Archive for December, 2006

Phase Shift

Saturday, December 30th, 2006

Phase, Frequency, Amplitude, and all that.. is an example of a university math course adopting the convention that identifies “phase shift” as angular shift as opposed to horizontal displacement or “time shift”

And at the time of this posting, the Wikipedia article on Phase (waves) takes the same point of view.

Phase Shift or Phase Angle?

Saturday, December 30th, 2006

Murray Bourne at squareCircelZ has taken the time to respond to a comment I made on one of his interactive math pages, so I thought I should make an effort to explain my concern in a bit more detail.

In high school and college precalculus courses, the material on graphing trig functions often includes a definition of “phase shift” which is contrary to the way the term is used by many in applied fields and also by many mathematicians (including me when I have a choice).

The usage demanded by high school examiners corresponds to the horizontal shift of the graph from a purely scaled basic trig function. So, for A*sin(bx+c)+d it would be given by s=-c/b since, with that value for s, we get A*sin(bx+c)+d=A*sin(b(x-s))+d , so the graph of y=A*sin(bx+c)+d comes from y=sin(x) by first scaling to get y=A*sin(bx), and then shifting horizontally by s units along the x-axis (and vertically by d units along the y-axis).
But in fact, the concept of phase arose from a need to identify the part of the cycle being considered (ie rising, peak, falling, mid-point, trough, etc) and is usually identified quantitatively by an angle. So we typically talk of two waves interfering constructively when “in phase” and destructively when “180degrees (or pi radians) out of phase”, and we also speak of a process such as reflection or refraction as introducing a “phase shift” of so many degrees or radians in the propagation of the wave. With this usage, the phase shift of A*sin(bx+c) relative to A*sin(bx) is just c (radians) rather than the math teachers’ -c/a.

Some authors seek to avoid the conflict by identifying “phase shift” as what the high school teachers insist on and “phase angle” for what the other camp prefers. But I think this is a mistake for several reasons. My main objection is that even if it might be a good idea to implement such a change, it should not be taught to students as fact if it has not in fact yet been established as a convention agreed to universally in the professional mathematics community. There is nothing wrong, and much to value, in admitting to students that not all terms have universally agreed definitions and that when they face such terms it is important to *ask* what convention the user intends rather than to blithely assume something that may be wrong (which is just the sort of thing that leads to expensive space probes crashing into Mars and causes international airliners to run out of gas in the middle of the Atlantic).

But if that particular convention were proposed I would argue against it as I believe it serves no purpose other than to “save face” for the math teachers, and does so at the expense of abusing the language. I say this for three reasons.

First, the word “phase” was introduced to refer to the position in a cycle (which is basically an angle), so to speak of a “phase angle” is redundant.

Second, there is a phase (angle) corresponding to every point on a wave and the term “phase angle” does not properly denote a shift.

Thirdly, to use the term “phase shift” for what in any other graph would be called the “time shift” or “horizontal shift” introduces a completely useless extra bit of language by having a special context-dependent term for something which already has a perfectly good name that works in every other context.

And fourthly (I know you weren’t expecting the Spanish Inquisition, but do you know the three kinds of mathematician?) wasting a term where it is not needed makes it unavailable for where it is actually useful.

When two split light waves are brought together again (as in the creation of a hologram) it is not the phase (angle) itself at each point but the angular shift between the two waves that is directly relevant to the outcome rather than the time shift between two signals. We could of course convert the time shift to a phase (angle) shift just by using the known frequency and velocity of propagation, but it would be silly to use both terms to refer to the time shift and leave ourselves without a name for the quantity that is actually most directly relevant.

The convention that makes most sense to me is therefore to use the term “horizontal shift” (or whatever term they’d use for the x-displacement in any other function) for what the math teachers call “phase shift” and keep “phase shift” for its traditional role as what is now being proposed as “phase angle”.

PNW Conifers–Genus page

Saturday, December 30th, 2006

PNW Conifers–Genus page

Oregon State Univ., LANDSCAPE PLANTS

Saturday, December 30th, 2006

Oregon State Univ., LANDSCAPE PLANTS

Batura Glacier Trek

Wednesday, December 27th, 2006
IMG_7655

IMG_7655,
originally uploaded by alqpr1.

Here is Tom near the end of our first day’s trek. Behind him is the foot of the black glacier.

Flickr

Wednesday, December 27th, 2006

This is a test post from flickr, a fancy photo sharing thing.

Langara College – Environmental Achievements

Monday, December 25th, 2006

“. . .identifying several simple directions to focus on and then getting on with the work, would work best I think.”-LH http://csap.envs.wmich.edu/pages/bestpracticeevaluation2.htm http://www.wilson.edu/wilson/uploadedfiles/offices/academic_affairs/fulton_ctr/163-177-policy-steven%20doherty.pdf (see page 8) http://www.ghgregistries.ca/challenge/cha_entity_e.cfm?no=2314 http://www.langara.bc.ca/news/archives/2004/news-040327-vcraward.html —

Carbon Footprint

Sunday, December 24th, 2006

Carbon Footprint includes a “calculator” for estimating one’s personal contribution of CO2 to the atmosphere and suggests various ways of reducing or offsetting it. But the encouragement to “plant trees” (or pay for same) may be misguided, since it seems clear that it is the lifetime carbon sequestration that is being assigned for each tree so the instruction “plant 5 trees” means plant 5 trees every year AND make sure that they all grow to maturity and are never used for fuel.

RealClimate – Climate Science Blog

Sunday, December 24th, 2006

RealClimate is a blog about climate science maintained primarily by Gavin Schmidt. It appears to be a forum for active discussion of current issues with input from a wide cross section of those active in the field.

The Carbon Dioxide Greenhouse Effect

Sunday, December 24th, 2006

This is a balanced complete and well referenced account of the history of our understanding of CO2 in the atmosphere.

Will at Work Learning: People remember 10%, 20%…Oh Really?

Wednesday, December 20th, 2006

This post by Will Thalheimer came to my attention via Harold Jarche and Stephen Downes. Unfortunately it’s not just in education that people are often impressed by fraudeulent mis-citation of derivative bunk.

phpMyID

Tuesday, December 19th, 2006

phpMyID

Wrong Problem, Wrong Solution

Tuesday, December 19th, 2006

This posting by Roger Shank
(found via Stephen Downes) uses widespread ignorance of the quadratic formula by successful people as evidence that mathematics requirements in our schools are excessive.

But I know that in BC it is quite possible to graduate from high school without knowing the quadratic formula. So, unless this jurisdiction is more unusual than I think it is, Shank doesn’t seem to know his head from a hole in the ground.

Of course it will always be true that “We need more people who can think. We need to teach job skills, people skills, and reasoning skills. And we need to make education exciting and interesting.” But Shank surrounds these observations with so much incoherent and contradictory posturing that I would consider his polemic virtually useless for persuading anyone who actually does know how to think.

For example, his “Here are reasons why” (teaching math and science “better”) “is simply the wrong answer“(to the question of “why American kids aren’t interested” in science and engineering) is followed not by reasons but by a series of rhetorical questions directed not at that issue but rather at the motives of foreign students – which he does not relate at all to the lack of motives for domestic ones.

Then later he says “The right answer would be to make math and science actually interesting” – but isn’t that exactly what teaching them “better” would consist of??? But then again, why *is* this the right answer if, as he asserts a bit further on, “What also makes no sense is the idea that math and science are important subjects.”? Of course they aren’t *essential* to everyone, and he seems in various places to acknowledge the need for at least some people to know these subjects, but someone who can’t correctly say what he means shouldn’t be pontificating about how to teach people to think.

Contrary Brin: Predictions Registries and Markets

Monday, December 11th, 2006

Contrary Brin: Predictions Registries and Markets look like a good idea.

More on Religion

Friday, December 1st, 2006

My experience may include something equivalent to what others call god, but whatever it is cannot be put into words – perhaps not at all, and certainly not with the certainty that most religions ascribe to their own very specific creeds and scriptures. Indeed, the conflict and hate that arises between these competing creeds is a source of much of the evil that we have experienced throughout human history. It strikes me that if a god does exist then it does not want us to talk about it, and if there is also a satanic force in the universe then it, not god, is the author of all scriptures. Perhaps god while allowing evil to exist and to tempt us towards the prideful sin of belief has given us a clue as to the reality by slipping into those scriptures items such as the sin of pride in our presumed knowledge of good and evil (embodied in judaeo-christian tradition by the story of the forbidden fruitĀ  – but note carefully that it is not the knowledge of heliocentric astronomy, relativity, quantum mechanics, or technology that we are forbidden but very specifically the “knowledge of good and evil”), or the commandment delivered via Moses not to “take the name of the Lord in vain”, which perhaps should be interpreted in the strong sense – ie not to identify any words utterable by man as being divine. I call this latter the “strong law of blasphemy” and suggest that the world would be much better off if it were enforced strictly – ie no claim by voice or text to represent the word of god should be taken as other than the work of the devil.

Deep Sixing

Friday, December 1st, 2006

My main reason for posting about this from David Brin is to see if any qualified comments come back on the feasibility of subductive disposal.

How Can Smart People Believe in God?

Friday, December 1st, 2006

How Can Smart People Believe in God?

is a blog entry at Stanford’s ‘Philosophy Talk’ about their Oct 22 show with Philip Clayton on ‘Believing in God’.

Commenter David Chilstrom revives the old saw that it takes as much faith to disbelieve than to believe – completely missing the point that not to believe in something is not the same as to believe in its negation.

Commenter Jody asserts that “Belief in a God is between God and oneself. Belief in a religion requires suspension of all doubts and questions that challange a religion’s writings and belief systems.” I agree.

In fact, personally, I suspect that if any God exists it cannot be described in words and that any attempt to do so amounts to blasphemy. This is particularly true of those scriptures which claim to be the word of god (ie all of them?). So if God and Devil exist then all religions are the work of the latter. But if a God does exist, perhaps it seeks to protect us from evil by inserting truth among lies and perhaps one of the truths of the Judaeo-Christian bible is the proscription against taking the name of the lord in vain which should be interpreted as condemning the very document which proclaims it.