A musing on mathematics and the existence of God

Either humans are capable of understanding everything in the universe or we're not. Given the facts of our fallible, fragile, and finite conciousness and comprehension, "we're not" is far more likely.

Just have a look at the Euler formula: e^ipi+1=0. It's a beautiful mathematical expression that contains all the fundamentals of mathematics: the fundamental constants e, i, pi, 1, and 0; and the fundamental operations addition, multiplication, exponentiation, and equality.

The constants in this elegant equation are all vitally important for describing and understanding reality. One is unity - existence iteself. Zero is nothing, except that it's not really nothing. (I had an interesting discussion a week or so ago with a very smart friend who noted that zero actually carries more semantic meaning than one. In a digital signal, no-voltage can mean Zero, or it can mean Off. Which is which makes a big difference.)

Pi of course is the ratio of the radius of a circle to its circumfrence. E is the natural logarithm, which is useful in all sorts of calculations involving real-world phenomena such as fluid flow. And note that both e and pi are by defintion irrational numbers - in any base number system (except base e or base pi), their decimals repeat *infinitely*.

And then there's i, which again is very useful for describing real-world phenomena, especially fractals, which shows the similarity between the jaggedness of the cost of Norway as seen from space, and the jaggedness of a pebble in a fjord when seen under a microscope. i is defined as the square root of negative one, a number that cannot exist in the real world. It's called "the *imaginary* number."

So... if the infinite, the irrational and the imaginary are so valuable in describing the reality that we *can* understand, why is it so difficult for people to accept the existence of an infinite, trancendent, and unseen God that we *cannot* understand?

Bleg for the Big Apple

My son has the chance to go to New York City with his Honors Social Studies class.

To raise the $500 he needs, he's selling candy bars for $1 each. (We buy them wholesale, he makes about .50 on each one.)

If you'd like to buy a few, please click the PayPal button and send me your sweet tooth preferences and shipping info. (We get charged a 3% fee for credit card payments.)

Thanks in advance for your support!

An AUP for kids

For your consideration...

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Parent-child agreement regarding the use of electronic communications devices and services

A. Definitions

1. The terms us, we, and our refer to the parents.

2. The terms you and yours refer to the minor (under age 18) child or children.
3. The term electronic communications devices and services (ECDS) is to be interpreted as broadly and inclusively as possible, including (but not limited to) laptop, computer, desktop, netbook, iPhone, iPod, cellphone, mobile device, internet, web, web-based service, website, online, social networking site, MySpace, Facebook, Twitter, email, IM, AIM, SMS, texting,IRC, chat, etc.
4. The term data is to be interpreted as broadly and inclusively as possible, including (but not limited to) documents, files, MP3s, photos, pictures, movies, videos, texts, messages, posts, programs, applications, plugins, etc.

B. Assumptions

1. We love you and want the best for you, now and in the future.

2. We expect the best from you, now and in the future.
3. You're a Good Kid and worthy of our trust.
4. We recognize that the 21st century is a different place than the age in which we grew up, and that the world you will inhabit as an adult is one that we can scarcely imagine. We have the responsibility to prepare you for that world. We hope that you can see what a daunting task that is for us.
5. The fluent and correct use of ECDS is an important skill for the 21st century. In learning these skills, you will make mistakes. Our job is to help you learn from them.
6. The digital footprint you create is global and permanent. You can expect potential dates, friends, coworkers, employers, and customers to look you up online.
7. As your parents, we are legally responsible for you and for your actions.
8. The application of law as regards ECDS is still evolving. Teenagers have faced lifelong branding as felony sex offenders for sending racy cellphone pictures to their friends. Others have been sued for downloading music.
9. As your parents, we have the legal authority and responsibility to impose appropriate discipline for misuse of privileges.
10. We have a legal and moral responsibility to notify the appropriate authorities if we have knowledge that a minor is (or might be) in danger.
11. You have no expectation of privacy as regards the use of ECDS. We have the right to access your websites, hard drive, cellphone, iPod, etc. at any time.
12. Your access to ECDS is a privilege and not an entitlement, and may be revoked by us in part or in whole at any time, for any reason, without recourse by you.

C. Terms

In order to have continued access to ECDS while a minor child living at home, you agree to:

1. Provide us with a correct and complete list of all websites, services, subscriptions, devices, etc, together with username and password for each
2. Keep that list updated in a timely fashion.
3. Remove data that we deem inappropriate.
4. Cancel memberships or subscriptions that we deem inappropriate.

For our part, we agree to:

1. Not eavesdrop unreasonably on your conversations with your friends.
2. Not reveal personal confidences unless a person's safety is in danger. (See B.10.)
3. Not post under your name without clearly identifying ourselves as your parents posting under your ID.
4. Not remove material posted by you without notifying you.
5. Not permanently cancel, revoke, or delete accounts or data without your agreement, unless we deem it necessary to protect you.
6. To listen to your reasonable arguments regarding our decisions and actions.

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Now, I think this is a pretty reasonable agreement. When I proposed this to my teenage son, he protested that that this would give us access to his friends' Facebook information that they had agreed to reveal to him, but not to us.

Interesting argument.

What's your take? (I have my own opinion, but I'll reserve it pending comments.)

The "New Normal"?

This was originally posted to an email list of educators who are ruminating on the future of educational technology in the light of Blackboard's acquisition of ANGEL.

Riffing on Neil's #5 (you only make one major change like this in your career / no one ever got fired for choosing IBM) and Joe's note re long-term company viability....

The comic strip "Funky Winkerbean" had a story arc (still ongoing) involving a character who developed terminal cancer. When she entered hospice, she remarked to her husband, "So... this is the 'new normal'."

"New Normal"...hmm.

I'm creaky enough to remember a startup company (a spinoff of the implosion of Control Data) that marketed a cool little CBT authoring application for the Mac called "Course of Action." For developers of interactive multimedia computer-based instruction, Authorware was *not* the greatest thing since sliced bread.

It beat sliced bread hands-down.

Partly as a result, Authorware was soon purchased by Macromind, Inc. (a larger company that had a world-beating animation program for the Macintosh called Director); the merged company being called Macromedia. Macromedia was HUGE. They OWNED the market for interactive multimedia.

Then Tim Berners-Lee and a few friends came up with HTML and HTTP.

Authorware and Director did not do well over HTTP.

Anyone here still use Director or Authorware?

Now, most of us are used to the idea that Things Change. We're pretty much okay with that, and we're pretty good at explaining changes - that's why we went into this business, right? (Okay, it's why *I* went into this business. YMMV.)

But we went into this gig expecting the changes to be incremental, not fundamental. We did NOT expect the world to turn upside-down every few years (Howard Rheingold and John Perry Barlow excepted).

But look what's happened:

The World Wide Web

cellphones

broadband

iPods

wikis

blogs

VOIP

RSS

YouTube

iPhone

UStream

Twitter

Skype

Wordle

et cetera, et cetera, in saecula saeculorum, ad confusium eterna...

Stop.

Take a deep cleansing breath.

Nothing has changed. Nothing (really important) will change.

Really. People are still people. We all have the same basic physiology and psychology as the ancient Greeks. We all have the same basic hopes, fears, and aspirations. Our tools are different than those of our forebears. But like all tools, they're just tools. They let us do some things (affordances) and don't let us do other things (constraints). But regardless, they are merely tools. It's what we do with them that matters.

The tools we use for learning still let us:

* Examine and explore content,

* Communicate and collaborate, and

* Assess and report our understanding.

We need to remember that the differences betwen tools we used a few decades ago, and the tools we use now, are superficial. We (and

faculty and students) need to focus on the processes of teaching and learning.

But as we know, people tend to have a hard time seeing the forest for the trees.

So how do we get the folks we support to stop panicking over the beetles in the bark, and lift their heads up above the forest canopy to note that the sun still rises in the east?

As I see it, that's the real challenge.

An observation about the Maersk Alamaba incident

Reports indicate that the Navy did not act immediately against the pirates - even when the boat containing FBI negotiators was fired upon - because President Obama had made it clear that only a "peaceful resolution" to the incident was acceptable. He later amended that to indicate that deadly force could be used if the Captain's life appeared to be in imminent danger.

The way the situation ended should make it clear that the U.S. Navy does not deliver ransom to hostage-holding pirates unless it is authorized by the President.

But when so authorized, the Navy delivers it quickly: At 2,900 feet per second.

Business Aviation gets the JetBlues

Small commercial carrier JetBlue jumped on the "Flying CEO" zeitgeist with a series of clever YouTube ads that poke fun at the image of CEOs who don't want to mingle with the hoi polloi. You can see them here, along with the unamused reaction of one self-decribed flying CEO.

The alphabet groups that promote business aviation seem to be taking a dim view of the ads. That's an entirely understandable, perfectly predictable response.

And it's dead wrong.

It perpetuates the popular image of CEOs as whiny rich men who are only interested in their money and their toys, with the business aviation industry being the chief toymakers.

Might I suggest something such as the following:

Scene - outdoors, general aviation airport. Middle-aged man in suit (carrying jacket, tie loosened) is walking across tarmac to an airplane, speaking to camera.

"Hi. I'm a corporate CEO. That means I make decisions every day that affect the people who work for my company. If I make a bad decision, they suffer the consequences. So, I try to make smart decisions - and wasting time is not a smart decision."

*looks directly at camera*
"That's why I don't fly on JetBlue."

*gestures at aircraft behind him*
"This little airplane gets me into more than five thousand small airports across the country. That's where my customers and suppliers are - nowhere close to the big airline hubs. And when I need to get someplace right away, I don't have to wait around for the next available flight. As a matter of fact, a customer in another state called me early this morning with an urgent problem. If I had to fly commercial, I'd be lucky to get there before noon, and really lucky to get home in time to put my kids to bed tonight. Most of my day would be wasted at the airport. But with this business tool, I can see my customer this morning, and be back in the office this afternoon. That's a smart decision."

*boards steps, looks back at camera, shrugs*

"I get to keep my shoes on, too."

Hat Tip Benet Wilson, via Twitter

Links at LinkedIn leave me a little sad

I recently realized that the professional SN site LinkedIn has discussion threads.

So today I was looking at this discussion about this article, and in the course of the discussion someone asked about this study, which she described as having "debunked reading and math software."

Now, five years of my career was spent making reading and math software for schools and para-schools. Really good reading and math software. Software we worked extremely hard on. How hard? In the project plans, I budgeted forty-five minutes for each multiple-choice question. Why so much time? Well, each individual incorrect answer choice was designed to tease out a specific misunderstanding of the topic at hand. Further, each incorrect answer choice was specifically remediated in the wrong-answer-feedback, without giving away the correct answer. After being written (a tough job in its own right) the question text had to be tagged, coded, compiled and tested. 45 minutes each.

We also developed an umbrella-sort mechanism using the magic of Regular Expression text-string comparison to do a reaonable job of analyzing free-entry text responses, going far beyond the typical exact-match of text-entry items. (Did I mention this was done on DOS on a 386 CPU, not using semantic cloud computing or neural networks?)

As I said, really good educational software, not just PDFs of worksheets or arcade-game drill-n-kill exercises.



So when I read that some study had supposedly "debunked reading and math software" my hackles stirred enough to send me to read the executive summary of the study. I read a lot of educational research. Not counting the journals I read tyrying to keep up in my field, I'm a reviewer for an international journal of education technology, and over the past several years I've reviewed more than fifty articles submitted for publication. SO I think I'm at least competent to read a piece of research and tell whether its any good.

The ED study is pretty good, though it has some major limitations, which the authors themselves note. It certainly does not "debunk" educational software.

Here's what I wrote in reply:

"Debunking" is rather a strong, and IMO inappropriate word. At worst, the survey reports no significant difference in learning outcomes. That's not necessarily a bad thing. As it happens I also have open on my desktop the site http://nosignificantdiffernce.org , which provides a meta-analysis of hundreds of comparative-media studies. The bottom line is that comparative media studies *usually* report no significant difference in outcomes.

And why should that be surprising? If Medium A and Medium B are both *designed to help learners achieve the same learning objectives*, we should *expect* to see no significant difference.

That said, the ED study reports a good deal of trouble in data collection. There was a serious lack of continuity from year one to year two - over 70% of the teachers dropped out of the study. There were no classroom observations in year two. The survey team administered their own tests where the districts did not, and it is not immediately clear whether the software that was evaluated was aligned to those tests, or whether the instruction given to the control group was tailored to the test.

In other words, is the software taking a hit because it didn't teach something that was on the test? Many of these software packages are highly modularized and can be adapted to fit state or local standards. If the software wasn't set up to teach the content that was going to be on the test (assuming it could have been), it's hardly the fault of the software developers.

In addition, the study authors issue some strong caveats about the limits of their own research. The summary notes: "Characteristics of districts and schools that volunteered to implement the products differ, and these differences may relate to product effects in important ways."

It concludes, "Products in the study also were implemented in a specific set of districts and schools, and other districts and schools may have different experiences with the products. The findings should be viewed as one element within a larger set of research studies that have explored the effectiveness of software products."

If the study authors themselves issue such caveats, it's a little over the top to call it "debunking." Just because it's not a magic bullet doesn't mean it's of no value.

Successful implementation of learning technology does not seek to replace the teacher (except in situations where there is no teacher to replace). Rather, it seeks to free up the teacher by assuming the role of content-provider. This enables the teacher to do what a machine cannot - to connect with the student as a person, to coach and encourage, and when necessary to admonish and correct (can we even do that anymore?)

The commentor to whom I had responded thanked me for my response and replied that she had gotten her information from a comment on a post on the liberal multi-author blog Huffington Post. I followed the link and found her reference in the comments section, which was filled with vitriolic partisan ignorance that is beyond my ability or desire to attempt to remediate.

I really feel sorry for people who are filled with fear and hatred for ideas that are different from their own. Can we not disagree agreeably?

The Upside-down Pop Quiz

Remember pop quizzes? "Class, take out a sheet of paper. I assume you've all read Chapter Three. So let's play the Read-My-Mind Game, also known as Gotcha! Bwahahahah...." Even if you'd done the homework and read the chapter, you never knew if what *you'd* gotten out of the chapter matched what the teacher thought was important. Oh, how we hated them.

A couple of years ago I was designing a new course with a History professor, and inspiration struck. Instead of punishing students for not reading the book (or not getting the "right stuff" out of it), why not provide a positive incentive? We want them to read the book. What do they want that we can provide? Grades! A simple transaction, really: You do what I want, I give you something you want. It's worked for generations of parents and corrupt government officials (until they get caught, anyway). It's called BRIBERY: Read the textbook, and it's worth a letter grade to you.

So we turned the pop quiz on its head. We created untimed, open-book online quizzes for the text chapters we assigned. The questions came directly out of the book, and were designed to be answered while looking at the text. (After all, life is an open-book test.) The quizzes were posted on the class website (Blackboard) the week before the discussion of the readings. Students could take the quiz as many times as they wanted. The feedback to incorrect answers directed students to the appropriate page of the text. We did not give the correct answers. The sum of all the quizzes amounted to 10% of the final grade.

Questions were a mix of high-level, conceptual, big-picture items that required students to integrate ideas across an entire section, and nitty-gritty detail questions that could not be answered apart from the text. Case in point: The text contained a passage from an original source document listing government jobs in Massachusets in 1690. The list included baker, brewer, collector of tithes, person to keep dogs out of church, rebuker of boys, and so on. So we put this question on the quiz: "According to the text, all of the following were government jobs in Massachusets in 1690 EXCEPT..." and then we listed the jobs above, inserting the red herring, "Admonisher of young ladies." Sounds reasonable, but it wasn't listed in the text. (I suppose colonial girls were better-behaved than their brothers.)

Now, I guarantee you, if you ask a question like that on a closed-book test, the students would be lighting torches and sharpening pitchforks, and with good reason. Expecting students to memorize a list like that is completely unreasonable. But it's perfectly reasonable to ask them to read that paragraph closely at least once, in order to kickstart a class discussion of colonial attitudes about the role of government.

Ok, fine, sounds great. Innovative teaching strategy, hoo-hah hurray, golf-claps all 'round. But does it work?

Yes. Emphatically so.

The data showed that most students took the quiz more than once, some up to four times in order to improve their scores. The time-stamps on successive quiz attempts showed how students were driven to the text, forcing them to ferret out the answers. The instructor could see which questions the students had missed, showing which concepts needed extra attention in the lecture and discussion.

In class, the discussions made it very clear that the students had read the assigned chapter, and read it carefully. And since the quiz questions reflected what the instructor thought was important, they were all on the same page regarding both the big ideas and the details. The instructor didn't need to spend time rehashing the chapter content; it became a starting point for the discussion.

So, I commend the upside-down pop quiz to you. Give it a try, and if you'd be so kind, let me know how it works for you.

Yak Shaving Razors - Take Two

List five useful things you know that others might find useful, but might not know. #yakshavingrazors

I got waylaid in my attempt to finish the earlier post, which lead Tojosan a bit off the path I'd intended. The idea wasn't to detail our own struggles with unshaven yaks, but rather to share ideas, tips, and tools that make the yak shaving - or any other activity - a little easier.

Think "Hints from Heloise" or the "lifehacks" tag in delicious.

So... My Five Useful Things to Know:

1. A dash or two of Tabasco improves almost any sauce, soup, or stew. It brightens the flavors. This is especially true of rich, creamy sauces such as alfredo.

2. Saliva is a remarkable cleaning solution. In reading about the recovery and resoration of rare artworks, you sometimes see the phrase "a mild, aqueous enzymatic solution," as in, "centuries of grime were carefully removed from the priceless painting with a soft brush and a mild, aqueous enzymatic solution." That's not magical mystery mix, but good old fashioned spit. Saliva is mostly water (aqueous) but contains lots of enzymes that break down and soften all manner of organic compounds (aka "pre-digestion"). So before breaking out the tolulene or MEK, rub a little spit on that spot. (Unless of course, you dip Skoal.)

3. Stretch out your guitar strings when you change them. The pitch of a guitar string depends on its length, unit mass, and tension. When you're tuning up a new string, the length and unit mass (.55 low E vs .10 high E) are constant, so the only variable is tension. Problem is, when you tighten the string up, it stretches. It literally gets longer, which reduces the tension, making it go flat.
Most materials (including guitar strings) stretch when they are under tension. You can graph the stress (tension) versus the amount of stretch (strain). At first, the stretch is like a rubber band - when you let off the pressure the string returns to its original length. But at some point, the "set" becomes permanent. The string will continue to stretch up to a point, then it won't stretch any more. That's the point you need to get to in order for the string to stay in tune.
So here's how to pre-stress your strings. Tune the new string up to pitch, then pick it up at the 12 fret (the midpoint). Pull it out an inch or so so you can feel it "give" a bit. Waggle it back and forth, then tune it back up. The stretched-out strings will stay in tune.

4. Experienced cooks know this, but here's how to make a nice pan gravy by "deglazing" the pan. Say you're browning some chicken, or pan-frying steaks. By the time the meat is cooked you've got some stuff stuck to the bottom of the pan. (We're assuming it's not burned, just browned.) I used to scrub it out with a scrubbing pad - such a waste of effort AND flavor!

Remove the cooked meat - it needs to rest for a couple of minutes before you serve it anyway. The pan probably still has some fat in it; drippings from the meat. If it's really dry, add some butter or oil, about a tablespoon. Heat the pan till it just barely starts to smoke, then pour in about a quarter-cup of liquid - enough to cover the bottom of the pan about 1/4 inch deep. You can use water, broth, wine, whatever. Use a spatula to scrape the bottom of the pan - the browned bits will come up easily and dissolve in the liquid.

Now you have several options. You can toss the pan in the sink, having saved yourself some elbow grease with a Brillo pad. (Booo! as the CommonCraft folks say) Or you can:

• Serve the pan sauce as is and call it "au jus"
• Boil the liquid down to concentrate the flavor (this is called "reducing").
• Mix a tablespoon of flour with some warm water, then add that and cook until the gravy thickens. You might add more broth for volume or to thin it. (Note - adding dry flour directly to the hot pan tends to form lumps - the hot broth cooks it up into little dumplings before the flour can get dispersed.)

5. Write offline. Whenever you're going to write a lengthy post for an online forum, do it offline in Word or Notepad. Because if you're typing right into Blogger or WP and your network connection crashes, you'll lose everything.

Twitter Tag Meme - Yak Shaving Razors

Today my postcard-sending pal Tojosan got tired of the "Several Things About Me" Twitter-tag meme that's been going around. He asked for a more useful topic. I replied, "OK, how's this: List five useful things you know that others might find useful, but might not know. #yakshavingrazors"

Yak Shaving Razors?!?!! Say WHAT?

Yes, Yak Shaving Razors. The term isn't my own, I first ran across it years ago on Joe Carter's old Evangelical Outpost blog. Yak-shaving is something that you have to do in order to do the thing that you actually need to do. For example, I want to move a study desk from the garage into the boys' room. But before I can do that, I have to clear out the back of the van. Why? Because the desk is going where the dresser is now, and the dresser is going to move into the closet, where the old TV is now, and there's a bunch of recycling int he back of the van where I plan to put the TV to take it to get it fixed so it can be used as a dedicated game console... you see where this is going?

So a Yak Shaving Razor is a tool or a tidbit of information that helps you get things done.

With that introduction out of the way, here's my list of Yak Razors.... dang. Lookit the time. I need to call in an order of Chinese takeout so we can eat before taking the kid to basketball practice...

Hey, who let that yak in here?