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Comment Re:Limits of Measurement (Score 1) 144

Electrons interfere with themselves, because the fluctuation (which is the electron) exists in the full region between the source and screen. The interference pattern is the same no matter how slowly (in terms of electron rate) you fire the electrons, so build up is not a concern.

And this is an important point. I'm not a physicist, but one thing that helped me understand this better is to consider firing a single electron (for example) at the two slits one at the time. It could be at the rate of one per minute, one hour or whatever.

Every electron that makes it through to the screen behind the two slits will hit it at a single point. Nothing unusual there. However, if you make a histogram on the screen based on how frequently each spot gets hit by an electron you'll see the interference pattern you'd expect from a wave being split in two from the two slits. So each electron is a wave that travels through both slits, not one or the other.

Comment Re:No real surprise (Score 1) 710

If there is true consensus about global warming, then science should be inviting opposing thought - not trying to stifle the discussion like a dictator.

But what if the opposing "thought" you're inviting is simply a bunch of specious reasoning debunked a long time ago? Repeated over and over. To the point that you realize that the ones doing the arguing have no interest whatsoever in any kind of objective truth. How long should you be inviting it then? How long do you pretend they deserve respect?

Comment Re:Progenitors? (Score 1) 686

...and we are indeed the first who will learn a lot of lessons as we swarm across the galaxy once we figure out how to get off this damn rock.

You know, I've heard this attitude many times before, and I just don't get it. The Earth is beautiful. We've evolved to see it as beautiful, and yet people still aren't able to enjoy they great things they have right here. Protip: if you can't be happy here on Earth then you're incapable of finding happiness no matter where you go.

Comment Re:This research should receive enormous funding. (Score 1) 202

It's true that the GP is just representing one interpretation. Just thought I'd throw out my favorite "interpretation", (objective collapse theory) as it doesn't seem to get much love. No multiple worlds. No living-dead cats.

Also, instead of thinking of things being fundamentally composed of objects that are sort of both waves and particles I find it easier to picture them all as waves that only occasionally act as particles under the right conditions. This seems counter-intuitive since most of the world we experience is a result of these interactions that make them appear as particles. But it makes it a lot easier when picturing how things work with QFT and the difference between virtual and non-virtual "particles".

Comment Re:danger will robinson (Score 1) 688

There is nothing deep about the concepts of addition and subtraction. Tell a young kid you have two different piles of a number of objects. Combine them into a big pile and count how many are in it. Now they've mastered the concept of addition. Take a pile of a certain number of objects. Remove a certain number from the pile, how much do you have left? By gum, the concept of subtraction has been mastered. The CC processes are tricks to do the calculations more quickly. And since we have calculators that can do that anyways, who cares?

Things get more complicated with fractions. One part that trips people up is how dividing a number > 0 by a fraction > 0 and 1 leads to a number greater than what you started with? (Assuming positive numbers). Say you have a medicine of 8 oz and you must drink 1 oz each day, how many days does it take to finish it? 8 days from 8 divided by 1. Now take the same 8 ounces and you have to drink 1/8 of an ounce a day - how long? Now the correct answer matches your intuition and it makes sense that you'd come up with something larger. THAT is an example of concepts, not calculation tricks.

My favorite example of a mathematical concept, something to introduce to students after they know simple arithmetic, is the method that a young Gauss came up with to quickly add the integers from 1 to 100. It's easy to understand, clever, can be easy to show how to generalize up to any number, and it begins to show the difference between arithmetic and math.

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