I don't understand why the author seems to discount anything remotely complex as not mathematical. For example, > Today's submicrometer transistors involve complicated effects that the earlier models neglected, so engineers have turned to computer simulation software to model smaller transistors. A more effective formula would describe transistors at all scales, but such a compact formula does not exist. What the heck does she think the code of the simulation software is? People wrote that code so that engineers can actually get work done at Intel. Furthermore, aren't those "complicated effects" at smaller scales due to quantum mechanics which are extremely well-defined by math? Why is there the assumption that describing something in the most general form (like "transistors at all scales") is still going to be simple? Is everything supposed to be as simple as E = mc^2?
I took transistor theory years ago. I remember almost nothing of the formulas, but I do remember the presentation. The engineering professor started with a quantum mechanical model, and he expanded the formula till it filled a chalk board. Then he said, notice that the dominate term is, and circled one of the terms. Then he took and erased everything but that term, and said we'll treat this as equal. He did this three times, with one of the formula expansions taking up 3 chalkboards. In the end, he said It's like Box said, and that is why we treat transistors as a linear amplifier, and it only applies across a certain range.
Then the next day we had the lab, and the challenge was to build a 2 transistor amplifier and show that it was linear across the desired range. You get the parts, and get them it all together up on a scope. It was a mess, there were odd side-bands and crazy noise points all through the spectrum, and I spent hours tuning the resistors to lock in the range. Wow, it was eye opening. Yes, one can model transistors as a linear amplifier, but it's good to know that the full model is a huge complicated noisy quantum mechanical problem that would probably take up 20 chalk boards fully expanded.all models are wrong, some are useful
The linear model of a transistor has proven very useful, but one needs to always be aware of the boundaries where it doesn't apply--for any model.
I still find it laughable that they call E=mc^2 simple, too. Sure, it's a simple formula. But it's applications, as far as I can tell, are FAR from simple. Personally, I'm fairly sure that the author knows very little of what they're talking about.
Armchair theoretical physicist rarely know what they're talking about. It's the same people who espouse ESP and stuff based on quantum entanglement.
Yeaaah that makes no sense. Telepathy/twin-thought would at LEAST make sense, but how the hell did they relate ESP with entanglement? Did they just went "Yeah that sounds cool" and stuck with it?
I don't even see how telepathy/twin-thought could be explained by quantum mechanics. I mean...I'm no physicist, but I don't see an explanation there. Electrons in two peoples brains are entangled so they think the same thoughts? That's not how your brain works. Everyone's neural patters are different. Flipping one electron's spin in one atom of one molecule of one neuron isn't going to make you suddenly read someone's mind. I think people aren't appreciating how complex this is.
I'm not saying it explains it. I'm saying it's a plausible stretch of the imagination that someone that's not versed (but not entirely ignorant) in the subject could think that it could happen. I know exactly how complex both the brain and quantum entanglement is. And it still baffles me that either are possible.