When people sneer at a technology for being too easy to use, it’s worth trying out.
If the only criticism is that something is too easy or “OK for beginners” then maybe it’s a threat to people who invested a lot of work learning to do things the old way.
The problem with the “OK for beginners” put-down is that everyone is a beginner sometimes. Professionals are often beginners because they’re routinely trying out new things. And being easier for beginners doesn’t exclude the possibility of being easier for professionals too.
Sometimes we assume that harder must be better. I know I do. For example, when I first used Windows, it was so much easier than Unix that I assumed Unix must be better for reasons I couldn’t articulate. I had invested so much work learning to use the Unix command line, it must have been worth it. (There are indeed advantages to doing some things from the command line, but not the work I was doing at the time.)
There often are advantages to doing things the hard way, but something isn’t necessary better because it’s hard. The easiest tool to pick up may not be best tool for long-term use, but then again it might be.
Most of the time you want to add the easy tool to your toolbox, not take the old one out. Just because you can use specialized professional tools doesn’t mean that you always have to.
Related post: Don’t be a technical masochist
A uniformitarian view is that everything is equally important. For example, there are 118 elements in the periodic table, so all 118 are equally important to know about.
The Pareto principle would say that importance is usually very unevenly distributed. The universe is essentially hydrogen and helium, with a few other elements sprinkled in. From an earthly perspective things aren’t quite so extreme, but still a handful of elements make up the large majority of the planet. The most common elements are orders of magnitude more abundant than the least.
The uniformitarian view is a sort of default, not often a view someone consciously chooses. It’s a lazy option. No need to think. Just trudge ahead with no particular priorities.
The uniformitarian view is common in academia. You’re given a list of things to learn, and they all count the same. For example, maybe you have 100 vocabulary words in your Spanish class. Each word contributes one point to your grade on a quiz. The quiz measures what portion of the list you’ve learned, not what portion of that language you’ve learned. A quiz designed to test the latter would weigh words according to their frequency.
It’s easy to slip into a uniformitarian mindset, or a milder version of the same, underestimating how unevenly things are distributed. I’ve often fallen into the latter. I expect things to be unevenly distributed, but then I’m surprised just how uneven they are once I look at some data.
Here’s an internal dialog I’ve had several times.
“What will happen when you’re done with this project?”
“I don’t know. Maybe not much. Maybe great things.”
“How great? What’s the best outcome you could reasonably expect?”
“Hmm … Not that great. Maybe I should be doing something else.”
It’s a little paradoxical to think that asking an optimistic question — What’s the best thing that could happen? — could discourage us from continuing to work on a project, but it’s not too hard to see why this is so. As long as the outcome is unexamined, we can implicitly exaggerate the upside potential. When we look closer, reality may come shining through.
Gaussian elimination is systematic way to solve systems of linear equations in a finite number of steps. Iterative methods for solving linear systems require an infinite number of steps in theory, but may find solutions faster in practice.
Gaussian elimination tells you nothing about the final solution until it’s almost done. The first phase, factorization, takes O(n^3) steps, where n is the number of unknowns. This is followed by the back-substitution phase which takes O(n^2) steps. The factorization phase tells you nothing about the solution. The back-substitution phase starts filling in the components of the solution one at a time. In application n is often so large that the time required for back-substitution is negligible compared to factorization.
Iterative methods start by taking a guess at the final solution. In some contexts, this guess may be fairly good. For example, when solving differential equations, the solution from one time step gives a good initial guess at the solution for the next time step. Similarly, in sequential Bayesian analysis the posterior distribution mode doesn’t move much as each observation arrives. Iterative methods can take advantage of a good starting guess while methods like Gaussian elimination cannot.
Iterative methods take an initial guess and refine it to a better approximation to the solution. This sequence of approximations converges to the exact solution. In theory, Gaussian elimination produces an exact answer in a finite number of steps, but iterative methods never produce an exact solution after any finite number of steps. But in actual computation with finite precision arithmetic, no method, iterative or not, ever produces an exact answer. The question is not which method is exact but which method produces an acceptably accurate answer first. Often the iterative method wins.
Successful projects often work like iterative numerical methods. They start with an approximation solution and iteratively refine it. All along the way they provide a useful approximation to the final product. Even if, in theory, there is a more direct approach to a final product, the iterative approach may work better in practice.
Algorithms iterate toward a solution because that approach may reach a sufficiently accurate result sooner. That may apply to people, but more important for people is the psychological benefit of having something to show for yourself along the way. Also, iterative methods, whether for linear systems or human projects, are robust to changes in requirements because they are able to take advantage of progress made toward a slightly different goal.
More linear algebra posts
In describing writing his second book, Tom Leinster says
… I’m older and, I hope, more able to cope with stress: just as carpenters get calloused hands that make them insensitive to small abrasions, I like to imagine that academics get calloused minds that allow them not to be bothered by small stresses and strains.
Mental callouses are an interesting metaphor. Without the context above, “calloused minds” would have a negative connotation. We say people are calloused or insensitive if they are unconcerned for other people, but Leinster is writing of people unperturbed by distractions.
You could read the quote above as implying that only academics develop mental discipline, though I’m sure that’s not what was intended. Leinster is writing a personal post about the process of writing books. He’s an academic, and so he speaks of academics.
Not only do carpenters become more tolerant of minor abrasions, they also become better at avoiding them. I’m not sure that I’m becoming more tolerant of stress and distractions as I get older, but I do think I’m getting a little better at anticipating and avoiding stress and distractions.
Contractors were working on my house all last week. I needed to be home to let them in, to answer questions, etc., but the noise and interruptions meant that home wasn’t a good place for me to work. In addition, my Internet connection was out for most of the week and I had a hard disk failure.
Looking back on the week, my first thought was that the week had been an almost total loss, neither productive nor relaxing. But that’s not right. The work I did do made a difference, reinforcing my belief that effort and results are only weakly correlated. (See Weinberg’s law of twins.)
Sometimes you have a burst of insight or creativity, accomplishing more in a few minutes than in an ordinary day. But that didn’t happen last week.
Sometimes your efforts are unusually successful, either because of the preparation of previous work or for unknown reasons. That did happen last week.
Sometimes you simply work on more important tasks out of necessity. Having less time to work gives focus and keeps work from expanding to fill the time allowed. That also happened last week.
* * *
I did get out of the house last Tuesday and wrote about it in my previous post on quality over quantity. This turned out to the theme of the week.
Diomidis Spinellis gave an insightful list of ways to reduce software development friction in the Tools of the Trade podcast episode The Frictionless Development Environment Scorecard.
The first item on his list grabbed my attention:
Are my personal settings and preferences consistent on all the computers I’m using? Are they stored under version control? Can I install them on a new computer using a single command?
Listening to the podcast provoked me to finally sync my
.emacs files on all my computers so that I now have the exact same file on all computers, maintained under version control. (Xah Lee gave me some sample code for creating the branching logic I needed for a few differences between Windows and Linux.)
Here is a small sample of questions from the podcast.
- Are my files getting backed up? Is the backup tested, accessible, off site, in multiple media, with regularly retained copies?
- Can I use the same editor for all my code and documentation editing tasks?
- Can I get context-sensitive help and code completion?
- Can I search recursively down a directory tree? Ignoring case? Only in a subset of files? With a regular expression?
- Can I open a shell from the graphical file explorer and vice versa?
- Can I quickly build the application I’m working on after a change? Can I test the application with a single command?
- Can I automatically check my code for common or tricky errors? Are these checks run by default? Are they clean?
- Does my application log its actions?
- Is documentation for the tools and APIs I use readily available? Is it hyperlinked? Available offline?
The last question from the podcast summarizes the whole list:
Do I regularly evaluate my development environment to pinpoint and eliminate the sources of friction? Do I help my colleagues do the same?
From “The Inheritance of Tools” by Scott Russell Sanders:
I had botched a great many pieces of wood before I mastered the right angle with a saw, botched even more before I learned to miter a joint. The knowledge of these things resides in my hands and eyes and the webwork of muscles, not in the tools. There are machines for sale—powered miter boxes and radial arm saws, for instance—that will enable any casual soul to cut proper angles in boards. The skill is invested in the gadget instead of the person who uses it, and this is what distinguishes a machine from a tool.
Related post: Software exoskeletons
Keith Perhac mentioned in a podcast that a client told him he accomplished more in three days than the client had accomplished in six months. That sounds like hyperbole, but it’s actually plausible.
Sometimes a consultant can accomplish in a few days what employees will never accomplish, not because the consultant is necessarily smarter, but because the consultant can give a project a burst of undivided attention.
Some projects can only be done so slowly. If you send up a rocket at half of escape velocity, it’s not going to take twice as long to get where you want it to go. It’s going to take infinitely longer.
Related post: A sort of opposite of Parkinson’s law
From Some Remarks: Essays and Other Writing by Neal Stephenson:
Writing novels is hard, and requires vast, unbroken slabs of time. Four quiet hours is a resource I can put to good use. Two slabs of time, each two hours long, might add up to the same four hours, but are not nearly as productive as an unbroken four. … Likewise, several consecutive days with four-hour time-slabs in them give me a stretch of time in which I can write a decent book chapter, but the same number of hours spread out across a few weeks, with interruptions in between them, are nearly useless.
I haven’t written a novel, and probably never will, but Stephenson’s remarks describe my experience doing math and especially developing software. I can do simple, routine work in short blocks of time, but I need larger blocks of time to work on complex projects or to be more creative.
Related post: Four hours of concentration