“It’s pretty hard to generate sequences of numbers that have any degree of randomness,” says BMCC math professor David Allen. “They’re expensive to create, and very hard to maintain.”
This begs the question, why would anyone want to generate randomness?
“The idea is to use it for pure math research, and also, for computer security purposes,” he explains.
“When you send emails or your credit card information, the technology is out there to encrypt it in ways that are very hard to break into—but not impossible, given the advent of really high-powered computers and quantum computing.”
The challenge, he says, is to encrypt that information—obscure its patterns; make it seem random to potential hackers—with an algorithm that even the most powerful software, can’t crack.
Another challenge is to find a computer powerful enough to be the testing ground for that algorithm.
That’s where the CUNY High Performance Computing Center at the College of Staten Island, directed by Paul Muzio, comes in.
Professor Allen, along with his research team including mathematician Jose La Luz of the University of Puerto Rico, Bayamon, and computer scientist Guarionex Salivia of Minnesota State University, are working at the Computing Center to find and code an algorithm that will unlock new levels of randomness, and raise the bar on encryption.
Pushing the limits
Both Professors Jose La Luz and David Allen earned their doctoral degree at the CUNY Graduate Center and have hard-earned academic credentials in the area of algebraic topology, which uses algebra to analyze global properties— properties that remain constant, even when an object changes.
As Professor Allen puts it, “You have some sort of randomized combinatorial object such as a polygon and the question is, if we cut edges off and add edges in a certain way, can we keep randomness as we extend the object into successive generations, or not?”
In the process of extending the object, he is creating an algorithm—a complex set of steps—and Professor Guarionex Salivia will take that algorithm and “code it, chop it into pieces, do work on each piece, get the results, then aggregate it,” says Allen.
This process is very expensive, computationally, he says, and “No doubt it’s going to push the system right to the limit.”
Fortunately, though, the CUNY High Performance Computing Center can handle that push, especially now that CUNY has selected SGI, a global leader in data analytics and management solutions, to support research activities through SGI's platinum partner Comnetco, Inc.
According to Paul Muzio, with the SGI UV 300 system—and its huge, shared memory—the High Performance Computing Center will be much better equipped to support the vital data component of CUNY-wide research across the social sciences, computer science and mathematics.
The allure of ‘real ideas’
Professor Allen joined BMCC in 2013. “This semester I’m teaching pre-calculus and math 56, which is a developmental course,” he says, “but over the course of my career, I’ve taught pretty much every math course.”
He didn’t always envision a career in math.
“I wanted to be an economics major and when I was in college, math wasn’t really my thing, but I couldn’t escape it, so I just said, ‘You know what? Rather than fear math, I’m just going to major in it’.”
Things turned around for him in a calculus class, “because that’s where you see a lot more interesting geometry and algebra and all this other stuff coming together, and the applications are more interesting,” he says.
“So I was like, ‘Wow, there are real ideas here’, fundamental ideas that are rather deep, and I realized that math was more than just calculating this, that and the other; that things are not trivial to understand, and to formalize them is even more amazing.”
That amazement carries into his work with randomness.
It’s important, he says, for professors to be involved in research in their area of interest, even if it doesn’t relate directly to the class content.
“Students know that you’re involved in something you care about, so when you speak, you have more credibility,” he says.
The human need for order
Whatever he’s teaching, he finds it heartening to see students’ misconceptions about math disappear, over the course of a semester.
“One misconception is that they think it’s useless,” he says.
“A lot of them don’t see where it’s used in the ‘real world’. So you try to explain to them, it’s everywhere. With high-powered computing and the way data is collected, it’s ubiquitous. When you shop online, when you’re sending texts, all that information is encrypted—it’s all mathematics at the end of the day.”
As for the math he is involved in outside of class; the algorithm he created with Professor La Luz, the coding of that algorithm by Professor Salivia, the High Performance Computing Center putting their theories of randomness to the test—do students relate to that at all?
Does anyone, for that matter, really understand randomness?
“I’m not sure I really understand it,” Professor Allen admits. “It’s not something that’s easy to understand. But students probably do understand it on some level.”
It’s human, he adds, to wrestle with the notion of randomness.
“People like to think that there’s order to everything, and also you have to ask yourself, ‘Can I trust my perception of something as being random?’ Maybe I just don’t have the tools to perceive the non-random qualities.”
In the end, “understanding things from different perspectives is very interesting,” he says, and while the theorizing and coding and distributing and aggregating is very hard work, “we’re making some progress. We’re much further along today than we were a year ago when we started.”