“…a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium.” (see Wikipedia).
Solitons occur in shallow water. Shock waves like Tsunamis can be modeled as solitons. Solitons can also be observed in lattices (see Toda-Lattice).
Among the many interesting properties of solitons is that solitons can pass “through” each other while overtaking – as if they move completely independently of each other:
This post is my own little theory on the mechanics of how an information (on a subject, person, anything) becomes relevant – over time:
An information on a subject, such as “Grails is very popular among Web developers” (of which I am not so sure anymore) or “No point in buying a Blackberry phone – they will be gone any time soon” (I bought one just last fall) or “Web development agency X is reliable and competent” (this time I really don’t know) spreads in a lattice of people (vertices) and relationships (edges) just like a soliton. It may pass others and it may differ in velocity of traversal.
Its velocity corresponds to how “loud” it is, its amplitude. It is louder, if it is generally considered more noteworthy when it entered the lattice.
As so many information snippets reach us every day, we sort out most as insignificant right away. So what makes a piece of information memorable and in particular recallable (e.g. when wondering “what is actually a good Web development agency?”) or even trigger an action like researching something in more depth?
It is the number of times and some (yet unknown) increasing function of the sum of amplitudes of all times that that piece of information (and its equivalent variants) has reached us.
Now that we have this wonderful theory, let’s see where that takes us.
It fits to common observations: Big marketing campaigns (high amplitude) send big solitons into the lattice. They do not necessary suffice to create action and so need to be augmented with talks, articles, rumors to add more hits,
Also it explains why that is equivalent to creating many small information solitons. There is great examples of open source tools that made it to impressive fame via repeated references in articles and books – without any big bang.
Most importantly, it explains the non-linearity of “return” on marketing: Little will lead to nothing in the short term. Not just little but actually nothing. Over time however hit thresholds will be exceeded and interest lead to action. As the speed with which solitons pass through the lattice does not change talking to many will not speed up the overall process – but increase the later return instead.
- Solitons in Wikipedia, http://en.wikipedia.org/wiki/Soliton
Surprisingly enough, some 15 years ago, as part of my dissertation work, I published some math papers on PDEs with solitons:
- “Solution of nonlinear equations by trace methods”, http://iopscience.iop.org/0951-7715/13/6/304
- “Solution of a discrete inverse scattering problem and of the Cauchy problem of a class of discrete evolution equations”, http://scitation.aip.org/content/aip/journal/jmp/40/9/10.1063/1.532973