Having come up through the UK educational system, where exposure to rigorous pure and applied math is (or was, my age may betray me here) a little more intense than in the US system, I have found myself with an interesting mental dichotomy after reading through Jim & Cash's books a couple of times. With every single description of the forces and math involved in piloting a motorcycle that I read, my mental response was "OK, yeah, of course." The math and physics is rigorous, susceptible to hard analysis and stands up to such scrutiny. So why was it necessary for them to write these books in the first place?
I will admit in advance that even amongst my peers I was (and am) something of a math geek. However to give an example of the difference I am seeing between educational systems, I and my entire cohort of math students were routinely solving 2nd order differential equations as classroom exercises in the equivalent of our junior or senior year of high school. Most US students don't get to that level until their junior or senior year of COLLEGE, and not even then if the student is not in a hard science or engineering major.
For me, the value of these books was to move the mathematical and physical mindset that I already possessed into the context of my riding. I cant begin to express how much it has changed my awareness of the issues involved in my riding. Just reading through the books has made me a better rider because of the increased awareness of WHY things work the way they do. The mental dichotomy comes because in the USA I see folks all around me that DIDN'T have the same mathematical and scientific background that I do - they are as smart as I am and in many cases more so, but they simply don't have the grounding in hard numbers that I do because they were never taught it. Those folks would have a VERY different take on these books than I would, but would probably gain a significant benefit from them.
Jim and Cash, it seems to me that you tailored your writing style to people with that kind of mathematical background. If I'm right in that then kudos to you. You've likely saved a few lives, possibly including mine, because you explained the math in a way that is accessible to anyone on the entire spectrum from minimal mathematical ability to "able to qualify for the lead on NUMB3RS".
I suppose the question I am asking is why are these conclusions not intuitively obvious when the context is presented? It may be a failing in myself, because with my background and mindset they are and I find it hard to conceive why anyone else would find them difficult. Is it a genuine difference in the approach to math in the national educational systems or is it a cultural difference in mindset? Or both?
Shadow Spirit 750DC
Posted - 07/30/2013 : 9:09 AM
quote:Is it a genuine difference in the approach to math in the national educational systems or is it a cultural difference in mindset? Or both?
As a product of the NYC public school system I can only speak to my experience and it may not be a reflection of areas with more limited resources. I am also referring to several decades ago and things may have changed, although I do not believe they have much.
I went to a regular NYC High School. I took a year of Calculus. I read and discussed Camus and Dumas in a French literature class conducted in French. English was not allowed in the class. These were opportunities that I chose which were offered in a "normal" HS. There are also HS that focus on particular talents. Mathematically gifted? then Bronx High School of Science for you. Interested in a job skill over academia then a Vocational HS for you (i.e. Aviation). Arts your thing, then NYC HS of Performing Arts.
*I* think this educational model reflects the US culture / mindset. Those raised in the US tend to have a "bottom line" and also a freedom of choice way of thinking. Do you force everyone to a level that most will never need or do you give everyone the opportunity to achieve that level but allow them the choice to pursue it in their area of interest?
I shared your interest in math but objectively speaking I can't think of one instance in more than 4 decades where advanced calculus has come in handy.
XR650L, 790 Adv R
Posted - 07/30/2013 : 9:40 AM
Although I've done much more with math than the average American, being in a technical industry, I don't see how math skills are necessary to be a safe motorcycle rider.
Okay, we can come up with an equation for the stopping distance from 30 mph, or the G-force when going around a corner, but it's easy enough to learn from experience how long it takes to stop or what sort of speed will let me comfortably go through a corner.
When I detect the need to make a quick stop, I'm not doing math equations in my head, I'm using the brakes to the best of my ability to get the bike stopped.
I'm not trying to be argumentative here, just pointing out a different point of view on the subject.
White House, TN
Posted - 07/30/2013 : 11:25 AM
I don't disagree with you about the benefit of understanding the physical/mathematical underpinning of motorcycle riding. But even theoretically understanding the theory completely, won't let you ride a motorcycle without actual training to acquire the physical and mental skills. There are simply too many simultaneous tasks to be performed for there to be time to work each one out from theory as it happens. They have to be internalised and separated from the need for conscious decision making.
BTW, I'm an expat Brit, and the two educational systems only match up at the Masters degree level. A Masters in America is a 3 year course, in the UK it's a 1 year course. Masters and PHDs are directly equivalent; Bachelors are not even close.
James R. Davis
Posted - 07/30/2013 : 11:39 AM
Needing to do mathematical computations while riding?
Sophistry at its worst.
You do mathematical computations while trying to understand the what and why of an endeavor (if you wish), or to design for future endeavors, or to prove truth and disprove lies (especially in court) like "I could not stop in time because I had a passenger", or "that skid mark shows that I couldn't have been going that fast before the collision", or "the brakes on my Harley are plenty good enough to stop me when I need to stop even if I'm pulling that 400 pound trailer".
"I don't need to know math" is perfectly true and appropriate ... for most entry level employees (though they may still be required to make change for a dollar), and justifies a minimum wage. It is also true for riding a motorcycle.
Thank you, ScooterCommuter, for your kind words.
Posted - 07/30/2013 : 11:45 AM
Scooter Commuter, I doubt if you would want to debate that with my engineer kids and grand kids. Likely also that you did not go to school in Brixton. You attended a school system where "A Levels" and "O Levels" determined your fate and a University System changed little since a time when a small number of elite civil servants were prepared to run an empire.
Congratulations on your math skills and hoping that some day your riding skills are on a par with a product of rural Kentucky public schools such as Nicky Hayden.
Saint Paul, MN
Posted - 08/05/2013 : 12:25 AM
Gentlemen, it appears I owe you all an apology. I appear to have given a very mistaken impression of what I was asking and why. I assure you I was not denigrating a different system than I was familiar with nor implying that I was running math in my head when riding - I do that in my comfortable armchair when analyzing my actions on my last ride, thats true, but when riding I'm just employing the stuff I've already been able to internalize. The intellectual approach just makes it easier to internalize the lessons I have to learn from each ride.
Having said that, however, I think it is better to simply leave it with an apology to you all and not attempt to justify my words and dig it deeper. There are many more skilled riders on this forum than I will ever be and for my part I am content to acknowledge that and simply aspire to their level. I will ask you to please excuse dumb questions that are aimed at that goal.
Shadow Spirit 750DC
Posted - 08/05/2013 : 7:32 AM
quote:Gentlemen, it appears I owe you all an apology.
I cannot fathom why you feel an apology is in order.
I took your post to have 2 parts. One was a positive review of the math and physics presented in the books authored by "Jim and Cash". I did not comment on that part because I felt the value to be self evident, in short, I agreed completely.
The second part I felt was a sincere question about the math level attained by the average product of the educational system here. I attempted to answer it using myself as an example and in turn I asked my own question. The question was a bit of a loaded question because of my personal philosophy on education which I will share with you now. I expect any educational system to teach reading, riting, and rithmetic. I then expect it to get the hell out of the way as we teach ourselves whatever strikes our fancy (or our need) to whatever level of competence we desire / decide. I personally measure the success of an educational system on the level to which it develops critical thinking. If one (anyone) reads or hears or learns of something and does not stop to analyze it but blindly accepts it as fact then IMO the educational system failed. But then again we all know the earth is flat and the sun revolves around it. How could it be otherwise? The town crier has told us it is so.
BTW, IMO, this second part of your post would have been a nice fit for the Get Your Motor Running forum. Open, respectful, discussion / debate is welcome throughout this site.
Shadow Spirit 750DC
Posted - 08/05/2013 : 11:27 AM
We're not far off in our thinking.
You've taken my brief answer and made certain logical assumptions which are probably contrary to what I believe. When I say get out of the way I mean do not impede my gaining knowledge. I am not saying do not aid the effort. For example a few decades ago I took an intensive COBOL class. I became drawn to JCL. The instructor was not happy with my lack of focus on the required material. He loaned me his JCL manuals, gave me access to an IBM mainframe, and answered as many of my questions as he was capable of. When the smoke cleared I knew COBOL, was pretty good at JCL, and picked up 360 assembler along the way. He could have stood in my way yet what he did was support my desire to learn. He was more interested in sharing what he knew then the impact my exit exam score would have on him.
This is a discussion that we could have over several cups of coffee and at the end of it I suspect we would discover we were on the same side of the fence. I realize the limitations imposed on teachers. IMO, the good (and great) ones have found a way around it. Many of mine did.
I don't want to hijack this thread but I suspect I could answer your points to your satisfaction.
Here is food for thought. Physics class should be a tool to teach / help one understand math and not something that expects you to already know it and apply it.
Shadow Spirit 750DC
Posted - 08/05/2013 : 10:14 PM
I had opened up a separate thread here where we can continue this conversation. I am interested in hearing your perspective and hopefully those of others.
Posted - 08/14/2013 : 9:39 AM
For me it works like this: understanding physics helps me understand physical situations better (and more quickly); understanding math helps me understand physics.
A quick example to illustrate my point: Many years ago I had a summer job (when in school) cutting grass on power line right of ways and around transformer stations. There was one transformer station that had a grassy slope that was extremely steep. We used to cut it by lowering a guy on a safety line, who would swing a fly-mo type lawnmower. (A wheel-less hovercraft. Remember those?) On the way there my first time I was told that, as the new guy, that would be my job. They were all looking forward to having a good laugh watching me slip and fall my way down the slope, which was apparently the norm. But they were disappointed when I didn't slip once. The reason, of course, was that I saw right away that it was necessary to stand perpendicular to the slope, restrained by the safety line, so that there was no lateral force where my feet met the ground.
Now some people are gifted at physical activity and quickly feel these things for themselves. But most people, myself included, aren't like that. Most of us would be helped a lot by understanding the physics of a situation, but the majority of people are neither physically gifted nor particularly insightful about physics. Where math comes in, I believe, is that better math education would probably lead to more people who have a good understanding of physics.
On a slightly different topic, though, one thing that has always bothered me is the pragmatic attitude most people take toward math. You always hear people say, "When am I going to use this?" But nobody every says that about art class, or music class. I think if we really want a more math-literate society it might benefit us to stop thinking so much about the practical uses of math and start trying to help people see the joy and beauty in it, like we do with art and music. "If you want to build a ship, don't drum up people together to collect wood and don't assign them tasks and work, but rather teach them to long for the endless immensity of the sea." --Antoine de Saint-Exupery