Gartnet’s Hype Cycle Gartnet’s Hype Cycle . . . Gartnet’s Hype Cycle . . . Gartner’s Hype Cycle: Our Explanation Our Explanation (cont-d) A Simple Explanation Our Explanation (cont-d) Our Explanation (cont-d) Jose M. Perez and Vladik Kreinovich Home Page Department of Computer Science Title Page University of Texas at El Paso El Paso, TX 79968, USA ◭◭ ◮◮ jmperez6@miners.utep.edu ◭ ◮ vladik@utep.edu Page 1 of 8 Go Back Full Screen Close Quit
Gartnet’s Hype Cycle 1. Gartner’s Hype Cycle Gartnet’s Hype Cycle . . . • In the ideal world, any good innovation should be grad- Gartnet’s Hype Cycle . . . ually accepted. Our Explanation Our Explanation (cont-d) • It is natural that initially some people are reluctant to Our Explanation (cont-d) adopt a new largely un-tested idea. Our Explanation (cont-d) • However: Home Page – as more and more evidence appears that this new Title Page idea works, ◭◭ ◮◮ – we should see a gradual increase in number of ◭ ◮ adoptees – Page 2 of 8 – until the idea becomes universally accepted. Go Back • In real life, the adoption process is not that smooth. Full Screen Close Quit
Gartnet’s Hype Cycle 2. Gartner’s Hype Cycle (cont-d) Gartnet’s Hype Cycle . . . Gartnet’s Hype Cycle . . . • Usually, after the few first successes: Our Explanation – the idea is over-hyped, Our Explanation (cont-d) – it is adopted in situations way beyond the inven- Our Explanation (cont-d) tors’ intent. Our Explanation (cont-d) • In these remote areas, the new idea does not work well. Home Page • So, we have a natural push-back, when: Title Page ◭◭ ◮◮ – the idea is adopted to a much less extent – than it is reasonable. ◭ ◮ Page 3 of 8 • Only after these wild oscillations, the idea is finally universally adopted. Go Back • These oscillations are known as Gartner’s hype cycle. Full Screen Close Quit
Gartnet’s Hype Cycle 3. Gartner’s Hype Cycle (cont-d) Gartnet’s Hype Cycle . . . Gartnet’s Hype Cycle . . . • A similar phenomenon is known in economics: Our Explanation – when a new positive information about a stock ap- Our Explanation (cont-d) pears, Our Explanation (cont-d) – the stock price does not rise gradually. Our Explanation (cont-d) • At first, it is somewhat over-hyped and over-priced. Home Page • And only then, it moves back to a reasonable value. Title Page ◭◭ ◮◮ ◭ ◮ Page 4 of 8 Go Back Full Screen Close Quit
Gartnet’s Hype Cycle 4. Our Explanation Gartnet’s Hype Cycle . . . • Any system is described by some parameters Gartnet’s Hype Cycle . . . Our Explanation x 1 , . . . , x n . Our Explanation (cont-d) Our Explanation (cont-d) • The rate of change ˙ x i of each of these parameters is Our Explanation (cont-d) determined by the system’s state, i.e.: Home Page x i = f i ( x 1 , . . . , x n ) . ˙ Title Page • In the first approximation, we can replace each expres- ◭◭ ◮◮ sion by the first few terms in its Taylor expansion. ◭ ◮ • For example, we can approximate it by a linear expres- Page 5 of 8 sion: � x i = ˙ a ij · x j . Go Back j Full Screen • A general solution of such systems of linear differential Close equations is known. Quit
Gartnet’s Hype Cycle 5. Our Explanation (cont-d) Gartnet’s Hype Cycle . . . Gartnet’s Hype Cycle . . . • In the generic case, it is: Our Explanation – a linear combination of terms exp( λ k · t ), Our Explanation (cont-d) – where λ k are (possible complex) eigenvalues of the Our Explanation (cont-d) matrix a ij , Our Explanation (cont-d) – i.e., roots of the corresponding characteristic equa- Home Page tion Title Page P ( λ ) = 0 . ◭◭ ◮◮ • When the imaginary part b k of λ k = a k + i · b k is non- ◭ ◮ zero: Page 6 of 8 – we get: Go Back exp( λ k · t ) = exp( a k · t ) · (cos( b k · t ) + i · sin( b k · t )) , Full Screen – i.e., we get oscillations. Close Quit
Gartnet’s Hype Cycle 6. Our Explanation (cont-d) Gartnet’s Hype Cycle . . . Gartnet’s Hype Cycle . . . • Why do we see oscillations practically always? Our Explanation • The more parameters we take into account, the more Our Explanation (cont-d) accurate our description; thus: Our Explanation (cont-d) – to get a good accuracy, Our Explanation (cont-d) – we need to use large n . Home Page • Any polynomial can be represented as a product of Title Page real-valued quadratic terms. ◭◭ ◮◮ • Some of these quadratic terms have real roots. ◭ ◮ • If p 0 is the probability that both roots are real, then: Page 7 of 8 – for a polynomial of order n , Go Back – the probability p that all its terms have real roots is: Full Screen p ≈ p n/ 2 0 . Close • For large n , this is practically 0. Quit
7. Our Explanation (cont-d) Gartnet’s Hype Cycle Gartnet’s Hype Cycle . . . • Thus, practically all polynomials have at least one non- Gartnet’s Hype Cycle . . . Our Explanation real root. Our Explanation (cont-d) Our Explanation (cont-d) • So, almost all systems show oscillations. Our Explanation (cont-d) • This explain why Gartner’s hype cycle is ubiquitous. Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 8 of 8 Go Back Full Screen Close Quit
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