Rantomamble: Flex Time and Office Space

Some ideas for office jobs that generally do not require a physical presence (i.e., programming, not teaching):

• No set hours.  Schedule is determined based on the job function.  In general, meetings and on-call schedules would be the primary drivers for the schedule.
• General expectation of 1900-2000 hours per year.  This is a little more than 40 hours per week, but the flexibility makes up for it.
• Expectations of responsibility are paramount.  Results matter.
• Vacation, sick time, holidays, etc. are somewhat irrelevant.  Leave (paid or unpaid) can be determined as an adjustment to the hour and/or responsibility expectation.  Employee may schedule explicit off-duty times without management approval.  Management must only approve adjustments to on-duty schedule.
• Adjustments to on-duty schedule, i.e. on vacation during meetings, on-call, etc., should be viewed as part of business.  Too many adjustments or adjustments that adversely affect the business in a significant way should be viewed as neglect of responsibility.
• Depending on the size and nature of the organization, distributed centers can serve as on-demand office and meeting spaces.  A central campus can be maintained for the physical structures that are necessary to the operation of the business.
• Phone line should be routed through cell phone with option to route through IP or land line on demand.
• LAN and intranet infrastructure (application servers, databases, etc.) should be limited to services necessary to support extranet infrastructure (cloud application servers, databases, employee portal, etc.).

What it means for the business:

• Reduced or eliminated need for physical office space.
• Reduced equipment costs.  Wires, routers, switches, etc. for computers and phones are expensive, as is their maintenance.
• Reduced utility costs.
• Fewer disruptions due to sick days, vacations, etc. as physical location is no longer an issue.
• Increased morale implicit in flexibility.
• Total increase in productive time (1800 per year is standard, assuming all time is used productively).  Employees can take breaks off the clock.
• Total increase in productivity.  Working in different locations makes employees more productive.  Variety inspires creativity.
• Employees are empowered with responsibility, and they can be held accountable for results, regardless of hours and logistics.
• Ability to hire a geographically diverse talent pool without the overhead of physical spaces and a reduced effect of timezone differences on the work day.

What it means for employees:

• Unprecedented flexibility with schedule and location.
• Take a cross-country trip without missing a day of work.
• Pick up children from school every day.
• Work four days each week.
• Work seven days in a week to make up for short days.
• No more awkward requests for time off or sick time.  This is built into conversations with manager about schedule.
• Increased responsibility means increased autonomy.
• Explicit off-duty time can guarantee rest.

How to get started:

• Just do it!  Work with your company to implement a pilot system.
• Pick a good, collaborative calendar system.  Make sure everyone knows how to use it appropriately.
• Pilot must be large enough to establish subculture within company.
• Ensure communications tools (video chat, phones, etc.) are set up and easy to use.

Why Math is Hard

There has been a lot of buzz around using "technology" for math education. Specifically, I have heard more people talking about using computer programming to teach math. While I think there are some real benefits to this, there are some major drawbacks if we just take the old methods and apply them to programming. Consider the standard algorithm for adding two positive integers:

• Start with the ones place. Add these. The result will be one or two digits.


• Take the ones place for the result and make it the ones place for the sum.


• Move to the tens place and add the digits. If the result from adding the ones was two digits, add this as well.


• Process the results for the tens place in the same way the result for the ones place was processed.


• Continue this process for each digit in the two numbers.


• Don't forget to add the carry digit at the end, if there is one.

WOW! No wonder kids hate math!

If you don't believe me, this is a snippet of the 75 lines of JavaScript code needed to add two numbers using this algorithm (this uses a bunch of helper functions and a 10-digit addition table):

function add(a, b) {
var digit = 0;
var carry = 0;
var sum = 0;
while (digit < numberOfDigits(a, b)) {
  var result = addSingleDigits(getDigit(a, digit), getDigit(b, digit));
  if (carry > 0)
    result = add(result, carry);
  sum = setDigit(sum, digit, ones(result));
  carry = tens(result);
  digit++;
}
if (carry > 0)
  sum = setDigit(sum, digit, carry);
return sum;
}

OK, so this could be trimmed with some clever programming tricks, and it should be made more efficient in special cases, but it is still a monster algorithm for just a simple operation. I'll happily send the full code to anyone who really wants it. By the way, binary calculations done by the most simple electrical circuits work in almost the exact same way.

Other arithmetic operations are no better. Think about the algorithms you use to multiply, divide or simplify fractions. Then add decimals and negative numbers.

If education is to move in this direction, we should think about how to simplify calculation algorithms into more logical, less comprehensive systems. Do people really need to add $473991 and $47838, or do they just need to know whether this means $500,000 instead of $1 million? Of course not!

Is it even important for kids to be able to describe and apply such an algorithm in plain language?

I think the answer is yes, due to the complex nature of the systems in modern society, but we should be providing tools to allow students to do this without the unnecessary complexity of the medium provided. I envision a sort of computerized graphic organizer that can allow students to express their thoughts through a path of least resistance. This is an education issue, not a technology one (the technology is easy).

As with so many of these initiatives, more work is needed on developing thoughtful learning tools before they are technologized so that kids can spend more time staring blankly at a screen.

You've Got to Keep 'em Seperated

School is not just a facility for learning. It is a social environment that children use to learn how to navigate the world. How unfortunate this arrangement is!

We have endeavored as a society to link academic achievement with social promotion (yes, I said those two words) for far too long. Why should these be related at all? The dire state of public schools in this country seems to indicate that, in attempting to perfect both, we have mutilated both beyond "reform."

Note: This is a commentary primarily of secondary schooling, but the implications thereof are applicable to other grades.

The easiest way to survive high school is to follow the social norms expected of both peers and teachers. Peers will respect anyone who can boost their egos, while teachers will appreciate a student who quietly struggles without making trouble. A smart student will learn to disengage during school, only to spend hours struggling on homework just to get by academically. The real question is why this type of student would go to school at all.

When students do not follow the social expectations of their peers, they are damaged horribly by bullying. Society's response? Anti-bullying campaigns! What is so amazing about this is that the schools often are creating the underlying conditions and pressures that cause this bullying in the first place. While the schools must react to bullying when it happens, the proactive measures necessary to prevent it are never even discussed. This is because bullying is based on a competitive model that the education system promotes and that schools rely on for efficiency.

The few students who thrive in high school do so despite the system. Intrinsic motivation and a well-adjusted home/social life keep these students moving in a positive direction. If no diploma existed to reward their efforts, they would create one. It is too bad that these students have to put up with school.

Why do we bother?

There is a belief in society that everyone has, at the very least, the ability to graduate from high school. Academically, this is likely true with very few exceptions. Socially, this is likely true with very few exceptions. Together, the statistics speak for themselves. In some areas, nearly half of all students drop out. Within the half that graduates, many attain a diploma by the skin of their teeth, barely accomplishing the minimum to warrant a piece of paper. They do this because colleges, jobs, families and other societal pressures deem it necessary for success in life.

Education is seen as a necessary component of modern society due to its ability to efficiently train people to perform complex job functions. Yet, when most people are asked how often they use the skills that they learned in high-school, college or post-doctorate studies in their jobs, they will readily admit that 90% of the material is lost. It is the experience of education, not the content that society places a value on.

What can we do?

The experience of school, the social aspects, the emotional supports, the rites of passage, and the growth of personal qualities can be partially separated from the academics. These skills should be taught explicitly and not by sitting in rows of desks. A large component of the value that society places on education is based on these experiences. Instead of pouring resources into flushing out the "best" wording for academic standards that everyone has a general agreement of, why not create new standards for learning how to manage time, resolve conflicts and work independently? Why not completely separate these classes from the development of essential academic skills? Academics will work themselves out. Personal qualities will not.

For all of those who loathe the state of academics in this country, this would seem to be heresy. Taking valuable time away from math and language to give to organizing calendars and learning to get along with others is simply unacceptable. That is, unless we change the entire model of school to fit a more realistic approach. Students learn very little in a classroom with 20-40 students where a teacher is lecturing as it is. It would seem ridiculous to argue that this model needs to be expanded for the sake of academics.

An implementation of this would include online coursework, but that is not a silver bullet. Simply making texts, lectures, assignments, etc. available for free to students and guiding them through an appropriate timeline is half of what students need. Teachers could actually have increased capacity if in-person lectures were removed from the model. The role of a teacher would be closer to coach and tutor than to public speaker. While this is already philosophically adopted by educational institutions, it is not adopted in practice.

School buildings could operate more like community centers, giving students access to resources, rather than imprisoning them. Schools have workshops, science laboratories, experts in multiple fields, AV equipment, theaters, gyms, computers, books and a host of other resources that teenagers would love to get their hands on. This could be an exciting place for teenagers, rather than the range of experiences that is currently anything but.

What about "accountability?"

How about "achievement" instead? A high school diploma is currently an explicit award for academic achievement and an implicit certificate of socialization. The meaning could be shifted to be certificate of both achievement in both academics and personal qualities based on rigorous standards for both. This is not difficult for most people to agree with. The difficult part is that, in the current implementation, the only way to do this is to severely compromise the quality of both aspects. By changing the underlying structure of schools away from a time-based in-person approach organized by academic subject, it would be possible to address both in a thoughtful way.

Time, age and grade would all need to take a back seat to achievement. This is a major shift from the current model. Course completion would be based on performance against standards, not seat time or assignment completion. Tests would almost definitely be used, but their impact would be limited to their ability to accurately measure achievement.

It is already happening! MIT's Open CourseWare and other, similar programs have opened the door to open access to educational resources. Online high-schools are emerging and there is growing interest in explicit instruction in personal qualities. In many ways, however, the implementation is preceding the philosophy in this realm. Most resources are purely academic in nature with little concern for the physical student. There must be a balance here, and there must be a recognition that this is not the future for a few, alternative settings. This is the only viable alternative for a 22nd-century education.

[JFF] Injective Functions and Left Inverses

Just For Fun

Postulate: A function is injective if and only if it has a left inverse.

Definition: A function, , is injective given the following condition.

.

Definition: A function, , has a left inverse given the following condition.

.

In order to prove the postulate above, it will suffice to show that both of the following conditions are true.

• A function is injective if it has a left inverse.


• A function has a left inverse if it is injective.

I will begin by showing that a function is injective if it has a left inverse.

• Let be a function with a left inverse.


• By definition, . Let such a function, , be defined for this section of the proof.


• Let .


• It is clear, from the fact that has a left inverse, that and .


• Then is can be shown that and .


• Since and is a function, . Had been true, would have mapped a single value to two different values, which contradicts the definition of a function.


• It can, therefore, be concluded that given .


• Thus, is injective.

Now, I will show that an injective function must have a left inverse.

• Let be an injective function.


• By definition, given .


• Let .


• Also, let there be a function, , such that .


• Clearly the fact that is injective shows that , ensuring is a function.


• . Since is unique to , a function, , such that can be defined.


• It can then be shown that .


• Therefore, .

I admit that the second part of this proof could use some refinement. Any ideas are welcome.
Since both conditions have been proven, the postulate is thus proven.

Video Games are Your Friend - A Literal Interpretation

Teenagers spend a ridiculous amount of time playing video games.* Any number of explanations could be given for the reason, but I would offer escapism as the primary culprit, as this hits on many of the main points contained within a video game. The education world has not yet found a solution for this virus that has spread through high schools across the country. Schools cannot control what students do at home (sorry!) - or school for that matter - and parents cannot control what students do anywhere* (news flash!). I assert that, rather than fighting an uphill battle, then Education (capitalization intentional) would could, and maybe even should, turn around and run in the other direction. What if students could escape into a virtual world of learning modeled after some of the most successful video games.

Disclaimer: I am not a gamer. I have played video games, but I can't stand the monotony and tedious nature of most of them. Also, video games are not, I repeat not, the cause of, nor the answer to all of Education's problems. This is merely one avenue that I thought worth exploring.

Why are video games so popular anyway? Teenagers are vain, conceded, insecure, hormonal, lazy, impatient maniacs. (It's late, so I'm being nice.) Video games are an ultimate source of ego. The player is paramount. Whether it's a simple game of Frogger (no, I'm not that old), or it's a not-so-secret online society like World of Warcraft, the main character is the player. Moreover, the object of the game is the success of the player. Essentially, the entire purpose of a video game is to boost the ego of the player.

This is not unique to video games. A million years ago, Dungeons and Dragons was played by socially awkward youth through old fashioned books, dice and collectible figurines. This form of RPG (Role Playing Game for the uninitiated) was the ultimate escape for those in need of an alternate reality. In addition to providing a fantasy world in which one could retreat -manipulating a character whose traits are strikingly similar to those in the dreams of the player - the game encouraged a twisted form of social interaction. People would need to gather in order to play the game, essentially creating the geekiest, nerdiest party culture every to graze humanity.

How does this relate to video games, you may ask? World of Warcraft, NeoPets (It's not just for boys (actually, most people don't realize just how gender neutral these games are (market share (nested parentheses (LISP)))) and a host of other online RPGs, including a Dungeons and Dragons one, by the way, all mimic this behavior in a virtual format. No longer does one need to risk even the slightest physical human interaction. Now, friends are no further than your computer. Moreover, other human beings can judge you entirely on what your virtual character does. Emotion is expressed through single phrases preceded by a forward slash in a global chat window. It is the ultimate poker face in the high stakes game of social interaction. (Yes, I did just use a gaming reference to describe another gaming experience, and, yes, gambling has a lot to do with video games.) What better way is there to exist than as an entity that you have complete control over.

Or do you have complete control...?

I said that teenagers are impatient, but they have remarkable patience when they are dealing with status. Just as they may painstakingly work toward the perfect outfit to show their fashion superiority, or at least acceptability, teenagers will work tirelessly on building up their characters in an online world. These worlds have entire economies with currency exchanges, rare collectibles, skilled trades, information industries and power hierarchies. Moreover, achieving a high status in any category has a clear and defined path. Complete the tasks that the game lays out for you, and you can gain power, money, skills or a host of other status symbols available. The path is generally crystal clear, and there is only one thing standing in the way of a teenager's current self and their ultimate ideal: time.

These games take an enormous amount of time, as we all well know (redundant, redundant, etc.). Most people take for granted the reason for all this time being spent on frivolous spinning of wheels. That reason being that it is not frivolous at all, at least not to a teenager. Every minute is another step toward a goal; a goal that means something very real in the adolescent mind. It might be many steps removed, for instance: kill the deer to get the hide to tan the hide to sew the leather to gain a "leatherworking" experience point, which contributes toward the status of "expert leatherworker," which allows the character to create unique leather armor if only they can find the magic rune to attach to it, etc. The goals are clearly laid out for the player, and the steps to get there are concrete, even if they would take forever, literally. In the teenage mind, however, the end result is (totally) worth the "effort" required.

The success of online, multi-player RPGs would be severely tempered, however, without the "multi-player" aspect. While single-player video games can have an incredible draw on teenagers, their appeal will inevitably fade when the realization sets in that nobody, anywhere, will ever care about their accomplishments in the game. A multi-player game, however, particularly one that is online with other people in real time, gives the player a new incentive for playing each time they log in. The thrill of achieving the 94th level is wonderful until a 103rd level player passes you on the road on their pet dragon, which is unlocked at level 100, of course. Power, money, ego. For an insecure teenager, the emotions (hormones) that get activated through the first few minutes of logging into a game are overpowering. The player simply "has" to get just a little further in order to restore some self-worth. This is a real need for a real person in a virtual world.

The social aspect of these games runs deeper than competition as well. Players can form alliances, groups, guilds, etc. to form whole societies, complete with politics and corruption. It is not only good enough to beat the game, but all the other players must pay homage to the founding member of the "Dragonbusters" (where do I come up with these ridiculous names?) guild. On a lighter note, it's 3:00 AM, and the teenager is alone at the computer in a quiet house. Obviously, the human interaction that they so desperately need can be fulfilled by chatting with other players on these games. They make virtual friendships, much like pen pals (whoa...there's a concept that has just died...yes, all you who are old enough to remember ALF, I went there). It's a social scene with no risk of rejection, at least not real rejection, because it's not real, but just real enough (grammar: it's a choice). It's escapism at its worst, as reality gets intermingled with fantasy, and a teenager cannot navigate the nuance to tell the difference.

I swear there's a message about education in here.

I propose creating a video game to replace all homework. It would, of course, have to be an MMORPG (Massively Multiplayer Online Role Playing Game). There would need to be an economy, skill structure, social institutions and just about all of the other major features that make these games so appealing. Students could challenge each other to academic duels in order to rise in the ranks. Graphics and music are key: it can't seem cheap (or "lame," which is worse than death). Goals need to have real, or in this case fake-real, incentives. For instance, achieving the ability to solve an equation could open up a new realm for exploration. Letters can be sent to an "oracle," who gives rare items to players who use topic sentences for their paragraphs. As the map unfolds, it will become clear that they are really travelling through the towns in rural Ireland. Later, they can travel to France, where all of the NPCs (non-player characters) speak only in French. etc. etc. etc. (The King and I)

Imagine the efficiency that could be gained if students concentrated on socialization and soft skills during school hours. They could work collaboratively on complex projects, free to explore and experiment. All the while, at home, they are playing video games to gain those hard skills that society requires of them when they get into the "real world" (there's a concept that will really make your head spin now). Moreover, they get so immersed in these games, that they have to be limited in order to maintain a healthy lifestyle. Imagine school becomes play and play becomes school. It could happen, but it won't; at least it will be a little while.

Creating such a game would obviously be a monumental undertaking. I don't propose that millions of federal and private dollars be thrown into such a venture without some serious foundational work. Unless, of course, I, personally, had complete discretion as to the appropriate handling of said funds. No, many academic studies would be needed to show which are the exact elements of a video game that give it the appeal to draw teenagers into it for hours on end. I hope that these ramblings give a hint of insight toward the themes of some of such studies. In the mean-time, let's hope Education survives long enough to see the day that video games become a tool, rather than a vortex. Happy gaming!

* All major claims in this article are completely unsubstantiated, yet entirely true*.

P.S. I capitalize "Education" in a few instances, although I invariably missed one or two. This refers to the current educational system in the United States. I see this as a massive entity with a character of its own that is so unique that it deserves to be a proper noun. Cue corporate culture (within Education) to adopt this whim as a standard. This has happened, to my great dismay, to the grammar rule that was held so dear to my English teacher and I**. Thank you.

** It physically hurt to type that.