Category Archives: Teaching

Friendly Triangles and Spectator Ions

There are many different ways that you learn things. You can learn things from school, from books, from videos, from sticking a fork in a light socket.

But we’re talking about the things you learn in passing, or by osmosis, as you’re growing up. Sometimes these are things learned so early on in your education, so basic, and built upon by thousands of other concepts. Sometimes they are the ways of speaking of your parents, their ways of thinking.

For me, this was Spectator Ions. Growing up, my dad would always talk about (aqueous) chemical reactions, for example, from Wikipedia:

2Na+(aq) + CO3 2−(aq) + Cu 2+(aq) + SO4 2−(aq) → 2Na+(aq) + SO4 2−(aq) + CuCO3 (s)

In this reaction, the carbonate anion is reacting/bonding with the copper cation. The two sodium cations and the sulfate anion have no part in this reaction. They are merely ‘spectators’.

So this is all reasonable, this makes sense. But I was trying to explain this to someone recently, and I realized that I didn’t know the phrase ‘spectator ions’, I just knew intuitively that sodium cations are basically never involved in reactions. The best way I can describe is knowing them as ‘small and bouncy’. (Perhaps ‘small, bouncy, and indivisible’, unlike N2(g), which is ‘small to medium-sized, bouncy, and divisible with significant effort.)

So, how do you explain something like this, when you approach it in such an intuitive way? I feel like it approaches or becomes an issue of privilege, like being the only person who can access the underpinnings of the system.

Sometimes, I feel the same way about ‘friendly triangles’. Probably the most famous of these is the ‘3,4,5’ triangle, which has been known (and presumably used in construction) since antiquity.

The other triangles commonly called ‘friendly’ are:
– 1,1,sqrt(2), or the ‘45,45,90’ triangle, used with unit vectors everywhere, also interestingly the right-angle triangle which has the largest percentage of its perimeter in its hypotenseuse.
– 1,2,sqrt(3), or the ‘30,60,90’ triangle, used most often probably with equilateral triangles and subsections thereof

Once these concepts are automatic, you start to see them everywhere. If you want a better explanation of ‘friendly triangles’, try here:

http://www.purplemath.com/modules/trig.htm

But back to our original question, which was all about how you deal with having a very intuitive sense of something, which underpins your world view in a subtle but fundamental way that is difficult to describe. I don’t know. All I can do is to try to notice when it happens, and try to learn how to best describe it, which is really all you can do to try to communicate something unconscious to you and which may be outside the other person’s experience. I think a later post will talk about some of my other interactions with math of this type, and how I learned to describe while showing and sharing.

alt.comp.risks and Swiss Cheese

If you’ve never read alt.comp.risks, you should do so. In fact, you can read the digest here:

https://catless.ncl.ac.uk/Risks/

If you don’t know what alt.comp.risks is, it is 30 years of all the things that can go wrong with complex systems (especially computers). Anyone who has done a post-mortem or incident report or accident report will familiar (if not happy) reading there. They will probably also notice that the same problems keep happening again and again and again.

Young Drivers mentioned a study* which said that a typical traffic accident requires four errors on the part of the drivers (two each). In the accident and risk analysis world, this is often referred to as the ‘Swiss Cheese’ model. https://en.wikipedia.org/wiki/Swiss_cheese_model

The ‘Swiss Cheese’ model is the idea that adding more layers of checks and protection can help make a system safer, as long as the holes in those layers do not align.

This is a major reason why it is just as important to investigate incidents as it is to investigate accidents. ‘Incidents’ are occasions where something ‘almost went terribly wrong’, where two or more of the ‘Swiss Cheese’ holes aligned, ‘Accidents’ are where all of the ‘Swiss Cheese’ holes aligned, and something terrible actually happened. In the Diagram below**, the ‘Accident’ is the arrow that made it all the way through, all of the other arrows are incidents, which left unchecked, could lead to accidents some day.

raeda-icam-image

Why do we not just spend our time and energy closing those holes in the ‘Swiss Cheese’ (or to making sure they don’t align)? All of that takes money or other resources***. So, given the modern legal system, most organizations balance money and safety in some way, shape, or form. This balance between resource allocation and safety is such an issue that there is an entire regulated profession whose purpose is to properly maintain the balance.

I’m speaking of course of Engineering. The perception of Engineering is perhaps of people building things, or Leah Brahms and Geordi arguing about how to make warp engines go faster, but fundamentally Engineering is about balancing safety with costs.

Probably the most pernicious obstacle to this proper balancing is the dismissal of incidents as unimportant or contained. Any incident which makes its way through 3 of your 4 layers of safety is one mistake away from a disaster, and should be treated accordingly.

*I can’t seem to find it at the moment, but I believe them, as it is consistent with my experience.

**From http://raeda.com.au/?p=115 “The ICAM (Incident Cause Analysis Method) Model Explained

***Often not stated is that spending time on safety-related things is a distraction, both in time and context switching.

Emotions and Control

So, I was listening to Adema’s “Everyone”, and one line in particular stood out to me:

“Why am I so angry inside my head?”

http://www.azlyrics.com/lyrics/adema/everyone.html

A classic question that people have been asking themselves for generations, and one of the questions that we’ve been trying to answer for the next generation I imagine for as long as we’ve been trying to answer things. (It also seems to be consistent fertile ground for many genres of music…)

Every generation brings new people, angry about new things (or the same thing, again and again).

Do we have more anger in our youth than usual?

Kondratiev wave theory would suggest yes:

http://en.wikipedia.org/wiki/Kondratiev_wave

At least in North America, there’s been a squeeze going on for probably 20 years (a whole slew of other topics, out of scope). Add that to they standard “Is that all there is?” as you approach adulthood, and that’s fodder for whole genres of music.

But really, the original question, about trying to control the non-grey matter portions of your brain…

When I was doing safety training, I used to say that I could deal with no sleep, or crappy food, but not both at the same time, or I would get cranky.

And how do you teach the next generation to control their brain? Do you want to?

How do you educate them to control the ‘proper’ parts of themselves, while still expressing their creative and exploratory sides?