Results matching “calculus” from Ye Olde Rad Blog III

Have a special treat for you today. Earlier this year I spent my Saturday mornings (8 weeks worth) up at Chapman University, here in Orange county. There I participated in a co-parenting course called » Kids First (.. for a second time, both court-ordered).

The curriculum is designed to help divorced parents put aside their disappointment & resentment and focus on putting their » kids first. (Hence the name.) Excellent course, taught by seasoned professionals who really care. ($300)

My particular classes were held in the same building where Chapman's Philosophy / Religion department is located.

[ The combatants, uh I mean parents, are assigned to different classrooms, as you might expect, to minimize the number of brawls. ]

Posted on the bulletin board outside the office to the Philosophy department was a large laminated poster that contained a list of the major philosophers throughout history, with a representative quote beside each name.

I enjoyed reading those quotes each week .. so much that on the final day I stayed late to copy them down, along with the name of each philosopher and their corresponding dates. I've been carrying around that piece of paper ever since. (Tho it's getting ratty.)

Today I finally transferred these quotes to 3 web pages (7 entries per page), and included a picture for each philosopher (which the original poster did not have). I also added a brief historical description to complement each entry.

Web typography. It would seem to be a fairly simple topic, no? While I was reviewing some related concepts recently, the following question popped into my head » What exactly is an em?

I've been using em's a long time, and knew they were based somehow on the letter 'M.' Wasn't sure however, if they were based on the size of the capital [M] or lower-case letter [m].

Also felt confident they were based on the horizontal measurement, but not certain. (In both cases, I was wrong.)

Trying to answer this simple question led to a surprising amount of confusion. Many sources on the web discuss ems, and detail their usage, without ever defining what exactly an em is.

Many pages are more complicated than need be. (It's not rocket science.) Finally have a handle on the topic, but my dang eyeballs are burning .. from reading so much.

First, let me answer the question I posed at the top, and therefore avoid the criticism I levied at many other sites.

An em is (drum-roll, please) » a unit of measure (.. defined by a certain number of pixels). So like inches & meters & light-years, which are also units of measure, the em is a » unit of LENGTH.

The thing that makes the em tricky is that » unlike inches or meters, or other fixed (or 'absolute') lengths, the em is a relative unit.

"Relative to what, Rad?" you might be asking. Relative to the font-sizing applied to (in pixels) its » parent element.

What this means is » the SAME font-size declaration (specified with ems) can yield DIFFERENT results (in pixels) .. when/if the parent element for each declaration specifies a different sized font. Hence, the confusion.

An article posted in last week's NY Times has been gnawing at me all weekend. It cites a study performed by two Israelis & a "leading American expert on the psychology of motivation." The single-page piece is titled » "When a Parent's Love Comes with Conditions" .. or » "When 'I Love You' means 'Do as I Say'."

The article can be summed with the following quote:

"The primary message of all types of conditional parenting is that children must earn a parent's love. A steady diet of that, Rogers warned, and children might eventually need a therapist to provide the unconditional acceptance they didn't get when it counted."

Doesn't it seem odd that a study was required to determine that rationing of love & acceptance (like gasoline during a shortage) based on 'performance' .. is detrimental to children? Duh.

First, conditional love is not love. Let's call it by its real name » manipulation. And it's the worst kind of manipulation, cuz children, especially young ones, are at the mercy of their parents.

Moreover, they do not yet possess the skills necessary to recognize and defend against such insidious tactics  .. from people they're so dependent upon (for eveything).

Now, do you know anyone who enjoys being manipulated? Cuz I don't. Heck, even people who enjoy pain don't like being manipulated. Cuz it doesn't really hurt; it just feels slimy. [Speaking of slime & pain, refer to my comments about boiling a frog near the end.]

Not very difficult to tell the difference, either. Kids (who happen to be particularly sensitive) can spot a fake all-the-way across the coffee shop and will turn away .. while gravitating wholeheartedly to the genuine. You can actually observe this play out.

There are many things a parent can use as leverage to encourage (or discourage) a particular behavior. But love should never be included in the leverage toolkit. Same goes for affection & attention .. things too precious to be used as mere bargaining chips.

Withholding love & affection based on behavior is cruel. Sure, it might elicit the desired response .. in the short term. But the child will grow to resent it (.. as does anybody who's being manipulated). Used consistently and frequently enough, it will instill deep-seated feelings of inadequacy .. that may never go away. (You might even know someone like this .. with deformed self-esteem.)

Many times, when a child is acting out, I'd wager it's *because* he or she is not getting the emotional support they need (from a parent). That would be like telling a hungry child » "Stop fussing or I won't give you any food."

[ In the military, we had a saying » "The beatings will continue until morale improves." Same principle. ]

Whichever side of the great nature vs nurture debate you tend to favor, you always return to » the parents .. as the prime causal agent for how a child turns out .. whether it be on count of their genes or their parenting methods (.. or a combination of both).

We were all kids once. (Well, most of us.) So we all have many years of first-hand experience from which to derive our opinions .. of what works, and what doesn't (.. and what really suks). My point is, it's not rocket science.

Changed the type of layout I use on the home page .. to » LIQUID-ELASTIC hybrid. If I did this correctly, you shouldn't notice any difference .. unless you change your default text-size (.. by selecting 'Text Size' from the 'View' menu in IE). Lemme know if you notice any display quirks.

There are 4 different 'types' of layout designs:

1. FIXED (column widths remain fixed, no matter what, used » here)
2. ELASTIC (column widths change with changes to your preferred font-size)
3. LIQUID (column widths change with changes to browser-window sizing, used » here)
4. HYBRID (combination of two or more of the above, used »  here)

I've long preferred LIQUID layouts (sometimes called » FLUID), which resize column widths as you resize your browser window (called the "viewport" by those in the biz). It's easier for me to understand the concept behind LIQUID layouts .. than ELASTIC.

Today however, I'm demo'ing a » HYBRID layout .. that combines elements of both LIQUID & ELASTIC. [ If you've read my SCSI guide, you know I'm a fan of hybrid config's. ]

The center section/column remains » LIQUID, while the two sidebars (blue-green colums) are now » ELASTIC. This means they will resize with changes made to your preferred font-size (e.g. » small, medium, large, gigantic, etc.). The center section will continue to change proportionally, as you resize your browser window - just like before.

Resizing your browser window will no longer affect the width of the blue-green sidebars (which are already skinny), while changing your default font-size will not affect the width of the center column/section.

The design itself of the home page has remained unchanged. Only the 'type' of layout has been modified (.. from LIQUID to » LIQUID-ELASTIC hybrid). This new type of page layout is considered more 'accessible' ..

.. especially for those who might have difficulty reading smaller text, and need to bump up their default font-size.

It's possible to learn to drive a car without ever understanding how one works. (e.g. » what the pistons do, the crankshaft, transmission, differential, etc.) And many drivers do just that. No problem. But I like to know how things work. This includes my study of Programming.

My degree-path specified one "sciencey" Computer Science class. So naturally, that's all I took.

The first half covered the various components of a computer and their functions (» the processor, memory, hard drive, etc.). The second delved into programming (with Pascal) on a rudimentary level.

Our instructor seemed more interested in the girls in the class than teaching. In fact, the hottie (red-head) who I studied with in the hours immediately prior to the Final exam, told me she'd spent the night at his place. (Her hair was messed & she referred to him by his first name.)

Based on the material she suggested we review, I did not doubt her claim. Because it quickly became clear, soon as the Final was handed out, that her suggestions mirrored the material contained therein. (Much of this material was never covered in class.)

I basically got an 'A' in that course cuz that girl spent the night at the instructor's place .. cuz many of those questions I'd never seen before. But that's ancient history now.

I have however, been delving into HOW programming languages work (crankshaft, pistons). I forget how I stumbled upon it, but there's an online version of this book: Programming Language Pragmatics .. located » HERE (Google books).

Actually, the online version is 2nd edition (2006), while the one for sale at Amazon is the 3rd (2009). But I doubt there's much difference .. that would matter to a rookie like me, anyway.

I'm learning programming. Not a specific language, such as Javascript or Ruby. Rather, the concepts of programming .. that can be applied to ALL programming languages.

[ By the way, I've completed my study of the Unix shell. You can retrace my CLI steps » here. ]

My particular style of learning emphasizes nailing down foundational concepts .. those primarily presented at the beginning of a course.

While this approach can be frustrating initially, because it slows progress at the outset, while foundational concepts are digested on an emotional level .. it allows me to crank thru with confidence (at an accelerated pace) once the foundation is set. [ See note #1 for an example. ]

Like any good geek, I've previously sought entrée into the world of Programming, but always settled for a cursory review of specific languages. (Most recently » Javascript.) Never found that global entrée I was seeking .. until recently.

The approach that is working for me .. is a combination of studying the HtDP text and watching the SICP videos (found » here).

• SICP = Structure & Interpretation of Computer Programs (based on Lisp)
• HtDP = How to Design Programs (uses Scheme)
• Both languages are similar. So the two courses complement one another nicely.
• The SICP videos and the HtDP text are freely available online, along with the SICP text.

The SICP course is legendary in the world of Computer Science. More people refer to it as the single best course on Programming .. than any other.

It was designed and presented by two professors at MIT (.. arguably the world's finest institution of geekdom). Moreover, it was recorded and the videos posted online, where they remain available for download & viewing (free).

I admit, I need to view each video multiple times before feeling comfortable enough to move on to the next lesson. But I *am* getting it .. and enjoying it.

The HtDP course is a simplified version based on the concepts presented in the SICP course.

Neither the SICP videos by themselves, nor the HtDP text alone works for me. But .. combining both courses really makes things click. I get it. I see what's happening .. how things work. It makes sense. And I look forward to learning more.

Today is the 40th anniversary of the first manned lunar landing (1969) .. a historic event for techies .. cuz it was techies who put us there. And techies used » calculus to put a man on the moon (some 240,000 miles away).

At the heart of calculus lies the notion of » limits (a concept I'm quite familiar with, unfortunately).

Calculus was invented to solve (among other things) the problem associated with finding the instantaneous rate-of-change .. as visualized by the slope of a line tangential to any given point on a curve (of a graph).

To calculate a slope, you might recall (dust off them algebraic brain cells) we pick two representative points, find their difference and divide the » "rise by the run" .. the change-in-Y / change-in-X (.. commonly referred to as "delta-Y over delta-X").

As the change in the X coordinates (recall from basic Algebra) gets smaller and smaller, we get closer and closer to determining the slope (rate-of-change) at a particular point.

The problem however .. is that a point has no size, so the "change" or 'difference' (in the X coordinates) becomes zero. And dividing anything by zero is a major mathematical no-no. (Defined as "undefined" .. a mathematical black hole that will crash your computer.)

See t=13:00 here, and especiaaly t=13:30.

Limits

The concept of » limits was introduced to address this problem. Imagine standing in your living room, and walking half the distance to the furthest wall. Then walk half the distance again. And again & again.

Each time, you keep getting closer & closer. But .. you'll never actually reach the wall (cuz you keep going only half the distance). A hundred years from now, you'll be very, very close (to the wall), but still not quite there.

Getting closer & closer to the wall is analogous to decreasing the size of the difference between the two X coordinates along a curve plotted on a standard graph (which contains an X & Y axis). But the limit (drum-roll, please .. here it comes) is » the wall! .. even tho, in reality, you never actually get there.

That's why the notion of a limit represents a mathemetical "concept" (not reality). If you think about it, you can't really have an instantaneous rate-of-change (.. cuz nothing can change in an instant, cuz an instant contains no time). And the word 'rate' implies "per-unit-something." That 'something can be (and often is) » time.

That's also why the result is called/termed a 'derivative' .. cuz you can't get there with conventional mathematical manipulations. It's kinda like what that old farmer told me down South when I asked for directions » "Son, you can't get there from here." =)

Today is Martin Luther King day. I find it interesting (and coincidental) that the very next day we swear-in our first black president. What are the odds these two (seemingly unrelated) days/events would occur consecutively?

I've always been good in math. I got the highest grade, for example, in my (first) Calculus class .. even after I opted to skip pre-Calculus, and hadn't had a math class in/for 10 years. (Pre-Calc is now a mandatory prerequisite, I hear.)

I also got the highest grade in my Statistics class (taken the same semester as Calculus). The professor who taught my 'Stats' class taught two classes that semester. He told me I got the highest grade in *both* classes.

Depending on how you categorize the variables, the odds of these two days/events occurring consecutively..

.. would be between 1-in-365 (the number of days in a year) and 1-in-133,225 (which = 365x365, since each event could theoretically fall on any given day).

I could spend today's entire entry discussing the nuances associated with probability & statistics, but my point is » the odds are miniscule .. no matter how you dice the math.

My brain, for some reason, seems predisposed to identify the statistical curios associated with seemingly unrelated events ('coincidences'). It's not something I try to do, mind you. Just seems to occur on its own.

We know that the inauguration date would've been the same whether Obama or McCain was elected. And (we know that) MLK could've been born on any day. Moreover, his birth (which we celebrate with today's holiday) obviously had nothing to do with our presidential inauguration.

So the proximity of these two events seem totally unrelated (from a design standpoint). Yet in reality, and certainly in influence, they are obviously very much related. So much so that many feel the accomplishments of one man could not exist without the efforts of the other. (See my point?)

I'm not drawing any conclusions .. merely identifying a curious coincidence. And it's obvious the work MLK did back in the 60's preceded Obama's rise to the presidency (chronologically). So even the ordering of the consecutive days aligns correctly with historical events.