# Network numbers

An article in the Guardian recently caught my eye: Why web.2.0 adds up to a revolution for our industry looked at the maths of networks and how they apply to different networks for carrying information.

It got me to thinking: how do the numbers really shape up? What would my ‘number’ be? And are they already too scary to contemplate given that the pioneers of broadcast media promotion would have started with much smaller numbers? Or is it just perception – was the risk still there even with smaller multiples?

She’s a model and she’s looking good

There are three models. I’ll try and summarise quickly so I can get to my point.

• The first, for broadcast, is one-to-many and named after the broadcasting legend David Sarnoff. It takes the relationship between viewers and possible interactions as parity: a broadcast to 20 recipients as a point value of 20. In other words, 20 people would receive the broadcast but that’s where the interaction, and possible number of connections, ends.
• The second, for email or telephone, is one-to-one. Named after Bob Metcalfe, it takes the number of participants and raises them to the power of two. This is because all the participants are singly interconnected. A network of 20 yields a Metcalfe score of 400.
• Then there is the web. This many-to-many relationship goes another order of magnitude higher. Because everyone can talk to everyone else, this network – named after Professor David Reed – calculates the number of connections as two raised to the power of the number of participants. So a network of 20 has a Reed value of…

… and this is where the article piqued my interest. “Over a million,” it said. “How many over a million?” thought I. So, in my slightly geeky, probably autistic way, I opened a spreadsheet, saved it under the name ‘netwroks.xls’ (sic – I have a headcold), and figured it out. Precisely, it’s 1,048,576. So, just over a million then.

The point of the article was that this is essentially the same interaction we see everyday but in the Web 2.0 world the constraints of time, geography and cost are removed. That is why these numbers are so real and so scary. They hold potential for huge gain or huge loss, and thereby huge risk.

Eins, zwei, drei, vier, fünf, sechs, sieben, acht

But what exactly are these numbers? Let’s employ netwroks.xls to find out.

Friendly Ghost, at time of posting, has 162 subscribers. Let’s chuck it into the spreadsheet and see what comes out. The maths states that I have a Sarnoff score of 162 – one to one – and a Metcalfe score of 26,244. In other words, if all my subscribers could email each other, they could have 26,244 separate interactions. Cool.

But my Reed score would be – stretch that column out and change the format so I can see the figure because those funny scientific notations don’t mean much to me – 5, 846, 006, 549, 323, 610, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

That’s an awful lot of zeroes. So many it even starts to spell ‘ooooOOOoooo’.

Let’s look at some of the more popular on the PowerPR index. Of those that advertise their subscribership, Neville Hobson is rated highest. His Sarnoff/subscription figure is 1,704. So, his Metcalfe score is 2,903,616. His Reed figure is – oops, here we go, Excel can’t handle it. We get a NUM! error. So, Neville Hobson is off the scale.

So are the Online Marketing blog (Sarnoff 8,983, Metcalfe 80,694,289) and PRSquared (Sarnoff 1,143, Metcalfe 1,306,449). Excel is borked.

Let’s down the ante. Wagner Comms has a Sarnoff of 334 and Metcalfe of 111,556. This gives it a more manageable Reed figure. It’s a mere 34, 996, 011, 596, 528, 200, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

Canuckflack is lower on the PowerPR index but has a higher subscribership (an object lesson in the weakness of the index if ever there was one). Sarnoff 535, Metcalfe 286,225 and Reed of 112,472, 844, 863, 580, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

Wow. This webpage would be borked too if I hadn’t put those spaces beween the zeroes.

Time. Travel. Communication. Entertainment.

I need to stop going ‘wow’. We’ve had a bit of number-related fun. Let’s think for a second. It’s hardly surprising that we’ve yet to embrace Web 2.0. These numbers scare the willies out of us. They are astronomical. But then, when newspapers came about, there must have been some brave soul who put the first ad in there. Same for broadcast: who put out the first commercial on radio, or TV? Who had balls enough to dip them in the cold waters of what was then ‘new media’? I’m talking advertisements here because, well, PR is probably more difficult to quantify in terms of who was influencing the influencers, so to speak.*

The first paid-for British TV ad was for Gibbs toothpaste – and, by the miracle of YouTube, here it is!

Its style is jerky and uncertain. Hardly surprising. It was after all a step into the unknown.

The first British radio commercial was for Birds Eye foods in 1973. Sadly there is even less information about that online (we need an audio equivalent of YouTube). My guess is that it was slightly more sophisticated by comparison. The first clickable banner ad was sold in 1973 by Global Network Navigator (GNN), to law firm Heller Ehrman LLP, when the total domain name database registered 4,000.

Beam myself into the future

These were all the acts of people with the foresight to see that the new media was simply another vehicle for promotion. And yet, even though they ramped up through the multiples of network numbers, they all started at a very early time in every media. Was the risk any less? The numbers were certainly smaller.

Web 2.0 is here now. It’s massive, and massively interactive. Quantitatively and qualitatively it is different. I cannot deny that the other day I read some broadsheets and the thought crossed my mind that the high quality of journalism displayed was a strong argument simply to concentrate on the industry-strength solutions, that is, the huge influence and comparatively low popularity of more traditional media. Perhaps we really shouldn’t get involved with the amateur rumour-as-fact blogosphere, and just let them talk amongst themselves while we get on with real jobs in the real world.

We’re charging our battery

But then, what would we lose? Action could provide us with so much. It could even cause us to lose so much. Inaction will certainly cause us to lose out. Perhaps we should stop worrying about the figures, get our heads down and just go for it.

* Advertising and PR are difficult to categorise anyway. Who’s to say what the first examples were? Signs painted on walls in Babylonia could have been the first adverts, but then again so could any cave paintings, which probably said “This is our domain” or “We have magic” or “Ouch, I wish I’d been more careful with that axe.”

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## 2 thoughts on “Network numbers”

1. Billyuns and Billyuns of connections!

You know, we can spend a lot of time trying to apply theoretical models to imperfect measurements – but I’ll tell you that my three blogs have very disparate audiences and goals.

For instance, sosaidthe.org has an imagined audience of three dozen, tops.

I think I’ll play around with these ideas over at my place.

Thanks!

2. Colin, just for the purposes of clarification…

…is that the standard “American billion” that equals 1,000 million — or the “British billion” that is one million million?

I’m guessing that your “billyuns and billyans” reference is to the late Dr. Carl Sagan, which makes it the American figure. Although the “British billion” would be more appropriate for these astronomical figure, by roughly three magnitudes.

Ghost – I may not know exactly where I fall in the taxonomy of communications bloggers, but add me to the Math Nerd Index.