Welcome To
Physimathetronics!This web site is dedicated to Physics, Mathematics and Electronics. It may be of general interest or useful as a study guide to people engaged in University studies in either of these three fields.
Some of the subject matter is related to my current Master's course in Physics and some is derived from previous work in R&D disciplines. I may add other ideas as I develop the pages over time.
I coin the phrase "Physimathetronics" as a quick-link to Physics, Mathematics and Electronics given the natural affinity all three disciplines seem to share. This is not exclusionist of course as other scientific disciplines also share common tools, philosophies and methodologies. The topics presented in these pages is simply reflective of my familiarity with the material and in no way should be seen as dismissive towards other equally valuable fields of inquiry.
As with web sites in general, the reader is advised to use their own judgment on subject matter presented. I make no claims for its accuracy, suitability, relevance or hilarity. I don't even claim that it is well designed. The only claim I make, is it is.
Science is used in common language these days and this is not surprising as we live in an age of science. Whenever we drive a car we give employment to the progeny of science, equally when we travel cross-continent, or chat on a cell-phone, or web-browse, or have a tooth repaired, or heat and light our homes we call on the many offspring that science has begat. Whilst science may not provide a panacea to humanity's plights, nor a paradise of eternal personal fulfillment, it would be hard to imagine anyone forsaking science's offerings in favor of a back-to-basics alternative. Even those people that might "return to the land" and just use "simple farming tools" will still evoke science. Agriculture, for example, could be seen as a scientific invention that enabled small hunter-gatherer tribal groups to establish "roots" and communities with some indication of structure and permanence. Horses that pull a cart of hay use the wheel from science; equally the plow is a tool that has its genesis in scientific enquiry. To retain farming therefore and yet claim to reject science would appear contradictory; is it ever possible, therefore, to completely abandon science in any real or practical sense? Unless we also abandon tools, clothing and vegetable crops selectively bred through time; thereby I guess so claiming a truly Spartan existence, can a true anti-science wish fulfillment be attained?
Not all scientific offspring could be viewed as humanitarian, ethical, social, spiritual or even useful. However these ambitions dance in the minds of philosophers, theologians and pragmatists rather than through pavilions of science. That we might expect some natural conflict for superiority between differing worldviews is more a reflection on our collective psychology than any intrinsic motivation to contest; it is simply better, I suspect, to allow each worldview its own domain and let people appraise each as they elect. This approach lets science get on with being science and faith get on with being faith and so on. If on their various travels they happen to chat then all well and good I reckon.
Having said this, each scientific discipline can now be discussed in it's own house of order. If I seem to anthropomorphize such subjects a bit I apologize - still in some ways ideas do collide and the history of human struggle shares parallels. In any case three web chapters follow; Physics, Mathematics and Electronics. These each contain some philosophical thought before leading into the real technical nitty-gritty web-linked later.
Physics is a branch of science concerned with the study of natural laws that we believe govern universal interactions. Its key philosophy is constructive skepticism towards theories that seek to explain physical phenomenon. Theories, however well intentioned, just represent our "best guess" at understanding our surroundings and so are available for appraisal through experiment. However a "guess" is perhaps misleading, as some guesses are arguably better than others. Physics tends to assess the "usefulness" of theories according to a few reasonable guidelines. For example, theories can be valued as "useful" if they satisfy the following criteria
 | Theories Must Make Predictions That Are Testable - Theories are then either Corroborated, Refined or Dismissed. |
| Predictions Made By Theories Must Be Consistent With Previous And Current Measurement Outcomes |
| When Competing Theories Equally Explain Measured Outcomes, Simple, Compact Theories Are Preferred |
| Good Theories Should Generate New (Preferably Unexpected) Predictions That Can, In Principle, Be Tested |
| The Best Theories We Propose Generate Widely Applicable Knowledge In Many Diverse Fields Of Thought |
The general public's opinions on science vary; some people may think that a theory can't be disproved is a good one for example. However the opposite is true - theories must be disprovable. For example, a theory based on "goblins" that "disappear when observed" may be impossible to disprove and therefore has little use. However a branch of physics called "quantum mechanics" has exactly this obstacle; the act of measurement forces experimental outcomes to some extent and we are unable to know the state of any system under investigation prior to this measured outcome. However, unlike goblins in the garden, predictions can still be made on global, repeated results that are consistent with what we observe.
In some cases, multiple explanations may explain an experiment's outcome just as many possible scenarios may explain a suspect's possible role in a criminal case. When "push comes to shove" we generally favor simple explanations over lengthy and complex descriptions, in other words "if it looks like a duck, it walks like a duck, it quacks like a duck, then probably, ... it's a duck!"
Physics also enjoys a history of being creative; Newton's laws of motion are one example. The common example of dropping a feather and an apple in a vacuum is one example. Prior to Newton's theory people might have expected the lighter feather to fall slowly but apparently both fall at the same rate. However on closer scrutiny, Einstein found flaws in Newton's theory that assumed, in effect, a static space-time geometry. Einstein predicted a curved universe that caused time, for example, to pass at different measured rates between equally valid observers. His space-time used a 4-dimensional description; current research considers many additional dimensions can be postulated that result in even better predictions that we can experimentally measure.
The foundation of physics is therefore progressive as opposed to doctrinal; as in many other braches of science its fruits of discovery fall into the hands of alternate disciplines. For example, Fourier invented his famous "Fourier Transform" in his study into the properties of heat. This transform is now widely used in remotely connected disciplines including electronics, optics, geology and even the search for extraterrestrial life "SETI"
I guess to summarize, Physics is a fairly practical old science and employs tools developed in other area such as mathematics and electronics in its quest for better understanding. As suggested, this is not a one-way usage as Physics contributes useful findings in return. It is reluctant however to dismiss its allegiance to refutability in it's consideration of theories whilst other disciplines of science may be more relaxed in that regard. For example, evolution is often cited as a contentious theory for scientific, emotive or religious affiliations. Without the benefit of Dr Who's time traveling Tardis we cannot return to an earlier point in time and see how things really did begin. Equally, we cannot construct an experiment spanning billions of years to test evolution in motion. At best we can gather a few snapshot relics of the past and compare what we observe with general predictions from this theory, or to witness some small scale outcomes in our very small window of time that may suggest some creation of life's precursors (e.g. amino acids) in a spark-fed chemical broth. Still all branches of science have value despite our physiological limitations of time and capability. Physics just happens to have a lucky draw on subjects that can at least be tested providing enough ready money can be found!
If Physics is the inquisitive cat of science then perhaps Mathematics is the cat's toolbox of stalking tricks. Or so the cat may believe - however "Pure Mathematics" would probably disown any such justification for its god-viewed status of personal existence based on some trivial feline application. But would a wider range of animal applications extend greater ennoblement to Mathematics? Probably not, although a Mathematician might own a cat I guess.
Perhaps I am unkind; this fortitude of ignorance should not residue in my nature. But in an other world view perhaps I should retain skepticism. After all, science is based on skepticism. Should not Mathematics also enjoy such harsh scrutiny? That I may be ignorant, or incompetent, should not dissuade me of question. After all, questions exist always as a state in a healthy mind, but do be need a "state" or do we need a "mind"?
Mathematics weighs low on such scales of questioning; in many ways it is a parading (i.e. conceited) cat at our footstep soliciting our favors. Will we pass such favors on in a saucer of milk or some vegetarian substitute - well no, the cat will command our attentions to the designs of its primitive own. We will follow it, empathize with its day to day routine in some parallel to our own and feel an acceptance.
Mathematics, like the cat, can only be accepted.
Perhaps I like cats but they make me sneeze.
Electronics has come a long way since its embryonic beginnings in static electricity - the physical phenomena of lightening perhaps represents our first charged experience with spectacular demonstrations of untamed natural power. Now electronics appears almost mundane; we flick a switch for light, we embrace high definition television screens with our eyes and take satellite communications around the globe almost as if for granted. However we are an electronic dependent civilization; take away the power and our EFTPOS machines fail, business based on financial transactions grinds to a standstill, road traffic lights turn blank, our airports close down and elevators stop awkwardly with contents of socially disengaged patrons.
Whilst we might have once seen ourselves prehistorically pitted against nature in some heroic struggle for survival, now we are divorced from such petty concerns; but how majestically will we respond if a protracted power outage occurred? Would we survive, would civilization retain fond vestigial components or would we quickly decay to disorder and ruin?
Electronics however admits no responsibility to the behaviors we might enact; instead it offers a wealth of toys that strangely entice initially and eventually make us dependant on such. The same technology found in computer video games might well be used to navigate galaxy wandering spacecraft; equally a surgeon performing a delicate operation might interface to a game-boy console instead of a scalpel and suture. The more electronic technology advances, then more captivated we become. Still, it's a fascinating captivation.
Perhaps now is a good time to shed some light on the technical detail of Physics, Mathematics and Electronics. In the first Physics chapter, strangely, the main topic I'll consider is optics. This will address linear and non linear concepts, involving ray tracing, lasers and wavelength conversion. The Mathematics chapter will address Linear Systems and cover topics on convolution, Fourier Transforms and Hilbert Transforms. The final chapter of this trilogy will examine electronic circuits with some emphasis of Field Programmable Gate Array (FPGA) development approaches.
There will undoubtedly be much similarity between these three. Within such mutual interest there should also reign some mutual respect I guess; however this remains to be seen. As these pages and perhaps the underlying themes of interest formulate some fundamental personality conflicts might arise - but then, at the time of purchase, my model of computer did not have the crystal ball option.
These opening illustrations might seem frivolous but equally construed of the stuff of plausible importance. If you wish to read deeper into the lower layers of detail I trust the tone will settle down a bit and portray more serious aspects; however should experience belittle expectation then I guess that's life. Science isn't serious to begin with; it deals with theories and all theories are just guesses awaiting measurement critique. It might be argued that Mathematics is not science as it deals with "proofs" derived from "axioms". However, even in this inner sanctum, axioms rest on accepted "articles of faith" in analogy to theological reasoning. Even if this suggestion receives coy audience, then Kurt Gödel's incompleteness theorem can be cited - if I remember one phrasing of it, "in any system that is sufficiently self referential, there exist statements that are true but not provable".
Science is about disproof, at least according to Immanuel Kant. If Mathematics enjoys the pontification of unquestionable truth, insofar as it argues discipline-centric proofs of inarguable validity, then perhaps Mathematics is doctrinal. How then can Mathematics be falsifiable in the sense that science is requested to be?
Alternatively, if Mathematics accepts its utility in the service of other disciplines then its saintly quest is reduced to paths mere mortals tread. Perhaps this is best for all but is humility in Mathematics' pseudopsychology? We have difficulties with which to struggle but within these conceptualisms useful meanings might reside - or maybe not.
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© Ian Scott 2009
