What is useful, he says, is to look at data arranged in shapes, using topology.
Topology is a form of geometry that relies on the way humans perceive shapes.
Dealers use pagers, cell phones and PDAs to create from this topology a sophisticated, and very lucrative, network.
Altair of Troy, Mich. has a lead over its rivals in a particularly interesting field called topology optimization, according to research firm CIMdata.
Network Magic provides users with an easily interpreted topology map that creates a diagram like a family tree of devices on the network.
ENGADGET: The Family is the Network: Pure Networks' Network Magic wants to make things simple
In 2006, for example, the entire editorial board of Topology, a mathematics journal published by Elsevier, resigned, citing similar worries about high prices choking off access.
In the early days of oil and gas exploration, geologists would largely rely upon topology at the surface of the earth to interpret the location of oil and gas accumulations in the subsurface.
FORBES: How The Internet Of Things Will Change Almost Everything
Network Magic can detect a network outage and mark it with a big red "X" on the topology diagram showing you where the outage occurred, and gives you some indication of how to fix it.
ENGADGET: The Family is the Network: Pure Networks' Network Magic wants to make things simple
Topology helps researchers look at a set of data and think about its similarities, even when some of the underlying details may be different, says Gunnar Carlsson, a mathematics professor at Stanford University who co-founded Ayasdi in 2008 with Mr. Singh and Harlan Sexton, a mathematician who holds more than 30 software patents.
Mr. SCHWEITZER: Well, we had to prove that it was both unique in terms of climate and topology, that there was a history of being called the Ramona Valley and that there were grapes growing here, not necessarily that there was any wine industry so much as that it was possible to grow grapes in the Ramona Valley.
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