Matt Bell is co-founder and CEO of Matter-port, a company building a low-cost 3Dscanning platform that allows anyone tocreate and share accurate 3D models of indoorspaces [Full disclosure: my venture firm Lux Capital isan equity investor]. When Matt left Google’s[GOOG] research team at 22, he wanted to createenvironments in which people interact with com-puters in an intuitive, natural way. Matt founded Re-actrix, where he formed the technology team andprovided the key computer vision innovations be-hind the interactive floor displays that let millions ofpeople play with virtual koi ponds and soccer balls.When Matt first saw Microsoft’s [MSFT] Kinectproduct, he recognized the huge spectrum of com-puter vision applications it could power. He chose tofocus Matterport on building models of real thingsbecause of the potential to help millions of peoplecommunicate in 3D. When Matt isn’t rallying theteam at Matterport, he likes to organize community

INSIDE • Ex-Google Guy Delivers 3D Visions

On-Demand• Science And Art In The Fold With Origami• Tied Up In Applications For Knot Theory• Word On The Street • Emerging Tech Portfolio

Volume 12/ Number 3 / March 2013 www.forbesnanotech.com

/Wolfe Emerging TechREPORT

This edition is all aboutspace—though not in theastrophysical sense, mind you.From digitizing our domiciles,to folding intricate forms, tocalculating the compliment of aknot—this month's interviewsare sure to bend your brain.We're also proud to report thatseveral of this month's intervie-wees are also participants in the3rd USA Science & Engineer-ing Festival—the nation’s mostentertaining and educationalscience festival. Culminating inan April 2014 expo in Washing-

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The Insider

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MATT BEL L

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JOSH WOLFE, EDITOR

Ex-Google Guy Delivers 3D Visions On-Demand

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Science And Art In The Fold With Origami

Tied Up In Applications For Knot Theory

COL IN ADAMS

Dr. Robert J. Lang has beenan avid student of origamifor more than 40 years and isnow recognized as one of theworld’s leading masters of theart, with over 600 designs cata-loged and diagrammed. Dr.Lang is also one of the pioneersof the cross-disciplinary mar-riage of origami with mathe-matics. He is noted for designs

Colin Adams is the ThomasT. Read Professor of Mathe-matics at Williams College. Hereceived his Ph.D. from theUniversity of Wisconsin-Madi-son in 1983. He is particularlyinterested in the mathematicaltheory of knots, their applica-tions and their connectionswith hyperbolic geometry. He isthe author of The Knot Book, an

/Wolfe /Wolfe

DR. ROBERT J. L ANG

hacking events. Matt earned a Bachelor of Sci-ence in computer science from Stanford Uni-versity.

How did you begin your career?I went to Stanford and majored in computerscience, but had a tremendous number of sidepassions—everything from psychology to elec-trical engineering. I went to Google after grad-uation, and it was a pretty exciting time to be atthe company. There were about 200 people,and I worked on a lot of interesting machinelearning problems. It was basically the largestsandbox one could possibly ask for—itdwarfed anything in academia. Google also ex-posed me to a range of best practices for oper-ating a small company—everything from engi-neering, to hiring philosophy, to productmanagement. My biggest passion was in com-puter vision though, and at the time, it was afield that wasn’t in a great state.

What were some of the challenges in thecomputer vision world?Ideas worked well in the lab but not in the realworld. I wanted to change that, and had someideas about how to use computer vision to

bridge the digital and physical worlds, by creat-ing camera systems that could recognize peo-ple’s position and movements. I ended up leav-ing Google and pursuing these ideas, creating astartup called Reactrix that built interactivevideo projections. We deployed interactive vir-tual ponds and soccer fields onto the floors ofmalls and movie theaters. This was way beforethe Kinect ever existed, and it was rather excit-ing in the early 2000s to see people learninggesture interfaces in public places in just a fewseconds. We were accomplishing our goal ofbringing computers out into the physical worldand allowing for that seamless interaction,where you don’t even think about the fact thatthere’s a computer there in the first place.

What is it about computer vision inparticular that you believe holds so muchpromise? Computer vision is basically a gateway forcomputers to interact in much richer wayswith the physical world. We all know that com-puters are good at dealing with highly struc-tured, curated information but there’s a hugeopportunity in enabling computers to recog-nize and interact with the messier visual data

from the physical world. That manifests itselfin everything from robotics to image captureand recognition.

When was your “A-ha” moment forstarting Matterport?I had been thinking a lot about the challengesin computer vision, and I realized that havinggood 3D sensors would enable many applica-tions to work a lot better. So when the firsttruly low-cost 3D sensors came out in theKinect (the sensors themselves are made by anIsraeli company called PrimeSense), we real-ized there was a pivotal opportunity to create anew company to try to revolutionize a varietyof industries using these sensors along withcomputer vision. In looking at the possibilities,we realized there are people in many differentindustries who need to work with physicalspaces. The tools that they have for workingwith those spaces are incredibly primitive—they consist of basically taking photos andusing measuring tape. These people live andbreathe in three-dimensional interior spacesevery day, so for them to not have a tool that isnatively 3D seemed like it was a ripe opportu-nity for innovation.

What were some of the key earlychallenges in building the company?The sensor gets you 3D snapshots, but youneed to be able to put all of those 3D snapshotstogether in a coherent model. When we startedMatterport, we found that almost all of thework that had been done in that area was lack-ing—the algorithms didn’t work well. Whenbuilding a computer vision company, you haveto make sure that your algorithms will workconsistently well in a wide variety of situa-tions—everything from an empty apartment toa complex garden to the crowded engine roomof a ship. So we really emphasized the develop-ment of a very robust set of algorithms thatwould work well across all types of situations,so our users can simply have a product thatworks reliably on its own.

What’s the status of Matterport today?We’ve now been in a beta program for severalmonths. Since we’re essentially creating an en-tirely new product category, we’re assessinghow our beta customers use our product so wecan be absolutely sure we create somethingthat’s useful to a broad range of companies in avariety of industries. Initially, we’ve targeted

ton, D.C., this year-round celebration of science is meant to re-invigorate the interest ofour nation’s youth in science, technology, engineering and math.

We begin with Matt Bell, co-founder and CEO of Matterport (full disclosure: my ven-ture firm Lux Capital is an equity investor in Matterport). Matt shares how state-of-the-art computer vision and low-cost 3D cameras are being combined to create a brand newmarket in communicating 3D spaces. The company promises to make it easy to captureour physical worlds for sharing via the World Wide Web, and hopes to revolutionizeeverything from real estate to remodeling along the way.

Next up is Robert Lang, who has the unique distinction of being both an origamimaster and renowned mathematician. The connection isn't coincidental, though, asRobert pioneered the mathematical techniques that allowed for the folding of previouslyunfathomable forms. Dr. Lang steps us through the art and science of origami, and howthe practice of folding has impacted everything from solar arrays to cardiac stents.

Lastly, we sit down with Colin Adams, an award-winning educator and erudite ex-plorer in the world of knot theory. A study that once suffered for lack of purpose, Colinoozes enthusiasm for how terms like "hyperbolic geometry" have new relevance in untan-gling mysteries of DNA, uncovering new synthetic molecules, and understanding theshape of the spatial universe.

As always here's to thinking big about thinking small...and to the emerging inventorsand investors who seek to profit from the unexpected and the unseen.and investors who seek to profit from the unexpected and the unseen.

The Insider Continued from page 1

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Ex-Google Guy Delivers 3D Visions On-DemandContinued from page 1

customers working with the home. The ration-ale behind this is some of the most importantfinancial decisions of our lives revolve aroundthe home—whether it’s buying or selling, rent-ing or remodeling, refurnishing or insuring—these are very big, expensive decisions peoplewant to make sure they get right. By having adetailed 3D model of the home, we believe allof these decisions become a lot easier. We’ll bemoving from our beta program to a scaled roll-out later this year to get our 3D scanning cam-era in the hands of a lot more customers.

What types of people and companies haveexpressed interest in Matterport’s 3Dcamera?A mix of professionals and companies, from in-dividual agents to much larger enterprises. We’veseen a lot of interest within the real estate indus-try—ranging from agents to photographers tolarger commercial firms. We’ve also seen a spe-cific interest in vacation rentals, since this is a sit-uation where you often have to make a very ex-pensive decision without visiting a location inperson. We also have customers in the insuranceindustry who are using our product to docu-ment insurance claims in a way that is faster andmuch richer than what was ever possible before.

What will Matterport’s camera cost? We haven’t announced a final price yet, but weexpect it to be in the range of a decent digitalSLR camera. There will also be a monthlycharge for the cloud processing of scans, sinceit is a fairly computer-intensive process. Priorto the existence of Matterport, if you wanted a3D model of a space, you had a couple of op-tions: Hire a highly-talented 3D graphic artistwho would spend several weeks taking photos,taking measurements and then recreating yourspace to the desired level of detail. That wouldcost thousands or tens of thousands of dollars.The other alternative: A 3D laser scanner,which would generally require a few days ofscanning plus another 10 days aligning all ofthe data. Hiring a laser scanning service wouldcost at least $10,000, and the laser scannersthemselves start around $50,000. What’s greatabout Matterport is that we expect 3D scan-ning to actually be free for consumers. Becausethe home is typically scanned in conjunctionwith a large purchase decision, there is a com-mercial party that is motivated to help the sale,and they will typically be the ones who buyscanners or pay for the scans.

If Matterport is successful in making 3Dscanning of indoor spaces widelyaccessible, how do you think that willchange the world?One thing that’s important to understand isthat 3D sensors themselves are getting smallerand cheaper very quickly. New sensors werejust announced that are capable of fitting insidea tablet or smartphone. We’ll soon be living in aworld where everyone is effectively carrying a3D scanner in their pocket.

Let’s take a simple example: imagine oneday in the near future you’re shopping for fur-niture. You could stand in your living room,quickly wave your phone around, and then allof a sudden have a virtual model of your livingroom on your phone. You’d then go online andstart dragging and dropping furniture from acatalog into your living room to see what itwould look like. Or what if you wanted to re-decorate? You could upload your 3D model tothe Internet and solicit ideas and bids from de-signers all over the world almost instanta-neously, and each of them could show you howyour new living room would look.

Now imagine you’re a first responder. Today,first responders rarely have much informationabout an emergency, and if they do have some-thing it’s usually a crude floor plan at best. Whatif you were a firefighter or SWAT team memberand before you arrived at the scene you had acomplete 3D model of the space? You’d be ableto run in knowing immediately what the spacewould be like. I actually have a related personalexperience of viewing a scanned space and thenvisiting it personally. While there, at one point Igot up and went to the bathroom. It took me afew seconds after I reached the bathroom to re-alize that I’d never physically seen it before—mymental model of the space from viewing thescan had guided me right to it.

This is all about helping people to commu-nicate in 3D and enabling them to quickly ma-nipulate 3D spaces.

What other industries do you think youcould disrupt?Let’s think about construction. It’s an incrediblymassive industry—something like $750 billion

a year in the U.S. alone. It involves large, com-plex projects with the involvement of many dif-ferent parties and subcontractors. Being able totake detailed physical records of the construc-tion process lets everyone stay in sync, and italso ensures that everything is proceeding toplan. If there is a disagreement, people canquickly make annotations and clearly commu-nicate those disagreements while viewing ashared virtual model. If we make their commu-nication process easy, even slightly more effi-cient, that’s a tremendous cost savings to them.

What are the next big milestones for thecompany, and what are you lookingforward to? We’re planning a large-scale launch in latesummer of this year. I’m looking forward toseeing the broad range of 3D spaces that peoplewill scan, and to seeing the communitiesemerge around those spaces, as people start in-teracting around them online and start work-ing with those spaces.

But we see 3D reconstruction as just the be-ginning of what we’re offering. We’ve spent agreat deal of effort to make sure that 3D scan-ning and viewing will be accessible and easy forpeople who are nontechnical. With Matterport,people will be able to just capture a space andhave it automatically reconstructed and easilyviewed and shared online—no additional workrequired.

Going forward, we plan to build on top ofthat platform, so that not only will people haveeasy access to 3D spaces, but they’ll be able touse apps that run on top of that platform to en-able a whole new level of utility. For example, ifyou wanted to auto-generate a floor plan, orvirtually shop for furniture, those will be toolsthat you’ll be able to invoke on our online ormobile platform. Or what if for fun, youwanted your house re-rendered and turnedinto a videogame as a post-apocalypticdwelling with zombies running around? Someof those tools will be built internally, but we’realso going to bring in an ecosystem of thirdparty app developers to add additional func-tionality to Matterport in a wide variety ofways. ET

“This is all about helping people tocommunicate in 3D and enabling them to

quickly manipulate 3D spaces.”

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Science And Art In The Fold With OrigamiContinued from page 1

of great detail and realism, and includes inhis repertoire some of the most complexorigami designs ever created. His work com-bines aspects of the Western school of math-ematical origami design with the Easternemphasis upon line and form to yield mod-els that are at once distinctive, elegant andchallenging to fold. His work has been ex-hibited in museums around the world, in-cluding Paris, Los Angeles, the Kaga Mu-seum of Origami in Japan, and the Museumof Modern Art in New York City. Dr. Langwas the first Westerner invited to addressthe Nippon (Japan) Origami Association’sannual meeting (in 1992) and has been aninvited guest at international origami con-ventions around the world. He has pre-sented several refereed technical papers onorigami mathematics, consulted on applica-tions of origami to engineering problems in-cluding medical devices, air-bag design, andexpandable space telescopes, and is the au-thor or co-author of fourteen books and nu-merous articles on origami. Dr. Lang is aregular lecturer on the connections betweenorigami, mathematics, science and technol-ogy. He received Caltech’s highest honor, theDistinguished Alumni award, in 2009 andwas elected a Fellow of the American Math-ematical Society in 2013.

How did you first get started in the worldof origami?When I was a small child, I acquired a bookthat had some instructions for a few tradi-tional origami designs, and I got hooked. Ifound no end to the possibilities withinorigami, all within the basic parameters ofone uncut sheet of paper. Now of coursethere are other forms of origami that usemultiple sheets, and some use cuts and I’vegotten into some of that as well over time. Butthe primary idea of using one uncut sheet hasalways been the most attractive part, andthat’s where I have continued to find greaterdepth and possibility in the art.

When I was a kid, this was a way of mak-ing toys with just a sheet of paper. I couldmake a wide range of toys and fun shapes forfree, using leftover materials or things Ifound. Paper was cheap and ubiquitous, so Icould try things with no worries that I’d ruinit. Those factors still appeal to me but I’venow added the factors of mathematical andstructural beauty.

Did you intentionally decide to integratethe study of origami into your academicpursuits?No, origami was always a hobby. When Iwent to Caltech for college, the plan was tohave a more conventional career path inmath, science or engineering—because I liketo build and make things. But Caltech is apretty challenging place that revs the braininto high gear, and it also revs up a problem-solving approach in engineering, where if youfirst understand the mathematical underpin-ning of the fundamental laws, then you canapply the tools of math to achieve the goalsyou’re after. Origami felt amenable to that ap-proach, in that it obeys basic mathematicallaws, and we can express those laws in thelanguage of mathematics. Most importantly,if we understand what those laws are, we canuse the tools of mathematics to achieve thegoals we’ve set—even if they are artistic goals,not engineering goals.

More simply put, by understanding andexploiting mathematical laws, we can reachan artistic vision that would otherwise beunachievable. That process got me inter-ested in applying math to the analysis oforigami, and the education that I receivedgave me a toolbox of mathematics that Icould apply to this art.

Before you began working at thisintersection of art and science, did youknow of others who studied themathematics of origami?I wasn’t aware of much other work when Istarted out, but since then I’ve learned thatother people had indeed been investigatingthe mathematics of origami and we can findsurprisingly deep roots to the mathematics offolding. Not all relate specifically to Japanesepaper folding, which is what origami is, butmathematicians have worked at describingthe folds on the surface of paper. Back in the1930s, Italian mathematician Margarita Bel-loch looked at the mathematics of geometricconstructions using folding.

The mathematics really came togetherstarting in the late 1980s, when a group oflike-minded origami researchers put to-gether the first of what has now become aseries of conferences on the mathematicsand science of origami. That first conferencewas held in Italy in 1989 and has since beenheld every few years. The next is scheduled

for 2014 in Japan.

Does the application of math to the artchange your approach, or your perceptionof the limits of what you can create?Years ago, I had lists of of things I wanted tomake, but no idea how to make them. By ap-plying new math techniques I could accom-plish the goals I was after. One vision was tocreate horned animals, like deer. There weredefinitely origami deer in the past, but mostused cuts. People would make a four-leggedanimal with a big flap on its head and thenmake lots of cuts in that flap to get branchedantlers. I found that unsatisfying because theidea of origami was to do it all by folding. Ialso wanted to fold a deer that could be iden-tified by the way the antlers branched, be-cause different deer have different branchingpatterns. I started by asking how to distin-guish different branching patterns, and howto quantify those features. The differentarrangements of points, the different lengthsand numbers, and how they’re connected toone another—those all can be describedmathematically.

That led to a question of the nature ofpaper, and how one arrangement of points ispossible but another is not possible. That ledto the mathematical laws and descriptions. Ibecame interested in pursuing the more ab-stract question: What are the laws that deter-mine the arrangements of points we can foldfrom paper? The question became purelystructural and completely separate from thedeer. What are the laws that let you fold thiskind of structure versus that kind of struc-ture? By creating an abstract question, youclear away all of the detail tied to a specificsubject, and then you can start to perceive theunderlying mathematics.

Eventually I found my way back to askinghow to create a particular structure usingmathematical ideas. The day that I couldapply these techniques to design a deer thatwas recognizable as a white-tailed deer, not amule deer, I realized I was onto something.

Some of your past work includes insectsthat seem like they’d be impossible tofold. How do you create these forms? Insects are a traditional figure in the historyof origami, and for years insects were con-sidered the hardest subjects. I use the terminsects informally because I’m including spi-

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ders, scorpions, crustaceans and othermany-legged shapes. These were considerednearly impossible in origami, and were verygeneric in historical designs, even up to the1950s and 1960s. A folded bug was sort of ablob with six legs, and getting six legs from asingle sheet of paper was pretty impressive.When we started developing mathematicalapproaches, we made it possible to designspecific types of insects. That led to an infor-mal competition through the ‘90s—theorigami bug wars, where people tried to foldever more complicated insects. We like sub-jects that pose structural challenges.

Do you reach a point where designsbecome so intricate that you can describethe way to create a form, but have nomeans to actually fold it? Oh, yes. We can design folding patterns forarbitrarily complex shapes, but the propertiesof the paper and of our own folding abilitieslimit what we can create. Two aspects limitorigami: first, even the best folding paper hasfinite thickness that builds up until it preventsmore folds. Second, some designs are so com-plex that you need to bring hundreds of foldstogether at once to make the form, and thatmight be too difficult to bring off.

What practical applications have emergedfrom our new understanding of the lawsof folding? Actually, a whole host of origami techniqueshave been applied to engineering problems.One example is an arterial stent developedby a group at Oxford University. Zhong You,an Oxford professor, along with post-doc-torate student Kaori Kuribayashi, developeda way of folding one of these tubes into avery small package that can be threadedthrough the artery until it gets to the loca-tion of blockage, where it is opened out intothe full tube. In the past, this type of stentexisted but was made from metal mesh—themesh tends to create blood clots, so a

smooth tube is preferable.

So origami techniques have helpedaddress heart disease! Are there otherapplications that come to mind?Origami techniques have been used in space.One of the first was developed by a Japaneseengineer named Koryo Miura, who devel-oped a folding pattern that could be appliedto a solar array. His array flew on a missionfor the Japanese Aerospace Agency in 1995.I’m also working right now with a group atNASA’s Jet Propulsion Laboratory on a designfor a different pattern for a solar array thatwill unfold.

If we think about the expression “formleads to function” are there areas whereyou believe origami could be used toimprove the efficacy of existingtechnologies?In general, origami can play a role when theproblem requires a surface—a flat shape asopposed to a solid 3-D shape—that needs toexist in two states: one small and one big. Inother words, something that needs to besmall for the journey and large at the desti-nation.

The heart stent, for example, needed to besmall for the journey through the artery, butopen out into a tube at the destination. Solararrays and space structures in general needto be small in their rocket ship but thenopened out at their destination. Things thatare flat and sheet-like, like solar arrays, an-tennas, telescope lenses—anything thatwants to be big and flat—these lend them-selves to folding.

We’re starting to see new applications oforigami in mechanisms that, for various rea-sons, are best made from a single sheet. Oneexample is the creation of microscopic mech-anisms, where it’s impossible to glue togetherlittle bolts and linkages. Instead, we litho-graphically pattern a sheet with a structure,and then fold that sheet into a mechanism

that manipulates or moves in some way. Moremechanical engineers are doing researchspecifically on the types of mechanisms thatcould be created by folding.

Can you describe in more detail some ofthese microscopic mechanisms?One that comes to mind is a little folding ma-nipulator for artificial insemination, where amicromechanical structure holds an egg andinjects it with a single specified sperm. A mi-croscopically machined structure uses a fold-ing mechanism to do the grasping and the in-jection.

Another project, currently going on atCaltech, involves a retinal implant that isconnected to an external camera, for peoplewith macular degeneration. The externalcamera takes pictures of the surroundingsand triggers electrical signals directly ontothe retina of the person, effectively replacingthe functions of their rods and cones. Theuser will perceive the images directly fromthe electrical stimulation of the retina. Theelectrode array that does this needs to be in-serted into the eyeball in a very small pack-age, and unfolded into a shape that con-forms to the back of the eye. The Caltechteam is developing an origami structure forthis electrode array.

How do you go about assessing projectsto understand whether folding is the bestapproach to solving a specific need?In pursuing any engineering question, youexplore what the requirements are to findout if an origami solution is actually the bestapproach, because if it’s not you’re going tobe wasting your time. You can come up withan origami solution, but if the requirementsof the problem don’t steer one towards afolding solution, then there’s probably anon-folding engineering technique that willwork better.

What would steer one towards an origamisolution? First, the material should be sheet-like, but with rigid sections that won’t flex (asopposed to cloth, that is arbitrarily flexible).You want a very well controlled deploymentwith a small number of degrees of freedom,so you know exactly how it is going to deploy.This is especially important in space, whereyou can’t go up there in person to shake outany snags. ET

“A whole host of origami techniques have been applied to engineering problems.

One example is an arterial stent developed by agroup at Oxford University.”

Science And Art In The Fold With Origami

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Tied Up In Applications For Knot TheoryContinued from page 1

elementary introduction to the mathematicaltheory of knots, Why Knot?, a mathematicalcomic book with attached toy, and Riot at theCalc Exam and Other Mathematically BentStories, a compendium of humorous mathstories. He has written a variety of researcharticles on knot theory and hyperbolic 3-manifolds. He is a recipient of the Haimo Na-tional Distinguished Teaching Award fromthe Mathematical Association of America(MAA) in 1998, an MAA Polya Lecturer for1998-2000, a Sigma Xi Distinguished Lec-turer for 2000-2002, and the recipient of theRobert Foster Cherry Teaching Award in2003. He is also the humor columnist for theMathematical Intelligencer. His next bookwill be Zombies & Calculus.

How did you get started in the field ofmathematics?As a child, my goal was to become an author. Iended up at MIT, and at that point I started tofall in love with mathematics. In graduateschool, I stumbled across this area of knot the-ory and hyperbolic volume—a professor chal-lenged us to solve a problem for a reward of$5. I worked on it for two months, and I didn’twin, but it set the course for my Ph.D.

Can you explain, in layman’s terms, theconcepts of knot theory and hyperbolicvolume?Hyperbolic volume is a quantity that we asso-ciate to a knot. Mathematically, when we talkabout a knot, we imagine a string with a knottied in the middle, and the two loose endsglued together, trapping that knot on thestring. The most fundamental question wecan ask in knot theory is whether we coulddisentangle that piece of string, without cut-ting the string?

Depending on how complicated the knotwas, you could play with it for years withoutsuccess. You need mathematical techniques todecide whether it’s possible to disentangle thestring.

How does the volume of a knot relate toits fundamental construction?The volume component is where it gets a littlemore technical. First, let’s define the compli-ment of the knot, which is space, minus theknot. That gives us a topological space, andwe measure distance on that topologicalspace in a way that is negatively curved, and

that makes it hyperbolic. Hyperbolic reallyjust means negatively curved. In this way, wemeasure the knot’s hyperbolic volume: thevolume of space minus the knot. Now, youmight think that’s got to be infinite, becausespace is infinite and space minus the knot isgoing to be infinite, right? As it turns out,measuring distance that’s negatively curvedwill give you a finite volume.

And so we can associate a finite, hyper-bolic volume to each knot, which gives us away to distinguish between the knots. If I giveyou two knots and you calculate the hyper-bolic volume of one knot to be 2.713 and theother knot to be 4.614, then you know thatthose two knots are distinct, and you cannotrearrange the one to look like the other.

What is one of the most basic knots youcan study?If you take a string and tie a simple overhandknot, and then you glue the two loose endstogether, you get a knot with three crossingson it. That’s called the trefoil knot, and that’sthe first nontrivial knot that cannot be disen-tangled.

However, we can make knots that are arbi-trarily complicated, at least in appearance,which in fact could be disentangled. Imaginetaking a string that is three miles long andgluing the ends together, and then messing itup and tangling it into a horrendous ball ofstring, an absolute disaster that would take sixmonths to disentangle. That would be an ex-ample of a trivial knot in a very nontrivialconfiguration.

Is knot theory a new field of study?Knot theory dates back about 140 years, backto the days when people were trying to comeup with a model for the atom. They were ask-ing questions like “How do we distinguish be-tween gold and lead? What is the fundamen-tal difference between those?” At that timethey believed that there was this ether thatpervaded all of space, and that atoms werejust little knots in the ether.

They thought that a table of distinct knots

would actually be a table of the elements,which would help distinguish between thedifferent atoms.The whole knots-in-ethertheory ended in the late 1880s, when theMichelson-Morley experiment showed thatthere was no ether, in fact.

What kept the field alive?Mathematicians continued to work on knottheory simply because of the beauty of thefield, but it was a bit of a backwater for thenext century. By the 1980s, people discoveredimportant applications of knot theory, includ-ing how it relates to DNA. DNA is a long,skinny, string-like molecule with a doublehelix structure, which has been stuffed intothe nucleus of the cell. It’s the equivalent ofstuffing 200 kilometers of fishing line into abasketball; it’s this horrendous tangle, yet ithas to be able to do recombination, transcrip-tion and various other things for the cell tofunction properly. If it’s all tangled up, howcan the DNA make copies of itself that can beseparated out?

Well, what’s the biological solution to theDNA knot problem?As it turns out, inside the nucleus there areenzyme molecules able to cut one DNAstrand open to pull another strand through,close the first one up and then let them go. Inknot theory parlance, the enzymes are mak-ing what’s called a crossing change, where onestrand is allowed to pass through another.The knot is changed in a way that allows theDNA to disentangle. In essence, the wholefield of protein theory is really a lot of knottheory—studying how proteins knot and un-knot.

What additional areas of study relate toknot theory?Knot theory also applies to synthetic chem-istry—synthesizing new molecules. Thinkabout any long, skinny molecule that comesaround and bites its own tail to form a cyclicmolecule. Benzene is a classic example of acyclic molecule. If you take that cyclic mole-

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“By the 1980s, people discovered importantapplications of knot theory, including how it

relates to DNA.”

cule, cut it open, tie a knot in it, and then gluethe two loose ends together, then you’veformed a knotted molecule. Syntheticchemists are incredibly excited about synthe-sizing knotted molecules, which use the sameconstituent atoms bonded in exactly the sameorder. By adding a knot, it has completely dif-ferent properties than the unknotted version.This means we could create a limitless supplyof new substances, because of the large num-ber of distinct knots. For example, if I drew apicture of a knot with 16 crossings, we knowthere are more than 1,700,000 different knotpossibilities. If you have a long enough mole-cule and you know how to knot on the molec-ular level, you could make over 1,700,000 dif-ferent substances out of that single sequence ofatoms! This concept holds incredible potentialfor dramatically expanding the set of sub-stances that can be created with just one chainof atoms.

Is this still a theoretical process, or areresearchers successfully knotting moleculesinto new configurations?So far, they’ve been able to synthesize trefoilknots, and they’ve been able to synthesize fivecrossing knots, but they have not yet found agood system for synthesizing more compli-cated knots. They’re still working on design-ing some kind of a template that allows theseparate creation of little pieces of knots thatcan be brought together when the template isdissolved. There are still very few actual knot-ted molecules, so we don’t yet have many ex-amples where we can say, “Here is this brandnew substance that is particularly useful forthis specific purpose.” Yet the knotted ver-sions seem to behave completely differently,and a lot of research dollars are supportingefforts to learn more about these possibilities.

Let’s go back to education for a moment.What excites you about teaching?I’m lucky to teach in a place like WilliamsCollege. The students are fantastic, and I loveto see their eyes light up when they under-stand and get excited by the mathematics. Ienjoy coming up with new and unusual waysto teach math, to get the messages across.That can mean a lot of different things in theclassroom. It means coming up with innova-tive classes for students and ways to get peo-ple’s attention. For instance, I’ve created a se-

ries of silly, tongue-in-cheek videos—the goalis to get people to pay attention long enoughto see the beauty in these important mathe-matical concepts.

Would you share your thoughts on beinginvolved with the USA Science andEngineering Festival?It’s a great opportunity to reach out to agroup of kids who have tremendous poten-tial, and excite them about science andmathematics. It’s critical to get young peopleinterested in science. We’re now competingwith television, video games and variousother opportunities that students can access.If we can’t keep their interest it’s going to bedisastrous in the long run, so the key is tocome up with ways to get people to pay at-tention long enough for them to get excitedabout the science.

What is your perspective on the currentstate of math and science education in theU.S.?At the college and graduate level, we have thebest schools in the world. People come to theUnited States from all over the world to go tograduate school in math and science. Ourcolleges are very successful, some more thanothers, but overall science and math at thecollege level is quite good. At the high schoollevel we struggle more. One challenge is toget enough people at that level who are bothstrong in teaching and in the sciences, whenthe monetary rewards are low and the frus-tration can be high. Often they work withstudents who come into high school unpre-pared, and it becomes difficult to take themto the next level. Mathematics, in particular,is very cumulative. A student who has a badexperience early on, or who misses one im-portant chunk, can have a hard time makingthat up later. That lag builds quickly and canbecome a disaster. We lose a lot of studentsthat way.

Outside of knot theory, what are someother fields that you think are reallyexciting right now?These days, I’m intrigued by a question in thefield of cosmology, which is related to knottheory mathematics. The questionasks,“What is the shape of the spatial uni-verse in which we live?”

Thousands of years ago, humans didn’tknow that our planet is a sphere. Locally, itlooked essentially two-dimensional. TheGreeks figured out one of the great victoriesof human intellectual history: that the surfaceof the earth is a sphere, as opposed to a planethat goes on forever or a disk where we couldfall off the edge.

Our next great intellectual achievement isto determine the shape of the universe. Onemight expect a three-dimensional spacegoing on forever in every direction, yet in factvery few cosmologists think that’s the case.Most cosmologists believe that the universe isfinite, yet you can head in any one directionforever.

How would such an arrangement of spacebe possible? Imagine a cube. What if I could glue the leftface to the right face, the front face to theback face and the top face to the bottom face,so I’ve glued them all around. I couldn’t actu-ally stretch a cube around like that, but justimagine it in the abstract. So if we head outthe right face, we’d come back in on the left;head out the front face, come back in on theback, and so on. That shape is called a threetorus. If that cube is the universe, imagineflying straight out of our galaxy. You’d even-tually fly right back into the place you left!

To study the shape of the universe, wehave a satellite that is collecting data from thecosmic microwave background radiation.That may give us enough information to con-ceivably determine the shape of the universe.To me, that’s a really cool problem. ET

© COPYRIGHT 2013 FORBES/WOLFE EMERGING TECH REPORT MARCH 2013 | 7

Continued from page 6

“Synthetic chemists are incredibly excited aboutsynthesizing knotted molecules…by adding a

knot, it has completely different properties thanthe unknotted version. This means we couldcreate a limitless supply of new substances.”

Tied Up In Applications For Knot Theory

8 | MARCH 2013 © COPYRIGHT 2013 FORBES/WOLFE EMERGING TECH REPORT

The Emerging Tech Portfolio

For editorial information, e-mail: nanotech@forbes.com

Company[symbol] Coverage Initiated Current Price 52-week range Mkt Cap ($mil)

INTELLECTUAL PROPERTY INCUMBENTS Leading researchers in the physical sciences, with big potential for spin-offs and revolutionary breakthroughsGE [GE] 8/07 $23.37 $18.02-$23.90 $243,010.00Hewlett-Packard [HPQ] 3/02 19.20 11.35-25.40 44,790.00IBM [IBM] 3/02 212.08 181.85-215.90 236,370.00

LIFE SCIENCES Companies that are working at the cutting edge of medical technologyLife Technologies [LIFE] 11/05 63.99 39.73-65.84 10,900.00Nanosphere [NSPH] 11/07 2.20 1.51-3.89 122.74

ELECTRONICS Companies that have corralled the key intellectual property that will be the foundation for next generation electronicsNanosys [private] 3/02 n/a n/a n/a

ENERGY Companies that are developing high-efficiency, low-cost alternative energy technologiesFirst Solar [FSLR] 8/07 28.85 11.43-36.98 2,510.00

ENABLING TECHNOLOGIES Tools and instrumentation that enable critical science and technology discoveriesVeeco [VECO] 3/02 34.96 26.15-38.39 1,350.00FEI Company [FEIC] 1/03 63.75 42.18-65.29 2,460.00Accelrys [ACCL] 3/02 9.66 7.44-9.97 537.21

INVESTMENT VEHICLES Funds that have investments in promising emerging technology companiesHarris & Harris Group [TINY] 5/02 3.64 2.98-4.57 111.91PowerShares Lux Nanotech Portfolio [PXN] 8/07 6.30 5.41-6.85 18.13PowerShares WilderHill Clean Energy [PBW] 8/07 4.58 3.46-5.78 140.87

Forbes/Wolfe Emerging Tech Reportis published monthly by Forbes Inc. and Angstrom Publishing LLC, 60 Fifth Avenue, New York, NY 10011

Editor: Josh Wolfe Contributing Editors: Zack Schildhorn, Suzanne Johnson

Forbes, Inc.Vice President/Editor, Newsletters: Matthew Schifrin

Senior Editors: John Dobosz, Tina RussoSubscription Director: Kasey Kaufman

To subscribe call 1-877-733-7876 from within the U.S. or 952-646-5381 from outside the U.S.; or visit Forbes.com Investment Newsletters(www.forbesnewsletters.com) on the Web. Copyright 2013 by Forbes Inc. and Angstrom Publishing LLC

NOTE: The Forbes/Wolfe Emerging Tech Report is neither a mar-ket-timing service nor a model portfolio. Companies listed in theEmerging Tech Portfolio are early leaders in nanotechnology and,as such, should interest investors seeking to orient their portfo-lios toward this revolutionary technology. It does not guaranteethat securities mentioned in this newsletter will produce profitsor that they will equal past performance. Although all content isderived from data believed to be reliable, accuracy cannot beguaranteed. Josh Wolfe and members of the staff of theForbes/Wolfe Emerging Tech Report may hold positions in someor all of the stocks listed. Josh Wolfe and members of AngstromPublishing LLC may provide consulting services to some of thecompanies mentioned in this publication.

Stock prices as of March 22, 2013

GE: Shares hit a new 52-week high before ending flat on the month. Investors see the companyas a proxy for the global economic recovery and increased capital expenditures.

H PQ: HP zoomed 20% higher as investors begin to believe in CEO Meg Whitman’s turn-around plans. The board also increased HP’s quarterly dividend 10% to 14.52 cents per share.While the company still faces huge headwinds, the stock is now up 62% YTD and has almostdoubled from its November 2012 low. Morgan Stanley raised its rating to Overweight (fromEqual Weight) and set a $27 price target. Revenue is expected to fall 6% in the current fiscalyear (ending in October), after a 5.4% decline last year. HP trades at 6.5x this year’s expected$3.45 in EPS.

IBM: Big Blue advanced nearly 5.5%, reaching an all-time high, which now values the world’slargest provider of computer services at more than $236B. Shares have climbed 11% this year,boosted by EPS gains, divestures of underperforming units, and a move into higher-marginsoftware businesses like data analytics. IBM has said it will deliver at least $20 in 2015 EPS,compared with $15.25 last year. It also has set aside $50B billion for share repurchases and$20B for dividends. The stock still trades at a 10% discount to the P/E of the S&P 500. 

LIFE: Life Technologies closed nearly 10% higher as buyout rumors reached a fevered pitch.The latest word is that M&A discussions have shifted in favor of strategic buyers as some pri-vate equity firms drop out. The odds are reportedly growing that either Danaher [DHR] orThermo Fisher Scientific [TMO] could buy Life, as KKR, Blackstone, TPG and Carlyle haveapparently withdrawn from the process. Cowen & Co. downgraded LIFE shares to Neutral(from Outperform) based on the expectation that the likely sale price won’t be much higherthan the current trading price. Analysts expect LIFE to earn $4.37 per share in 2013.

NSPH : Nanosphere rose 12.2% after brokerage firm Canaccord upgraded NSPH to a Buyrating, claiming shares were oversold and there was 150% upside. The firm believes thatNanosphere is poised to capture a large piece of the molecular diagnostics business after itshifted its focus to blood stream infections. Nanosphere obtained the CE Mark for its Gram-Negative Blood Culture Test. The Gram-Negative Blood Culture test notably expands Nanos-phere’s infectious disease test capabilities to include rapid detection of bacteria that can causedeadly bloodstream infections, an increasingly recognized health threat.

FSLR: First Solar shares lost 14.7% of their value after reporting disappointing Q4 results andguiding lower for 2013. First Solar earned $1.74 per share on revenue of $1.1B in Q4 2012,

below analysts’ projected profit of $1.75 per share on revenue of $1.3B. The company said Q1will fall far short of expectations, guiding to revenues of just $650-750M (versus forecasts of$822M) and EPS of $0.70-0.90 (versus forecasts of $0.89). Bank of America Merrill Lynch cutits rating to Underperform and lowered the price target to $25 (from $35). RW Baird alsodowngraded the stock to Neutral with a $25 price target. Goldman Sachs reiterated its Neutralrating, but cut the price target to $27.

VECO: Veeco jumped 17.9% as investors anticipate a strong rebound in the LED equipmentmarket. The company received a letter from the NASDAQ on March 5 notifying Veeco that itis not in compliance with Listing Rule 5250(c)(1) because its 2012 Form 10-K was not filed ona timely basis with the SEC. As previously announced, the Form 10-K, as well as the com-pany’s Q3 report on Form 10-Q could not be filed timely because the company is reviewingthe timing of revenue recognition of MOCVD systems and related upgrades to these systems.Northland Capital initiated coverage on Veeco with a Market Perform rating and a $29 pricetarget. 

FEIC: FEI shares edged higher on no news. Shares are up more than 15% YTD.

ACCL: Accelrys eclipsed a new 52-week high before slipping almost 2% after reporting fourthquarter results. Q4 non-GAAP revenue increased 16% to $47.5M. Non-GAAP net incomewas $4.5M ($0.08 per share), compared to $4.6M ($0.08 per share) for the prior year period.Analysts had expected revenue of $43.5M and EPS of $0.07. Accelrys recently completed threeacquisitions (HEOS, Aegis Analytical Corp. and Vialis AG) that complicate its GAAP finan-cials. The company said the acquisitions have helped position Accelrys as the leading providerof scientific innovation lifecycle management software. For FY 2013, Accelrys expects non-GAAP revenue of $185-190M, and non-GAAP EPS of $0.36-$0.39.

TINY: Harris & Harris Group nudged lower after reporting Q4 2012 results. The firm’s NetAsset Value fell to $4.13, versus $4.70 a year earlier. Most of that was attributable to the declinein Solazyme [SZYM], its largest holding. TINY exited its entire investment in Neophotonics[NPTN] and began selling Solazyme shares.

PXN: The PowerShares Lux Nanotech portfolio advanced almost 5% on the month.

PBW: The PowerSharesWilderHill Clean Energy portfolio fell 4.2%.

Word on the Street