Monday, August 7, 2017

Number Bases

It was Christmas time when the kid and I started talking about number bases.  The air outside was more than normally chill for San Francisco.  In the winter here, thanks to the fog, the air’s still damp, so cold feels really cold, but the chill was compensated for by town being even prettier than usual; sporting all it’s holiday lights.  People on public transit were more tired than in other seasons; the holiday rush, and December’s early sunsets combined to make a sleepy, almost lethargic atmosphere.  The season also seemed to have made our generally friendly fellow bus riders even a little more affable.  Smiles swept across their faces a little more quickly.  People scooched and shuffled to help each other get into the crowded buses.

The kid and I were on one of these buses, returning to the house from who knows where when, mostly just to liven up the ride, and with only the slightest hint of an ulterior motive, I asked her, “How many numbers can you make from a single digit?”

Why’d I do it?
I did in fact have an ulterior motive even if it was just a smidgen of one.  In my work with computers I use a lot binary, a number system that only has two values per digit, 0, and 1.  I also use a number system called hexadecimal.  Hexadecimal has 16 different numbers.  They are, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, and f, (seriously, not making it  up).  I wanted to be able to talk to my kids about what I do at work.  Hence the question, “How many different numbers can you make with a single digit?

Technical terms (a brief interlude)
Please excuse one more interruption in our tale.  Before we go too much further, let’s get the fancy technical terms out of the way.  Binary and hexadecimal are specific names for two specific systems of numbering.  Mathematicians, (who for various syntactic and semantic reasons are probably cringing as they read this), call these systems of numbering ‘number bases’.  The binary system is called ‘base 2’, (there are two single digit numbers in the system, 0, and 1).  Hexadecimal is called base 16.  That’s because there are 16 single digit numbers, (go ahead,count them above… yes, a - f are numbers in hexadecimal).  None of us can really escape number bases, we can just choose not to discuss them; the system we all use every day is  base 10, (0 - 9: 10 numbers).

Learning our native base
So, back to the kid’s and my conversation. You’ll recall I asked, “How many numbers can you make with one digit?”  She was unsure, so I suggested counting them.

“1, 2, 3, 4, 5, 6, 7, 8, 9, 10…”

As the bus veered off of Ocean, to enter Persia, in our little neighborhood called Excelsior, I interrupted, “Stop!  Can you write down 10 with one digit?”


“When you write down 10, how many digits—characters—do you have to use?  What do you write down on paper for 10?”

“A 1, and a 0,” she answered.

“OK, so 10 doesn’t count because we only want to know how many single digit numbers there are.  Ten takes two digits, a one, and a zero,” I said as I wrote the digits in the air with my finger, being careful to get the one on her left, and the zero on her right as I faced her; a trick I’d learned in my college beer-money job—tutoring physics.  I continued, “So, how many number can you make with a single digit?”


“What about 0?  It’s a single digit right?”

“Oh yeah, 0!”

“So, how many single digit numbers are there?”

 “Nine plus one more for 0,” she said counting on her fingers.  “So, 10.”

 “Awesome!  You just figured out what number base we use!  The number of single digits in a number system is called its base.  We use base 10.”

“OK,” she said with a grin.

We stopped to pick up new passengers at the corner of Persia and MIssion.  The kid and I were able to grab seats as people filed first out, and then into the bus.  As we sat down, our neighbors got on carrying pink boxes of Salvadoran pastries from the bakery near our stop.  The warmth of their aroma hit us as the boxes and their associated passengers scattered throughout the bus.  As we got back under way, I jumped back into our conversation.

“So, what number system do we use every day?  What base?”

“10,” the kid exclaimed as we got a sideways glance from a sleepy fellow passenger.

“Good job!  So, what’s the biggest number you can make with single digits?”

“10?” she pondered.

“Really?  Doesn’t that take two digits?”

“Oh yeah!  OK, 9 then.”

“Cool deal!  So, what number base do we use?”

“Base 10!”

“What’s the biggest single digit number?”


The bus squeaked to a stop at Naples.  Lots of people live near there.  They all trundled off.  The doors closed and the bus continued to power up the hill..

“What if we were in base 4?  How many single digit numbers would we have?”


“So, in base 10 we have 10 single digit numbers.  If we had another system called base 4, how many single digit numbers do you think it would have?”


“Yup!” I beamed as we crossed Vienna.  What would they be?  Which numbers?”

“1, 2, …”

“What about zero?” I interjected.

“Oh, 0, 1, 2, 3, and 4.”

“Really 4?  How many numbers is that with 4 in there?  Count them.”

Hammie started out counting.  “1, …”

“Make sure you start with zero.”

“0, 1, 2, 3, 4,” she took time to look at her five fingers that were now up.

“Too many numbers right?  We only want four numbers for base 4 just like there were 10 single digit numbers in base 10.  Got it?”

“I think so.”

“So, how many single digit numbers in base 4?”


“What are they?”

“0, 1, 2, and 3.”

“Sweet!  What’s the biggest single digit in base 4?”


“Cool!  So, the biggest single digit is always one less than the base.  In base 10 it was 9.  In base 4 it was 3.”  We got off the bus at our stop, and trundled up the hill, talking about number bases as we made our way through the chill night air up to the house.

The Base Game
We spent time on the next several bus rides going over all sorts of bases.  I figured worst case, the kid was working on counting and on subtracting one.  What could we lose?

Before long, she could habitually respond with the correct answers to my questions about number bases.  As the game became easy, I began to plan my next question.  What happens when you run out of room in your single digit?

When digits are all filled up.

Monday, June 26, 2017

Steal Like an Artist by Austin Kleon

An excellent thought-provoking book that's fun to look at and to hold. Yes, I'll steal the size of this book for my homeschool travel book, and well, that was one of the points! Austin Kleon who serendipitously came to live in Austin, TX wrote this book of on how to best experience being creative. The book covers more of the how than the what I'd say. Some of the advice Austin offers filtered through my reading:

1. Think of your heros' lives, not just their creative input. Let their lives inform yours.
2. Dress for the job you want. Keep being a kid, keep pretending.
3. Get bigger pockets if you need to but keep a journal(s) on you at all times.
4. Who influenced the people who influence you?
4.a. Who does influence you anyway?
5. Don't worry about your ideas being stolen.
6. Everything that needs to be said has been, but no one listened.
6.a. Say it again.
6.b. Say it your way.
7. Write not what you know, but what you like to read.
8. Touch your work. Rearrange it. Tape it to the wall.
9. Tune out while you experience the world. Take the bus. Keep your head up.
10. Keep a log book. Ask yourself what's the best thing that happened to you today?

All of it's so, so good!

No. 1 our 6 y.o. demonstrates how to tape your work to the wall! (And some of Leroy Neiman's).

Monday, June 5, 2017

Living Light

We practice minimalism in a different way. We’ve applied it to our out-and-about living.  We travel light, and I love it!

Minimalism, and thoughts of living mindfully are in the air this week.  On Racheous, Rachel talked about her family’s recent move, and how switched to a more mindful set of possessions on the way.  At Jitterberry, Jessica discussed her family’s transition to a minimalism lifestyle.

We practice minimalism in a different way, we’ve applied it to our out-and-about living.  We travel light, and I love it.

Before we had kids I was spooked by strollers.  They inevitably seemed to be loaded with numerous items on their bottom tray.  They also seemed to inspire the use of diaper bags, or other parent-laden luggage.  My typical outing at that point involved throwing a collapsible fishing rod, a tackle box about a quarter the size of a shoe box, a few pancakes wrapped in a paper towel, and perhaps a cup of earthworms into a small pack.  I enjoyed fishing in hard to reach places off the trail, behind brambles, and away from people.  If I carried too much, I couldn’t get there.  I wanted to share these experiences with my kids.  Consequently, the stroller/diaper-bag combo gave me the willies.  I need not have worried, a solution was close at hand.

I’d seen women in Boulder coffee shops with babies in wraps.  Their lives looked delightful.  They bounced into the shop with a small bag, and a kid strapped to their torso, and ordered their coffee.  If the baby was awake out of the wrap they’d come for some lap-time.  If the kid was asleep, they’d let them continue to snooze.  These moms had skills that even I would never develop.  They’d take the wrap all the way off.  When they were ready to go, they’d inevitably tie it back on with the baby in a different comfy potion.  Baby on the chest on the way in, on the back or perhaps tucked onto the side on the way out.  Showboats!

So, before we had kids, my partner and I talked things through.  We decided we could have a wrap if the kids were wrapped to me.  We don’t do diaper bags.  We just throw the minimum equipment we need for an outing into one of our packs.  We take snacks, (the kids and I travel on our stomachs), a few diapers, a package of wipes, and a few plastic bags to hold the old diapers in.  Of late, it’s all gone into our 6-year-old’s bag.  I’ll give you that as the kids grow, we need to bring more food, but this is balanced out by the smaller kids getting backpacks to carry their own things in as they get larger.

Our experience at outwards-bound minimalism has been incredible!  We can leave to go on adventures at a moments notice.  We can change routes and plans easily.  And, it’s a piece of cake to take public transit, and maneuver around town—dividing up to scamper through crowds, and having a great time!

How do you lighten your load? 

Sunday, June 4, 2017

Respectful Parenting, Electronics System Theory, and Faith

Inspired by the Sara’s recent post about respectful parenting +Happiness is here vis-à-vis Minecraft screen time.  The end analysis there?  Trust your kids, and parent respectfully.

In electrical systems theory, we divide circuits up into two categories, differentiators and integrators.  Differentiators make circuits more sensitive to every little change.  The circuit doesn't miss much, but it might flail around quickly.  Integrators on the other hand cause the system as a whole to be less sensitive to small changes.  Systems with integrators won't respond to a small change, they simply add it to a total response, and wait for more information.  If the changes continue to happen in the same way, ultimately the system will respond, but it takes time and consistency.

This is how I view Sara’s description of handling video game screen time.  I would have been inclined to shutdown all the screens after two days spent exclusively on a video game.  If I'd done this, I wouldn't have given the 'system' of our kids the time to organically respond to their new environment.  By taking a more integrated approach like Sara did, it's easier to see what the system wanted to do for itself, and how it normally behaves without outside influences.

I like the integrating approach better, though it's occasionally difficult to remember to use it when I'm caught up in the moment.  I find myself thinking, 'something's changed, change it back.'  I might also phrase the whole thing with integrators and differentiators in a different way—in terms of faith.  It’s sometimes difficult, but it’s always been helpful for me to have faith that the kids are competent, and are going to figure things out for themselves in a healthy way.  Sure, I can offer advice if they want it, (and I do), but they get the best results, and grow the most, I think, when I’m not involved.

Saturday, June 3, 2017

Our Bus Our Living Room

 Public transit…  Our living room activities mostly take place on the buses and trains of San Francisco.  If we get on a bus at an early enough stop, we can consume the entire back row of seats; there’s five of us and there’s five seats.  Our deepest conversations happen there, we talk about things like “How do number base systems work?”  “Why is it not OK to pick up food from the ground close to a train station,” (answer Pee).  “Where do puddles underground in train stations come from,” (same answer.)  Some of our conversations like the pee exploration gather other bus passengers.  A young lady with her one year old strapped to her chest figured she’d have to have the conversation with her kid soon enough, and wanted to get the youths’ take on public pee in the city.  This often leads to utter hilarity—our 4 year-old No. 2 wasn’t sure it was such a bad thing to pee on walls.  Most of our conversations draw more quiet audiences—the ladies grinning and chuckling as our oldest, then four years old, and I discussed how we eat meat, muscles are meat, and therefore we eat muscles.  From there it was on to more draconian topics like blood.  (Yes, No. 1’s a died-in-the-wool meat-eater).  Sometimes our reverie is interrupted by others who feel the need to contribute to our entertainment.  Who needs cable?  Did I see the Super Bowl this year?  I didn’t need to.  A tipsy gentleman give us the complete play by play on the way back from Oakland to San Francisco.  He even acted out some of the more linear plays for us in the aisle of the train.  Other we provide unexpected ‘entertainment’ for others.  I’m sure, not everyone in the back of the bus was interested in listening to the travails of Scooby Doo overlaid with the adventures of Groot as we trundled home from last Sunday’s birthday party.    That gives us what feels like a clubhouse on the bus.  

What about you?  Do you spend the majority of your quality time in or out of the house? What’s your favorite quality time activity?