Author Topic: Sick of ridiculous KVL infighting  (Read 7556 times)

0 Members and 2 Guests are viewing this topic.

Offline SandyCox

  • Regular Contributor
  • *
  • Posts: 141
  • Country: gb
Re: Sick of ridiculous KVL infighting
« Reply #50 on: January 15, 2022, 12:32:54 pm »
The point is that circuit theory is a (very useful) abstraction. The notions of electric and magnetic fields are not part of this paradigm. There is no Faraday’s law or Ampere’s law within the paradigm of circuit theory.
In circuit theory, components are represented by symbols and the “wires” form a graph, describing the way in which the components are connected. Components are represented by their terminal properties, in the form of mathematical equations, i.e.
v = Ri,
i = C dv/dt,
v = L di/dt,
etc.
While these equations are derived from the laws of electromagnetism, the actual physics of how the components work do not form part of the paradigm. Semiconductors are also represented by symbols and their terminal properties. Circuit theory tells us absolutely nothing about the underlying semiconductor physics.
The loops we draw in circuit theory and the actual physical loops are not the same. The physical loops have parasitic resistance, inductance and capacitance. Magnetic fields can couple into the physical loops. We can model these effects, to a certain extent, by creating symbols and equations that capture the underlying physics. For example, the equivalent circuit of a transformer.
Within the paradigm of circuit theory, Kirchhoff’s laws are perfectly valid.
Circuit theory remains an extremely valuable abstraction. Most of us simply would not be able to design circuits if we had to take the full Maxwell’s equations, and semiconductor physics, into account at every step of the design process.
Dr Lewin, with all respect, you are wrong!
Apparently, you are unaware of the fact that circuit theory is an abstraction. You are mixing concepts from two different paradigms.



 

Offline thinkfat

  • Supporter
  • ****
  • Posts: 2161
  • Country: de
  • This is just a hobby I spend too much time on.
    • Matthias' Hackerstübchen
Re: Sick of ridiculous KVL infighting
« Reply #51 on: January 15, 2022, 01:32:42 pm »
And back to square one...
Everybody likes gadgets. Until they try to make them.
 

Offline snarkysparky

  • Frequent Contributor
  • **
  • Posts: 418
  • Country: us
Re: Sick of ridiculous KVL infighting
« Reply #52 on: January 15, 2022, 02:47:17 pm »
Aren't we talking about a completely static situation.  No field quantities are changing with time?  That was the original question?

If so isn't the line integral of E * dl    path independent?

 

Offline SandyCox

  • Regular Contributor
  • *
  • Posts: 141
  • Country: gb
Re: Sick of ridiculous KVL infighting
« Reply #53 on: January 15, 2022, 04:06:03 pm »
Not static. Note the di/dt and the dv/dt in the equations.

There is no concept of electric field within the paradigm of circuit analysis. It is only introduced in the next level of understanding. Also no concept of distance or path along which to integrate. Just symbols described by their terminal properties and links (virtual wires) connecting them.
« Last Edit: January 15, 2022, 04:15:47 pm by SandyCox »
 

Offline snarkysparky

  • Frequent Contributor
  • **
  • Posts: 418
  • Country: us
Re: Sick of ridiculous KVL infighting
« Reply #54 on: January 15, 2022, 04:44:06 pm »
The original problem is a battery powering a light bulb.  So yes the fields have no time varying component after the transient.   

And after the transient the power flows entirely in the wires.   

Veritasium is WRONG in his statement.

 

Offline SandyCox

  • Regular Contributor
  • *
  • Posts: 141
  • Country: gb
Re: Sick of ridiculous KVL infighting
« Reply #55 on: January 15, 2022, 05:06:39 pm »
I fully agree, but this thread is about KVL.
 

Online RoGeorge

  • Super Contributor
  • ***
  • Posts: 6793
  • Country: ro
Re: Sick of ridiculous KVL infighting
« Reply #56 on: January 15, 2022, 05:09:54 pm »
Aren't we talking about a completely static situation.

No, there is nothing static in Lewin's paradox.

He said:  I'm gonna show you how two voltmeters connected in parallel can indicate two different voltages.

And everybody was, "yeah right, maybe if one is defective, you are trolling us, right?".  And then Lewin said something like:  "you know what, even more, I'm gonna make one show +0.9V, and the other show -0.1V, both in parallel, how about that, do you believe me?".  And everybody was:  "chill down professor, you must be drunk, or something".

Then the professor cobbles up a circuit with 2 voltmeters in parallel, and "bang!" he released a full blown EMP (Electro-Magnetic Pulse) in the middle of his circuit.  And one voltmeter goes +0.9V, the other goes -0.1V, just like he predicted, yet with both voltmeters connected in parallel.

And the professor is: "told, you!", and everybody else was:  :o
Then after a second, "wait a minute, you weren't suppose to do that!" (as in, we all assumed a static situation, or else said a conservative field).

Well, "assumption is the mother of all fuck-ups", I never said it was static, and my point is one of the most glorified of yours EE rules doesn't hold in some very particular situations, like I just shown you with my clever circuit and this EMP, or else said instead EMP, a non-conservative field for the most pedantic, sais the professor.

Well, the professor never actually said all those words, that was just my artistic rendering of how the whole debate started, technically.

-----------------------

From here on, even more human feelings and emotions are thrown into the game, electricians and engineers saying "my rules you point out as limited/sometimes wrong are working just fine for me, and I have my ways to deal with that particular EMP you showed, we use induced voltage in the probing wires instead", and the professor said "but that really is because your rule doesn't hold for non-conservative fields", and so on.

From here, each side gets more and more stubborn into its own interpretation, and bang!, 40 pages of fights on EEVblog only, and countless other debates elsewhere!  :rant:

 ;D




See for yourself at minute 50:50 (and those experimental results are not coming out of nowhere, it was all explained how something like that is possible, just watch the lecture(s) preceding the minute 50:50 demo):

8.02x - Lect 16 - Electromagnetic Induction, Faraday's Law, Lenz Law, SUPER DEMO
Lectures by Walter Lewin. They will make you ♥ Physics.
« Last Edit: January 15, 2022, 06:02:20 pm by RoGeorge »
 

Offline Simon

  • Global Moderator
  • *****
  • Posts: 18061
  • Country: gb
  • Did that just blow up? No? might work after all !!
    • Simon's Electronics
Re: Sick of ridiculous KVL infighting
« Reply #57 on: January 16, 2022, 09:51:35 am »

Carrying that mentality forward, I've seen things go wrong in industry because people ignore this -- if you forget about fields, you forget that you shouldn't route over splits in ground planes (or, really, split ground planes without rationale -- but that's a whole different religious argument). I worked on a receiver board for a LiDAR on an upcoming lunar mission and the receiver is borked for this reason (SPI bus routed over a GND split near the signal path) -- needs substantial, costly, time-consuming redesign and respin, complicated by the fact that the designer doesn't understand the issue and won't concede that it's a fields problem (despite every fingerprint being there, from qualitative EMC to being able to measure the SCLK signal rising edge on the TIA output). Forget about fields and you'll never be able to solve many of the noise issues you're dealing with -- and don't hold any hope for understanding why your boards have failed EMC.

So, I put it to you -- are we educating new engineers right? Are we motivating the issues at hand well, and are we giving concise and intuitive explanations? If we're triggering holy wars then the explanations at hand are not good enough, and we need to do better. As to what those might look like? Well, I've no idea what's intuitive to newcomers of the field; I've been at this too long. What helps? How do we avoid more of the kind of 39-page inane fighting on this forum, and between YouTube electronics education superstars?

You don't need a degree in physics to know that you should not route a trace from one ground plane to another, this is because you don't need to know down to the atomic level why it's a bad idea, at a basic level you just need to know not to do it, a slightly better engineer will know the verbal reasoning but won't need to worry about the math. It is the physicists job to tell you the math detail but for the purposes of designing a PCB that's irrelevant, because as a good engineer you know not to do it.

i have no idea about fields, but I put items including a SMPS through military EMC testing successfully, no physics knowledge required, I'm just a good engineer. If you asked to to prove down to the math why my method worked I will tell you to consult a physicist. I can tell you broadly what is going on but I won't be calculating the rf emissions for you. No one sits down and makes calculations to that level when they design for EMC, they learn what works and what does not and hopefully get mentored by anther experienced engineer. Theoretical evaluation of an EMC scenario is far more complicated than designing with well informed instinct based on intuition and experience. That is the difference between engineers and physicists.

So as he is the ultimate physicist why did he do a demo to disprove a theory but not explain that the theory was not meant to hold at this level and then explain what was going on. He just seemed to disprove someone with no explanation himself.
 

Offline PlainName

  • Super Contributor
  • ***
  • Posts: 7303
  • Country: va
Re: Sick of ridiculous KVL infighting
« Reply #58 on: January 16, 2022, 11:15:47 am »
Quote
at a basic level you just need to know not to do it

I think this is what distinguishes, say, a script kiddy from a programmer. Anyone can follow rules, but knowing why you follow them allows you to apply them properly and appropriately (and, sometimes, not to). As they say, "Rules are for the obedience of fools and the guidance of wise men."
 
The following users thanked this post: nctnico

Offline Simon

  • Global Moderator
  • *****
  • Posts: 18061
  • Country: gb
  • Did that just blow up? No? might work after all !!
    • Simon's Electronics
Re: Sick of ridiculous KVL infighting
« Reply #59 on: January 16, 2022, 01:33:40 pm »
Quote
at a basic level you just need to know not to do it

I think this is what distinguishes, say, a script kiddy from a programmer. Anyone can follow rules, but knowing why you follow them allows you to apply them properly and appropriately (and, sometimes, not to). As they say, "Rules are for the obedience of fools and the guidance of wise men."


Knowing why is different to doing the mathematical proof about it. If I already understand enough to know that it is not a thing I should do. Do I need to to the theoretical math and prove it ? no I don't, because I know enough to know broadly that the outcome is a fail.
 

Offline SiliconWizard

  • Super Contributor
  • ***
  • Posts: 15425
  • Country: fr
Re: Sick of ridiculous KVL infighting
« Reply #60 on: January 16, 2022, 05:17:59 pm »
Quote
at a basic level you just need to know not to do it

I think this is what distinguishes, say, a script kiddy from a programmer. Anyone can follow rules, but knowing why you follow them allows you to apply them properly and appropriately (and, sometimes, not to). As they say, "Rules are for the obedience of fools and the guidance of wise men."

Yes. But you'd also be a fool thinking that just because you apply more complex rules, then you're not just following rules, and that you actually understand something. =)
 
The following users thanked this post: bdunham7

Offline PlainName

  • Super Contributor
  • ***
  • Posts: 7303
  • Country: va
Re: Sick of ridiculous KVL infighting
« Reply #61 on: January 16, 2022, 10:26:17 pm »
That's a nice scarecrow (aka strawman) with the ever more complex rules :)

All I pointed out was that it's better if you know why a rule is there. You don't need to go down rabbit  holes or have more complex rules, just know why that rule is the rule. For instance, you put a diode across a relay coil as a matter of course. It's a rule. But if you didn't know why it's a rule then you don't understand what your circuit is doing. Sure, it will survive better than if you didn't know the rule was there, but you're just tickboxing. However, knowing why you put the diode there doesn't imply anything about quantum mechanics or the 40 lower layers of sub-rules that might be invocable.

In the specific case of the ground planes, why do you not route over gap? If you don't know and just follow the rules, the probability is that when you need to do it (perhaps you have no choice) you won't be able to choose the least worst way of doing it. Perhaps it doesn't actually matter in this design and having separate planes is more important. Who knows? (Clearly, not the person who unknowingly rule-follows.)
 

Offline SiliconWizard

  • Super Contributor
  • ***
  • Posts: 15425
  • Country: fr
Re: Sick of ridiculous KVL infighting
« Reply #62 on: January 17, 2022, 12:33:44 am »
That's a nice scarecrow (aka strawman) with the ever more complex rules :)
All I pointed out was that it's better if you know why a rule is there. You don't need to go down rabbit  holes or have more complex rules, just know why that rule is the rule. (...)

That was just a pinch of humility, which never hurts, and which some seem to be severely lacking here (not talking about you).

But of course, the more you know... the more you know. In a way. =) (Jokes aside, because beyond some point, excessive "knowledge" can actually end up counterproductive.)

Yes, applying rules without understanding them is never a good thing. You should at least understand the basic principles underlying them - which will help applying them wisely.

You don't necessarily need to resort to Maxwell equations  - or the Schrödinger equation  ;D - to design and analyze electronic circuits. The moment you think you do, either you *really* do, or you are probably going to teach physics rather than design things.

Of course knowing why you use some rules while routing PCBs *is* a necessity. But knowing the principles doesn't mean you need to dig ultra deep. When was the last time you used Maxwell equations to route a PCB?

And precisely, I think a good engineer (and admittedly not all are "good") must be good at applying physics. Engineering is applied science. And believe it or not - I'm pretty sure a few will fiercely disagree - good engineers are often better at applying physics than many physicists (at least, those that are theoretical physicists). Experimental physicists are a different matter. I have a deep respect for them (I have for theoretical physicists too, don't get me wrong, it's just that we are talking about applied science here!) Many theoretical physicists are not good at experimental physics. Which is why it's not unusual that the ones having devised sophisticated theories and the ones that have been able to observe them through experiments are different people/teams.

So anyway, just a few random thoughts. My point is, certainly, if you don't understand the underlying principles, you're going to have a tough time, but conversely, just because you perfectly master the underlying principles to the minute details doesn't mean you'll be good at applying them in all circumstances.
 

Online nctnico

  • Super Contributor
  • ***
  • Posts: 28071
  • Country: nl
    • NCT Developments
Re: Sick of ridiculous KVL infighting
« Reply #63 on: January 17, 2022, 01:10:52 am »
In short: engineers apply science; turn applicable theory into something that works in the real world.
There are small lies, big lies and then there is what is on the screen of your oscilloscope.
 

Offline Nominal Animal

  • Super Contributor
  • ***
  • Posts: 6956
  • Country: fi
    • My home page and email address
Re: Sick of ridiculous KVL infighting
« Reply #64 on: January 17, 2022, 06:05:43 am »
And precisely, I think a good engineer (and admittedly not all are "good") must be good at applying physics. Engineering is applied science. And believe it or not - I'm pretty sure a few will fiercely disagree - good engineers are often better at applying physics than many physicists (at least, those that are theoretical physicists). Experimental physicists are a different matter. I have a deep respect for them (I have for theoretical physicists too, don't get me wrong, it's just that we are talking about applied science here!) Many theoretical physicists are not good at experimental physics. Which is why it's not unusual that the ones having devised sophisticated theories and the ones that have been able to observe them through experiments are different people/teams.
I agree.  Similar difference exists between mathematicians and physicists, too.  Things like galling have a rather funky causation chain, and are obvious in hindsight, but very, very difficult to predict from the theory alone.  Yet, just about anyone dealing with metal-to-metal sliding contacts knows about galling, and how lubrication helps avoid it.  (Even then, cold welding (in vacuum) was a bit of a surprise when it was discovered in the 1940s.)

Kirchhoff's circuit laws precede Maxwell's equations for classical electromagnetism.  Neither is exactly correct: they are both limited models.  As far as we currently understand, for a full description of electromagnetism, we need to turn to quantum electrodynamics.

QED is also currently used for the most precise simulations of chemistry (including molecular dynamics and materials physics), by only modeling the outermost interacting electrons for each atom.  Even there, because of its calculation-intensive nature, we are limited to cases with at most some tens of thousands of electrons, plus the volume must repeat in every direction (periodic boundary conditions).

Now, mathematically, you do get from QED to Maxwell's equations at the limit of taking the reduced Planck constant to zero, \$\hbar \to 0\$.  This is deceptively simple, because it really does not just mean that we ignore the quantum nature of the universe –– even though there are a lot of highly respected theoretical physicists that will laugh at that and say that of course it does –– because that difference is what produces some of the unexpected effects: just like galling I mentioned before is unexpected to those considering atomically perfect metallic crystalline surfaces sliding against each other, but obvious and easy to explain in hindsight, when you already know it does happen.

(Do remember, that physicists still cannot exactly agree if and why hot water freezes faster than cold water in the exact same conditions.  This is easy to experimentally verify.  I do believe the reason has been found through simulations, and is essentially that heating water will affect the O-H bond length decreasing the heat capacity of the molecule, but when shedding the heat, the bond length shrinks slower than the other degrees of freedom that comprise the heat of the molecule (various vibration modes).   This is why I don't see anything "strange" in arguing whether KVL or Maxwell is correct in some specific situation, because to me, it is normal argument about which imperfect model is better applied since the "correct" one, QED, is too complicated to apply here.  But remember galling: math alone does not say what effects there are if you simply approximate a single constant a bit.  A lot of things go wonky in geometry if you assume e.g. \$\pi = 3.14\$ i.e. rational, for example.)

Full disclosure:  I don't like QED.  I am not a mathematician, and getting my feeble brain to work with QED and the approximations required to work with it (like the Hartree-Fock method) so overwhelms it that I then have no touch with the physical systems I'm trying to work with.  Lagrangian and Hamiltonian mechanics I can just about grok, and I can work with quantum physics in general (since it has a nice definition of observables that keeps me in touch with the actual physical systems I can measure and, uh, observe).  So, I won't be offering much wrt. KVL-vs-Maxwell.  I'm best suited to making the computational tools for others to work with, really.
 
The following users thanked this post: RoGeorge

Online RoGeorge

  • Super Contributor
  • ***
  • Posts: 6793
  • Country: ro
Re: Sick of ridiculous KVL infighting
« Reply #65 on: January 17, 2022, 04:32:01 pm »
e.g. \$\pi = 3.14\$

Can be between 3 and 4, according to mathematicians:  ;D

When Pi is Not 3.14 | Infinite Series | PBS Digital Studios


though Pi is 3.0 for construction engineers and that's nothing but a scratch, because cosmologists often assume Pi is 1.0!  :scared:

Offline PlainName

  • Super Contributor
  • ***
  • Posts: 7303
  • Country: va
Re: Sick of ridiculous KVL infighting
« Reply #66 on: January 17, 2022, 05:41:06 pm »
Her hands need tying down or the video cropping or something. Very hard to watch with those beating time.
 

Online RoGeorge

  • Super Contributor
  • ***
  • Posts: 6793
  • Country: ro
Re: Sick of ridiculous KVL infighting
« Reply #67 on: January 17, 2022, 06:09:07 pm »
She was a very good host for that channel, that good that after she left the channel in order to have more time to finish her PhD, they tried a few replacements but none were as charismatic and skilled as she was, and after a few more months of trying, PBS decided do end the "PBS Infinite" channel.

"PBS Infinite Series" was a very good channel, always with outstanding content and making complicated concepts easy to follow, brief but showing just enough to make one curious and wanting to learn more.

Online RoGeorge

  • Super Contributor
  • ***
  • Posts: 6793
  • Country: ro
Re: Sick of ridiculous KVL infighting
« Reply #68 on: January 17, 2022, 11:58:15 pm »
you do get from QED to Maxwell's equations at the limit of taking the reduced Planck constant to zero, \$\hbar \to 0\$.

He, he, nice!  I didn't know that before, so I've thought "how's so" while peeling potatoes, trying to cherry-pick for an explanation.  Well, \$\hbar \to 0\$ would mean making quantization smaller and smaller, until instead of quantities coming in certain chunks, it all become a "smooth" continuous function, just like we used to have before QED.  Q.E.D.  ;D

But the idea of energy coming in chunks was introduced in order to patch the wrong prediction of the so called ultraviolet catastrophe.  With smooth energy exchange, the calculated spectrum of a black body radiation was very different from the measured spectrum.  And somehow, adding a new rule about energy exchanges happening only in certain chunks of energy, the quantization, fixed that wrong prediction.

Now, I would expect to get some failed prediction in terms of QED, too, when \$\hbar \to 0\$ (as it is in Maxwell), similar with the failed predictions from the spectrum of the black body radiation when the quantization aspect was not considered, but I don't know any examples where Maxwell fails to predict correctly.

What would be such an example?

Offline bsfeechannel

  • Super Contributor
  • ***
  • Posts: 1668
  • Country: 00
Re: Sick of ridiculous KVL infighting
« Reply #69 on: January 18, 2022, 03:34:50 am »
You don't need a degree in physics to know that you should not route a trace from one ground plane to another, this is because you don't need to know down to the atomic level why it's a bad idea, at a basic level you just need to know not to do it, a slightly better engineer will know the verbal reasoning but won't need to worry about the math. It is the physicists job to tell you the math detail but for the purposes of designing a PCB that's irrelevant, because as a good engineer you know not to do it.

i have no idea about fields, but I put items including a SMPS through military EMC testing successfully, no physics knowledge required, I'm just a good engineer. If you asked to to prove down to the math why my method worked I will tell you to consult a physicist. I can tell you broadly what is going on but I won't be calculating the rf emissions for you. No one sits down and makes calculations to that level when they design for EMC, they learn what works and what does not and hopefully get mentored by anther experienced engineer. Theoretical evaluation of an EMC scenario is far more complicated than designing with well informed instinct based on intuition and experience. That is the difference between engineers and physicists.

So as he is the ultimate physicist why did he do a demo to disprove a theory but not explain that the theory was not meant to hold at this level and then explain what was going on. He just seemed to disprove someone with no explanation himself.

"All generalizations are dangerous. Even this one." People attribute to Alexandre Dumas. We can't generalize and say that knowledge of physics is dispensable for the "good" engineer. Electronics engineering is a vast field. Some areas can get away with basic knowledge of circuits. Other areas are at the edge of the technological advancement and require really knowledgeable people.

So, the difference between an engineer and a physicist not always can be translated into the knowledge of physics. And in many cases you can have a bit of overlap between the two camps. Just to cite two classical examples, Michael Faraday, a physicist, while discovering the phenomenon of magnetic induction invented the very first transformer, which is now an ubiquitous engineering device. Moritz Jacobi, an engineer (and also a physicist) proved the theorem of maximum power transfer.

Lewin never wanted to disprove Kirchhoff's laws. What he wanted to show is that those laws are not applicable to all circuits and in that case the more general theory is Maxwell's equations. He left the explanation of his demo as a homework to his students. The "ridiculous" KVL threads we have is us responding to the challenge, and discussing why some have flunked it miserably. I have learned an awful lot with it, especially with Sredni's and Huronking' posts and with several others'.
 

Offline Nominal Animal

  • Super Contributor
  • ***
  • Posts: 6956
  • Country: fi
    • My home page and email address
Re: Sick of ridiculous KVL infighting
« Reply #70 on: January 18, 2022, 06:04:03 am »
Now, I would expect to get some failed prediction in terms of QED, too, when \$\hbar \to 0\$ (as it is in Maxwell), similar with the failed predictions from the spectrum of the black body radiation when the quantization aspect was not considered, but I don't know any examples where Maxwell fails to predict correctly.

What would be such an example?
The Wikipedia article lists a few.

The photoelectric effect is probably the easiest case to verify and understand, where Maxwell's equations fail to predict the phenomena.  Maxwell's laws suggest that a low-frequency (long-wavelength) light beam at high intensity would accumulate enough kinetic energy in the outermost electrons of the atoms, exciting them until they're kicked out from the atoms, and thus releasing photoelectrons, but that does not happen.  The photons need to exceed a threshold energy (frequency, wavelength) for it to happen.

A typical silicon photovoltaic cell has a minimum bandgap of about 1.12 eV.  Photons having this energy have wavelength of about 1100 nm, which is near infrared, just outside human visible spectrum.  Maxwell's equations don't predict any kind of threshold effect, and photons with longer wavelengths (and thus lower energies) should work just fine, just provide less energy.  However, in reality, photons with lower energy (higher wavelengths) won't produce a photoelectric effect.

This is easier to see with semiconductors with bandgaps in the visible spectrum, for example gallium phosphide (as used in e.g. old-style green LEDs), which has a bandgap of 2.26 eV, corresponding to photon wavelength of about 550 nm.  Use a red laser (over 600 nm) to exite gallium phosphide, and nothing happens.  Use a blue laser (under 500 nm), and it exhibits the photoelectric effect.

(A laser, such as a cheap laser pointer, is just an easy source of monochromatic light, which is the point here: the photons all have the same wavelength.  In a laser, they also have the same phase, but that is not important here.  This experiment works with non-coherent monochromatic light of suitable wavelengths.)

[Lewin] left the explanation of his demo as a homework to his students.
Funnily enough, I see this as the biggest difference between mathematicians or theoretical physicists, and experimental physicists or others who apply mathematics as a tool.

Mathematicians show the formulae and their derivation, and leave the interpretation and application to the student.
Experimental physicists and those who teach applied mathematics describe a family of problems, their description in mathematical terms, and the applied tools that can be used to find the solutions –– exactly the part that is left to the students by mathematicians.

To some people, the latter is the natural, better approach.  To some people, the former is the natural, better approach.  A lot of people can work things out either way.  Very, very few people can teach both ways effectively.  And this creates a big part of the dichotomy, since very few people can bridge the two effectively.  It also explains why some believe string theory is physics, while others consider it only mathematics thus far.
 
The following users thanked this post: RoGeorge


Share me

Digg  Facebook  SlashDot  Delicious  Technorati  Twitter  Google  Yahoo
Smf