For Reactor & Einstein

[RainmanTime]

While I realize that Einstein would rather claim that mathematics is "wrong" as that is easier than learning why it is "right", I also realize that reactor is more willing to knuckle down and learn something on his own. Well, I have an excellent tool for you both...

I have been trying to help one of my nieces who is an engineering student understand and work differential equations. She lives in Ohio and I in California, so it is not like we can just meet up and have a conventional tutoring session. So I found some VERY good instructional videos on YouTube that cover a great many topics in math, physics, finance, etc. (Yes, even a playlist for differential equations that my niece Molly is using!).

Here is the list of playlists... I would suggest starting with the calculus videos, assuming you are both "good" with basic algebra and trigonometry. There is even a linear algebra playlist that will help you understand vectors and coordinate transformations.

Khan Academy Playlists

Enjoy...
RMT

 

[Einstein]

RMT

Reactor is probably off playing with computer code. Me? I'm off playing with time waves. And you? Why not give that vector and basic algebra video a view? Sort of practice what you preach. Then maybe we could have an intelligent discussion on temporal mechanics.

 

[RainmanTime]

Einy:

Then maybe we could have an intelligent discussion on temporal mechanics.

RMT

 

[Einstein2087]

Reactor is probably off playing with computer code. Me? I'm off playing with time waves. And you? Why not give that vector and basic algebra video a view? Sort of practice what you preach. Then maybe we could have an intelligent discussion on temporal mechanics.

Yeah... RMT came off abit patronizing there, I agree. But if you're honestly searching the truth about the world we live in, you won't let that stop you, will you?

Listen. Forget those videos, and let us have a good honest discussion about whether math works or not. Let us have a discussion with the goal of finding the Truth, rather then the goal of "winning". Are you willing to do that?

 

[Doghead]

I am. I used to work with the mentally ill so I am used to the level of discussion I am expecting.

How or why does mathematics not work?

 

[Einstein2087]

I am. I used to work with the mentally ill so I am used to the level of discussion I am expecting.

Well... that opener doesn't really invite a discussion, does it?

My suggestion to Einstein was serious, and mockary isn't going to get this discussion anywhere.

 

[RainmanTime]

Yeah... RMT came off abit patronizing there, I agree.

And I would even agree with that, myself!

Well... that opener doesn't really invite a discussion, does it?

My suggestion to Einstein was serious, and mockary isn't going to get this discussion anywhere.

You'd have to have an appreciation for our history. We mock each other...it's what we do. Doesn't make it right, tho. You see, I have attempted to have the conversation with Einstein that you are suggesting...many times. And over those many times I have gotten small inklings into just how far his mathematics education had progressed. When he starts to show these cards is when he will begin distractions and bring up his "common sense" approach, rather than sticking to understanding why math can accurately model reality.

For instance, recently in our discussion of why a gyroscope "works", I got a glimpse of his mathematical knowledge that told me he either never had a proper education in vector mathematics, or he may have had such an education but never realized a proper understanding of why it works. Most notably was his misunderstanding (or lack thereof) of the vector cross product (pretty fundamental to explaining gyroscopic precession). I'd say it is a fairly fundamental operation which, while not "intuitive" and while it might not speak to "common sense" we have many extant examples that verify its accuracy.

In any event, I wish you luck in the discussion of mathematics you are calling Einstein to have with you. I would truly like to see such a discussion, myself. So much so that I will promise to do my best to limit my searing sarcasm, as long as Einstein stays on the topic and does not bring up non-veridical issues that take us off-topic.

RMT

 

[Doghead]

I am all for this.

How or why does mathematics not work? Seriously, all jokes aside and with no intention on my part to be snarky, let's thrown down and get this out in the open.

 

[Einstein]

RMT

For instance, recently in our discussion of why a gyroscope "works", I got a glimpse of his mathematical knowledge that told me he either never had a proper education in vector mathematics, or he may have had such an education but never realized a proper understanding of why it works. Most notably was his misunderstanding (or lack thereof) of the vector cross product (pretty fundamental to explaining gyroscopic precession). I'd say it is a fairly fundamental operation which, while not "intuitive" and while it might not speak to "common sense" we have many extant examples that verify its accuracy.

My oh my oh my.... I don't believe we ever got to the point of why a gyroscope works the way it does. If we had, you wouldn't be making these statements. As for cross product? Mathematical dung. But honestly I think your mind is too closed to look at the answer. Either that or you are deliberately trying to suppress the truth. Honestly at the time I thought you were interested. But I was mistaken.

 

[Einstein]

Einstein2087

Listen. Forget those videos, and let us have a good honest discussion about whether math works or not. Let us have a discussion with the goal of finding the Truth, rather then the goal of "winning". Are you willing to do that?

One step forward and two steps back. My path to knowledge. Learning the rules of operation for the reality we live in is my goal. Some of those rules have been incorporated into mathematics. But not all. Mathematics isn't the scope into reality that we have been led to believe. It is a tool, but not a very good one. Recently I have been viewing reality as having multiple directions in time. An upcoming experiment will confirm my suspicions. The text books say one lorentz force. I say two. Newtons laws are dominate. If I do succeed in my search, then time has many directions. Just follow the rules for reality. No math needed.

 

[RainmanTime]

My oh my oh my.... I don't believe we ever got to the point of why a gyroscope works the way it does.

I did. You did not. Instead, you simply refused to accept the verified mathematical explanation.

http://www.upscale.utoronto.ca/IYearLab/gyroscop.pdf

If you think you have a different explanation, you had better be able to lay it out mathematically, as this link does. It had better relate to the spinning mass' moment of inertia about its spin axis. And it had better obey Newton's Second Law in rotational form (at the subluminal limit, where relativistic effects are negligible).

If we had, you wouldn't be making these statements.

Crackpot.

As for cross product? Mathematical dung.

That pretty much says it all.

But honestly I think your mind is too closed to look at the answer. Either that or you are deliberately trying to suppress the truth.

Dude, I teach the truth of gryoscopic precession to aerospace engineering students in not one, but two classes. I teach the concept in my intro to propulsion course when we talk about the impact of gyroscopic torques induced by a jet engine on the airframe. I also teach it in an advanced control systems course where we model a 3-axis gyro package in MATLAB/Simulink.

Since you are using the word "honestly" so much, then I should do the same: Honestly, Einstein, I don't think you have a clue that the standard vector mathematics for gyroscopes perfectly explains its operation based on the rotational form of Newton's Second Law. But honestly, I can tell you are too afraid of the mathematics that you do not understand.

RMT

 

[Einstein2087]

Learning the rules of operation for the reality we live in is my goal.

Me too. It's a good thing we already agree on something. This will make progress much easier.

Some of those rules have been incorporated into mathematics. But not all.

Agreed.

It is a tool, but not a very good one.

Here we disagree. And of-course, this is where the discussion gets interesting /ttiforum/images/graemlins/smile.gif

Math is only a tool. I agree. But why do you think it isn't a good tool?

Let me explain my problem with you statement:

I've been using math for years, and it served me wonderfully. I've been using it not only in my professional life (as a physicist) but also in my personal life. Of-course, it has its limits, but every tool has limits. So it's really hard for me to understand where your coming from here.

Can you explain, please?

Recently I have been viewing reality as having multiple directions in time.The text books say one lorentz force. I say two. Newtons laws are dominate. If I do succeed in my search, then time has many directions. Just follow the rules for reality. No math needed.

Okay, now I am completely lost.

You have this theory. Fair enough. More time dimensions, two lorentz forces, and a return to newtonian physics. How does this jive with your claim that "no math is needed"? And what is the alternative framework you are suggesting?

 

[Doghead]

The level of this discussion is surprisingly simplistic from the anti- side...

Is the suggestion seriously on the level of semiotics? Mathematics is no more than window dressing for a hallucinatory consensus? If so, that's old hat. And not logically sound. Or psychologically sound.

 

[Einstein2087]

You'd have to have an appreciation for our history. We mock each other...it's what we do. Doesn't make it right, tho. You see, I have attempted to have the conversation with Einstein that you are suggesting...many times. And over those many times I have gotten small inklings into just how far his mathematics education had progressed.

You speak of this, as if it is some dark terrible secret. So the guy doesn't know calculus. What's the big deal? Is that a federal offense now?

If you want to have a good discussion, you gotta try and understand where the other fellow is coming from. And one doesn't need to be rocket scientist, in order to understand that Einstein is coming from a very different perspective then you or me.

BTW I'm not telling you this in order to preach you that "you did wrong". I'm being strictly practical here. Mockery is simply not going to get us anywhere.

When he starts to show these cards is when he will begin distractions and bring up his "common sense" approach, rather than sticking to understanding why math can accurately model reality.

Of-course he does! Why do you expect anything else?

Do you expect people to drop their common sense just because you tell them to do so? Maybe you, with all your professional training, have a very good reason to believe that his "common sense" is in error, but don't expect him to accept it on basis of authority alone.

I'd say it (the cross-product) is a fairly fundamental operation which, while not "intuitive" and while it might not speak to "common sense" we have many extant examples that verify its accuracy.

What do you mean "its accuracy"?

The cross-product is nothing more than an abstract concept. It's nothing more than a definition dreamt up by engineers to simplify their calculations.

Does it work? Of-course it does. But other than that, the concept has no existence of its own. Indeed, the cross-product isn't even defined in a space with more or less than 3 dimensions. So what's so "fundamental" about it?

And the same goes for many other mathematical constructs. The only reason we use them, is that they work so well. And this is something that Einstein will have to figure out for himself - whether these things work for him or not. You know, even the real Albert Einstein wasn't particularly fond of math. He used it simply because he couldn't do without it.

To sum things up:

Let Einstein find his own way. Let him decide for himself what's needed and what's not. And realize that whenever someone chooses to mock instead of learn, that's his problem.

 

[Einstein2087]

My oh my oh my.... I don't believe we ever got to the point of why a gyroscope works the way it does. If we had, you wouldn't be making these statements. As for cross product? Mathematical dung.

So what's the alternative you are proposing?

See, engineers all over the world have been using this "mathematical dung" to get good practical results. They've been using it to build bridges and skycrapers, and to power our homes. They've been using it to design your computer. They've been using it to design... pretty much everything.

Modern civilization simply won't exist without ideas such as the cross product. It may sound like an absurd concept, but it does work, and it works well.

At least that's my take on it. If you have an objection to anything I've said, I'll be more than happy to hear it. But please, support your statements with some sort of logicial argument and/or evidence. Just shouting "it's dung" or "you're too close-minded to see the truth" isn't going to get us anywhere.

 

[Einstein2087]

If you think you have a different explanation, you had better be able to lay it out mathematically, as this link does.

Um... Since Einstein is claiming that math isn't the right way to go, why are you asking him to lay his alternative in the language of mathematics?

I understand that you can't imagine any accurate explanation that doesn't involve mathematics. To tell you the truth, niether can I. But it is exactly this incredible claim that Einstein is making. He claims he can do without math, doesn't he? Very well. I'd like to see him present us with his alternative.

 

[Einstein]

Einstein2087

You'll excuse me if I skip over replying to RMT. He as usual never has anything constructive to add to a discussion. In my theoretical analysis of the gyroscope I noticed a similarity between its behavior and the magnetic lines of force about a wire sitting in a magnetic field.

In the picture on the left side of the center cross section of the wire, the magnetic lines of force are in the same direction. Forces add. On the right side the magnetic lines oppose. Forces subtract. This results in an orthogonal force causing the wire to move to the right. A very simple and easy to understand visualization.

The same drawing can be used to observe the behavior of a gyroscope with an applied force. The vertical lines represent the applied force. On the left side of the rotating disk, forces add. On the right side forces subtract. MV^2/r is more on one side of the rotating disk than the other. The center of mass is no longer on the axis of rotation. This results in an orthogonal force to the applied force. So it appears mother nature has found a way to rectify centripetal acceleration. But this gets even better. The rotating disk is moving to the right under an internally generated force. That force adds to the top of the rotating disk and subtracts from the bottom creating an additional orthogonal force in the opposing direction to the initially applied force. The push back force. Or my interpretation is that this is how mother nature makes mass. I did take a stab at developing the math for this too. The equations are around here in another thread somewhere.

At any rate I was also curious about precession reversal of a gyroscope under the action of the gravitational force. My current interpretation for this phenomena involves using a negative magnitude vector space as a solution for the observed behavior. Imagine that, even spacetime may have a negative counterpart.

 

[Einstein2087]

In the picture on the left side of the center cross section of the wire, the magnetic lines of force are in the same direction. Forces add. On the right side the magnetic lines oppose. Forces subtract. This results in an orthogonal force causing the wire to move to the right. A very simple and easy to understand visualization.

A drawing! Now, why didn't I think of that.

Well, Einstein, I gotta hand it to you: Drawings can, indeed, circumnavigate the need to use algebra. It's still math, though. Geometry is part of mathematics, no less then algebra is.

As for the specific discussion regarding the gyroscope, I'll have to think about it. Since my major is high energy physics rather than engineering, my understanding of magnets and gyroscopes is a quite rusty.

But we digress. The topic here isn't the gyroscope (luckily for me :oops:). The question we are discussing here is whether math works or not. You've yet to respond to any of the posts I've made on that topic. And what about your statement about the cross product? Do you still maintain that it's "dung"? Or did you just say that to annoy RMT, while not really meaning it?

 

[Einstein]

Einstein2087

The question we are discussing here is whether math works or not.

As a descriptive tool, yes. As a predictive tool, no. A very ambiguous question.

And what about your statement about the cross product? Do you still maintain that it's "dung"? Or did you just say that to annoy RMT, while not really meaning it?

RMT just recently introduced me to the cross product. I was never exposed to it while taking algebra or calculus courses in high school. I studied it extensively. It does appear to be a fictitious mathematical construct. Hardly something I would use to describe anything in the real world. It's almost as if it were designed to replace something. Sort of like a mask. A mask without an author. Although it didn't occur to me at the time that it would annoy RMT. There has been occasion where I have deliberately tossed him a bone just purely for entertainment.

 

[Einstein2087]

As a descriptive tool, yes. As a predictive tool, no. A very ambiguous question.

Sorry for the ambiguity. I meant as a predictive tool.

So you say math isn't a good predictive tool? Then how come scientists and engineers are using it for centuries to get the right result?

How do astronomers predict eclipses? How does the autopilot of a plane stays on course? How does a GPS satellite give you your accurate position within a few feet, even though it has to take into account the rotation of the earth (as well as relativistic effects)?

And even the case of the gyroscope. Gyroscopes have many applications, and the people who design them follow the conventional mathematical approach (including the cross product). And it works. Perhaps there is some deeper layer of reality hidden underneath these calculations, but how can you deny their predictive value?

RMT just recently introduced me to the cross product. I was never exposed to it while taking algebra or calculus courses in high school. I studied it extensively. It does appear to be a fictitious mathematical construct.

You are right, Einstein. It is a fictitious mathematical construct. And the name "cross product" is quite misleading, because it isn't really a "product" of anything. It's nothing more than shorthand for a combination that engineers find useful.

But you see, the key word here is "useful". The cross product does works. Odd? Definitely. Indeed, the fact that such abstract constructs give such accurate results is a dead-on miracle. But they do. Every time you go up a plane, you trust your life in the cross product.

It's almost as if it were designed to replace something. Sort of like a mask.

You may very well be right.

The question is: What's hidden behind the mask?

I'd love to know the answer to that. Especially in the case of the more abstract math of quantum physics. All those Lagrangians and Feyman Diagrams and Gauge Symmetries... Bah! There gotta be some underlying simple truth behind it all. Something we've missed.

See, I agree with you completely on this point. I simply don't think that finding the answer is going to be as easy as you think it is. I wouldn't even know where to begin looking for it.