I’d like to extend a heartfelt thank you to everyone who visits this site to read the mathematics posted here. Mathematicians are ultimately normal people, and their work is valuable, even if it’s the gravity you can’t see.

PS: Thank you to all the delegates who contributed to this discussion: Jon Hudson, Rob Markovic, Dr. J Metz, Robert Novak, W. Curtis Preston, Leah Schoeb, John Troyer. Many thanks to the organizer, Stephen Foskett and Ben Gage as well.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

#### Footnotes

- Thanks to Nick Traylor for the great title
- For mathematicians reading this, I am absolutely not advocating that we should only study pure math that has obvious potential implications for industry. This talk was trying to reach those in business making funding and investment decisions, and an attempt to “speak their language”, if you will, by showing the value pure math would have to them.
- I did make a mistake while presenting and mistakenly attributed Budweiser as Gosset’s employer. It was in fact Guinness.
- I realize this can get controversial. It certainly did in the discussion. There is a place for advanced development, and that is necessary to grow a business and remain financially competitive. But advanced development is marginal without that exploratory pure research.
- I intend to make a video about this soon, and the importance of this is in the upcoming Tech Field Day video and a future post.
- I’ll work on publishing the rest of my dissertation on here.
- Small cost, very large benefit