Yet interestingly Einstein forgot this secret in his later years (perhaps being called 'a genius' went to his head or something?). His famous remark 'God does not play dice' was hardly the exclamation of a modest five year old. That would have been 'hmmm, interesting .... so how does God play dice then?'.
Math is not an intentional barrier at all. For an engineer, math not only helps provide a basic understanding of the principles involved it also allows a deeper insight into how it all relates. Instead of removing a so-called barrier, mathematics training needs to be more intense with smaller classes and more courses. For me, the bell never rang until I saw and understood the mathematical equations and how they were derived and how they could be manipulated.
John
Nonsense. Maths is not an intentional barrier, any more than musical notation is an intentional barrier. Whether we like it or not, maths happens to be the correct way to describe the behaviour of the physical universe. If you want to understand English literature, you have to understand English language. If you want to understand physics, you have to understand maths. You can make some progress at a superficial level with minimal maths, but as soon as things start getting counter-intuitive (first-year physics, second-year engineering?) the 'maths-lite' people either have to stop or blunder on with an increasing level of misconception. I am not saying that physics is just applied maths, there is much more to it than that, but you can't do it without maths.wbeatty said:
I would like to know how to determine the atomic energy levels (and so the emission spectrum) of hydrogen without using maths! Do you have a formulation of quantum mechanics done just using words or pictures?
Actually, it is very much on topic.
You have intended to show everybody how what is taught is "wrong", why it is wrong, and what is "right". Despite no formal education or training on the topic. As a result, your page (or two) on flight is not internally self consistent, a key item I look for when evaluation of information outside of my area of expertise.
When one builds an entire site based upon correcting the faults of everybody else and substituting one's own beliefs, it is imperative the new content be immaculate. Otherwise, corrections which would really be little things will destroy the image one wishes to present, that of absolute accuracy.
Your flight stuff is certainly not internally self consistent, nor is it consistent with the link you provided to another site. Your electricity/electronic stuff is the same way.
As I've said, I believe your goal and intentions are worthy. But the methodology needs work.
Cheers, John
Nope. Try Newsgroups back in early 1990s. Fun!
Actually, DIYaud is a rarity in having quite a bit of that old spark.
There's still one unmoderated electronics Newsgroup going strong: SED, sci.electronics.design. It's accessible via Google Groups:
Discussions - sci.electronics.design | Google Groups
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Sorry, not clear enough with the phrase "math that keeps people from understanding electricity." I refer to non-expert common people, the general public. Those articles are mostly aimed at 11yr old kids. At that grade level even Ohm's Law is a significant barrier. Why 11? That's the target audience when writing science explanations for the public: USA grade 6. It's the knowledge level of subscribers to Wall St. Journal (although this was only the case at the start of the project in 1985. Perhaps it's moved a bit since then.)
And math certainly is an intentional barrier. I've had lots of direct contact with people who react badly to any attempt to remove that barrier.
Once Fortran/JCL/assembler served as the same barrier, but then the high priests of the mainframe lost their lofty position to hoards high school kids with Pascal on Apple II. Like the sealed doors around the IBM-360, math keeps the riffraff out of physics, acts as an ingroup-outgroup boundary, separates the Women from the mere girls. Even here last month in Seattle there was a minor kerfuffel at the local hackerspace over "breaking down math barriers" versus "go out and learn the hardest stuff." One group left in a big huff to start their own meetings free from the contaminating philosophy of we, the disgusting anti-intellectuals insisting on explaining linear algebra and diff eqs so even little kids and grandmothers get it.
Hmmm. Has anyone yet written a For Dummies book on "Shrodinger eqn and matrix algebra for QM?"
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In the same sense that possession of socket wrenches and screwdrivers acts as an ingroup-outgroup boundary between automobile mechanics and the rest of us. You can't do matrix mechanics or predict phenomena quantitatively without the math tools anymore than you can loosen engine mounts using your teeth.
Machian? Ooo, a term I've never heard used in physics forums, with quite nice googling results. machian analogy - Google Search Ha! Historical dirt!
As for semiconductors, if one is tasked with explaining them to Grandmothers, one strikes conceptual gold. How is silicon different than copper? Besides all the low-temp behavior and band structure stuff, there's one huge issue which I'd never encountered in any physics explanation...
In doped semiconductors, the electricity is compressible.
In metals, every atom donates one or more mobile charges of electricity into the "electric fluid" or "sea of charge." In doped semiconductors the number is a bit less. Millions to billions of times less.
The above idea fits with the corrected version of a widespread student misconception that "conductors" are transparent to electrons. Wrong, "conductors" are materials which contain mobile charges. Vacuum is a good insulator except in the case when something has added an electron cloud. What happens if we have a conductor with very few mobile charges? It means that we can use relatively tiny voltages to push those charges off to the side, which changes that conductor into an insulator.
What would we be able to build, if we had a metal-ish conductive material which could be magically converted into glass? And what if we could do this in fractions of a microsecond?
And that's basically why the science, tech, and business communities all started freaking out about those "transistor" things back in the late 1940s. It was almost as big as inventing Fire, or The Wheel.
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Serves the same function in economics too. Nassim Nicholas Taleb's recommendation is to give it (math in economics) a wide berth.
True! But in the case of QM, it's as if the socket sets had long been invisible, kept obscurely named, and never used in plain view of outsiders. Write a visual-based QM/spice program aimed at grade school, and let my Grandma take it out for a spin. Nope, doesn't happen. The Masons were another group that knew the power and respect that comes from carefully-maintained secrets.
You canna be han Expert if any littul kid kens easily all yr vaunted Works.
Fred Alan Wolf and John Gribben have gone far in changing that situation. In fact they brought community-wide embarrassment to physicists by revealing to the public the great and terrible von Neumann Mistake qm "von neumann's error" "hidden variables" - Google Search as well as demonstrating that all those top professionals confidently explaining QM theory on sundry PBS specials had all along been hiding their smoldering disagreements with each, all while carefully presenting a very different face for public consumption. Smiling for the camera while kicking each other under the table. After Lehrer: "The poor folks hate the rich folks, the rich folks hate the poor folks, the Manyworlds folks hates the Collapse folks, and everybody hates that Bohm!" 🙂
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Mystical? 🙂
Thems you shoot with bullets cast from a melted-down Silver Seven. Hammer an OFC spike through their heart, place a huge slab of granite directly on their grave[1]
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[1]Supposedly gravestones originally got their start from ancient superstitious fears of the whompeer. Massive stone slabs laid direct on top of grave-dirt keep your undead relatives from rising in the night.
Also good on Microphonics.
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QM a secret? Puh-leez.
Indeed, Granny and the kids will not be able to predict nodal behavior in electron clouds, or why the charge carriers in polyacetylene are spinless. Too bad, but that's the way it is. You can explain some of the weird effects at a Granny-and-the-kids level (Feynman's illustrations of the one and two slit experiments are a classic of the genre), but it does take a reasonable grasp of math to understand QM- to the extent anyone CAN understand it. Not hugely advanced math, but certainly basic linear algebra and differential equations, not exactly obscure or unreachable subjects for anyone with half a brain and some motivation.
With these VERY basic math tools, one can then tackle the Feynman Lectures or a more conventional treatment like Gottfried or Schiff. This is not arcane stuff, but there's no way around it- it cannot be understood or used without basic math tools.
Indeed, Granny and the kids will not be able to predict nodal behavior in electron clouds, or why the charge carriers in polyacetylene are spinless. Too bad, but that's the way it is. You can explain some of the weird effects at a Granny-and-the-kids level (Feynman's illustrations of the one and two slit experiments are a classic of the genre), but it does take a reasonable grasp of math to understand QM- to the extent anyone CAN understand it. Not hugely advanced math, but certainly basic linear algebra and differential equations, not exactly obscure or unreachable subjects for anyone with half a brain and some motivation.
With these VERY basic math tools, one can then tackle the Feynman Lectures or a more conventional treatment like Gottfried or Schiff. This is not arcane stuff, but there's no way around it- it cannot be understood or used without basic math tools.
Yes it does flow, but the electrons aren't moving at anything like the speed of light.
Think of it like this: all the wires are already full of electricity. All metals are full of movable electrons all the time. When you close the switch, the wires' electricity begins to circulate. If electricity is like a drive belt, then closing the switch releases the brake, and the entire "belt" starts moving slowly in a circle. There must be at least one drive-wheel which is pushing the belt along, of course.
One very important part is the "starting up" process.
Have you ever been near a long freight train which was sitting still on the tracks? When it starts up, you hear a noise like "BANG BANG Bang Bang Bang bang bang" going off into the distance. That's the sound of each train car being yanked in succession as the engine starts pulling on the long chain. The column of train cars might start moving leftwards slowly, but the "bang bang" goes rapidly in the other direction.
The train cars are like the flow of electricity inside the wire. The series of "bangs" shows the high speed flow of electrical energy. The electrical energy doesn't follow the flow of electricity. Electricity is the train itself. Electrical energy is the wave that goes down through the column of train cars.
Or, if electricity is like water in a pipe, then electrical energy is like sound waves traveling through the water. You can have sound propagation, and you can have water flow ...all inside the same pipe!
And that reveals one large problem: where electric circuitry is concerned, basically most people don't know the difference between water and sound! Inside circuits they call "it" by a single name, and speak as if a single thing is flowing.
That was my point as well- anyone with half a brain and the curiosity can learn the basic math tools needed to understand the physics. There's a million introductory books on calculus and linear algebra. But one DOES need the basic tools, and whining that it's some sort of conspiracy to keep "outsiders" from understanding quantum mechanics is contradicted by the facts.
Try suggesting to a literary circle that non-readers can appreciate literature. Try telling athletes that anyone can race, no matter how unfit they are. Try telling a surgeon that knowledge of physiology and anatomy are intentional barriers to wielding a scalpel. I suspect you will find a similar reaction, and for the same reason. In science you can get so far by using simplistic mechanical analogies, but eventually these will lead you astray.wbeatty said:
There are a few scientists who have been able to explain, at a very superficial level, how stuff works. One of the best is probably Richard Feynman on QED: the strange theory of light and matter (I think that is what the book is called). But someone reading it and understanding all of it still won't be able to actually do any physics. For that you have to learn some maths and read his textbooks. As SY says, the maths to get you started with quantum mechanics is not too bad: linear algebra, vector spaces, low order differential equations (or matrices), complex numbers. You also need to be able to cope with non-commuting operators. In the UK this roughly corresponds to late first year or early second year undergraduate physics. The difficult stuff comes later!
A very quick look at the list suggests that the maths you need for elementary QM is there, but the physics is not (except possibly in the chemistry section). Maybe come back next year?
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