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What a Slinky Knows

Monday, September 10, 2012 - 07:00 PM

Looking through a slinky at the sky (SashaW/flickr/CC-BY-2.0)

"Hey kids," said physicist Tadashi Tokieda, "Wanna see a magic trick?" He pulled out a Slinky and did something that amazed the kids, & their dad Steve Strogatz. Steve, along with Neil deGrasse Tyson, explains what the gravity-defying Slinky trick reveals about the nature of all things great and small (including us).

If you've played with a Slinky for more than five minutes, you've probably mastered all the classic moves. But it turns out those humble coils have a surprise up their sleeves. Do this:

1) Dangle a Slinky above the ground as though you were holding a fish by the tip of its tail.

2) Let it extend to its full length.

3) Let go.

For a fraction of a second, something amazing happens: the bottom of slinky hovers in midair, seeming to defy the laws of physics, while the top collapses toward it.

The reason the bottom just floats there, according to Steve Strogatz, is simple: it hasn't gotten the memo yet. We're not just being cute here. Information flows have a lot to do with how our physical world works. And this little experiment, when extrapolated out, might reveal some pretty surprising truths about... well... everything. From anti-tank weaponry, to what would happen if the sun suddenly disappeared, Steve and and our astronomical friend Neil deGrasse Tyson help us unravel the implications of the "wonderful toy." The bottom of the Slinky, friends, is us!

Also check out:

Steve Strogatz's new book The Joy of X

And this slow-mo video of a falling Slinky...

Guests:

Steve Strogatz and Neil deGrasse Tyson

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Comments [41]

Dante Lovecraft from Florida

Tadashi sounds really talented 12 languages whoa that’s a lot. I find it really interesting that the bottom of the slinky just stays there, I would not have expected that. I really like the idea about plucking out the sun and on Earth we would not notice a difference for eight minutes! But when you really think about it, that makes sense because of the speed of light. Yet would we really continue to orbit the previous position of the sun?

Oct. 27 2014 09:28 PM
Dave K from NYC

Very disappointed, especially in Neil, someone I deeply respect. As many others have said, when the slinky is released, it will be affected by gravity AND it will return to its state of equilibrium (coiled up). Said less technically than the other posts, the bottom of the slinky is coiling UP as the rest is coiling/falling down. All parts of an object feel the pull of gravity, so this time delay theory is, honestly, dimwitted.

Still love you guys tho.

Feb. 01 2014 11:19 PM

What a disappointment this podcast was! After listening to some powerful episodes that moved me deeply and shifted my frame of mind, this was just not good enough. The whole episode is basically trying to wrap the most basic concept of physics in mystery and enigma (as Woody Allen would phrase it). The concept is nothing more than inertia. Any school textbook on physics will have the definition, explanation and examples. It is just a property of matter, no mystery about it. The original trick with the slinky is a great way to demonstrate what inertia is to students, but not worth the entire podcast. I think, there is more mystery to the Pythagorean Theorem than to this phenomenon. Not worth the time. Sorry.

Oct. 05 2013 11:51 PM
Adam B from Denver, CO

I generally enjoy the deep and sometimes logic bending questions that are asked on this show, but I was disappointed with this episode. The concept of an objects "awareness" seems pointless. The examples used are all simple physics problems involving force and momentum. The natural state of the slinky is compressed. The force of the hand and the force of gravity stretch the spring and that energy is stored within the coil. Once the top is released, the forces are no longer balanced and so the object begins to fall. The center of mass moves toward the ground at exactly the same rate as any other object would, however the energy stored in the coil is acting to contract to spring. This results in a downward force on the top and an upward force on the bottom which causes it to remain stationary for a short time. Sorry, that's not mysterious.

Mar. 20 2013 04:10 PM
Guille Puerto from Mexico

You guys should invite Neil de Grasse Tyson more often.

Mar. 05 2013 01:11 PM
duff howell from Felton CA

As a point of semantics, shock waves usually mean wave fronts traveling faster than the normal speed of sound. That's why you don't hear an explosion before the shock wave hits you, and don't hear supersonic (relative to air) planes (or bullets) until they're well past (or through) you - the plane or bullet is traveling faster than the sound energy can travel through the local air.

Those shock waves on Mythbusters are explosion-compressed air moving outward so fast that the other molecules on the shock-front can't dissipate the energy into random motion yet. The molecules moving outward from the blast move outward, and the next molecules they hit can only transfer some of the energy, but the net momentum of both molecules still has to be outward.

If you have an arrow or armor-piercing sabot, there is a lot of energy, force impulse, and momentum that can only be dissipated in the material it hits (physically touches) at the point of contact. A kitchen knife works the same way - a modest hand pressure of force on a very sharp (small area) blade edge is huge pressure on a thin line. The fleshy material of a carrot or pork chop fails (cuts) before the force transfers, while the different material of the cutting board deforms and spreads the force enough to just be scuffed. For an arrow, I think a better question is 'between the sharp tip and the oblique sides of the arrowhead and shaft, how much force can be applied by friction, and how much energy can be dissipated by friction or cutting flesh, and when does this add up to what the arrow had when it hit? The arrow usually stays intact, so the energy /momentum dissipation is pretty much all heat and friction work. The arrow isn't traveling faster than the speed of sound in wood (around 3 km/s), so there isn't going to be much 'information not yet received' piling on before the back end of the shaft is very clear that there's been an impact. This is just energy and momentum conservation.

For the tank round, there will be material deforming in both the armor and the sabot, but it's the same - you can dissipate energy by deforming or breaking armor, deforming the sabot, heating things up, - aka turning organized motion of the projectile into random motion of individual molecules. From wikipedia - uranium speed of sound 3100 m/s, kinetic penetrator velocity, 1500-2000 m/s. So they are supersonic in air, but subsonic for their materials. If you concentrate the impact in a small area, the pressure (force/area) rises, and if you get a direct perpendicular impact, you have to stop the sabot completely. (another reason why tank sides are angled as steeply as possible, to deflect weapons, and why advanced antitank weapons fly high in the air and then straight down on the top of the tank, where armor is thinnest and the angle of impact will be 90 degrees. Articles on armor piercing rounds put a fair emphasis on the hard pointed casings, again pointing to an emphasis on high initial peak pressure.

Dec. 14 2012 07:51 PM
duff howell from Felton CA

The speed of sound for the slinky as a spring-like object will NOT be the speed of sound in steel. It's determined by the speed at which the compression wave travels down the medium. Do a push-pull compression on one end of a slinky and you'll watch a slow compression wave travel down the spring with a speed a small fraction of a percent of the speed of sound in the steel. You watch it happen easily with your eyes. That's not hundreds or thousands of meters a second, it's probably not even a meter per second. That's why this works with the slinky as a composite object.

The spring constant and the density determine the speed of sound. Stiff spring, low mass = fast, weak spring, high mass = slow. The manufactured slowness is the whole point of the slinky. If it was really stiff, you couldn't bend it and do cute walk-down-the-stairs tricks.

Since the speed of sound, down the slinky, is slow, that's the speed that information can travel from the just-let-go-of end to the bottom.

Gravity indeed does pull on all of the parts of the slinky at once, but the whole point is that the bottom of the slinky has more than the force of gravity acting on it during the drop. It also has the force of a stretched out spring pulling it upwards. As mentioned above, the center of mass of the spring does dutifully travel downward in the same trajectory as a point-like-object.

A good parallel example is standing on the ground. Gravity is still pulling on you, but the ground is pushing up with equal and opposite force. (This is the 'Normal' force that can cross your eyes a bit at the start of a freshman physics class). There is zero NET force on you. You have to add up all the forces before you start doing motion calculations.

This was a fun and terrific segment - great cool visual science, and introductions to the deeper waters of information flow and delayed action. Plus, getting Neil deGrasse Tyson on pretty much always ads to the fun, regardless of venue. Bravo.

Dec. 14 2012 07:48 PM
Lexie from California

This information gives me nothing...................

Nov. 19 2012 10:05 AM
Sloppy from Stockholm, Sweden

The reason I like this story is because of the language used and the descriptions being presented. I appreciate that there are mathematical reasons why the slinky does what it does but those are not the "why" so much as they are the "Why we can see it" in the slinky rather than any other object.
I think "know" is a great word for it. "Is it the knowing of being observed that may change the behavior of a given particle?" Could do a great show on "knowing" with several crossovers to other shows.

A great short episode, Thanks

Nov. 03 2012 10:09 AM
Andy from California

Robert and Neil, near the end, and Neil especially, seemed almost ready to quote Hamlet on fate: "...if it be not now , yet it will come." Great episode!

Oct. 08 2012 07:44 PM
John Kerry from St. Louis, MO

So, in a sense, if part of your feet passed the event horizon of a singularity, your head would be the bottom of the dangling slinky.

Oct. 03 2012 05:07 PM
ProfAJO from UK

At what speed was the video clip captured and using which model of camera?

Sep. 27 2012 11:46 AM

I agree with "Ron Schoonmaker from Awake in science class" This is a simple physics problem, the slinky is trying to return to its original state, and thus the upward pull of the slinky from the bottom is offset exactly by gravity and thus the two forces cancel each other out.

Sep. 24 2012 01:32 PM
thisishannah from New York City

A fun video to illustrate NdGT's point about bullets: bit.ly/SgYPKz

Great breakdown! What's really interesting is the fact that we somehow expect matter to "know" what it is supposed to be, when in fact it's all just a bunch of molecules blindly following the laws of physics. What's really being illustrated here is that matter doesn't perceive itself the way we perceive it - a pencil doesn't know it's supposed to be "one thing." The molecules that comprise it just respond to the molecules immediately adjacent to it and to the forces that act upon them directly. The idea that objects have some kind of internal integrity beyond this is a simply a mental shortcut - its easier to call the thing you're writing with a pencil than a collection of molecules bound together in a temporarily stable solid form.

That's makes Radiolab so fascinating - it brings to light common ways in which the lazy or over-simplified ways we perceive the world and actual reality disagree.

Sep. 22 2012 12:47 AM
Tobias Toll

Sadly, none of the examples given in the show has anything to do with locality (except for the sun example).
When talking about locality one must talk about the speed by which a signal can travel through a system. For the examples of the tank ammunition and the arrow, the shockwave of the impact would travel through the projectile at the speed of sound in that projectile, in the case of the arrow that's at approximately 10 times faster than the speed of the arrow, which means that the back of the arrow knows about the impact much before it reaches the target. In ballistics this is a good thing, what you want is all the momentum in the projectile to hit the target at a small surface during a short time for maximum impact, you don't want many mini-impacts from each segment of the projectile.

When it comes to the slinky, some commentators have got it almost right. Again, the information travels much faster than any other scale in the system, in this case it's the information about the decreased tention in the slinky. What happens is that the tention in the slinky, T, is a function of its length l: T(l). If you think of the slinky as two equal masses m, connected by a massless spring, the downwards force on the upper mass is: mg+T(l), while the for the lower mass its mg-T(l) (notice the sign). When the experiment starts, mg=T(l), so the bottom part is in rest while the top mass accelerates by the force 2mg. But the tention is reduced when the spring is contracted so the bottom part accelerates as well, slowly in the beginning and then more and more. The center of gravity for the whole system though will accelerate with 2mg the whole time. Try to put a ball at the center of gravity of the slinky and let go of both at the same time, they will hit the ground simultaneously.

The information about the decreased string tention in the slinky travels again basically at the speed of sound in the slinky, which is much faster than what you can see with your eye. The example with the pencil, is basically the same as the slinky, but the spring-tention is MUCH larger.

Sep. 20 2012 10:46 AM
Murzi from San Jose, CA

I am ready to buy a RadioLab t-shirt, which says "I am the bottom of the Slinky". I may buy a few for my family and friends, too.

Sep. 19 2012 03:00 PM
Angel from Miami, FL

I would replace "know" with "hit". The bottom cannot "know" but it can be hit by the middle parts of the slinky. So when it's suspended in mid-air it's because it hasn't been hit by the segments above it. Since most other objects cannot dissect themselves like a slinky, the "segments" are actually rows of atoms. So when the arrow hits a tree the atoms making its tail end continue at the same speed until they fly into the atoms at the front end. It's a seemingly solid object so we can't see this compression the same way we see it in a slinky. How about an electron [microscope] camcorder? We'd be able to film the reaction at an atomic level when a flying arrow hits an object.

Sep. 19 2012 01:36 PM

I didn't buy the slinky explanation in the show (information flow) so I decided to try and solve it as if it was an assignment from a physics class. I created some free body diagrams to see all the forces at play and how they interact over time. My conclusion: Everything is behaving exactly as it should according to Newtonian physics - although if you had asked me before I heard the show or watched the video, I would not have predicted that the bottom would stay put like that. It is very cool.

No part of slinky is "waiting" for a memo. In fact, if you want to stick with the information metaphor the bottom part got a memo instantly saying "wait for us before you drop so we don't violate the laws of physics" - the law being that the center of mass of the entire slinky must fall at the rate of gravity (with the usual caveats about air friction, etc). If you watch the video closely, you will see that the top shoots down very quickly and slows down as it nears the bottom so that it can catch up with the center of mass by the time it reached the bottom of the slinky.

If you are intereted in how I calculated all this: I started with 4 masses connected by 3 springs at equilibrium. After the top is let go, I calculated the net forces/acceleration on each mass due to gravity and the springs and from that calculated the new position of all the masses and springs 0.1 seconds later. Then again 0.1 seconds after that, and again, etc, etc. The interesting thing was that the bottom mass really did stay stationary until the 4th time interval then it started to move. With 5 masses it would take 5 intervals, with 6 masses it would take 6 intervals. Extend this to an extremely large number of tiny masses, connected by an extremely large number of tiny springs, with an extremely small time interval and you basically have the slinky experiment.

Sep. 17 2012 10:06 PM
dmcg

Jtreml, I had the same exact question after I listened because my brain hurt after thinking about it and asked it to r/askscience on reddit. http://www.reddit.com/r/askscience/comments/1001n0/gravity_light_radio_lab_and_a_hypothetical/

Sep. 16 2012 10:22 PM

But what about Neil DeGrass Tyson's comment about the sun?

He had explained that it takes time for information to travel. I'm completely good with that and everything makes sense. What is the sun were suddenly whisked away. We wouldn't know it had happened for several minutes until the light that was 'in transit' all arrived at Earth and suddenly, it appears to us that the sun has disappeared.

But then he said something that peaked my curiosity. He said that, not only would be not know that the sun was missing because of the light, but also because we would continue to orbit the empty space where the sun was for those same couple of minutes. This raises the question - how fast does gravity 'travel'? That is, sure, light moves at speed = c. Is gravity also limited at speed = c?
Would we continue to orbit empty space for several minutes?
Or would we immediately fly off at a tangent because the mass of the sun wasn't there?

How can this question be asked? Has it been answered in a physics lab somewhere? I know that there is a lot about the nature of gravity that we don't know, but is this amongst those unknowns, or has someone cleverly worked this one out? If you can answer this, could you also please provide a citation for the work - I'd love to check it out myself (to the best of my ability)

Also, thanks Scott Woelber. You were able to clearly state what I was thinking was the answer to the slinky problem.

Thanks

Sep. 16 2012 04:56 PM
Pablo

I don't buy the vertical domono effect theory. Gravity acts on all parts of the slinky at all times, so to say the bottom rung levitates until the compression of the rungs above it gets to it and moves it just seems wrong. The constancy of gravity alone suggests there is something else going on. Also, since we are talking basicly about a spring in freefall, anyone got video of a slinky in space?

Sep. 16 2012 01:59 PM
Poet Economist (Jason) from Orlando

Inspired by this show:

Decentralization

Accounting for rounding,
Amongst such data as
The star’s circumference
And its distance from our Earth,
And the exact speed of light:
Eight minutes and seventeen
Seconds, maybe twenty.

If God should pluck the Sun
From the smack center of
Our system—no longer
“Solar”—we would not know it
Until such time had elapsed:
Blissfully prevailing,
Eyes blind to doom’s approach.

Working on flawless abs,
A minute per each pack;
Creating two perfect
Soft-boiled eggs in succession,
With yolks ideal for sloshing
Fingers of hoppy, whole-grained
Wheat toast into, just twice.

Eight minutes, seventeen:
A densely-packed short film;
Reading Whitman’s, “Song of
The Exposition,” aloud;
Indulging in Beethoven’s
Fifth Symphony, Movement one,
Andante non troppo.

Sex, nap, stroll,
Chat, Scowl, love
Smile, grow, fill,
Stir, spoil, live,
Tick, tock, tick.

Past the rising action,
Beyond its climaxed crest,
In fifteen’s second half,
Approaching fame’s denouement,
In early-ending spotlight,
Yet unfinished cosmic script,
Lectus interruptus.

Seventeen or twenty
Short seconds after eight
Minutes, some, now matter.
Only then, now, day darkness—
Forever night—consumes us
(a last three second gasp)
Sending Earth from orbit’s flight.
Uncentered, God-whimsied
ended light.

http://poeteconomist.blogspot.com/

Sep. 15 2012 02:14 PM
Burkhardt

Ron, you are incorrect. Information cannot travel faster than the speed of light. This was one of the breakthroughs of Relativity. Turns out the effect of gravity travels at (almost exactly) the speed of light. If the sun were to instantaneously vanish, we would have no indication for 8min 20sec, as stated in the podcast.

Your explanation of the slinky is also flawed. Without going into details, it appears as though you've forgotten that the entire slinky feels the force of gravity.

Sep. 15 2012 12:28 PM
Ron Schoonmaker from Awake in science class.

I respectfully disagree with the idea that the "let go" information is passed from the top down. When held, the turns of the Slinky have two forced in equilibrium: The desire to spring back together where it is held at the top (compression) and the force of gravity which pull them downward and apart. At the point of release, the Slinky is divided into two halves: the top half sees combined forces pulling DOWN (Gravity + compression), while the lower half still feels the compression in the *opposite* direction of gravity. Thus, the lower portion of the Slinky does not move because the opposing forces cancel each other out. Each turn of the Slinky starts to fall when the gravity force overcomes the upward compression starting from the top and moving downward.

Also, I disagree with the explanation of the bullets vs. rods as being only due to shape. Assuming the rod is still the same weight as the bullet, it's still basic physics of momentum being stopped by a small area. It's why a ball peen hammer can be more deadly than a sledgehammer.

Finally, there is some information that is propagated much faster than the speed of light. "Action at a distance" is very important in quantum physics and gravity. If the sun (and its mass) were to be instantly poofed out of existence, we would have a wild ride for eight minutes, twenty seconds until the light reached us and let us know what happened. The light propagates at "c" but action at a distance is instant.

Sep. 14 2012 09:24 PM
Tony

I think this concept was the inspiration for the entire Roadrunner series: http://www.youtube.com/watch?v=Gq_bjaI0NTo

Sep. 14 2012 04:10 PM
Jayla Diggins from lewisville texas

Hey Guys,

Thanks for the Podcast and thanks for taking you time to make such. I wanted to say good story and i have learned alot.

Sep. 14 2012 02:49 PM
eight18pm

if I'm always the bottom of the slinky, then I'm always levitating!

Sep. 13 2012 12:15 PM
Kellam Clark from Brooklyn

Hey Guys,

Anti-tank ammunition is made from Depleted uranium. I mention it because it is important to know. This does not mean a rod will not behave the way suggested in the show but deleted uranium works way better. It is very dense and brittle, also when it fractures apart it enters combustion to create a greater amount of heat then just your standard friction from say steel. We have (Americans) for a long time (since the gulf war) been using depleted uranium in our ammunition (smart bombs as well) and tried very successfully to keep it out of common knowledge. The fine vapor and dust from the munitions are fatal. They give off beta? gamma? Rays that would normally not be able to penetrate even a news paper let alone skin but when they enter the blood stream through inhalation are deadly. I just don't want people going around thinking that antitank munitions are made of simple steel rods. They are way more potent and high tech then that. Most importantly they are much more lethal and contradict several treaties we have signed that address leaving long lasting ill affects on the battle field. Also excuse the laymen's tone. I happen to know this stuff but am not an expert. I love the show and thank you for your interesting work.

Best Kellam

PS, Depleted uranium was also for a short while used to make cheap metal products like forks and knives, it can be found in planes as a ballast due to its ex stream density aka weight.

Sep. 13 2012 01:29 AM
Troy McConaghy from Burnaby, BC

Information will propagate along the slinky at the speed of sound (in the slinky material). If the slinky is made of steel, that's about 6100 m/s.

The slinky top starts at rest, and accelerates downward once it's let go, but it will only get up to a speed of around 10 m/s (an order of magnitude estimate from v = gt where g ~ 10 m/s/s and t ~ 1 s).

The explanation given assumes that those two speeds are the same, but they're not. They differ by two orders of magnitude.

Sep. 12 2012 11:06 PM
DA from Pasadena, CA

It’s a cool “trick” and looks awesome in super slow motion, but as others have said, why the terminology, personification of the slinky, and philosophical implications? Physical actions, whether they are vibrations, sound waves, light waves, or otherwise, take some amount of time to propagate through their medium. Like Jose Murillo said, the bottom rung only needs the tension that exists between it and the rung above it in order to remain in equilibrium. That tension doesn’t change until the rung above it begins to fall, and so on up until the top rung, beginning when the hand is removed.

Sep. 12 2012 12:43 PM
Ms. from NYC, NY

Perfect fun--animated ideas are perfect for kids and kids at heart--the associations to weaponry, the nature of everything, the wave reality and it's metaphorical potential extending into the philosophical, psychological implications resulting in that fabulous "You are the bottom of the slinky."--Brilliant!

Sep. 12 2012 08:40 AM
Scott Woelber

At t=0, the bottom of the slinky is not in motion because the force from its mass and g (F = mg) is equivalent to the upward force from the spring constant (F = kx). The slinky is stretched to its equilibrium length because x will increase until kx = mg. As the top falls, both the force from g and the spring constant are decreasing at the exact same rate. So, just as the upward force from the spring is decreasing, so is the mass that the spring is supporting. The downward force and the upward force are constantly equal and opposite so the net force on the bottom of the slinky is constantly 0.

Sep. 11 2012 11:12 PM
Johnny Logic from Portland, OR

If anyone is interested in the relationship between physical information, the principle of locality, and measurement, this paper provides an interesting (if mathematically and conceptually demanding) summary: http://arxiv.org/pdf/1110.4630.pdf

Sep. 11 2012 06:33 PM
Johnny Logic from Portland, OR

Regarding those disputing the terminology-- 'information' is an ambiguous and possibly misleading term, but there are notions of physical information which are substantive and widely used in physics: http://en.wikipedia.org/wiki/Physical_information

However, the slinky "knowing" about the situation is pretty straightforwardly problematic unless we are speaking metaphorically (which they are unless they are pansychists).

Great episode, in any case!

Sep. 11 2012 06:15 PM
Max Osterhaus from Oakland, CA

I agree with some other commentors, it makes no sense to talk about knowing in this context. The slinky doesn't "know" anything so you are making this more profound than it is! It's just Newtonian physics: the bottom of the slinky does not move until one half of the force holding it in equilibrium is removed, then it falls (or is pulled more toward the earth).

Anthropomorphization can be fun, but can also be dangerous scientifically and even socially!

Sep. 11 2012 05:58 PM
Jose Murillo from Tijuana, Mex.

This "hasn't gotten the message" explanation doesn't work for me. That bottom rung doesn't fall because it is supported by the rung above it, and so on.It is all the support it requires. It does not need the support of the upper already falling rungs. Just the one above it.
Think of it sideways like dominoes. You knock over the first one but the last one doesn't fall till something change for it. It is struck by the preceding one.

Sep. 11 2012 04:52 PM
Brian from Minnesota

I love thoughts like this! However, I disagree with the notion that "You're always the bottom of the slinky." How does the top of the slinky feel? It's been on a downward spiral for some time now and the bottom of the slinky does nothing but bury its head in the sand! Is the top discouraged that no one listens to it? That no one has heeded its warning?

"Dear bottom of slinky, you're next. Don't think you're immune from this." - T.o.S.

Does it get sick of always being the trendsetter? Perhaps we're sometimes the bottom of the slinky but sometimes we're also the top.

Sep. 11 2012 04:33 PM
Theo

Without gravity the slinky would collapse from both ends towards the middle. With gravity, the force of the retraction upward against the mass of the top cancels out with downward force of gravity at the bottom end, until the top gets to the bottom and the slinky doesn't retract anymore. Am I at all correct?

Sep. 11 2012 03:38 PM
markodore64 from Philadelphia

Fascinating subject—but why this terminology? "Knowing" and "information"? Either it's not sufficiently explained in the episode, or there is a problem here: Personifying physics (like personifying, or attributing 'mind' to, say, evolution) is a misleading leap, no?

Sep. 11 2012 01:27 PM
JT from Lebanon, TN

Fascinating!

Sep. 11 2012 01:01 PM

What a great description of information flow - it reminded me, in a way, of the idea of the "adjacent possible" as described in Steven Johnson's book Where Good Ideas Come From and WSJ article http://online.wsj.com/article/SB10001424052748703989304575503730101860838.html

Information, ideas, possibilities... all travel from point to point to point through individual connections.

Sep. 11 2012 08:33 AM

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