In the preface to the second edition of Science, Order, and Creatvity, F. David Peat writes of his co-author David Bohm:
… Bohm’s thinking was like a spiral – for a time he would focus on one area and then appear to leave it for some quite different interest, only to return, months or even years later, with a much deeper sense of the original topic.
I like to think that this is my thought process as well, as reflected in the breadth and depth of the WordPress categories I post to 
Not too long ago I blogged about Google Notebook as a tool for annotation.
Of course, annotation isn’t a new concept, and therefore there are other tools that allow for it.
Not surprisingly, Microsoft Word is one of these tools. By use of comments, Word allows for annotation. I’ve made available Word and PDF examples elsewhere. In addition to annotations via Word comments being author and date stamped, my example illustrates how annotations via Word comments:
My example also illustrates how annotations via comments are distinct from tracked changes, the latter being another very powerful capabilty in Word.
Although Word can annotate to at least the degree described here, there is one aspect that is limiting. To be wholly useful in the context of annotation, Microsoft needs to expose its mechanism of fragment identification. This is the Word equivalent of an XPointer entry. (The same applies to Google Notebook. Microsoft and Google may have already allowed for this through some API, Application Programming Interface. I just haven’t spent any time looking for them.) Using my Mac, I converted the Word example into HTML. (Sorry, WordPress wouldn’t allow me to upload it!) Comments become linked footnotes. Although this is understandable, aspects of the annotation are lost in translation. I’ll look at an XML-based representation next time I’m at my desktop PC to see if that does any better. Stay tuned.
In closing, it’s important to note that Word is representative of current office productivity software in its ability to convey annotations. In other words, I would expect that OpenOffice and others could do the same. Somewhat related Adobe Acrobat also allows for a similar capability in the case of PDF documents.
About 3,000 km beneath our feet lies Earth’s third ocean. Quite unlike the water-based first and air-based second, this third ocean is an iron-based alloy. Because this liquid-state alloy (aka. Earth’s fluid/liquid outer core) is an electrical conductor, currents can exist. Owing to a well-known reciprocity between electrical currents and magnetic fields, this third ocean factors significantly in an observable known to any of us surface dwellers who have ever wielded a compass.
Although there’s no question that Earth possesses a magnetic field, there are a number of open scientific questions about this pervasive, natural phenomenon. A number of these questions are directed at the sustainability of this magnetic field over geologically significant timescales. Well evidenced in the geologic record over a few billion years, Earth’s magnetic field requires a self-sustaining mechanism (aka. a geodynamo) to account for its very existence and peculiarities (such as reversals).
The starting point for scientific investigators is that this electrically conducting region is under rotation. (Taken from the appropriate scientific perspective, a perspective that takes into account planetary scales and fluid dynamical properties, it turns out this region is rotating rapidly.) The same Earth’s rotation that causes deflection of trade winds in the atmosphere (via the Coriolis effect) also figures significantly in the energetics of Earth’s magnetic field. Rotational effects alone, however, cannot account for the existence, longevity and peculiarities of Earth’s magnetic field over the visible geologic past.
This conundrum has forced the scientists who study this phenomenon to speculate on mechanisms for Earth’s magnetic field. Many of the suggested mechanisms call from some degree of additional stirring. This additional stirring causes deviations from the otherwise steady state of solid body rotation. Simply put, these deviations cause motion in the electrically conducting fluid that in turn result in magnetic fields.
Since the late 1970s, the favored mechanism for additional stirring has been based on buoyancy. In the case of Earth’s third ocean, buoyancy is thought to result from solidification. More specifically, as Earth’s centremost region (know as the inner core) grows by iron crystallization, the residual light element(s) in the alloy is/are released buoyantly. This combined effect of chemistry and fluid dynamics is thought to result in compositional convection.
Compositional convection, however, can be challenged on a number of fronts. Rather than pursue that here, my present purpose is to relate another mechanism for Earth’s magnetic field. As with the previous mechanism, deviations from an otherwise steady state of solid body rotation are key in this case as well. Rotation enforces cylindrical symmetry. This enforcement even applies when the body that’s under rotation (Earth in this case) has an almost spherical symmetry to it. Almost is definitely the operative word here, as Earth isn’t perfectly spherically symmetric. In fact, Earth is an oblate spheroid that bulges at the equator and is depressed at the poles. This combination results in an opposition of symmetries, cylindrical (owing to Earth’s rotation) versus spheroidal (owing to the boundary that contains Earth’s third ocean). As has been demonstrated experimentally and theoretically, the introduction of deviations in the presence of such symmetry oppositions can cause significant instabilities. In Earth’s case, periodic deviations might originate from precession and/or tides.
Experimental, theoretical, numerical and observational studies of such instabilities have been one of Keith Aldridge’s research themes for over a decade at Toronto’s York University. In addition to ongoing experimental studies with graduate student Ross Baker, Keith has been collaborating with post-doc David McMillan and I on supportive observational evidence. Because the instabilities we’re all interested in are periodic, we’ve been looking for indirect evidence in historical records of Earth’s magnetic field. Deep-ocean sediments, extracted as drill cores, are proving useful in our attempts to analyze relative variations in Earth’s magnetic field intensity over the past 70,000 years. In short, our analysis of variations in paleointensity allows us to further support fluid-flow instabilities as a viable mechanism for Earth’s magnetic field.
A scientific account of this investigation has recently been accepted for publication in an appropriate journal, Physics of the Earth and Planetary Interiors. A preprint is currently available online.
