Fuzzy Math

[Glenn]

Once you get comfortable with not having to be exact, or at least correct to 4 or 6 decimal places, fuzzy math gets you numbers to work with right now.

The following was from a discussion of chimney diameter size vs inside area of the pipe, specifically how much of an increase in area is achieved with the each additional increase in pipe size.

Fuzzy math:  Forget for a moment the formulas for circles and just use square measurements.  8 x 8 inches square is 64 square inches inside area. 10 x 10 inches square is 100 square inches inside area. and 12 x 12 inches square is 144 square inches inside area. That is 150% increase in area with each additional pipe size.

 

Time to get out the calculator:

8 inches diameter is actually 50.625 square inches, 

10 inches diameter is actually 78.54 square inches, 

12 inches diameter is actually 113.10 square inches

 

Going from 8 inches to 10 inches diameter is actually a 155% increase

Going from 10 inches to 12 inches diameter is actually a 144% increase

 

Fuzzy math said 8 to 10 inches was 150% square (actually a 154% round) increase and 10 to 12 inches was 150% square (actually a 144% round) increase.  That means fuzzy math from 8 to 10 inches was off by +5% and from 10 to 12 inches was off by -6%. 

Fuzzy math for a right now answer to work with beats a calculator (if you can find one and remember the formulas) hands down. 

If you want close, fuzzy math works. If you want exact, find a calculator and look up the formula. Remember that if you do not have a number close to the right answer, the calculator can lie to you, and you will never know. 

 

[ThomasPowers]

What we called "back of the envelope" calculations or even "order of magnitude" calculations---quite common when using a slipstick and needing to determine where the decimal went.  I even had a class in it at engineering school in the mid 1970's when pocket calculators were just taking off.

[Glenn]

Slipstick, Long or round?

[Frosty]

Approximation and interpolation, Dad called it ballpark and he could do calc and trig in his head.

Long, easier to carry in a pocket than round.

Frosty The Lucky.

[ThomasPowers]

I remember reading an old SF story where they had a motorized 300' long slide rule in a hanger to do calculations for their rocket's trajectory and get the precision they needed.   I can do a simple "slide rule = pocket calculator" substitution in my mind reading the old stuff now.

[Frosty]

Ah, 1940s Sci fi! I remember vernier slide rules with microscopic lenses in the cockpits of space ships to calculate course. 

I recall reading the triply redundant computers in Apollo capsules totaled about 64k. My Casio calculator watch has more than that. The astronauts had to use a special book to use the right commands. It was all pre-programmed and the input keypad had large buttons with graphics. Buttons about the size of a quarter so you could use them wearing a 1960s space suit glove and graphics because each one was a command. 

The more you now about the early manned missions the scarier they are.

Frosty The Lucky.

[arkie]

I wonder how many folks here know what a slide rule is, or more so, how to use one.

[rockstar.esq]

Glenn is spot on about "having a number" to check against the calculator.  I've met a whole lot of people who get their order of operations wrong when they're using a calculator.  Same numbers, same operations, different answers.  

One aspect of this that jumps out at me is how people love work out a rough percentage or ratio without much consideration for the driving relationships.  That leads to a lot of incorrect assumptions.  

For example, you could take the total cost of a construction project and divide it by the square footage to get a square foot cost.  OK fine.  Now, you decide you want to build something the same size or slightly smaller with a more efficient layout and the budget jumps.  What happened?  

Well, things like restrooms are driven by occupancy not square footage. Depending on local building rules, restrooms have to be made in groups of pairs or triplets.  Restrooms require just about every skilled trade to work sequentially in a limited amount of space which makes them  expensive.  The further these rooms are away from the utility sources, the more the price will rise.  Crossing the "occupancy threshold" where you have to add a bathroom group might also require that the groups be placed at opposing sides of the space which can boost their cost.

The "right" way to ballpark this is to use a parametric estimate.  Bathrooms can be priced as a standalone parameter.  That gives you some way to quantify the cost impact of changing the occupancy.

 

 

[ThomasPowers]

I tend to keep track of stuff at the store; I've had several incidents when I told the checker something like: I had 10 items, each of which cost less than $3---how could the total before tax exceed $30?"  They generally can't understand what I am saying or that I could do simple math in my head...

[Frosty]

Yes, having an approximation in mind before you start punching buttons can be a life saver. Close approximation is why I REALLY like the formula I use for finding the area of a circle. A= .7854 D sq. It's easy to do in your head and D 3 x .8 is close enough to cause a double check if your calc says much different.

Approximating Dia. from the middle by dividing the circ by 3 is easy brainwork, if you need closer you need a cloth or pi tape as a steel tape measure won't follow close enough, even face down.

It's harder to score if you're not in the ball park you know. 

Frosty The Lucky.

[ausfire]

And some young people have become so reliant on calculators that common sense has gone on holiday. I remember a few years ago when calculators first came into use and we went into a jewellery shop to buy a crystal on display in the window for $60. The shop advertised a 1/3 off sale. The young assistant punched the calculator to figure out that we were to pay $40. And she was perplexed because the answer came up as $40.02. She had been instructed to use -33% to calculate the discount.

[ThomasPowers]

In my numerical methods class the first day the Professor had us run specific calculations on our calculators to force an over-run or under-run and looking at what the calculator coughed up he could tell us which chipset it used...A good start to a class that had the basic premise that you didn't need the exact value for an answer as long as you could get close enough. (Rough on some ringers from the math department whose brains popped when told that 2 + 2 does equal 3.999999999999999999999999999999999999999999999999999999999999999999999999999999 for most purposes.)

 

[rockstar.esq]

ausfire,

I got all the way to college before I encountered a teacher who presented a lesson showing how fractions were more precise and intuitive than decimal approximations in practical applications.

Huge physics calculations could be done in your head if you kept everything in fractions.  Trying to get the solution using decimal approximations just made it a lot harder.  That teacher had a knack for writing exam questions that were virtually impossible to solve any other way.  

 

[Glenn]

The highway project had dirt to waste, or get rid of. The decided to fill in a hollow 30 to 50 feet deep by 2-3 miles long. The now flat ground was to be used for a rail road, main road, secondary road and some 250 + houses. At the end of a couple years of work the plan were ready to be checked. It was required to hit every single survey point in the calculation. This was done by two individuals working separately and independently of each other, on two different platforms.

Their numbers DID NOT match. So they re-ran the calculations and still did not agree. Panic time.

Using two different operating platforms, each was correct. They just did not agree with each other. The problem was chased down to one system rounding up in the 13th decimal and the other system rounding down in the 13th decimal. The size of the project and the amount of survey points made the difference accumulative, until it created a problem.

[rockstar.esq]

Glenn,

As a professional estimator with ten years of experience, I can say that it's very rare for competing bids to perfectly agree on quantities, but very common for them to be virtually identical in cost.  

The principle difference is the round up/ round down function of judgement.  People get hung up on precision because it gives them something to measure, so they feel better about it.  Accuracy is hitting the right answer. Good judgement can look a lot like luck to an uninformed bystander.

Really often, the influential factors aren't that difficult to roughly calculate.  The hard part, is knowing which factors to look for.

 

[Frosty]

Glenn: That's why AK DOT doesn't use more than one surveyor for road projects. Contractors building a project might but if they're quantities are off they eat the difference UNLESS they can prove the State's estimates are off and that's typically by the number of truckloads required. Empirical data trumps estimates.

Frosty The Lucky.

[Dave51B]

 % of moisture in the cut verses % of compaction in the fill, makes for an interesting estimate, just sayin'..........Dave

[Frosty]

Neither has anything to do with the surveyors Dave. Moisture and compaction tests are lab work. Volume can only be estimated by survey, actual quantities are in the As Builts largely in the form of tons of various gradations of compacted fill. 

Road building is planned with best guesstimates and a conservative margin of error. 

What really stinks is when the contractor convinces a politician who has to approve construction projects lots of money can be saved by using a building technique that works fine all over the world. . . EXCEPT in earthquake country. The pic is of Vine Rd. about 3/4 miles N. of our place. This is a fill section over a silted in pond, it's about 40' or more of saturated organics and silt. The fill technique is called "surcharging" they spread geotextile and load it in lifts. The weight of the fill material forces the water from the original "ground" when it stops settling for a given period of time they compact and build the road. Roads and buildings are built on surcharged ground and it's MUCH less expensive than sub excavating 40' +/- of saturated mud and peat. It works great where it doesn't shake. What looks like ripples in a pond on either side of the road are just that, waves where the displaced saturated materials were driven out from under the road.

No soil survey (drilling) company, soils lab or design engineer recommended surcharging this fill section, it was all contractor and politicians deciding based on their criteria. 

Best information and estimations in the world is at the mercy of the purse holder.

Frosty The Lucky.

[ThomasPowers]

Liquefaction was extensively covered in my geology courses as a major issue with quakes, especially the fill in San Francisco Bay and issues from the 60's? quake in Alaska.

 

[Dave51B]

  No courses here.....Just retired from moving dirt for 40+ years.           Thanks                 Dave

[Frosty]

That was Good Friday 1964 and when you talk money to politicians lessons don't count.  I moved here in 72 and there were still places where you could see pieces of buildings and vehicles sticking out of the rotational slump failures along the bluffs. (Earthquake Park) Much of Anchorage sits above a lens of saturated Cook Inlet clay about 25' - 40' thick. The only thing keeping it in place in some areas is the weight of silt in Cook Inlet. The 64 quake liquified the silt and the weight of aluvials on top of the clay lens literally squirted clay fountains in places. The stuff that "stayed" in place turned into a liquid bearing and the bluffs just rotated out and down. 

It was no accident I picked a lateral moraine composed of glacial til to build on and zero structural damage in the Nov quake makes me smile.

You're right Dave, moisture content of OG vs fill does make a difference. I just got lost in thought there, my head has plenty of room for random wandering. Driving an end dump was a much more enjoyable job than sifting, weighing and analyzing or recovering samples. My favorite was snow removal in a belly blade sander, converted from end dumps. 

Frosty The Lucky.

[rockstar.esq]

There's a 13 mile stretch of interstate near me getting a lane added in each direction.  It's pretty much straight as an arrow, perhaps five overpasses, and no seismic activity to worry about compared to AK.

The project is anticipated to take nine years.  Just for giggles, I googled the production rate of the transcontinental railway.  On their most productive day, they laid ten miles of track.  From what I can tell, that doesn't include time cutting and grading.  It was however twelve hours of setting ties and track.  All work done by either man or beast.

I had a few classes on road construction so I'm not an expert by any means.  That said, I've worked for firms that hired paving firms to build public and private roads.  When the road designs were identical , the private roads consistently took less than a quarter of the time to get built.  In my experience, most of the additional time was generated by  leaving the site after the prep was completed, and not coming back until a day or two before the deadline whereupon the paving is completed in one or two hard-driving shifts.  Typically they'd be gone for several months between prep and pave with all the traffic control stuff left in the public's way.  There were no inspection, permit, or weather related delays to justify this behavior.  This delay was built into their schedule. Every paving company was basically the same.  All of their estimators/salesmen would swear up and down that it simply couldn't be done any faster.  

 

[anvil]

dang, and i thought reading a 6' metal folding ruler to a 64th was good.  I think the "th" makes it a fraction.