I gave a version of this talk this morning at the excellent “Digital Landscape” event at UCD. Colm Long (Facebook), John Herlihy (Google), Martin Murphy (HP), Eamonn Fallon (daft.ie), Dylan Collins (Jolt), John Breslin (DERI and Boards.ie) Kim Majerus (Cisco) and Damien Mulley were the panellists in two excellent panel sessions. Minister Eamon Ryan opened the conference. Aileen and Fiachra at Amas have written a posting on some of the discussions. Silicon Republic has also posted on John Herlihy’s views of the future of desktops; Dylan Collins’ views on the efficiency of internet start-ups; Colm Long on virtual money; UCD’s Paul Haran’s views on fixing the Irish economy; and Eamon Ryan’s comments on broadband and a CIO for the Government. (Happy to cross-reference any further posts here on the event if you would let me know of any that I’ve missed…)

I myself had been asked to speak about “digital strategy”. I was asked at short notice to keep my presentation short, since it was nearing the end and the event was running over time at that point. My posting here therefore is not exactly the same as I presented, but close enough.

I started what I hoped would be a fun talk by observing the importance of mathematics in the economy, and that Engineers Ireland (of which I’m current non-exec President) had recently published an extensive report on the education of mathematics and science in our primary and secondary schools.

I also noted that I am an engineer, and felt a little misplaced amongst the elite of the UCD Business Alumni and Smurfit Business School – I have never done any sort of business degree… 🙂

For me personally, the true value of mathematics is the training it gave me in spotting patterns. Observing commonality in different situations, abstracting and learning from these to produce a generalisation, and then finally applying a specific generalisation to solve a new situation which I have never met before. As an engineer, and even more so as a software developer, these are absolutely critical core skills. In the world of rapid technology change – “we are currently preparing students for jobs that don’t yet exist, using technologies that haven’t been invented, to solve problems that we don’t even know are problems yet” as “Shift Happens” notes – we need analytical skills for life..

I then teased the audience – can you spot the pattern in the following powerpoint slide ?

So: what happens to the newpaper industry when advertising revenues collapse ?

What happens when customer acquisition costs run down your investors’ shareholder funds ?

What happens when a highly popular TV journalist is inspired to join a political party, attracts votes but then languishes on the back stage ?

What happens when a car runs out of fuel (gas) ?

All of these systems appear to be examples of negative feedback. In engineering terms, negative feedback is the fundamental technique used to enable an output signal to track and follow an input signal, albeit amplified or diminished in some form. For example, an amplifier bolsters an input signal, but is designed so that the output signal faithfully follows the input. If the input increases, so does the output in proportion. If the input falls, so does the output. The amplifier works by comparing the difference (subtraction, negative) between the output and input signals, and tried to ensure that the difference in trend is minimised, and distortion is minimal.

Cool for amplifiers. But not cool for the systems above. If the advertising revenues dry up, a media business may be in deep problems. If the cost of customer acquisition is not being met by the rate of new customer growth and purchasing, then investors funds will be run down and your company dies. If a highly popular TV journalist loses the steady stream of plaudits while in the bowels of some political party, he/she may become a little disillusioned. If the car runs out of fuel, the car slows and then stops.

Control systems, such as amplifiers, work on negative feedback. But what we want — what you need to engineer for your business and for your digital strategy – is positive feedback.

In control systems, positive feedback means the output signal is added back into the input signal:

Positive feedback is cool for a business. It’s magic! It’s what we all strive for. It’s like a perpetual motion machine. It’s like nuclear fission, where a chain reaction is established of neutrons from each exploding nucleus go on to cause more to explode, releasing yet more neutrons.

Positive feedback is self sustaining. Even though the input has disappeared, the output keeps growing. Acoustic (sound) engineers do not like positive feedback in their amplifiers: but in business we do want to engineer positive feedback:

Here, even though the input (green line) falls back again to zero (the car’s fuel is exhausted…there are no more investor funds….the plaudits have gone…there’s no advertising revenue…) the output (red line) just keeps getting bigger and bigger, even if it does take a little temporary set-back for a while when the input falls.

This is what the web guys call going “viral“. This what twitter, facebook, skype and ning – and several others – have successfully done. For each new customer, at least one further customer prospect is introduced to the system and becomes yet another customer – and the loop repeats.

In considering your business strategy – including your digital strategy – have you thought about the flows in your business – particularly your customer and prospect flow ?

For each new customer prospect you have, what is the conversion rate – the probability – that that prospect converts into a real customer (K1 in the diagram) — and how long does it take for the conversion to actually happen ? And for each successful conversion, does that customer create at least one and hopefully more prospects (F1 in the diagram) which each in turn are potentially converted, and so on ? And how long does it take for each successful customer to create the new prospect(s) ?

What can you do to increase the conversion probability (K1) ? And the multiplicative effect (F1) ? And what can you do to reduce the transit times through the flow, and drive the “engine” faster ?

In IONA, I’ve written elsewhere in this blog (eg here and here) about various tactics we used to manage this positive feedback loop – driving out business on cash-flow; leveraging competitor’s marketing spend; applying a “trojan horse” model to get a beachhead; the network effect of technology adoption; and so on.

Of course, in practice, your company may have a more complex flow:

For example, prospects who turn into real customers for one offering (K1) may in turn be prospects for a follow-on “upsell” offering (K2), with both streams potentially generating further prospects (F1 and F2) for the first offering. Or:

Here customers of your second offering only generate further prospects (F2) for your second offering; and likewise for your first offering (F1).

You can envisage many different potential flows, with multiple stages, depending on your business. Do you know what the flow model is for your business – and what do you want it to be ?

Its all very well building a flow model, but how do you optimise it ? If you have limited resources (shareholder funds, debt, retained profits and staff) is it better to place a higher priority on the first stage (K1) or the second (K2) ? Do you want higher viral rates for the first stage (F1) or the second (F2) ? How do these various parameters play off against each other, and where is the maximum bang for the buck ?

Interesting questions. Pattern time again – mental shift.. Imagine you are given the responsibility of creating a smart economy. And you only have limited exchequer funds. What do you do, and what policies should you have ? Precisely the kind of questions we have faced in the Taoiseach’s Innovation Taskforce, which I have written about elsewhere.

A (simple…) model of a smart economy might be a positive feedback loop as follows:

The cumulative number of new start-ups entering the economy, from new entrepreneurs for which this is their first start-up in the economy, at a given time t is N(t).

The number of successful firms produced at time t is S(t) – by success, I mean in this case, successful exit – change of majority ownership via an IPO or acquisition.

The number of entrepreneurs serially starting their next business after a success (or fail), together with the number of new spin-outs from existing companies, at time t, is R(t).

E(t) is simply N(t) + R(t) — we want positive feedback!

Let k be the average probability that a start-up is successful. Let r be the average probability that an entrepreneur serially starts a further business. Let p be the average number of spin-outs created by each successful company. Let d be the average (delay) length of time it takes a start-up to succeed or fail.

Let’s assume that the number of new entrepreneurs entering the economy to create start-ups grows at a steady rate, so that the cumulative number of start-ups at time t is N(t) = at — a is the steady rate.

What then is the number of successful companies S(t) at any time t ?

To solve this, a mathematician or engineer (maybe perhaps a macro-economist ???….) can probably show you:

where I have used the usual Laplacian transform to convert from the time domain t to the s domain:Then it is simple arithmetic gives (remembering it is a positive feedback loop) E(s) and hence S(s) in terms of N(s):andwhere B is just shorthand for r(1-k) + pk.

Now, if we assume a cumulative steady ramp of new entrepreneurs and start-ups, as we discussed above, then:and:and hence in this case (cumulative steady input ramp):Some reasonably standard mathematics, which I won’t reproduce here in the interest of space, uses both the sum of an infinite geometric series and the second Laplace shift theorem, to convert S(s) above back into the time domain S(t):where Un is the usual unit step function Un(t) = 0 for all t<0, and Un(t) = 1 for all t>=1.

Looking at the equation carefully, it is indicating that the number of successful firms S(t) emerging from the innovation process pipeline is in fact a series of ‘ramps’ or ‘steps’, almost like ‘shifting gears’. Initially there are no successful firms at all, until the first ones emerge after a delay of d (years say). Then successful firms start emerging at a rate of ak (per year say): a is the input rate of entirely new start-ups entering the pipeline (per year), and only k % of them are succeeding after a delay of d (years) – hence the output rate is ak. This represents the transition from ‘neutral’ to ‘first gear’; or the first ‘ramp’.

Then, after a delay of 2d (years), a second wave of successful firms start emerging at a rate of Bak, in addition to those who are still emerging at a rate of ak. This second wave is those firms which have been spun-out from successful firms d years ago and now themselves are emerging as successful; together with those firms which entrepreneurs recycled d years ago to start, and which also now have been successful. This is then a shift from ‘first gear’ to ‘second’; ot the second ‘ramp’.

After a further d (years) – or 3d (years) in total – a third wave of successful companies start arriving at a rate of B^{2}ak. These are those firms founded by entrepreneurs who recycled twice and succeeded; and spin-outs who succeeded and in turn created spin-outs. And so on.

Plotting this using some selected values for k, p, r and d, we get graphs such as follows:

Initially, the number of successful start ups (the red line) emerging is less than the cumulative number of fresh start-ups (green line), but after a time, the number of successful start-ups rapidly climbs as the positive feedback loop takes effect.

All of this is to say, that with suitable policies and eco-system, in principle an environment to encourage a large number of start-ups is possible. And for the Irish smart economy, we cannot wait around for the red line to overtake the green one – we need jobs now as well as in the future. So this feedback analysis is only part of a possible total solution…

More complex circuits – such as the double stage systems we looked at above – are also readily amenable to normal circuit analysis.

A similar analysis to that of the smart economy strategist of course can give you valuable insight into how to best construct a positive feedback loop, to “go viral”, in your company and in your digital strategy.

Or perhaps to design a perpetual motion machine 🙂 Or a car which would not need fuel 🙂 Or newspapers that would not need advertising revenue 🙂 Or happy politicians 🙂

We do need mathematics skills in our economy….

Chris,

I like the feedback loop you show and, having observed the success rate of the spin-outs from each of the teams that have completed good technology exits in Ireland, it is clear that increasing the number of people who have had this experience is ultimately key to scaling up the smart economy.

I’m amused by your mathematical presentation of it though, in the light of an experience I had last week. I’m trying to bring forward some of this feedback by creating an incentive for large Irish-based companies to spin-out some of their in-house developed technologies. To this effect I’ve drafted an amendment to the Finance Bill 2010 (with a subtle change to the R&D tax credits regime) and it was proposed in the Dáil last week by Fine Gael. It got a guarded welcome from the Minster for Finance and may yet go through.

Last week I tried to get some press coverage for it but was repeatedly told that it was too complex to cover. Good luck to them trying to present your model!

Pearse Coyle

PS Before it comes back before the Dáil or Seanad in the coming weeks I’d welcome an opportunity to explain the amendment to you in an effort to get your backing for it.

Pearse,

The Innovation Taskforce report is due to be published late next week I believe (11th) and also contains some recommendations specifically on tax R&D credit, as one part of creating the feedback engine which my post discusses – so it will be interesting to compare notes between the thinking of the taskforce and yourself.

Once the report has been published and you’ve had a chance to take a look, maybe we could grab a coffee ?

best

Chris

Chris,

Will do – thanks for the reply. Please send on an email address or phone number.

Pearse pc@CorporateSpinouts.com

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Chris, this maybe of interest, its an idea for a feeback mechanism in the public sector, its very simple but ties in with you speak about above.

Its on the your country your call website.

http://proposals.yourcountryyourcall.com/ct/ct_a_view_idea.bix?i=3B6E98B8

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