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# Educating in Steps and Where Have Too Many Stopped

Posted by holy-cow on August 20, 2016 at 3:32 amWay back when we were all just little tykes some of our older relatives might quiz us with silly questions about numbers. Things like, “How many fingers old are you?” Their goal was to make us aware of numbers. People use numbers to count things. Some number of years later some teacher introduced us to the term “integers” which we were supposed to recognize as being those numbers we had been learning about. Meanwhile we had learned to do certain things with numbers, like add, subtract, multiply and divide. Then some teacher introduced us to fractions, again using only integers. But, eventually we discovered both regular and irregular fractions existed. Then “real” numbers, as opposed to what our silly little brains wanted to ask. Of course they were real. Oh, my. Some real numbers are the result of integers plus fractions which become numbers on both sides of a thing called a decimal point. Wow. Oh, oh. Then there’s this weird thing called a power of a number which simply means multiply the number by itself that many times. Somehow that gets all turned around to demonstrate that even stranger stuff called square roots and third roots exist. If we are lucky they go on to explain how the combination of powers and roots can result in something similar to that number with numbers on both side of a thing called a decimal point. Geometry? What’s that? Triggernomutree? What’s that? Wait a darned minute, now, I’m not buying this wild story about imaginary numbers. Calculus, LaPlace, L-Hospital????? Matrix what? Series of what?

Once upon a time a guy took a stick and stuck it in the ground and then he took a few other sticks and stuck them in the ground and then he told everyone he saw that everything between those sticks was his land and to stay off of it. Through some long, twisted similar series of steps to the math example, the survey example evolves. From as solid as a rock to as fleeting as a gust of wind. Something you can touch to something that exists only in theory. Individuals are introduced to something known as land surveying and then begin a journey of continually feeling ignorant because no matter how much they learn they are constantly told that what they have assumed to be true really isn’t true. And, you need this new regimen of training to become semi-functional until further adjustments can be made to further prove that you are still generally ignorant.

The only way to climb the survey tree is to first climb the math tree. That, or punch blindly at buttons that spew forth strings of text that seem to somewhat satisfy the gods of employment .

mathteacher replied 7 years, 8 months ago 12 Members · 21 Replies- 21 Replies

I disagree, while the understanding of mathematical principles and the ability to problem solve through mathematics is certainly important to the surveyor. The ability to visually read the land, the physical evidence available, and a firm understanding of the deed as written is of far more importance in surveying than ones ability to apply simple mathematics. In my opinion the only way to gain true knowledge in surveying is to apprenticed under a surveyor who has true understanding of boundary law. And the experience to back it up.

I started out surveying with a large corporate company. I learned many things from the older chiefs I worked with, how to calc a lot, how to calc a house, how to figure grades and their thoughts on boundaries. But it wasn’t until I worked for a small family company with a licensed surveyor who was the chief and a father that owned the company did I learn the importance of the deed and reading the land for evidence of the boundaries mentioned in the deed or not.

A hump in the woods might be an old edge of a field or a indentation in the ground an old wagon road, a piece of barbed wire in a tree and being able to determine the patent date of that wire are far more important than the math.And unfortunately that knowledge can’t be taught in a college curriculum.

Math is power and provides a great foundation for the commencement of a surveying career. Certainly one can cobble in the math along the path of acquiring knowledge of evidence analysis, survey procedure and boundary law, but having a solid math background first is my recommendation. Especially if I’m going to be the mentor. I much prefer teaching youngins who have a math foundation.

**Holy Cow, post: 387274, member: 50 wrote:**

The only way to climb the survey tree is to first climb the math tree.I agree. My favorite part of surveying is the math. I like to know what all those numbers are on my data collector’s screen. Also, simple stuff. Like looking at stationing and through simple subtraction, knowing how far it is to the next station. Elementary school math. No need to inverse! But, also needing to know if I should worry about a scale factor of 0.99954132.

**Holy Cow, post: 387274, member: 50 wrote:**

That, or punch blindly at buttons that spew forth strings of text that seem to somewhat satisfy the gods of employment.How do you know those strings are even close to being correct if you have no idea how the math works?

MH**Ron Lang, post: 387284, member: 6445 wrote:**I disagree, while the understanding of mathematical principles and the ability to problem solve through mathematics is certainly important to the surveyor. The ability to visually read the land, the physical evidence available, and a firm understanding of the deed as written is of far more importance in surveying than ones ability to apply simple mathematics. In my opinion the only way to gain true knowledge in surveying is to apprenticed under a surveyor who has true understanding of boundary law. And the experience to back it up.I think knowing the purpose of a survey is important. Is a 0.10′ really that important in a topo of a wetland?

MHNumbers vs evidence? Well, those who cannot do numbers, cannot do anything. It’s like the 2 wheels on a bicycle. You really cannot take either one for granted. (Unless it’s my kids, and their unicycles!)

Part of the learning curve in math is always knowing there is something about it we haven’t learned yet. The simple stuff only seems simple now because we know there are more complex things.

Part of the learning curve in land surveying is always knowing there is something about it we haven’t learned yet. Some of the most complex boundary solutions are the ones that appear to be simple when first presented to us by the client. Once we get started, we begin to see the first can of worms, then the second, then third, etc.

Imagine a job to cut out a new parcel of an exact number of acres. The north side is a section line or block line. The west side is to go south from a specific point on that section/block line until the to-be-determined south line is calculated. The easterly side is an apparently straight westerly r-o-w line of something like a railroad that runs at a bearing other than south, say south twenty degrees east. Simple. Only four sides. Simple math. Anyone can do it. No, not anyone can do it. Only those who understand geometry, trigonometry, algebra and basic math can do it.

Meanwhile, the land surveyor who is going to do the calculations above must delve into the history of how the section/block line was established, how it can be correctly located today and, also, discover the history of how the r-o-w line was established, if there have been any modifications since first establishment and if it is truly a straight line or if it is a circular or spiral curve with a very long radius. May the Lord help the surveyor if a couple of extra kinks exist in fact but are not evident by how the fence was built along the assumed line a few decades ago. Especially because the math exercise above just became far more complicated.

Then the land surveyor discovers the cans of worms mentioned above involving title issues, access issues, line of sight issues and so forth. There is another tiny little issue. The client wants the final area to be not just 4 acres but precisely 174240.00 square feet. The surveyor can’t really do that because for each additional 0.01 foot of depth multiplied by 1 foot length of the south line there is an additional 0.01 square foot of area and the south line is going to much more than one foot in length. That’s when the third side of the process comes into play…………client coordination.

Math is often just the framework or the model that lets us quantify the real world. Accountants use Assets = Liabilities + Capital as the general model of a company. Geodesists use an ellipsoid to model the earth. No matter what, a company’s assets are always the sum of its liabilities and capital, and 36N, 80W is always at the exact same spot on a given ellipsoid.

The accounting model won’t run a company and an ellipsoid model won’t complete a survey. They can guide some of the work, but they can’t complete it. They can help determine if the work was successful, but they can’t make it so.

Surveyors have multiple models to satisfy. There’s the math model, the legal model, the regulatory model, the moral model, and perhaps a dozen more that I’m ignorant of.

School cannot teach everything about every one of those models. School should, at a minimum, identify all of the models and teach why each is important in every survey. It should strive to be efficient and comprehensive in doing that.

Then the student is ready for the real teacher to appear.

Gotta have a solid math background in order to properly proportion in all them lost corners:)

**Field Dog, post: 387295, member: 9186 wrote:**I think knowing the purpose of a survey is important. Is a 0.10′ really that important in a topo of a wetland?A 0.10′ vertical error, that is!

MH**Ron Lang, post: 387285, member: 6445 wrote:**And unfortunately that knowledge can’t be taught in a college curriculum.Yes it can, it just isn’t.

Take another field that requires one to read the evidence of man’s past possessions on the land – archeology. No one claims that archeology can’t be taught in a college curriculum. But take a look at the degree requirements at the top schools and you’ll multiple classes in field procedures, graduation requirements for field internships, capstone field projects in the senior year, etc..

One thing to keep in mind though is that university courses of study like archeology and geology have been in existence since the 19th century and the teaching of advanced field procedures has evolved as an academic field of study over more than a century. Most college surveying programs are only a couple of decades old and there is no history of academic / reseach surveying evolving in tandem with practical field surveying like there is in, say for example, geology.

boundary surveying combines archaeology and law. Brilliant. I’m having a vision of the future of surveying in academia. Mostly math, Archaeology, law, and a few engineering courses to learn how to measure. Astute observation.

Edit: geodetics of course. The point is that with enough math one knows how the measurements are or were made and can analyze them without being a servant of the buttons.

One of the great things about this site is that we learn about how things are different in different places. Individually, we can be absolutely great at what we do in a specific place but without the knowledge of the differences between various local laws and practices that does not automatically infer that we would do absolutely great in any of those other places. We would have most of the tools and knowledge but not the specific knowledge.

At the educational program I attended yesterday being led by Jan Van Sickle he told of working on a massive project in Mozambique. It has it’s own unique datum. The first challenge was translating between that datum and anything else. No simple button pushing allowed.

Progressing through the more and more rigorous mathematical training prepares us well for progressing through the more and more rigorous survey training we need over the decades of our career.

Math isn’t a step on a ladder. It is one of many blocks in our foundation. If properly laid and maintained it will provide part of a stable platform for decades (though few of us are a model of stability). When we elevate any part of the foundation over others, things get whacky. Usually they fall apart fairly quick.

Remembet- Balance Danialsan…My problem with math came about 25 years ago when my 3 sons came in from school needing help with their math homework.

Dad sat down with them and they learned how to add, subtract, multiply and divide.

Their teacher would not accept my old math skills saying it did not follow her teaching based on what she called “new math”.

She did not understand that there was no new math.

Somebody simply wanted to sell all the schools new textbooks to teach number sense skills instead of math.

I got my sons calculators and taught them my old math.**gschrock, post: 387332, member: 556 wrote:**The schools do not teach just math and button pushing. I read where someone said a particular school taught no boundary so I visited the school and found out they taught a heap. No, no one is saying that education without experience is the answer; that is a real straw man stance and I really wish folks would stop with such battle lines. The education part provides the basics; then experience makes sense of it. How long would it take a new surveyor fresh out of high school learn everything they need to know about the math, and professional evaluation of evidence? Probably many many years and only if their mentor is so well rounded as to completely and effectively teach them all aspects (only if). The schools will at least give them a running start. I think it does a great disservice to the dedicated educators, schools, and students to dismiss their value. It is all too easy for folks with 30-50 years experience to stand on their high horse and dismiss the young folks just getting started as being inferior and useless – absolute bull – everyone starts somewhere. I have been visiting the schools; the programs and most of the students are amazing and are gobbled up by forward thinking firms that do not pine for the good old days. It is not lightweight math they are being taught. We have it kinda easy here; in many countries if you want to do any work in the cadastre (official registries of land) you have to have the equivalent of a masters and a lot of verified (strictly verified) experience.Those that say the college path is bad are no better than those who reject the experience path. I do find it ridiculous that only 7 of 127 hours in our 4 year program have any connection to boundary law. That’s less than half of one semester. I would rather see a 2 year degree with double the law…

**Holy Cow, post: 387274, member: 50 wrote:**f we are lucky they go on to explain how the combination of powers and roots can result in something similar to that number with numbers on both side of a thing called a decimal pointInfinity to the power of infinity is still infinity…

I hope everyone has a great day; I know I will!What happened was the English being the English would transfer property in a very complex and elaborate title system but with the subject matter being mentioned almost as an afterthought. The subject matter is what we call the legal description. It might be just “the Smith Place.” Where is the Smith Place? What are the boundaries of the Smith Place? The answer is what Smith showed you is what you get.

Over here some attempt was made to describe the boundaries. Beginning at Smith’s corner, thence in the line of Smith N 10 W 50 poles to a stake, thence S 80 W 100 poles to a stake, thence S 10 E 50 poles to a stake, thence N 80 E 100 poles to the place of beginning. Simple right? A rectangular tract 50×100 poles. Maybe it was surveyed in 1750 and by 1770 they couldn’t find the stakes so it was run out again. Maybe the tract was really not close to rectangular or the new lines did not agree with the adjoiners. Late 18th century and early 19th century courts often upheld the new lines if they had been in place more than twenty years.

Math came in as an attempt to remove systematic errors by quantifying them, often mechanically. Hold the chain level or reduce slope to horizontal probably using tables. Use mechanical means to determine north other than by use of the magnetic needle, mainly by use of a solar compass.

Of course this led to confusion, do the erroneous stakes control or the numbers in the description? Not always an easy question to answer. Surveyors look for an answer in something objective and quantifiable (how close is close enough). The Courts look at what the parties did and it is crucial to find out did they know or not know where the line is located? If they knew then their parol agreement may be invalid; if they did not know and they acted with respect to the agreed line then that will likely be enforced. But here is the big but, if the original stakes can be found then those will usually control over the mutually mistaken agreed line.

Note the breadth of Gauss in surveying as well as mathematics.

http://www.ams.org/samplings/feature-column/fcarc-surveying-one

http://www.ams.org/samplings/feature-column/fcarc-surveying-two

Back in the days when we rode our dinosaurs to school and a computer took up a 20′ x 60′ space in an environmentally-controlled, highly-guarded location, computer classes focused on teaching how to think the way the computer was programmed to think (machine logic). This was like learning how to speak by first learning all the parts of speech, their eccentricities, preferences, plural forms, gerund forms and sentence diagramming. Ninety-five percent of the work was in communicating what you really meant to the stupidest machine in the world. Today, people think they are computer whizzes if they can type without looking at the keyboard.

Back then we were forced to think out in great detail where we wanted to go and the best way to get there. Today prompts appear suggesting what you probably want to do and warnings appear to guide you back onto the correct path. Back then it was do it right or don’t do it at all. So, we learned to do it correctly on the first try. That no longer applies. Just toss something at the wall and see what sticks.

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