I was teaching mathematics to complete beginners, and finding that while they were fine with arithmetic, algebra completely eluded them. The moment one said “let x be the number of apples”, their eyes would glaze and one knew they were lost. But the same people had no problem entering a number into a spreadsheet cell labelled “Number of apples”, happily changing it at will and observing the ensuing results
This is one secret of the mass accessibility of spreadsheets: they don't require abstraction—you build a concrete working example, then tweak it. This differs from other programming environments—even the simplest scripting languages—which require you to build abstractions first and only later instantiate them. That is a high cognitive hurdle.
Indeed. Ultimately a spreadsheet is a REPL for a functional programming language. Makes you wonder why we worry so much about teaching everyone to code when the average office admin does it every day!
I agree wholeheartedly. Common wisdom states that 'spreadsheets don't scale' but I wonder if that is because we haven't built good enough tools to facilitate that. Imagine if developers developed in spreadsheets and as much effort went into creating new paradigms within them as has gone into programming language design.
You can even add another layer of abstraction that people seem to do OK with, which is "Goal seek". Excel will tweak an input cell until the output cell reaches a given condition.
I find doing mathematics in this paradigmatic non-abstract form to be utterly impossible, pure slaves to arithmetic. Whenever algebraic notation is barred from me I just break down and fail.
I'm completely the opposite. Mathematical equations and proofs make my brain shut up shop.
One day we will figure out what parts of the brain allow some people to prefer working using one way rather than the other. Until then, I'm glad that we have both.
How much did spreadsheets influence how we think about the structure of data? I know (well, I read in Wikipedia) that RDBs were proposed in 1970, but probably weren't in popular consumer use by the time VisiCalc came out. While row-column can't perfectly encapsulate objects and attributes in our world, they do a good enough job that I wonder if they compelled us to think in flat tables?
If not anywhere else, then surely on a hacker news site, one would expect not to see a statement of the form "this way that things have always been done is the only way to do it" (especially if 'it' is a subjective thing like presenting data clearly; think about the totally changing UI paradigms that could authoritatively have been predicted to be impossible before the widespread availability of touch-based interaction).
I took that to mean that it is now, rather than only that it was in the 17th century, the only way to present data clearly. Certainly if I misread that, then it undermines some of my argument.
(Even so, I don't think that the onus is on the doubter of a claim of impossibility to provide evidence of possibility, but rather on the claimant to show evidence of impossibility. That is, even if the claim is about the 17th century, then I buy that no-one has thought of a better way, but not that there is no better way—especially since 'better' is ill defined.)
Social conditioning or not, brain malleability decreases rapidly after 25. Neuroplasticity is no longer what it was, and the quicker one reconciles themselves to that fact the quicker they can figure out what they both excel at and enjoy. There's tons of things that are just in the brain. I come from a family of academics where every male in my family was either a PhD or an MD except for my paternal grandfather. Most of them are of Oxbridge pedigree, ranging from post-docs with Nobel Laureates to tenured faculty at those East-coast liberal schools Ann Coulter hates so much. Math came ridiculously easy to me, nature or nurture I'm not sure. Then I started going to conferences and seeing people who were of Terrance Tao caliber. No matter how hard I train, I'll never win a Fields medal. My brain is no longer malleable. One of the reasons I went into industry instead of academia was meeting people 20 year old first year grad students who were of one subset of mathematics, take 4 months to sit down and study an entirely different subset and start collaborating, then outperforming post-docs who've spent ~10 years on it. I'm convinced we all have more or less the same ability to perform at that level, just in different fields. Most of us will never be able to out-return Andre Agassi, but they might just be naturally[I use this term loosely since we know so little about the neurological methodologies by which we acquire and integrate knowledge, problem solve, etc we can't quantify what differentiates one's propensity for a skillset from anothers] great at poker, tearing down an engine in 20 minutes, or precision pilotry.
None of this is considered hard fact. There are studies that support what you say and there are studies that completely dispute it. And neither have been replicated with very much success. However, if you are correct, it would suggest our modern efforts at treating stroke victims are a complete waste of time and effort, a statement I think the patients and their families post-treatment would find puzzling.
People who have early success within an area of study will tend to think of themselves as a natural and will put in more practice time than a person who has not had early success. People who had early failures will continue to see themselves as "struggling" at the subject, regardless of their actual skill level. The only advantage the "natural" has is that this emotional response to the subject makes it easier to decide to practice: people of equal practice level are almost always equally skilled, even in opposition to their subjective self-evaluation, barring general mental deficiency.
There's no "math" gene. There's no "art" gene. There's only intelligence and it can be applied to any subject. The idea that people's neuroplasticity somehow "hardens" in the mid-20s or whatever is just an excuse that people make for themselves for why they bought an electric guitar but then never practiced at it. When you're a kid, you don't have a lot of different concerns competing for your time. When you're an adult, it's easy to put off a new subject when you can be productive doing something else. It's completely social.
This is one secret of the mass accessibility of spreadsheets: they don't require abstraction—you build a concrete working example, then tweak it. This differs from other programming environments—even the simplest scripting languages—which require you to build abstractions first and only later instantiate them. That is a high cognitive hurdle.