Since the golden era of arena rock, guitarists have played tube amps – monstrous, fire-breathing multi-hundred-watt heads with vacuum tubes glowing red-hot beneath grills that bore names like *Marshall*. *Orange*. *Mesa*. There has never been anything quite like them; nothing has put out the unique sound of a tube, and nothing has offered the interplay between a guitarist’s fingers and the tone coming forth from the cabinets supporting those heads. Solid-state amps, behind a surge of marketing money, briefly took a foothold in the amp market during the 1970s and 1980s, until guitarists realized a simple but terrible truth: *the new tech was nowhere near as good as the old tech*. And so tube amps continued on, Jurassic technology that somehow managed to fend off the incursions of electronic advancement for decade after decade.

And then a German scientist realized something: namely, that what made a tube amp a tube amp was pretty simple, from the physics perspective. A tube amp applies a variable modification to an input waveform, based on the volume and sonic envelope of that input waveform, and then outputs the resulting modified waveform to a speaker. Capture the delta between the input and the output waveform – in all of its complexity – and you can truly put a tube amp into the digital environment. That’s it. And, just like that, the entire amp industry changed, overnight – some artists adopting Kemper tech, others using its competitor and close cousin, the Fractal Axe-FX. It’s a technology that has been nothing short of transformational. Don’t get me wrong; there are still plenty of tube amps being sold, just like there are plenty of gas-powered cars and plenty of Windows 8 laptops being sold today. But, just like those products, guitarists have started to get the sense that maybe,* just maybe*, we’re looking at the beginning of the end.

Why do I bring this up? Because I’m writing this between sessions checking E’s algebra homework. She’s working on equations involving radicals and roots, and it’s a topic that’s got her complete attention. I can actually see the content spinning up the Big Engine to full speed. That’s rare anymore; it’s nice to see. But what’s got *my* attention is the fact that she’s meticulously solving these equations by hand over the course of minutes, and I’m checking them with Wolfram Alpha in mere seconds. Things have changed, fundamentally, once more.

Thirty years ago, algebra teachers wrote and checked homework problems by hand, just like we did. Why? Because absolutely *nothing* like Wolfram Alpha existed. For them, it would have been impossible to conceive of a world in which algebra should be taught with solving technology when there wasn’t any such thing. We’ve always had some sort of solving tech for arithmetic; slide rules have been around since the 1600s (fact!) and cheap four-function calculators have been around since the early 1970s. Most of us reading this blog grew up with slightly bemused and befuddled math teachers who told us that calculators weren’t allowed. Today, there’s been some grudging acceptance of calculators for sixth-grade math and beyond (apparently, five years of hand calculation is sufficient penance in 2013). But if you rolled into a high-school algebra class today with Wolfram Alpha running on an iPad, it would be considered heresy.

Yet this is the age we live in: applications and services and technologies are coming forth that fundamentally change our lives overnight. Five years ago, unless you owned a copy of Wolfram Mathematica, there was no such thing as opening an app and typing:

Not only does Alpha solve that, its cheery OCD nature also checks for complex roots, graphs the result in a handful of different, potentially-useful ways, and even offers a step-by-step solution to the problem (in case you’ve, *ahem*, grown *rusty* in your manual formula evaluation skills). It is, quite simply, revolutionary, and at some level, I sincerely hope it changes how algebra is taught in this country.

Before you get out your *I-walked-to-school-uphill-both-ways* pitchforks and torches, let me set your minds at ease: I don’t think Alpha is a *substitute* for learning the theory of algebra and developing skills in solving equations manually. I think it’s important to see the results come together under your pencil – *for some period of time*. But at a certain point in elementary-school math, we now allow kids to use calculators. Why? Because given better tools, we’ve elected to raise the bar for what can be done with them. The questions are harder, so we allow some computational support in getting to the right answer. Computation is no longer the important part of the problem; setting up the problem is.

Now we need to do the same in algebra. Algebra chapters in 2013 focus on much the same end goal as they did in 1981: *solve this equation*. Sure, story problems get a bit more difficult, but there’s nothing in E’s copyright-2013 Algebra I book that would have looked out of place in my 1981 copy. We need to acknowledge the existence of solving tech by asking *more* of algebra students. Specifically, we need to begin to emphasize those tasks that only a creative human mind can perform: namely, setting up complex equations and systems of equations, with multi-step problem solving. Solving them, over time, should begin take on that you-can-use-a-calculator mindset: *go ahead and use it – you still have to do the most important work. *

From the longer-term view, though, we need to start adopting a mindset that accommodates, embraces, and – eventually – *goes looking for* disruptive tech. Alpha is, ironically, an omega technology; it brings to an end a particular era of doing things in one way and one way only. It breaks the paths of mental endeavor into new forks and branches, and asks a fundamental question of us: do I keep doing manually what this new technology will do for me, or do add the tech to my toolkit and push myself to do more complex, more intricate, more beautiful, more inspired work with it? After all, I can now carry a warehouse full of multi-thousand-dollar tube-amp heads around with me in a gig bag. Should I feel threatened by that, or empowered to make more interesting music?