Our Colorful Mathematics Revolution

Education bureaucrats are trying to gently and safely tweak a broken system so that fewer students fail math.

Meanwhile, a colorful revolution is taking shape outside the walls of a crumbling institution. A populist movement in creative math is empowering an unlikely crowd.

Authors of Wikipedia math pages aren’t contributing to this populist movement. They are intent on impressing each other; competing to see who can reduce a mathematical concept to its most accurate, most precise (and least comprehensible) definition.

A debate rages on a “new way” to do subtraction. Oh does it rage. But step back from that debate and consider that these tricks, algorithms, processes, hacks, become less relevant as new tools take their place. When calculators entered into the classroom, something started to change. That change is still underway.

Do students no longer need to learn to do math by hand? No. But calculators (and computers) have changed the landscape.

Rogue amateur mathematicians, computer artists, DIY makers, and generative music composers are creating beautiful works of mathematical expression at a high rate – and sharing them at an even higher rate. This is a characteristic trait of the “new power“.

Technology

(1) Computers are better at number-crunching than we are. If used appropriately, they can allow us to apply our wonderfully-creative human minds to significant pattern-finding and problems that we are well-suited to solve.

(2) Computer animation, generative music, data visualization, and other digitally-enhanced tools of creativity and analysis are becoming more accessible and powerful – they are helping people create mathematically-oriented experiences that not only delight the senses, but express deep mathematical concepts. And they also help us do work.

(3) The internet is enabling a new generation of talented people (amateurs and professionals) to exchange mathematical ideas, discoveries, and explanations at a rate that could never be achieved via the ponderous machinations of university funding, publishing, and teaching. There will never be another Euler. Mathematical ideas now spread through thousands of minds and percolate within hours. It is becoming increasingly difficult to trace the origins of an idea. Is this good or bad? I don’t know. It’s the new reality.

Five things You Need to Know About the Future of Math

According to Jordan Shapiro:

1. Math education is stuck in the 19th Century.
2. Yesterday’s math class won’t prepare you for tomorrow’s jobs.
3. Numbers and variables are NOT the foundation of math.
4. We can cross the Symbol Barrier.
5. We need to know math’s limitations.

We can (and will – and should) debate how math should be taught. Whether the “symbol barrier” is a actually a barrier, and whether memorizing the multiplication tables is necessary, no one can ignore the seismic changes that are rumbling underfoot.

-Jeffrey

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The Unicorn Myth

I was recently called a “unicorn” – a term being bantered around to describe people who have multiple skills.

 

Here’s a quote from http://unicornspeakeasy.com/

“Dear outsiders,

Silicon Valley calls us unicorns because they doubt the [successful, rigorous] existence of such a multidisciplinary artist-engineer, or designer-programmer, when in fact, we have always been here, we are excellent at practicing “both disciplines” in spite of the jack-of-all-trades myth, and oh yeah – we disagree with you that it’s 2 separate disciplines. Unicorns are influential innovators in ways industries at large cannot fathom. In a corporate labor division where Release Engineer is a separate role from Software Requirements Engineer, and Icon Designer is a separate role from Information Architect, unicorn disbelief is perfectly understandable. To further complicate things, many self-titled unicorns are actually just programmers with a photoshop habit, or designers who dabble with Processing. Know the difference.”

Here’s David Cole on the “The Myth of the Myth of the Unicorn Designer“. He says:

“Design is already not a single skill.”

There are valid arguments on either side of the debate as to whether designers should be able to code. What do you think?

-Jeffrey

Programming Languages Need Nouns and Verbs

I created the following Grammar Lesson many years ago:

Like many people my age, my first programming language was BASIC. Next I learned Pascal, which I found to be extremely expressive. Learning C was difficult, because it required me to be closer to the metal.

Graduating to C++ made a positive difference. Object-oriented programming affords ways to encapsulate the aspects of the code that are close to the metal, allowing one to ascend to higher levels of abstraction, and express the things that really matter (I realize many programmers would take issue with this – claiming that hardware matters a lot).

Having since learned Java, and then later…JavaScript, I have come to the opinion that the more like natural language I can make my code, the happier I am.

Opinions vary of course, and that’s a good thing. Many programmers don’t like verbosity. Opinions vary on strong vs. weak typed languages. The list goes on. It’s good to have different languages to accommodate differing work styles and technical needs.

But…

if you believe that artificial languages (i.e., programming languages) need to be organic, evolvable, plastic, adaptable, and expressive (like natural language, only precise and resistant to ambiguity and interpretation), what’s the right balance?

Should Programs Look Like Math? 

Should software programs be reduced to elegant, terse, math-like expressions, stripped of all fat and carbohydrates? Many math-happy coders would say yes. Some programmers prefer declarative languages over procedural languages. As you can probably guess, I prefer procedural languages.

Is software math or poetry? Is software machine or language?

I think it could – and should – be all of these.

Sarah Mei has an opinion. She says that Programming is Not Math.

Programming with Nouns and Verbs

First: let me just make a request of all programmers out there. When you are trying to come up with a name for a function, PLEASE include a verb. Functions DO things. Like any other kind of language, your code will grow in a healthy way within the ecology of human communicators if you make it appropriately expressive.

Don’t believe me? Wait until you’ve lived through several companies and watched a codebase try to survive through three generations of developers. Poorly-communicating software, put into the wrong hands, can set off a pathological chain of events, ending in ultimate demise. Healthy communication keeps marriages and friendships from breaking down. The same is true of software.

Many have pontificated on the subject of software having nouns and verbs. For instance, Matt’s Blog promotes programming with nouns and verbs.

And according to John MacIntyre, “Take your requirements and circle all the nouns, those are your classes. Then underline all the adjectives, those are your properties. Then highlight all your verbs, those are your methods”.

When I read code, I unconsciously look for the verbs and nouns to understand it.

When I can’t identify any nouns or verbs, when I can’t figure out “who” is doing “what” to “whom”, I become cranky, and prone to breaking things around me. Imagine having to read a novel where all the verbs look like nouns and all the nouns look like verbs. It would make you cranky, right?

The human brain is wired for nouns and verbs, and each is processed in a different cortical region.

There are two entities in the universe that use software:

(1) Computers, and (2) Humans.

Computers run software. Human communicate with it.

-Jeffrey