I asked on Twitter today “What steep learning curves do you wish you’d climbed sooner?” Here’s a summary of the replies:

- R
- Version control
- Linear algebra
- Advanced math
- Bayesian statistics
- Category theory
- Foreign languages
- How to not waste time
- Women

IgorCarron‘s response didn’t fit into the list above. He said “I wish I had known that sensing all the way to machine learning is about approximating the identity” and gave a link to this post.

I wish I had learned that steep learning curves actually mean fast learning and gentle learning curves mean slow.

@John: or maybe a steep learning curve means you need to learn a lot in a short time?

Did anyone recommend resources for tackling those steep learning curves?

@John, @JW: I think people typically use “steep” in this context to mean “hard,” not necessarily “fast.” The metaphor may make more sense if you think of the vertical distance as being fixed rather than the height.

I also think of “steep learning curve” as meaning “delayed return on investment,” something that isn’t useful in the short term, or even counter-productive in the short term, but that pays off well eventually.

@Amit. Nobody recommended resources, and I think that goes with steep learning curves. Part of what makes a learning curve steep is the lack of resources, or the limited usefulness of resources if they do exist. If you want to learn French, for example, the best textbook can only help so much.

Do you find much use of the advanced math as a consultant, say in comparison to simpler* math and simulation/programming-based solutions?

*E.g. basic linear algebra and (multivariate) calculus

@Benjamin: It’s all over the map. Some clients need very simple math, some need graduate/research-level math, and everything in between.

For the most elementary math, what they really need is not the math per se but someone to tell them what is appropriate in their context, what is important and what can be ignored, etc. Sometimes the elementary math is not really elementary. There may be an advanced theory in the background justifying or leading you to an elementary result.

By the way, clients are often excited about simple solutions. You may be a little embarrassed that something turned out to be trivial, but they’re only interested in the result and don’t really care how you got there. They may be more impressed by something they find comprehensible than by something more advanced that’s just gobbledegook to them.

LaTeX. I wasted so much time fighting with word, it crashing, moving figures around and corrupting documents. Not to mention all the CS stuff I did in Word in first use using keyboard shortcuts to insert logic symbols or OpenOffice’s equation editor.

As a woman working in tech, I’m not sure how to parse the women list item.

Are your twitter followers mostly straight men? Do they not understand half the world’s population? What does that even mean? Are we building tech just for men?

Dear John,

Great work with the blog. I always enjoy reading it. Keep up the good work!

I’m a little puzzled by the entry on Bayesian statistics. In principle, it’s actually very simple — posterior equals prior times likelihood. The rest is just examples and special cases. In my experience, it’s really frequentist statistics that has the much steeper learning curve, and which requires much more sophistication to understand properly. Sure, it’s easy to teach people how to run a few simple commands in SAS or Stata or even R, and the theory is so well-mechanized at this point that people can do a lot of analysis just by knowing what numbers to read off of a printout. But actually understanding *why* they are doing it, what the rationale is — that’s a very different story, and in my experience a lot of people with fairly extensive training still can’t explain even simple ideas such as the difference between a standard deviation and a standard error. The fact that frequentist statistics didn’t even make it onto your list really suggests that most people don’t even know what they don’t know.

@Theodore: I agree that Bayesian statistics is more coherent than frequentist statistics, fewer principles more widely applied.

One thing that may make Bayesian statistics harder to learn is that you may have to learn more on your own since more classes are taught in frequentist statistics. Also, I think people who don’t really know what they are doing can do more harm with Bayesian methods than with frequentist methods.

Dear John,

Well, I’m not so sure that Bayesian statistics is more “coherent”. But perhaps this is just a debate about semantics.

Sure, there are lots of classes on frequentist statistics that train people in the mechanics of the process. But my point is that many people come out of those classes without understanding the underlying ideas, so in that sense the learning curve is steeper. Speaking personally, my experience has been that it took me a lot longer and required much more work to grasp what was going on in frequentist arguments, whereas the Bayesian approach was relatively straightforward to comprehend.

@Theodore: I could see that. A frequentist confidence interval, for example, is harder to understand than a Bayesian credible interval.

C++. Bayes. Maths. Book of Mormon. Christianity.

Oh yeah – vim!

And by definition Bayesian statistics is more coherent, because all frequentist methods can be shown to be incoherent. To be coherent is to be Bayesian.