191–200 of 216 posts
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Except that there are wrench sizes in the /64 range as well. https://www.google.com/search?q=13%2F64%20wrench
Rather than 4/32, 9/64, 5/32, you'd have 4, 4.5, 5. That actually seems even better.
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A practical impact of this - tool users from metric countries don't think in fractions. The notion that the next larger wrench after 1/8 is 5/32 is alien to people brought up with the metric system. Metric bolt heads are integral numbers of millimeters.
The irrational part of this is that the 'wrench system' is actually sized in 32nds of an inch, and thus would be much easier to comprehend with 'improper fractions'. 4/32, 5/32, 6/32, 8/32 ... etc
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From the linked notes: I never really understood capacitors until I started trying to construct proper water-analogies for them. Then I discovered that my electronics and physics classes had sent me down a dead-end path with their garbage about "capacitors store electric charge." Since my discovery, I've gained significantly more expertise in circuit design, which leads me to a sad thought. Maybe the more skilled of…
I still remember struggling with fractions when I was young. The funny thing is that I ended up majoring in math in college (at a highly ranked one at that), and I did very well, even publishing research in differential topology as an undergrad. How can someone who struggled to even grok fractions end up being successful in pure mathematics? I think it's because all my teachers operated off the assumption that kids c…
(By the way if anybody out there does have children that age, I recommend the game Fraction Formula which has tubes in which you put cylinders in to representing different fractions).
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From the linked notes: I never really understood capacitors until I started trying to construct proper water-analogies for them. Then I discovered that my electronics and physics classes had sent me down a dead-end path with their garbage about "capacitors store electric charge." Since my discovery, I've gained significantly more expertise in circuit design, which leads me to a sad thought. Maybe the more skilled of…
I still remember struggling with fractions when I was young. The funny thing is that I ended up majoring in math in college (at a highly ranked one at that), and I did very well, even publishing research in differential topology as an undergrad. How can someone who struggled to even grok fractions end up being successful in pure mathematics? I think it's because all my teachers operated off the assumption that kids c…
I believe it. I've known a lot of adults who don't quite get fractions. They generally also have no trouble working with money and giving change, but no ability to understand interest, especially compound interest. Somehow, the educational system is failing here, not the kid.
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What?? Okay then count by lengths of the spacing of carbon molecules in graphite, or Plank lengths, or whatever. I don't see why your objection is on inches or otherwise any unit I chose for dimension of length.
If you compress a spring, and then heat it, what happens to the stored inches?
Hmm. I learned about E&M theory from Halliday and Resnick, and the practical stuff from Horowitz and Winfield (The Art of Electronics) and they were pretty precise about distinctions between electrons, holes, charge, flow of charge, and so forth. Sounds like I dodged a bullet by not being drawn too much to electronics as a youth, waiting instead to learn about it as a college physics major.
In fact, it isn't so hard that they would like you to believe - it just seems that way when they remove the best parts due to national security :D You would have to go back to James Clerk Maxwell's original 20 equations to see what it's all about. Okey, quaternions are kind of hard, I'll admit to that, but all in all it makes much more sense.
Like QM, doing it analytically clears away misconceptions and gives a consistent view - but it isn't exactly something you can teach to children. It's useful to be able to explain things to laypeople and the not mathematically inclined, which means tightening up the metaphors.
What's the difference between ionized hydrogen and electricity?
Hydrogen gas is insulating matter. Ionized hydrogen is conductive matter. Too bad we don't have metallic hydrogen. It would be a solid conductor, just like any other metal. "Conductor" actually means "contains mobile charges." Conductor doesn't mean "a hollow pipe which electricity flows through." Conductors are more like long, narrow ponds. They're made of 'electric fluid,' so if we have a ring-shaped pond, we can p…
It took 495 GPa pressure to create. The sample is being held in the cryostat in liquid nitrogen.
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How significant is this when you work at the level of Coulombs (high count of charges) ?
Sorry, I don't think I fully understand your question. Again, what I say could be wrong, but if there's a flow of charge it could mean the outer electrons have more charge than they can contain whilst remaining part of an atom, resulting in either electrons breaking free of atoms, or the energy being passed on to another atom (causing a chain reaction as each atom does the same). I'd suggest a higher count of charges…
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I didn't agree with what you wrote and maybe I can explain why. Springs store inches. You measure displacement in inches. Spring constant is just the value that relates stored inches to available force. (You can swap roles of force and displacement if you wish, the point is the same. It sounds bad to say springs store force or displacement, to me.)
But inches are an abstract measurement of distance. Electrons are a thing. (Well, depending on who you ask... no one has ever seen one, and some people have claimed half-jokingly there's only one electron in the entire universe: https://en.wikipedia.org/wiki/One-electron_universe .)
Given that this was decades before the Standard Model was formalized (one-electron, ca. 1940; Glashow electroweak spontaneously broken symmetry, 1967), I think that the one-electron thinking was incredibly productive (especially since Feynman credits it with some insights into what became his path integral formalism).
It's not that one-electron was (or even could be) fully in line with available evidence that was important, but rather that it connected the full symmetries of the Poincaré group (the isometry group of Minkowski spacetime, which is the spacetime of Special Relativity, particle indistinguishability, and representation theory.
The results of the this excited and informal conversation are still found in particle paradigms of quantum field theories (e.g. the Standard Model).
"Electrons are a thing" gets much trickier outside of Minkowski spacetime, however. In non-flat spacetime, the Unruh effect "is a thing", and one consequence is that different observers will disagree on particle count, and even on the interpretation of quantized excitations in the fields as (asymptotic) particles. Unless general covariance is abolished, which seems really hard to do, none of these observers is any more right than any of the others; the number of particles is simply not well-defined locally. Worse, a generally covariant formalism exposes that this is the case in flat spacetime too (e.g. Rindler observers of a patch of a quantum field are not "less right" than another observer at a constant interval from that patch, even if one sees a huge lake of energetic particles and the other sees no particles there at all).
An everywhere-in-spacetime electron field thing is probably a thing in our universe, though. But there are several different descriptions of it... :)