Man nearly falls off roof after ladder buckles - GIF

[mklotz]

Oh I totally agree. But I am taking about the people who FIRST discovered and began to actually use it. Before anyone can study it, someone had to realize that it existed.

As a retired teacher, I do agree that many school and teachers schools are failing badly.

In many cases, math was the tool used to predict the existence.

You don't realize the earth's orbit is elliptical until you make a lot of observations and then attempt to fit a curve to them, a mathematical operation. In modern times our theories of atomic structure have predicted the existence of unknown elementary particles. Experiments based on their predicted features have then demonstrated their existence. Einstein utilized his general relativity to predict the existence of black holes long before they were discovered.

The schools are so busy with social claptrap that they never get around to teaching the stuff that will form the platform for lifetime learning. Nor do they instill the understanding that learning doesn't stop at graduation.

[neilbourjaily]

Hemmjo, "But I am taking about the people who FIRST discovered and began to actually use it."
Generally, mathematical concepts began with accounting (how much is owed the king), measurement of time (when do we plant), and measurement of land area (how much wealth have I). Nearly everything following those concepts is built on those concepts. Math is the field where discoveries are made while "standing on the shoulders of giants." It is incremental in the growth of its understanding. We're it not for Riemann, ca 1860, there'd be no General Relativity, ca 1915. Maxwell's work may have given rise to Special Relativity. Lorentz, LaGrange, Euler, Copernicus, Galileo, Pythagoras (did not discover the Pythagorean theorem)..., each built his work on his predecessors' work. Einstein found a use for the geometry of curved spaces after Riemann discovered it.

[tonyfoale]

It has always fascinated me how those early thinkers figured out all of these vitally important details. The mathematical concepts, relationships of the stars and the planets, etc.

They did all of this with their own minds, no computers to help them.

As Marv pointed out, they studied mathematics. The same is still true, there is still lots of scope for improving knowledge through purely theoretical mathematics in the fields of the large and small - the greater cosmos and the quantum arena. Much if not all of Einstein's contributions were a result of pure thinking and mathematics. Those people from centuries and millenia ago had similar intellects to those of today. They had less starting knowledge and less computational tools, but that is not a hinderance to analytical thought. Although some also had to content with religious doctrine which in some cases was a hinderance. The opposite is actually the case, with less starting knowledge they had more scope in which to apply some mathematics to both observed and unforeseen phenomenon.
My own meagre experience shows the value of mathematics as an aid to understanding the world. From the age of 8 my hobby was electronics and to understand more I had to study maths from books way ahead of classroom teaching. I studied and understood algebra, geometry, vectors etc. but I just could not get my head around the calculus from books. I lied and managed to get into university quite young, I was 15 and to pay my way I got a job as a lab technician at the university, that meant that I was exempt from tuition fees and had good access to the lecturers. Before going to my first lecture on the calculus I asked an engineering lecturer from the department where I worked to quickly explain differential calculus to me before the lecture. He explained that the derivative was a rate of change. Wow! That was what had alluded me through my book studies and the subsequent first lecture. Suddenly a whole new world of understanding opened before me. Stuff that I couldn't get beyond previously became crystal clear. A couple of years later I was involved in the simulation of various physical phenomena and I learnt the extraordinary power of mathematics to predict stuff that nobody had thought of previously.
It is a big mistake to think of our ancestors as being mentally less capable than ourselves, just because they rode horses instead of cars. The difference between those of earlier eras such as Euler, Newton, the Bernoullis, Galilao et al and their equals of today is that the ancients dealt with things that were within the human intellect to comprehend. Anyone could understand that apples fell to the ground. Today's smart chaps are dealing with things that even they themselves can understand only through the mathematics. Yet the predictive power has been amply demonstrated.

[ductape]

The uppermost ladder bent nearly in half without breaking then showed little deformation after popping back straight. It would be interesting to know what material it is made of. Bamboo is fairly flexible but not like that in my admittedly limited experience working with it. Good thing that vent was there to stop the fall.
Also, the discussion of mathematics here is very interesting. Always nice to learn something.

[mklotz]

Perhaps there's a key to why so many people can't deal with mathematics. Most things in life offer a chance for interpretation. Trends in history, the author's message, the meaning of an artwork - each is open to varying views by different people. In fact, often when taught, these varying interpretations are exploited in the instruction methodology. Who hasn't encountered a question in a humanities exam where one is invited to discuss the 'meaning' of a passage or outline the most important features of a book?

Math, on the other hand, is absolute. It offers no latitude for interpretation. If asked for the prime factors of a number, you must come up with the same answer as everyone else or you're wrong. No "well that's another way to look at it, Johnny" in math.

Faced with an absolutist system, people irrationally feel they're losing their freedom. They can't relate to a world with absolutist laws that are completely beyond their interpretation and manipulation. Their reaction is to mentally "run away" from a system they view as confining although most will manufacture some rationalization for their retreat.

The hard sciences, chemistry and physics, are similar. What's taught at the high school and lower college level is pretty much immutable. Sure, at the higher level, there may be future alterations to the laws of these disciplines, but at the lower level things are pretty much cast in concrete. There's even a principle in physics that says that any future laws or changes to laws have to reduce to known laws when used at the scale at which the known laws work. Relativity must, and does, become Newtonian physics at speeds well below that of light.

So, again, at the lower education levels, the physics/chemistry student is faced with a system he can't possibly manipulate if he wants to produce realistic and acceptable answers. As with math, the first impulse is to run away.

And run they do. Even when faced with a simple tidbit of math from which something could be learned, e.g. a simple linear equation that wraps up a collection of hard to remember tidbits in a chart or table, most mathophobes will refuse to read it, much less attempt to understand it.

For me, the most curious thing about their refusal to learn is the fact that they are so proud of it. Use math to answer a question and immediately a group of the listeners will trumpet how little of math they know, how they flunked math courses, how confused they are by it. I can only imagine that they think their ignorance marks them as more "normal", more like the mob, more ordinary and they want everyone to know they aren't contaminated by all that education stuff.

[hemmjo]

... snip... For me, the most curious thing about their refusal to learn is the fact that they are so proud of it. Use math to answer a question and immediately a group of the listeners will trumpet how little of math they know, how they flunked math courses, how confused they are by it. I can only imagine that they think their ignorance marks them as more "normal", more like the mob, more ordinary and they want everyone to know they aren't contaminated by all that education stuff.

There are way too many uncontaminated people in the world today.

[neilbourjaily]

[QUOTE=mklotz;238016]"...freedom. They can't relate to a world with absolutist laws that are completely beyond their interpretation and manipulation. Their reaction is to mentally "run away" from a system they view as confining although most will manufacture some rationalization for their retreat.

The hard sciences, chemistry and physics, are similar. What's taught at the high school and lower college level is pretty much immutable. Sure, at the higher level, there may be future alterations to the laws of these disciplines..."

There is the beginning and the end of it, freedom and discipline. What the un-disciplined refuse to realize is the disciplined life is the life of freedom. Without discipline, there is no freedom only chaos. Creative freedom for the scientist comes when she or he learns the discipline and applies it to new thought. Even the artist learns and creates through discipline or produces scribbles, blobs of paint, or word salad, It's the same as when someone makes a statement improperly using words, for example confusing chaos for freedom. They make up their own meanings and become incensed when others do not adopt their meaning.
There, I said it.

[Jon]

Previously they were not supported by a society that enabled them by offering a backdoor around absolute fact. However, there are signs that academia is regaining its footing. For example, last week MIT announced that they would no longer require diversity statements for hiring faculty.