O~,IEG4 The Int. JI of 5,1gmt Sci. Vol. 11. No. I. pp. 99-105, 1983 0305-0.-t83 83 010099-07503.00 0 Printed m Great Britain. MI rights reserved Copyright ~ 1983 Pergamon Press Ltd

Innovation as a Cause of Organizational Strain

COXStDER a company as a black box with an input function f(t) and an output h(t), the transfer function being g(t). which describes the company - - t he black box - - and the transformation from the cont inuous input into the output.

Industrial dynamics, developed by Forrester E2], is a computer modelling technique for describing the com- pan.~ as a system. The description is made by difference equations and a set of different dimensions or par- ameters describing the operation of the system. The pure mathematical approach to a black box problem, often t.tilized for a coherent set of signals (e.g. electronic impulses to and from an electronic circuit`), is by means of Laplace CI, 7] transforms.

The black box approach can be used as an analogy, since while a company handles a large number of inputs and outputs which do not have a smooth analytical form. the simplifications used here are useful in that they indicate what the system might ideally be like. I am making two basic general assumptions: first, that a smoothly changing input signal creates a smoothly co- varying output signal, and second that some time delay is involved in generating the ou t pu t - - t ha t is, the ups and downs of business cycles are responded to with some time lag. Ideally, the company would like to see them smoothed out.

Thus. if a business cycle variation is introduced, starting from zero it could take the sinusoidal form of

f(t) = a sin wt

where a is the amplitude and w the angular frequence. The response is described as

h(t) = b sin(wt + ~,)

where b is the resulting amplitude of the signal (in most cases b should be smaller than a, representing the smoothing out of the variation) and ~ is the time delay.

The second assumpt ion is that radical invention- innovation means a quan tum step, i.e. it can be described as a step function suddenly changing the "level" of a s ignal-- implying the sudden emergence of a new signal where previously there was none.

The Laplace transforms of f(~,) and h(t,) are

w F(s) = u ,

s - + w -

and

(w-cos :~ + s-sin c0 H(s) = b ,Q + w-'

respectively. The transfer function G(s) is then given by G ( s ) F(s) = H(s). i.e.

w ',v'COS ~ + .s.sin 0~ G(.~)-a- , . = b S- + ,..2 $2 + W2

so that

G(s) = " co s : ~+ - ' s i n ~ . w

The Laplace transform of the step function, here representing radical innovation and assuming that the step has a height of one unit (equal to omitt ing a proportionality factor), is l/s. In this case the response Hi(s,) would be:

i cos , + '_ s n,) G(S) ' s = a ks w /

Thus the response to the simple step function ( 'innovation'} consists of two terms in the response function:

b - . cos :(, (step function) (1') a

konst. 6(t), (delta function, nail). (2)

From the first term {1) we see that the step function is, essentially, passing through the system attenuated by the same amoun t b/s as the sinusoidal function. We also see that the effects may diminish the more the time lag in the system approaches 90" (cos:~ = 0 when

= 90°). It was only to be suspected that the step function would generate another step as an output.

The second term (2) is of greater interest, however. Again the at tenuation factor b/a appears, together with sin ~. which has its maximum value when cos:~ is 0 and vice versa. But what is most interesting is the generation of an even more genuine discontinuity than the step function, the delta function 6(t~, often described as a "nail' of infinite height and infinitesimal duration.

Wha t we have demonstrated is that a system developed to cope in a cont inuous way with a cyclic change of a smooth signal responds to a step function in a very nasty way. Strains and disruptions are in- evitable. The discontinuity is of a singular nature and cannot be coped with. Either the system breaks down, or the step function is rejected. The conclusion is simple: the same system, the same transfer function, cannot take care of both the smooth change and the radical.

From the outset, I have been modest about the extent to which one may draw upon this hypothetical compu- tation. Still, one should remember that a more complicated signal pattern can be divided up into harmonics, that is, into a sequence of sinusoidal waves with wavelengths that are multiples of the smallest in the series. The results obtained in the analysis would hold also for such a treatment, only there would be a whole set of delta functions generated.

Actually, if response is immediate, sin -, would be 0, and consequently the delta term would be zeroed out. And with w a small number equal to a system designed for slow changes, the impact of the step would be larger. Again, common sense and the mathematical properties derived from the simple assumption converge. For example, if it is true that the electronics industry is more responsive, then it should find innovation easier to cope with; and, in fact, organizations do innovate.

99

lot) 3.l emorunda

Either the black box the organizat ion-- is designed to treat ,tep ft, nc t ions- inno~at ions- -separa te ly , or it is des*gned to take c,.cltc, smooth changes less seriously.

DISCUSSION

The most ob vious current example of technical change. taking place nearl.~ as a step function, is the rapid de- velopment in electronics. There are numerous examples of companies which reacted in accordance with the mathematical analogy developed here. i.e. they believed change would take place in an incremental way. But e~en companies that were aware of the drastic change ahead failed to act on that knowledge sufficiently rapidb despite their own previous experiences[l 1~].

One conclusion to be drawn from the mathematical treatment of the problem might be that, within the same company, one organization shovld care for the smooth current business and a separate parallel organization should be set tip for the realization of radical change. The literature, of course, abounds with such advice [4. 5.8] and some companies seem to have acted upon it [10]. Another prescription profitably implemented in the case of electronics was to establish a task force to introduce the inno~ation, so far separated from regular operations that it was even kept a secret [3].

The mathematical treatise here would seem to substantiate the advice often given to American in- ventors: offer your invention to a company that is in a lot of trouble. Such an organization has anyhow failed to cope with smooth change and its ability to fend olt step ch:mge innovations would therefore be smaller.

At first sight, the description of one company and its relation to one innovation, one step change, might seem dillict.lt to link to long wave theory, where innovation itself, in aggregate, follows a cycle. Following Mensch [6], howe~er, innovation is radical at the beginning of a ne~ cycle. Apart from the fact that the fate of one company might be of considerable importance to its owners and employees and even to a small country, the result of the mathematical ex~:rcise here lends certain credibility to Mensch's idea of the long waves being effected throt, gh 'metamorphoses" [6]. The mathe- matical functions might possibly be linked up so as to cause a final "breakthrough'-- the wholesale departure from old investments and embarkat ion on a new wave. The importance of this subtle argument is underlined by the fact that no company that did not participate in the early development of a new innovation has ever succeeded, by internal adjustments only, in adopting it in a substantial and successful way [9]. (The acquisition route is. of course, a different matter.I

Finally, the results indicate some ideas for future and more empirical research. As hinted, organizations

de~eloped to cope with "step functions'--Iike the elec- tronics indus t ry- -might pro,.ide patterns that could guide other industries as well. The idea ~ould then be to look for management teams, managerial practices and organizational features which diminish the efficiency in handling incremental change while enhancing the tolerance to drastic change. Such a study must. of course, be carefully designed to a~oid becoming merely tautological.

Another prediction also resutts from the mathematical analyses. Organizations which are. basically, following the business cycle and those which behave counter- cyclically would seem to display ~ery different potentials for bolstering step change {though the value of :c might be said to be set arbitrarilyL Again, carefully collected data might help to improve on our current organizational theories.

REFERENCES

I. DoliTsctt G (19431 Theorie and Anwendung der Laphtce-TransJbrmation. Do~er Publications, New York.

2. FORRESrER JW (1961} Industrial Dynamics. MIT Press, Boston, Massachusetts.

3. HOLLOMON JH (1980) In Current lnnoc~ttion (Ed VvDtx B-A). Ahnqvist & Wiksell, Uppsala.

4. Lt~vrr-r T 41963) Crcativit? is not enough. Harc. Bus. Rec. 41 (31.

5. Mal,tC'l! JG & SIMON HA {19581 Org~mizution.s. John Wiley, New York.

6. MENSC,I G (1979} Stalemate in Technologlv. Ballinger. Cambridge. Massachusetts.

7. SAVANT CJ Jr {19621 Fundamental ~g ttte Laplace Trun.sJbrmution. McGraw--Hill. New York.

8. SrI-:I'LE L (1975) Innocation in Big Business. Elsevier, New York.

9. UrTF.RI~ACK JM (1981~ Innovation Seminar at MIT Industrial Liaison Symposium. 13 November 1981, London.

10. VEI)IN B-A (1980) Corporate Culture ti," lnnorution. Studentlitteratur, Lund.

11. WALLANDER J (1979} Om proqnoser, budgeter och Ifingtidsplaner. Svenska Handelsbanken. Stockholm.

Bengt-Arne Vedin {July 19821

Studief6rbundet N&inqslic & Samhalle SkiJhlunyagatan 2 S-I {,t27 Stock!udm Sweden