Category Archives: Nostalgia

How do you math?

Analysis, Idle Speculation, Nostalgia, Teaching, Thoughts on Thoughts

In an earlier post, I was talking about ‘friendly triangles’ as an example of unconscious things that inform my interactions with problems and math. Today, I wanted to talk about some other aspects of solving math problems that I didn’t notice I did until I had to teach mental math*, a number of years a.

I was trying to describe mental math, when I noticed all of the little assumptions I made, all the little tricks that I used to make math and mental math easier and more likely to end up correct**.

Some of these tricks were:
– The curve on the bottom of the lower case ‘t’, so it didn’t look like a ‘+’ sign
– Curved ‘x’, I’m guessing so it doesn’t look like a multiplication symbol (this one is lost to the mists of history for me
– Lining up equals signs
– Being very conscious of only having one equality per line
– Friendly triangles (1,1,sqrt(2), 1,2,sqrt(3), 3,4,5)
– Looking for radii of circles in geometry problems
– Various methods for making sure that I always itemized all of the permutations or combinations***

Once I noticed that I was doing these tricks, it was a matter of figuring out which were useful enough to spend my students’ time on. Many of them would probably be most usefully conveyed by demonstration in passing, like the way a painting instructor would demonstrate brush stroke by example.

Knowing then what I know now, I might have tried to help them come up with rules for each type of situation, but in hindsight, it’s probably best I didn’t****. What I do remember is teaching geometry problems with the advice ‘draw a big picture*****’, and ‘label everything you know or can figure out’, which feels like sound advice for solving all sorts of problems.

To this day, it’s probably why all my notebooks are slightly-larger-than-larger blank sketch pads.

*To adults, as part of standardized testing preparation.

**I remember being one of those school math students who did really well overall, but was constantly doing ‘stupid mistakes’, where I would drop a sign, or reverse something/etc… I think I compensated for this be extra checking and all the little tricks I’ll be talking about above. Or have already talked about above, it you’re reading the footnotes after all of the post.

***I actually learned this

****I don’t actually remember what I told them. I seem to recall it was just a bunch of working through problems.

*****Thanks prof. Collins!

Friendly Triangles and Spectator Ions

Nostalgia, Science!, Teaching, Thoughts on Thoughts

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.

What is the Difference Between a Duck?: Mu Jokes and Mental Push Hands

Analysis, Idle Speculation, Internet Culture, Nostalgia, Puns, Words!

UPDATE: While I was writing this, this blog passed 1000 page views since I started counting on Dec 29th! You people are awesome!

******************************************************

Yesterday, I briefly touched on the concept of ‘the space between meaning’.

One way to demonstrate this concept is with a Mu-joke (not really an anti-joke*):

Q: What is the difference between a duck**?

A: One of its legs are both the same!

The goal here is to say some words which sound not too much like nonsense, such that the listener really tries to understand.

Like a good pun, you want to draw the listener in by making things the correct level of ‘difficult to understand’. Too easy, the listener groans and moves on. Too difficult, the listener times out and moves on. (Note that this changes with each individual audience member. If ever there was an argument for (education) streaming, this is it. 😀 )

By analogy, you want your Mu-joke to make the listener feel like they would understand it if they ‘just tried a little harder’.

Also, a good Mu-joke will play with language and parts of speech, the goal being to make the listener more aware of the structure and inner meaning of what they are saying and what is being said around them. Normally, the word ‘between’ refers to two things, but we are using it to refer to one object, a duck. This gives the listener a mental ‘cache miss‘ or ‘branch misprediction‘ error, and it can throw them off balance as they try to reassemble their mental model of the conversation.

This trick can be used in a ‘Mental Push Hands***’ competition. I have fond memories of doing this with MC as we reshelved books at the library in high school. I suspect many of the best debaters use variants of this, and the best politicians have well-developed defenses against these kinds of tactics.

But back to ‘the space between meaning’. It is the space in your head where you are comfortable with ‘between’ referring to any number of things, where you are comfortable with ‘both’ referring to one thing.

It is a space I enjoy, and I hope you can help put me there. 😀

*Anti-jokes are not quite what I mean. They seem to be defined online as jokes with a standard leadup and an opposite-ish punchline. Many of the punchlines seem to take a ‘standard’ punching-down joke and subvert it. Funny, interesting, useful, but not what I’m taking about.

**I first saw this joke in one of those ‘choose-your-own-adventure-rpg’ books: https://en.wikipedia.org/wiki/Grailquest. Probably my favourite series in the genre.

***I learned ‘Push Hands’ as a martial arts balance exercise. You plant your feet and touch palms with your opponent. The object is to make your opponent move one of their feet without moving yours. For me, it was all about being as flexible as possible while trying to find my opponent’s inflexibilities.

Three

Nostalgia, Thoughts on Thoughts, Words!

Warning: 25-year-old TNG spoilers below! Imbibe at your own risk! If you wanted to see Dr. Crusher at her finest, read further!

It’s always interesting how certain things lodge themselves in your brain, to be retrieved only at certain personally defined times…

There’s a scene from ‘A Matter of Perspective*’ where Riker says “Riker to Enterprise, I’m ready to leave. Now.” I often replay these words to myself when it is clearly (in my head) time for me to leave. 8 words from a TV show I saw once 25 years ago, and yet it has stayed with me and the memory has perhaps only gotten stronger with time.

This brings us to the title of the post, ‘Three’. This is from a different TNG episode: ‘Cause and Effect****’, where the Enterprise is caught in a time loop, and Data** sends himself a message so that they can break free. This message is ‘Three’, which represents the number of pips on Riker’s collar that Data glances at just before the Enterprise is destroyed. Data surmises that he was trying to tell himself that Riker was correct and he was not***, and vents the shuttle bay doors, saving the ship. Earlier, he and Geordie had described the effect as a ‘post-hypnotic suggestion’. Interestingly, this may have been more powerful than they realized. Often, when I am asked a question, I will randomly answer with ‘Three’. Sometimes I do this because I enjoy putting people into ‘Mu*****’ space, but sometimes it’s probably just because of my memories or subconscious effects from this episode.

Incidentally, this was probably my most favourite episode for Beverly Crusher. I feel like she was the only one who could play the part she played, bringing together the early detection of Deja Vu, with the scientific and analytical mind to analyze what was going on and to gather the data that no one else would think to do. Data may have sent and received the message, but Beverly told him and Geordie that something was going on, and gathered and analyzed data to prove it. If you like this character (or want to), watch this episode.

Also incidentally, it felt almost like the scenario may have been designed by Q (or some being like him), as there are just enough clues for the crew to figure it out, without that legendary crew, they would have been trapped for 90 years, just like the Bozeman, but also because it hints at helping humans understand space and time just a little bit better, like Q was talking about in ‘All Good Things…’

*A really interesting look at perception and consent, as well as other things.

**And Geordie. They have an excellent bromance, from before such a thing was named.

***Riker wanted to decompress the main shuttle bay to move the Enterprise away from the collision, Data wanted to use the tractor beam to push the other ship away. Why they didn’t simply use both from the start, or have established emergency procedures for moving the ship when engines and thrusters are down is anyone’s guess.

****Incidentally, one has to google ‘data three tng’ to retrieve this episode. ‘data three’ is a data center, and ‘tng three’ is the third season of TNG. Interesting to think how Google and its pseudo-venn-diagram method of searching has changed the way we think******.

*****I like to refer to this as ‘the space between meaning’, similar to the effect of asking the question ‘What is the difference between a duck?’. (This will be the subject of a later post.)

******I used this when I was playing a party game many years ago. (I thought it was Cranium, but it looks like it was more likely Taboo.) I would get a word like ‘Superman’, then name two words which, if you googled for them, would return ‘Superman’.

Waving Shipfish

Fiction, Nostalgia, Science!, Space!

The waves existed, as they always had. Well, as they assumed they did. There was not much memory in waves. Every so often, they would etch some comments onto shore rocks, or read comments from before. These comments were all-too-transitory for the waves, as they would inevitably erode them away all too soon. There were also the old stories kept alive by the deep waves, those of the time before waves, when the waves were rocks and rocks were waves. The old stories also told of times when sky water was different liquids, but those times were long gone.

But something different was happening now. Normally, the waves would be fed by sky water, nurtured by winds, but there were organics coming from above? Organics had not come from above since the sky water was different, and never in sizes larger than droplets. The waves were not concerned, as waves never are. But the waves felt the pain of the shore beasts diving under the waves for protection. At the same time, the underwater beasts seemed almost giddy, swarming to the surface and feeding voraciously everytime the strange organics fell. The fliers would wink in and out, sometimes feeding, sometimes with fire, sometimes evading the sky organics.

Time passed. The waves existed. The organics stopped falling from above. They started again. They stopped. They started again. The waves were no longer visited by large shore beasts. The underwater beasts multiplied and proliferated. The fliers kept flying. The cycle continued. The waves existed. Time passed.

Something changed again. Large beasts from the sky! Some of metal! The waves had new friends! Large water beasts who talked to each other and played with the waves. The land beasts also played with the waves and traveled among the waves in mobile artificial land. As much as waves could feel joy, they felt joy.

The cycle progressed. The sky organics returned. The waves saw less of the beasts. There was less time for play. There was much fire above the waves, much pain from the land beasts. There were different chemicals at play. Runoff from the land beasts now included residue of strong dissolver. The Southern waves stopped seeing the land beasts. They heard word from the Northern waves that land beasts had appeared there and seemed to hide under rock, some artificial, some carved by waves. The waves were happy that their eons old carving work had served some purpose. The waves existed.

The waves existed. Time passed. The large water beasts played with the waves. The larger water beasts went deep under the waves and sang to them. The waves existed. The waves were happy. The waves existed.

Resisting Regulatory Capture

Economics, Nostalgia, Organizing Systems, Politics

Most people, if you asked them, would agree that corruption is a bad thing, and should be reduced or avoided. Most of them will not have heard about Regulatory Capture, though.

‘Regulatory Capture’ is the process by which an industry ‘captures’ the governmental bodies which are assigned to regulate that industry. It is generally thought to happen because of two factors:
– The people who are assigned to perform the regulatory tasks spend most of their time talking to people in the industry they’re regulating
– There are huge financial incentives for the industry to persuade the regulators to change the rules in their favour

These rule changes can take many forms. They can be laws, regulations, even constitutional changes.

The rule changes can diminish penalties, replace jail time with company-paid fines, make it more difficult for new competitors to disrupt oligopolies or monopolies, lessen oversight or protections against fraud, and many other forms.

The bribery or coercion of regulators can also take many forms. Most countries have rules in place which make it difficult to perform the obvious ‘money in brown paper bags’, but there are many other ways to induce regulators to rule* in your favour:
– Many industries have laws about the amount of time between when you can work in an industry and when you can regulate it (and vice versa), but this does not seem to have stopped anyone
– Many industry consortia write the regulations** which regulate them, so the regulator (who may feel overworked and underpaid) doesn’t have to spend the time to do so.
– Most people have family or other tribal associations of some sort. A spouse’s job has been suggested to influence even supreme court justices
– The politicians who are in charge of the regulators are often persuaded by campaign contributions
– Various illegal inducements such as drugs or ‘favours’
– Threats, extortion, etc. may also come into play

So, how do we solve this? The closest we seem to have come to this is an interlocking set of checks and balances, including freedom of speech, lobbying laws, freedom of information acts, and the occasional incorruptible investigator.

We haven’t solved this yet, and it might not be solvable, given the power dynamics. Next time, we’ll talk about some current and possible solutions.

*Ha!

**There is a lot to be said for including industry as major stakeholders when regulations are written, as for the same goal, there may be very different ways to implement them, which would have vastly different costs.

alt.comp.risks and Swiss Cheese

Analysis, Engineering, Nostalgia, Teaching, Thoughts on Thoughts

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

Idle Speculation, Nostalgia, Organizing Systems, Teaching, Thoughts on Thoughts

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?

TNG: What Might Have Been

Nostalgia, Reviews, Space!, Thoughts on Thoughts

So, we were watching the TNG episode ‘Reunion’ http://memory-alpha.wikia.com/wiki/Reunion_%28episode%29, and it got us thinking about what TNG might have been.

K’Ehleyr was such a big and interesting and *alive* character. Imagine if she had been a cast regular. The place she seemed to fit best in our mind was replacing Riker as the Enterprise First Officer.

First, a bit of backstory to set the stage:

It’s often been said that the original Star Trek was based around a ‘Freudian Trio’ of the Ego (Kirk), the Superego (Spock), and the Id (McCoy).
http://tvtropes.org/pmwiki/pmwiki.php/Main/FreudianTrio

Gene Roddenberry’s vision for TNG was that humans would have evolved to no longer ‘need’ the interpersonal bickering which characterized the Spock/McCoy interaction. Some say that this led to ‘too safe’ personal interactions amongst the crew, with the only sources of conflict being Worf’s conservatism, Riker’s devil’s advocate, and the management/engineering interaction* between Picard and Geordi.

This made the writers need to look outside the main cast for sources of conflict. This generally worked well, but wasn’t Wesley’s best performance in the series when he played the sulky teenager being called on the carpet by Picard?

All this is a long winded way of saying that it could have been a very different series with a more varied and emotionally expressive cast.

Back to Susie Plakson as K’Ehleyr as First Officer. You would have a very different take on the ‘Freudian Trio’, with the calm and rational emotional readings from Troi, and the more aggressive emotions from K’Ehleyr, with Picard bringing it all together. There’s a beautiful scene with K’Ehleyr and Troi talking just after K’ehleyr has broken a glass table in anger. So much interesting emotional depth to discover and explore!

Also, you’d have the fun dynamic between K’Ehleyr and Worf, with her as his superior officer, much more interesting than the never-really-explored-outside-of-the-book-Imzadi relationship between Riker and Troi.

But alas, TNG was a product of its time and executives. Riker with his daddy issues (which are important, and he carried the part well) must have spoken to those casting, and it must have not just been because he had the second highest rank on the ship that he got second billing, above all the ‘supporting cast’.

Also, the two women who were most like what we’re suggesting for K’Ehleyr were both written out of the show after the first season, both because they wanted more from their parts on the show. Denise Crosby left to pursue feature films, and Gates McFadden was pushed out because she was insisting on more substantive parts for her character.

It wouldn’t be until Kira Nerys that we would have a character close to what could have been with K’Ehleyr. Maybe in a Mirror Universe someday…

*It’s actually really fun to watch this, especially in the early episodes, where they have a number of classic ‘management/engineering’ conversations, including such gems as ‘I don’t want you to use the word impossible’.

Other interesting notes:

Apparently, ‘Wesley Crusher’ was almost ‘Lesley Crusher’: http://trekmovie.com/2010/08/26/1987-paramount-memo-reveals-actors-auditioning-for-star-trek-tng-cast/

Pages 293-7
http://www.amazon.com/The-Continuing-Mission-Star-Trek/dp/0671025597#reader_0671025597
Interesting notes include the fact that each of the actors had to pass personal interviews with the studio execs, that Marina Sirtis and Denise Crosby were originally cast in the opposite parts, and that Gene had to be convinced at length to choose Patrick Stewart.

Touch Typing

Games!, Idle Speculation, Nostalgia, Thoughts on Thoughts, Writing

It’s the little things that you notice. I was writing something, and just happened to notice that I was looking off into the distance while I was typing. It was one of those choices I made when I was very young. I was in High School, our school didn’t have a typing class, and I decided I needed to learn how. I don’t even remember why. It might have been my mom’s stories about learning, with those typewriters with no letters on the keys, when she was growing up.

Anyways, I remember taking one course, one of those summer enrichment things, up at Northern Secondary. I seem to recall I also took magic, stained glass, and board games, but those might have been different years. (Come to think of it, it might even have been before high school…) Interestingly, I remember this being my choice, perhaps an odd choice for a 12 year old. I don’t even remember why I thought it would be useful, but I remember acutely that I knew it would be. Perhaps similar to my choice to pursue chemical engineering over computers, as I knew that no matter what I did, I would be using computers.

I remember taking that one course, and it being fun…They had these cool puzzles where they gave you a sequence of commands to type, making simple versions of what I could only find online as ‘typewriter art’: https://www.google.com/search?hl=en&site=imghp&tbm=isch&source=hp&biw=1250&bih=694&q=typewriter+art

(Kind of early ASCII art, I wonder how much crossed over…)

In searching for the above, I found:

http://www.rapidtyping.com/online-typing-games/isogram-puzzle.html

It’s Mastermind, but with words! 😀

Which apparently has also been published:

https://boardgamegeek.com/boardgame/5662/word-mastermind

In a couple of different forms:
https://boardgamegeek.com/image/1029413/word-mastermind
https://boardgamegeek.com/image/1151419/word-mastermind

Anyways, I took these classes, but I don’t remember really using my typing until we had an email group in undergrad called the ‘Mailstrom’, often hitting 3 digits of messages per day, where quick wit (and quicker typing) was key.

I suspect there was also some training from playing computer games, but that would really only train a few keys (mostly ctrl and alt, from that era), and the mental mapping probably wouldn’t be from the hand motion to the letter.

And right now, I’m touch typing this, and it seems so normal/natural. Such a weird skill. Happy typing! 😀