On Mathematics: Base Not-Ten Systems and Abacii

Chapter one (that is, the chapter following chapter zero) of Here’s Looking at Euclid started off with an extensive analysis of the base 20, base 12, base 2 (binary) and other number systems. Aside from the brief realization that when converting between TBSP and cups or cups and gallons I can actually think in an essentially base 16 system, I find it hard to wrap my head around non-base 10 systems of numbers, so on that subject I simply refer you to Toby’s defense of the base 12 system: http://geekofmanytrades.blogspot.com/2014/03/math-and-sciences-monday-cheaper-by.html

The more intriguing (or at least less brain bendingly intriguing) part of the chapter was the discussion how becoming proficient with an abacus (specifically a Japenese style soroban, with five beads to a row) can improve the speed of mental calculations. I’m beginning to wish that I learned how to properly use my childhood abacus instead of arranging the beads into patterns and rolling my eyes at manipulating the beads to show answers to basic math problems I could already do faster in my head.

After reading about the intensive mental calculations achieved by school children who master the soroban it seems like a very good way to teach basic math skills. Manipulating physical objects as a way of doing math changes which parts of the brain are used, which means that not only could it make basic math concepts much easier to grasp for more creatively and less logically minded children, but even for logically minded children, the crossover of using multiple parts of the brain should improve their ability to recall what they’ve learned. Add to this the fact that soroban then becomes a basis for much more complex calculations later, and I’m a bit tempted to go back and learn to use a soroban in my spare time myself.

Maybe right after I finally tackle quantam physics.

On Mathematics: Approximation and Exactitude

The first chapter of Here’s Looking at Euclid (which is numbered at Chapter Zero) deals with the cultural differences between dealing with numbers and instinctive human reactions to dealing with numbers, which leads to a lot of discussion of approximating numbers versus exact counting.

The author ends the chapter with the conclusion that numbers are a human construct imposed on the outside world as a way to try to make sense of it. I find this conclusion baffling as it follows on the heels of this question, “If our brains can represent numbers only approximately, then how were we able to ‘invent’ numbers in the first place?” Perhaps the whole thing would make more sense if one assumed that God created numbers and mathematics, and that even our attempts at exactness are derivative from His truly exact calculations. (Pi, anyone?)

To me, the most interesting part of this exploration of the human brain and numbers was the idea that we innately tend to think logarithmically rather than linearly. That is, we tend to think in terms of comparisons and ratios rather than exact numbers as laid out on a number line. Don’t believe me? Which sounds more drastic, the difference between one and a million or the difference between one million and two million?

See what I mean?

Even those of us who lean toward logic and precision of calculation still have a human inclination to view numbers in an approximate and comparative way. (Possibly because this is more useful in everyday life, as people who tend to get caught up on precise calculations are often reminded. Counting how many items are in the carts of each person in each line of the grocery store isn’t going to save you any time, even if you do manage to calculate which line is mathematically shortest, but a quick estimate and comparison of heaping full carts vs one nearly empty cart might save you quite a bit of time.)

Now, here’s one of the interesting bits: Teenagers who were tested on their ability to rapidly compare groups of dots and accurately estimate the differences in sizes of the groups varied greatly in their ability to make these estimates. The ones who scored highest on these tests correlated to those who tended to score highly  on their school test in the precise calculations of formal mathematics. In other words, the better you are at estimating and comparing, the better you likely are at precise calculations.

This brings to mind teaching approaches that focus on the natural developmental stages of children. Perhaps rushing children past the early, colorful, comparative stages of learning math into ‘proper’ academics actually slows down their progress in the long run. I have no idea off the top of my head what that means about teaching math as specific ages, but it does seem to lend general support in the direction of allowing younger children time to focus on creative play instead of formal academics.

This chapter of the book sparked one last ponderable thought for me: If most of our formal mathematics are based on a logical, linear scale, are there similar levels of advanced mathematics yet to be discovered along the path of more intuitive, logarithmic scale?

Best Birthday Freebies in the Peoria, IL area

Before my birthday last week I signed up for a bunch of birthday clubs and such for restaurants in the Peoria area. A lot of the coupons you get with these are BOGO, which is nice if it’s for a place you frequent anyway, but not really worth for places you only go on occasion. I did collect a few nice completely free freebies (most of which I still need to use as my original plans were derailed by have having so much fun shopping with friends that I lost track of time), and I promised a couple different people to post about them here so they’d know which birthday clubs are worth signing up for.

(There are a lot of lists of birthday freebies on the internet, but I got tired of having to wade through a bunch of chains that don’t have locations near me in order to find the pertinent deals, which is why I figured this list would be useful to others in the area.)

Pro tip: you’re going to get a LOT of promotional e-mails if you start signing up for a bunch of clubs like this. Gmail now has a separate tab for promotional e-mails, which helps, but if you’re an obsessive notification checker, or just really like to cut down on e-mail clutter, I highly recommend getting a secondary e-mail address someplace (I use Yahoo) to use when signing up for offers like this. I also use that e-mail address when registering at most store websites, when signing up for freebies, etc.

Baskin Robbins: free 2.5 oz scoop of ice cream OR 3 oz soft serve swirl

Format: printable only

Fine print: free + applicable sales tax

Expires: mine expired 5 days after my birthday

I got my offer over e-mail. I don’t know if the text club offer gives you anything additional or different for your birthday or not.

UPDATE: I have now used the Baskin Robbins free scoop coupon. We presented the coupon after ordering and were informed that the coupon is for a kid’s sized scoop, but he did go ahead and take off the $2.09 value of a kid’s sized scoop, so we got my scoop of ice cream for $0.40. It was still a very pleasant experience and a good deal, but I’d suggest showing the coupon before you order, or specifically ordering a kid’s size scoop to make sure you get your ice cream free.

Caribou Coffee: free medium drink

Format: present Perks card (or account linked phone number)

Expires: valid only on your birthday

I’ve used this one without any problem on previous years, though this year I had a little problem with remembering which phone number was linked to the account, so I was sadly not able to use my free drink reward.

Culver’s: Free one scoop sundae

Format: printable only

Fine print says: Sundae includes two toppings, Additional charges may apply for nuts.

Expires: two weeks from when they send your coupon (they sent mine on the day of my birthday)

I joined the e-club so I got my offer over e-mail. I don’t know if the text club offer gives you anything additional or different for your birthday or not. I haven’t used this coupon yet, but I’ll try to come back and update the post if and when I do, and tell you if there were any additional restrictions or hassle with using my coupon.

Denny’s (click join now in the Rewards box): Free Grand Slam breakfast (the picture shows two eggs, two small sausage links, two strips of bacon and two pancakes)

Format: printable only

Fine Print says: Present ID upon ordering to redeem coupon.

Expires: Valid ONLY on your birthday

FYI, there are no Peoria locations for Denny’s, so you have to go to East Peoria to use this one. I haven’t used this coupon yet, but I’ll try to come back and update the post if and when I do, and tell you if there were any additional restrictions or hassle with using my coupon.

IHOP: Free order of Rooty Tooty Fresh and Fruity pancakes OR of World Famous Pancakes (second option listed in fine print)

Format: printable only

Fine print says: Valid ID required to redeem. Dine-in only. Limit one coupon per table.

Expires: two weeks from when they send your coupon (they sent mine the day before my birthday)

I was a little disappointed to see they have a limit of one coupon per table, because we also got a coupon for free pancakes for signing up for the e-mail list, and I was hoping we could use both in the same visit. Though, realistically, my husband I would probably both be fine doing a light Saturday breakfast of splitting the order of pancakes and just do lunch a little earlier… I’ll try to come back and update the post if and when I do use this coupon, and tell you if there were any additional restrictions or hassle with using my coupon.

Logan’s Roadhouse: Free Dessert OR Appetizer

Format: printable (not sure if you could show the coupon on a smart device or not)

Fine print says: Good on any menu item $7.99 or under OR one full size dessert. Not valid on alcoholic beverages.

Expires: thirty days from when they send your coupon (they sent mine one week before my birthday)

I haven’t used this coupon yet, but I’ll try to come back and update the post if and when I do, and tell you if there were any additional restrictions or hassle with using my coupon.

Panera BreadFree pastry

Format: present Rewards card (or account number)

Fine print:Cannot be redeemed for bulk pastries, souffles or bagels.

Expires: mine expires nearly three months after my birthday

I haven’t used this coupon yet, but I’ll try to come back and update the post if and when I do, and tell you if there were any additional restrictions or hassle with using my coupon.

Red Robin: Free Burger

I didn’t complete my sign up (which requires getting a call or text with a verification code) in time to get this coupon so I don’t have any details on it. Do note that there are no Red Robin locations in Peoria, so you have to go to East Peoria for this one.

Ruby Tuesday’sFree Burger

Format: printable, or show code on smart device

Fine print says: Recieve a free burger (up to $9). Not valid on limited time offers or daily specials.

Expires: mine was valid from the day before my birthday until two weeks later

FYI, there are no Peoria locations for Ruby Tuesday’s, so you’ll have to go to Morton to use this one. I haven’t used this coupon yet, but I’ll try to come back and update the post if and when I do, and tell you if there were any additional restrictions or hassle with using my coupon.

In case you’re interested, here are additional birthday clubs in the area that give you a discount (usually something free with purchase):

Applebee’s: BOGO entree

Auntie Anne’s: BOGO pretzel product (Auntie Anne’s also has a perks app which offers a free birthday pretzel. I don’t know if that’s also a BOGO offer or not.)

Dairy Queen: BOGO medium blizzard

Einstein Bros Bagels: free breakfast sandwich with drink purchase (We used this coupon because Einstein Bros is a favorite breakfast spot for us anyway. On the same visit we also used the free bagel and schmear (with other purchase) coupon we got for signing up for the e-mail club, and between the two coupons we ended up paying about $12 for two breakfast sandwiches, a latte and a bagel with schmear. No hassle whatsoever about using the coupons, and they didn’t even make me show my ID to prove my recent birthday, though the fine print said they would.)

Famous Daves: Buy one entree get one 1/2 off

Flat Top Grill: Free ‘birthday bowl’ with purchase of equal or greater value

Hometown Buffet: BOGO dinner buffet

Longhorn Steakhouse: free dessert with purchase of entree

Red Lobster: $5 off purchase of two dinner entrees

Sonic: Free medium tater tots with purchase (I also got a coupon with the option of free creamslushie or tater tots, but I think that one was for the anniversary of my signing up for their e-mails. It’s a little confusing though, because both used the word ‘birthday’ in the coupon.)

Here are a couple more non restaurant coupons and freebies that seemed worth mentioning:

Driscoll’s Berries: .50 coupon off your next purchase of Driscoll’s Berries. I’m a fan of coupons on fruit, but this would would be more awesome if my birthday happened while berries were in season…

Famous Footwear: $5 off $5 or more shoe purchase coupon (Officially only ‘Gold’ members get a birthday offer, but I haven’t spent enough there to possibly be a Gold member, and they still sent me this coupon. It’s not valid on accessories, slippers or a few select shoe brands. Oh, and limit 21 pairs of shoes, in case that was going to be a concern with a $5 coupon…)

Redbox: free movie rental (near your birthday they’ll email you a code that’s valid for two weeks)

I’d love it if you would comment below and let me know of any good birthday freebies in the Peoria, IL area, or of any experience you’ve had redeeming the above birthday coupons (restrictions, etc). I’d especially like to hear of any local restaurants or coffee shops that have some kind of birthday reward, because I’d often rather get a small discount at a favorite local place than drive out of my way for a minor freebie at a chain restaurant I never ordinarily go to.


On this crisp almost winter morning, I thought perhaps I’d throw back the curtains, let what light there was come streaming into the house, and enjoy the cusp of the new season. On opening the blinds I discovered that not only was this cusp of winter the usual drab snowless transition one might expect, but some bird had a case of diarrhea so intense as to manage to hit my window through the screen.

You know what’s really lovely this time of year? Curtains. Curtains are a great look. I think I’ll stick with those.

Always Winter

It is culturally unacceptable to be cheerful about winter time. People bundled deep in layers of coats and scarves swathe themselves with grumbling as if in added protection against the cold. They range from startled to offended if you dare to suggest that the snow is actually rather pretty. And that’s on an average winter.

When the temperatures stay low for longer than normal and the clouds are thick with any manner of winter precipitation about to drop down on our heads and power lines, the only acceptable response is grumbling. After all, clearly, if God really loved us, it would be spring. Right. Now. (And probably forever.) A few little rays of sun between the clouds are not going to cut it when we know we deserve better.

And obviously, with our clear vantage point on all eternal knowledge, we know exactly what God should do if He really loved us.

Or at least, isn’t that what we’re really saying when we complain about what God is sending us?

Now I know everyone is rolling their eyes, because I’m that crazy winter person who really does think the snow is pretty and rarely gets cold and doesn’t even like summer all that much. But before you tune me out entirely (and leaving aside the fact that even I reach the point where I start thinking green plants might just be prettier than gray slush), let me remind you that I know something about waiting.

I understand being stuck in a season that you can’t change that feels like it should have been over a long time ago. I know what it feels like to ache, not in a theoretical sense, but in a physical, ‘I wonder if this is what a heart attack feels like’ kind of pain in the chest, every time you really know that God is saying ‘not yet’. I know that feeling of convincing yourself that you’re really perfectly fine and being slightly exasperated to find tears rolling down your face anyway.

And if you think I’m going to try to downgrade Winter to the status of a lesser problem, you’re mistaken. Winter may qualify as a major trial in your life, but even if it’s a small trial I wouldn’t write it off as nothing.

Sometimes the ‘big’ trials in life are, in a way, the easiest to deal with. They come at you head on, over and over again, and you can’t ignore them or pretend that you’re not supposed to be dealing with them. I can go straight from working through big trials in my life, and finding a place of peace and calmly trusting, to being completely exasperated that I can’t find a clean pair of socks.

Because overarching life stages are one thing, and God probably has those planned out, even when I don’t like it so well. But really, I have a morning schedule to keep, and I can’t do that if I spend ten minutes trying to find a decent pair of socks to wear, and since I don’t know of any huge life altering consequences to having clean socks, clearly God just doesn’t care enough to arrange these details for me, exactly the way I want them and on my own schedule.


Not like there’s any obvious pride issues that need to be dealt with there or anything…

But the funny thing is, if we can just accept the fact that God really does know what He’s doing, that He really does love us, and it’s all part of this huge happy ending fairy tale He’s writing in the world, it changes how we see things. Instead of being an insult to the eternal summer we think we deserve, that tiny ray of sunlight between the clouds is a promise that it won’t be gray forever.

A Not So Perfect New Year

Every year (several days after the new year starts) I post something about how the last year went and how I’m hoping the next year will go better. This is usually accompanied by me making many lists, coming up with way too many areas in which I want to improve, and angst over the fact that it’s January and I’m already behind on my blog posts.

This year I didn’t really feel like analyzing 2013. Good stuff happened, my health improved and I failed a lot. Moving on. Rah 2014! Maybe 2014 will be the year I stop failing! More lists! More goals! More… angst…

I didn’t even plan on starting my brand new 2014 schedule on January 1st. The fact that this new clean slate of a new year begins immediately after staying up past midnight the night before has always seemed a bit ironic to me. Plus, Colton was able to get quite a few days off around Christmas and New Years this year, so I figured vacation would just stretch until he went back to work. My official new year blank slate would start on the first Monday of the new year.

On the first Saturday of the new year we discovered that we were about to have lots of snow and the coldest temperatures in a long time. We could have just holed up at home for the weekend (church had already been canceled due to the uncertainties of travel in those conditions) but the dangers of being snowed in during a record cold and then having our power go out seemed a little too risky. We could handle a power outage, and we could handle record cold, but not at the same time.

So we spent the weekend with Colton’s family, experimenting with how long we could stay out in subzero windchill throwing snowballs at each other and then proceeding to play games and watch Bleak House (which I must say, is less depressing than it always sounded from the name). Not my plan for the weekend, but fun.

This is where my plans for the new year really started to fall apart. A frozen car meant not getting back to Peoria until Monday evening, which meant skipping my new Tuesday schedule so as to do my Monday chores, notably laundry. Wednesday, the cold I’d had was finally getting quite miserable and my husband made me take a sick day. Thursday I finally caught up on dishes and got the laundry folded, but still lacking a car, grocery shopping was not going to happen. It wasn’t until today that I really got to try out my new schedule, and by then something had changed.

This wasn’t the new start to a new year I had planned, but somehow it was exactly the start I needed. It was the start of letting go of my plans and my lists and my schedules. It was the start of refusing to feel guilty for getting sick while I had work to do. It was the start that forced me to relearn what it means for God’s grace to cover my failures.

And that, I think, is an excellent way to start 2014.