Learning Arithmetic

 Learning Arithmetic

By Bobby Neal Winters

Arithmetic was never my favorite subject. (Can I have an AMEN?) Indeed, I hated it. I used to get my mother to do my long division homework for me.

What an irony then that I am now a Professor of Mathematics at a respected state university.  They probably won’t want to include that in their press release.

Actually, the take away from that is mathematics is quite a bit more than arithmetic.

But here I am now, turning 62 next month, relearning arithmetic. 

Having stepped out of administration, I’ve been having a sabbatical of sorts before going back to the classroom, and I am using it to equip myself to step into my university’s growing Computer Science program.

As a part of that, I’ve been learning the architecture (that’s the term they use) of a particular integrated circuit and learning how to program it in assembly language.

I will be getting a little technical but will try not to fly off into full geek mode. You will need to tell me how I do.

Computers store numbers in binary form.  The number 0 is still zero, and the number 1 is still one. Okay, hang on, here we go: The number 10 is two; the number 11 is three; the number 100 is four; and the number 110 is five. I could go on, but it’s not important that you understand the particulars, but that there is a different way numbers are stored in a computer.

The numbers are stored in “bytes.”  This is a pun on the word byte. (Geeks have always been geeks.) Historically bytes have had different sizes.  It’s now been pretty well settled that a byte is 8 bits, i.e. 8 binary digits.  So 11001010 would be a byte.

The unit of memory that a processor works with is called a “word.” The size of the word varies from one type of processor to another.  In most computers these days, you can figure that the word is 32 or 64 bits long.

To bring me back to my topic, the longer the word size the more arithmetic you can do.

The chip I am working with uses the 8-bit byte for its most basic operations and you have to build up from there. You have to know some arithmetic. Let me show you what I mean.

An 8-bit byte can represent a number between 0 and 255 (between 00000000 and 11111111). If you want to add say 17 (00010001) to 20 (00010100), you can do that easily enough to get 37 (00100101). But if you want to add 250 (11111010) to 10 (00001010), you’ve got a problem. The answer is 260 (00100000100). I’ll save you the counting; it requires more than 8 bits to represent.

On this chip, you have to write your coding to extend the addition process.  It’s not hard. The designers of the chip knew this limitation was there and prepared for it.

They did this with multiplication as well. By its very nature, multiplication gives you bigger numbers quickly. The chip I am working with anticipates this by assuming that multiplying two 8-bit numbers will require 16-bits of storage. So right off the bat you can have a product that is as big as 65535 (1111111111111111).

As nice as that is, it will only get you so far, but you can get around this limitation by doing a little math and a little more programming.

Subtraction is handled in a way more similar to addition than it is to multiplication, though there are some complications in the way negative numbers are handled. (Buy me a coffee and a cookie at Signet, and I will tell you about it. You might want a whiskey. Signet can’t help you there.) 

We can even do the equivalent of decimal multiplication using this chip, but I am still getting my head wrapped around it.

Here we come to my favorite subject: division.  This chip doesn’t have 

If I am going to deal with division, there is not going to be any help from the chip. It’s all going to have to be done by programming.

I wish my momma was around to help, but I think she’d just tell me I was on my own.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

Fighting about words

 Fighting about words

By Bobby Neal Winters

Is a tomato a vegetable or a fruit?

A lot of time has been spent--not to say wasted--arguing this point. We think of fruit as being sweet, and a tomato is not sweet, so one would then argue it’s a vegetable. And the argument goes round and round, unresolved.

This is because the question is set up wrong.

First of all, this is not an either or sort of question.  It’s what is called a “false dichotomy.”  The world of objects is not split into disjoint sets, one of which is fruit and the other vegetables. What we have here is different sets of nomenclatures coming into conflict.

When we talk of vegetables, it is almost always in the context of food for human beings. We think of a meal as being constituted of meat and vegetables.

Fruit, by way of contrast, is the name of part of a plant, that is the fleshy part of the plant that contains the seeds. 

So a tomato is both a fruit and a vegetable.

This may disturb you, but this is just logic and using a dictionary.  If you are disturbed, hold on to your horses, it gets worse. 

An apple is a vegetable and a fruit as well.  So is a grape; so is a banana.

The devil lies in the word vegetable, because vegetables are just parts of plants that people eat.  We don’t speak that way in English, though.  We like to give fruits a special place--because they are sweet for the most part--and refer to fruits and vegetables.  But in reality we are just singling out fruit as a special kind of vegetable.

Another question that suffers from a bad set up is this: Mickey’s a mouse; Donald is a duck; Pluto is a pup. What is Goofy?

Here we are referring to classic Disney characters.  Characters they had long before they became the Borg of the entertainment industry and acquired Marvel, Star Wars, etc, etc.

It was a much simpler world made complicated by a deliberately bad question.

Mickey, Donald, and Goofy are characters who interact with each other. They possess the ability to speak what appears to be English to each other, though be it in annoying accents.  They are natural creatures who are caricatures of human form.  To put it in Greek and make it sound scholarly, I could say, Mickey is an anthropomorphic mouse and Donald is an anthropomorphic duck.  Pluto is still a pup, but Goofy, with this nomenclature in place, is an anthropomorphic dog.

As Disney has taken its Star Wars intellectual property and made all sorts of new back stories in the setting, do you think they would ever go back and create a mythology of how Mickey, Donald, and Goofy attained the power of human speech but how little Pluto was left out?

We now come to what is to me a more serious matter:  The story of Jonah and the Whale.

Any serious Bible scholar will know that the Bible doesn’t refer to the creature who swallowed Jonah as a whale, but as a fish. However, in popular telling of the story it becomes a whale.

Here’s the thing. It makes no literary difference to the story: Being swallowed by a big fish and being swallowed by a whale are exactly as dramatic as each other. It makes no theological difference to the story: Jonah prefigures Jesus with the time in the belly of the fish/whale as the time in the tomb.

This is a pointless argument from every dimension.

But more so pointless because at the time of the writing a whale would’ve been considered a fish because the ancients (the ancient people in general and the ancient Hebrews in particular) had a completely different way to classify animals that we do. Linnaean taxonomy was far in the future; DNA after that.  Distinguishing fish from mammals was not one of their major problems.

Considering they were sheep herders who had very little business to do with the sea, I think they left a remarkably large impression on the world.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

 These Precious Days

By Bobby Neal Winters

In June and July, the sun remains in the sky until late in the evening, and to us it feels like youth. Not to say that we feel young, but rather to say it feels normal. It feels as if it is due to us. It is owed us. We are entitled to it.

The long, warm days will go on forever, and we will be young and vigorous forever, until the end of days.

But June passes and then July is gone.  August disappears like an ice cube on a Dallas sidewalk, and we find ourselves in September.

The days don’t last as long now.  The sun remains abed later and it pulls the curtains earlier. It’s as if the days themselves are entering into old age.  Those that once bounded out of bed like they were mounted on springs now have to sit on the edge of the bed awhile to get their balance before staggering off for the start of their day.

We are still at the part of the year where there is more daylight that night.  We can still hear the grasshoppers singing in the grass. (Or is that my tinnitus?) Light and warmth still have the upper hand, but the Old Ones know those times are ending.

In a few weeks, there will be the equinox, and after that, darkness will have the upper hand for six months. The darkness will come and the cold along with it.

There was a time when I hated the cold and dark of winter. There was a time when I hated the heat and aridity of summer. There was a time when I resented spring’s unpredictability.

At some point, I decided to stop wishing my life away, to stop rushing through the seasons, to stop hating the moment, to stop hating life.

The summer may burn our faces with the blistering sun; the winter may chap our skin with its cold wind; the spring may rob our sleep with thunder and hail; but everyday is still another day of life.

All that said, I do love autumn in particular.

Here on the Great Plains, we see the extremes. Sun and snow; Darkness and dust. From ten degrees to a hundred and ten in the same calendar year.

But God owes us nothing in compensation. 

I am owed nothing.

But if we were, if I were, these coming days of September with cool mornings and warm afternoons are days of blessing, days of grace. They would make it worthwhile.

I love them.

Sometimes I just stand still and try to record the moment, to put it into memory for later. I just want to make a mental tape of the way the sun and the air feel against my skin and play it on a loop.

We come into this world naked and we take nothing with us when we leave.  If we are truly wealthy, it will be known from what we leave behind: friendship, love, truths said and knowledge passed along.

Everyday is a gift, but these glorious days of September, days of the Fall are especially so.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.