Logarithms For The Only Slightly Off

Logarithms and steel.

Remember logarithms? There was a time I used them constantly. If you think a logarithm is something an aborigine might bang out on a fallen tree, you're not getting my drift.

Umm. No.

From Wikipedia:The logarithm of a number is the exponent by which a fixed number, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10³ = 10 × 10 × 10. More generally, if x = b^y, then y is the logarithm of x to base b, and is written log_b(x), so log₁₀(1000) = 3.
Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by scientists, engineers, and others to perform computations more easily and rapidly, using slide rules and logarithm tables. These devices rely on the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors:

The present-day notion of logarithms comes from Leonard Euler, who connected them to the exponential function in the 18th century.

Forget all that.

I suppose mathematicians still use them somewhere, but back in the days before portable computers and scientific calculators, logarithms were a necessary tool.

When I started as a draftsman just out of college there were no handy electronic calculators of desktop computers. No one had even conceived of a laptop computer. Mainframe computers were around, actually, but mostly in large businesses. It would be ten years or so before Alamo Steel, the company I worked for, would have access to a mainframe for accounting.

I was a draftsman, fresh out of college. My math skills were, umm, a bit shaky. Sure, I was okay with basic math, and I had geometry licked. In high school I basically taught my geometry class. The math teacher used to duck out of class for a cigarette in the duplicator room after telling me to explain the homework to the rest of the class. I'd had trigonometry in college, although I'm afraid little of it stuck.

I finally learned, though. When I started working on hip and valley beams and stairs and handrails I was using trig constantly.

This means doing higher math while juggling feet, inches and sixteenths of an inch!

Sure , you can convert to decimals to calculate some things, but ultimately you have to convert back since the required outcome of the procedure was to produce drawings for our shop employees to fabricate steel members with. Our shop guys were great guys, I was friends with many, but quite a few barely spoke English, others could not read. They learned to use a steel tape measure, but it was considered a bit much to subject them to more than the most simple measurements to work with.

So, we in the drafting room were called upon to simplify, and especially to do all of the math and conversions in advance.

One of the first calculating tools I worked with was a slide rule. 

This was, by the way, toward the very end of the heyday of the slide rule. Slide rules use logarithms. The beauty of logarithms is to simplify calculations. When you have multiplication, division, and other complicated operations to perform, you only have to use a conversion table to change the factors to their logarithms, then all operations become addition and subtraction problems.

We all learned multiplication tables in school. Those work great for simple whole numbers. If you are working with complex numbers of many decimal places it can be tedious to sit there and multiply or divide the whole thing out the long way. For instance, if you are multiplying two numbers, you use the tables to convert them to their logarithms, add the two logarithms together, then convert the logarithm sum back to real numbers. That's your answer.

Remember, electronic calculators were not available!

A slide rule, or slip stick, manually added and subtracted logarithms. The scale was a logarithmic scale. If you lined it up to multiply two and two, the answer was four. What it was doing was adding the logarithms for the two numbers graphically, and letting you read the answer.

For a while slide rules, well, ruled! A skilled engineer could read one to several decimal places, and do complicated problems all day long.

Other sorts of slide rules appeared. Not really technically slide rules, as they didn't use logarithms as such, but they did match up factors to show pre-calculated answers. They were common for many fields that required quick and practical calculations. My chosen field before drafting was electronics. I made use of, and still own, several cardboard cutout calculators that were this sort of slide rule. Very practical and quick to use. I still use them from time to time. 

Ohmite Capacitor Calculator

 Once in awhile one of the hobbyist magazines would even print a similar one to copy, fold and tape together.

Did I mention useful?

 Anyway:

Eventually my original K&E slide rule, or slip stick, got replaced.

 

For simple adding and subtracting of measurements, we did have electrical adding machines with special keyboards and a paper tape readout. 

Monroe Foot-Inch-Sixteenth Machine

Victor Foot-Inch-Sixteenth Machine

 These were great. Some of us even used mechanical adding devices, known as Addiators, that used a metal stylus. You used the stylus to advance numbers in one direction for adding, the opposite direction for subtracting. With many of them you kept track of sixteenths of an inch manually, literally, by holding up a pinky finger when you had a sixteenth in the number, folding it away when you didn't. A very few of the Addiator models actually handled sixteenths of an inch.

Addiator

 

No electricity, but so much more portable! That was important for those of us who, shall we say, labored with side jobs in the same industry?

The engineers in the company often used a specialized adding machine that allowed you to reset the decimal point, to more rapidly work with big numbers. It did require the conversions to be made from feet and inches to decimals, but once those conversions were made, their calculations could be carried out and the answers converted back at the end. 

Shifty Monroe Machine

You actually manually moved the carriage over to the correct decimal place column. Some of these had a little crank below the keyboard to do this! Sure, it was electric, but still, can you say Fred Flintstone?

An integral part of the calculating process was a book. Several of our available books did have the foot-inch-sixteenth to decimals of a foot conversions available, but one book was our math “bible”. 

Smoley's

Smoley's Tables were available either as four separate books, or all four combined into one volume. The fourth volume, Segmental Functions, was useful for circular calculations, critical when needed, but rarely used. The first three volumes had to do with decimal equivalents, squares, logarithms, and trigonometric functions. Those we used constantly. We were each required to obtain our own Smoley's books. When we could, we got the first three together in one volume, and the fourth separately. That fourth Segmental Functions volume would last forever, and did! We could often wear out two or three of the first three volumes before the fourth would even show wear.

Those logarithms and trig functions really came in handy! Perhaps I should also mention that this was in the days of manual drafting as well. Lead pencils, T-squares, triangles, lettering guides, drafting tape, tracing paper. CAD programs did not exist. Dinosaur days. This was in 1971 and years following.

We had to know the mechanics of drawing a pencil line, and construct various shapes to put together a useful drawing, and then to hand print the lettering to explain and dimension everything. Then, copies were made with a smelly ammonia Ozalid process to produce real “blueprints”.

We ended each day with liberal amounts of graphite and rubber eraser dust on ourselves.

TI Calculator

Well, after a few years, Texas Instruments came along with a series of hand held electronic calculators. Now THAT was revolutionary! We still had the conversion problem to deal with, but suddenly it was less of a chore. The so-called “scientific calculators” appeared with more and more functions, including trigonometric functions that made things easier. We were able to rely less and less on the Smoley's tables, and go straight to calculating.

Bigger than a breadbox Wang

About the time that mainframe computers became more accessible and user friendly, programmable calculators appeared. The first were pretty large affairs. The Wang programmable was one we utilized for awhile. Pretty nifty! I actually taught myself to write programs for it! (As a mere draftsman, this was a bit above my station, but I tended to color outside my lines a lot!) Two number pads with memories meant you could perform more than one operation at a time and merge the answers. Also, it sported a cassette tape program storage, so you could record and reload several programs as you needed them! Display screens were still in the future, all usable output was preserved on paper tape printout.

After only a couple of years, those same hand held calculators we were using became programmable as well. First one, then many programs could be stored and used. The Wang was fairly obsolete in no time. It still worked well for some situations, but for everyday calculations the hand helds were the thing.

It was not until the mid '80's that we were able to finally ignore that conversion problem. Development of calculators that actually worked with fractions and inches was ignored until then. The United States was considering going metric for many years but there was a lot of resistance. Most of us dinosaurs didn't really want to learn a new system. 

The manufacturers finally gave in and designed a few calculators that actually worked in feet-inches-sixteenths. This is the one I have now. It has taken the place of every machine/calculator/book that came before.  This is the Jobber 6 by Calculated Industries. It's great! Online versions are even available, so you can use it without taking your hands off the computer keyboard.

That's important, since Computer Aided Drafting also took over from manual drafting. Of course, most of the major CAD programs like Autocad have several calculating functions built right into them, but... remember those aforementioned dinosaurs? 

I still have my board and pencils, too. I might even have my copy of Smoley's around somewhere!

I admit I've gotten a bit rusty on interpolating logarithm tables. On the other hand, it's been awhile since I've detailed steel as well. Still drafting, though, with CAD and my Jobber!

To The Far Blue Mountains!

I don't repost others' blogs often, but Bish really nailed it in this one:

 BISH'S BEAT: FORGOTTEN BOOKS: TO THE FAR BLUE MOUNTAINS!: FORGOTTEN BOOKS: TO THE FAR BLUE MOUNTAINS! LOUIS L’AMOUR About twenty years ago, I read my way through two dozen or more Louis L’Amour ...

"Oh behive!" News from EarthSong Retreat.

In a wonderful barter arrangement, we are getting chickens, a small chicken house, and bees from our friend India in exchange for two weeks of house and animal sitting. We were planning to add chickens to our place soon anyway, and we got this chance to get ten grown hens. I've got plans to build them a nice coop of what is popularly called the "Amish" style, but they are coming with their own coop that will work till I get the new one built.


I've had chickens several times over the years. The picture above is from a small setup I had when I lived in Round Rock in the '80's. It worked quite well for the time and place. I love those Rhode Island Reds! The new ones will be a mixed bunch, and we're happy to be getting them. 


We're also getting a hive of bees. Now, personally, I like bees. However, I'm a bit spooked by them. I seem to be a bit allergic to their stings. Over the years I've been stung several times, and each time has been worse. I'm not sure how much risk it will be to be stung again. However, we want bees here at EarthSong Retreat, and so this is a good thing. Cat Dancing has wanted bees also for some time, and she feels that she connects with these already. In a couple of weeks we'll be getting the hive. We've both been studying up on the art of beekeeping. I'm looking at the structural aspects of housing, etc. Cat has enlisted Michael to actually help with the hands-on bee working.


Both of us feel that adding bees will contribute to fighting the decrease in bee populations all over, as well as greatly aid in pollination of the various plant life here at EarthSong.  We've also seen that bees are in serious difficulties in this area already from the drought and heat. 

We've already delved into our first controversy concerning bees. Some of my Permaculturist friends introduced me to "Top Bar" hives as being very simple to build, natural, and beginner friendly. The "Langstroth Hive", however, is more common and more used commercially. Both designs have assets and drawbacks. The clincher, however, is that the season is late, and a Langstroth is what the bees are already established in. We've been looking at various designs to build our own, and we will see about trying different types as we divide the hive or add more bees later. I'll keep you posted. 

On a related note, Cat has been looking at the "space suits" for working with bees. She is considering just going with the head veil and gloves, knowing that many keepers work their bees with no extra covering at all. Not to be outdone, I've been looking at bee suits as well. I'm considering this model:
















On the other hand, perhaps she would appreciate me getting her another assistant:

Nothing is too good for my darling beekeeper!


To be honest, I showed her this suit, and she pointed out that it might not fit me. Sigh.





In other news, we are having our first work day for volunteers here at EarthSong in association with our partners at Vajra Azaya. I've designed a series of wicking bed garden beds to be hooked into our proposed gray-water system. We'll be building those this Sunday, Sept. 18, 2011. My back has been a bit out of whack, so I may be the geezer in the chair pointing others where to dig!


I'll end this with a lovely logo my friend Larry Santoyo has on his t-shirts.

See you!

A Typical Holiday

You know, typical hot summer three day Labor Day weekend. Catch a movie, eat out, maybe plan a barbecue with beer and watermelon and mmmmmmmmm beef ribs and sausage. Did I mention cold beer?

Add the thrills of seeing huge clouds of roiling smoke as a north wind driven wildfire of gigantic size sweeps by within spitting distance of your place burning whole neighborhoods to the ground, melting cars to puddles while you and thousands of your neighbors are evacuated and most spend days huddled within hastily organized (or not) shelters while you wonder what the hell (literally) is happening to your house and family members.


Damn, do we know how to party in Texas or what?


All joking aside, it was a horrendous experience. Our firefighters and emergency services, and even local government folks really showed and continue to show their worth and humanity! Thanks all of you! 


And, to so many who lost their homes, their loved ones, even their pets,  it is impossible to express words close to being worthy of the loss that you feel. We do feel, truly sickened by what happened. Those of us who were bypassed, this time, were incredibly lucky, and we each know we could be next.


Pray for RAIN! And keep your bug out bags packed!

It's Far From Over But We're Home!

It's far from over, but we are home at least. 
We are among the lucky ones. 

The Bastrop Complex Fire of Sept. 4, 2011 is the largest of many that broke out around Central Texas on Labor Day Weekend. It came during a horrendous drought that still continues. Following months of daily temperatures of 100 plus degrees F, (as high as 112 near us), and constant southerly winds, the weekend brought strong northerly winds and a break in the temperature. This felt wonderful. However, the gusty winds also apparently brought down dead limbs onto power lines and sparked this fire Sunday afternoon. It started east of us and traveled fairly straight to the south, missing us by only two miles or so. There was a huge wave of boiling smoke high in the sky all afternoon as the firestorm raced through dry grass and dry pine trees into the Bastrop State Park and through wooded neighborhoods. Everything was bone dry, and the winds pushed the fire farther and farther. 

We were finally evacuated Sunday evening at about 8. We grabbed our four cats and stuffed them into carriers, grabbed food and clothing and left, taking both cars and my motorcycle. Not sure where to go, we rendezvoused at the Bastrop Library. Cat had been in touch with a good friend, Amanda, in Austin, who has a vacation rental that was vacant. Amanda immediately put it at our disposal at no charge, so we headed into town. It looked as if all the world near Bastrop was on fire. 


There we were, evacuating EarthSong Retreat, our new home, and on our way to Austin, not knowing if we would lose everything or not. As an added incongruity, Cat witnessed a motorist tossing a lit cigarette out of a window onto the pavement, sparks flying. It made her very angry, as it did me when she told me about it later. What an IDIOT! In the next couple of days fires broke out all around Austin and another in Bastrop. Some of those fires were accidental, others were apparently arson. In the midst of all of this, other instances of smokers tossing lit cigarettes out of windows were witnessed by friends. The stupidity was mind boggling.


Amanda and her family welcomed us to their home and rental unit, we moved in and started the wait. It was very comfortable, a beautiful place just off of Barton Springs and Zilker Park in Austin. 


We used the wifi to follow the news and updates on the fire. More and more people were pouring into the evacuee shelters in Bastrop, making us glad that we had come on into Austin. It took us several days to get through the busy phone lines and register ourselves as evacuees so that we might be notified of changes. 

More and more businesses in Bastrop and Austin were helping out the folks who were waiting. We were treated to a free dinner at La Fonda San Miguel in Austin, free to evacuees. It was a fabulous meal, in a place we would normally dress up to go to. The staff was wonderful, the food was great, and they offered us the full menu. Our server, David, had been an evacuee from Hurricane Katrina. That meal was such a bright spot in a dreary waiting game! We were also constantly getting calls and messages from friends and relatives who were checking on us. That meant a lot as well!

We were constantly watching updates and monitoring the Bastrop County Office of Emergency Services page on Facebook for news. KXAN News was a good source, as were the Facebook pages of "Texas Storm Chasers" and  "We Are Okay in Bastrop", and others. Several pages had sprung up on Facebook for groups monitoring the fire, most had some good information. A lot of it was also on Twitter.


Finally, on Thursday, Sept. 8, 2011, the news came out that folks in some areas were being allowed to re-enter. Ours was one of those areas. Another good friend, Maria, and her family, who live North of us had already returned. They had gone by our place and reported to us that all was well. The fire maps we had seen all indicated that the fire hadn't come as far west as us, but it was great to have confirmation. Of course, we also had concerns about looters. A few weeks before the fire we had already suffered some vandalism. When we got the news about re-entry we were ecstatic, we couldn't get loaded fast enough. It was great on another level, as the rental we were using was booked for the weekend. We needed to be out anyway. We had received offers from other friends of places to stay, but going home is SO much better!


Everything at home was okay, other than some wind damage from the blustery norther. It seemed very quiet in our area. A lot of people have not returned. Just a couple of miles away families have lost everything. My cousin lives four miles away and was burned out. At this moment the count is nearly 1400 structures burned. Most of those are homes, with a few barns, offices, and other buildings. I believe there have been only four human fatalities so far, but innumerable animal casualties. The fire is still only 30% contained now, but it has moved further south. At latest count close to 35,000 acres has burned. This includes almost all of Bastrop State Park, parts of other parks, and so many neighborhoods. A huge blackened area is visible by satellite. 

This is the satellite picture. We are located just above Lake Bastrop seen on the left side of the map. This is a shot from a French satellite, processed by UT. 


In our area, however, the continuing northerly winds carry the smoke away from us. We smell very little of it here. Air quality is down, but not too bad. The smoke is not even visible from here. 


We were so lucky!

For those who may be interested. Check out the beautiful vacation rental we stayed at. It is called "Wren's Nest" in Austin, Tx. It can be seen on www.homeaway.com , listing #293833. Phone 512-788-1044. Tell Amanda that William RainCrow sent you!