There is (approximately) the same amount of energy on both sides of the lens (presumably a small loss into the lens itself). If you measure that energy directly off of the lens on both sides there won't be much difference (you can touch both sides of the lens without getting burnt), but because the direction of the energy has changed, the density of the energy at the focal point is higher than at the lens. So, there is more energy per square mm at the focal point, and presumably less energy per square mm in the area around the focused light than in the ambient area unaffected by the lens shadow (I wonder if that is measurable).
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JimFive

Walkers can stop instantly, Cyclists take a bit longer. In addition, there is a much longer time window for the car and pedestrian to see and avoid each other at a driveway than there is for a car and a cyclist.

Cyclists are, generally, safer on the road than on sidewalks. Drivers see and stop for road traffic, not for sidewalks. By being in the road, a cyclist is where the drivers are looking. In addition, sidewalks have many more crossing intersections than roads do. Every driveway crosses the sidewalk, but none of them cross the road.

It should also be noted that in many places bicycles are forbidden from being ridden on the sidewalks.

The truly important thing is for everyone to follow the rules. Cyclists on the road must stop at stop signs, not pass on the shoulder, signal turns and stops, etc. And the cars around them should treat them respectfully, move over to pass, don't pass and turn, don't honk, etc. Cyclists on the sidewalk are pedestrians and should act as such, ride more slowly, cross in crosswalks, wait for cross signals and traffic, etc. Additionally, cyclists transition from sidewalk to road (pedestrian to vehicle) should do so safely and should not do so for convenience (don't pop up on the sidewalk to avoid traffic and then pop back onto the road).

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JimFive

Reading your links makes me happy that I don't live in North Carolina.
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JimFive

You seem to be implying that we can never know anything about diet because each specific case differs from the general case. That seems to be a fairly pessimistic attitude regarding the ability of experimental science to tease out commonalities and processes in human biology.
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JimFive

You realize that the existence of school lunch standards does not preclude the parent from packing a lunch for their children, right? The school lunch program is not shoving food down the kids' throats. If you want your kid to have whole fat, white milk, then pack it for them.

I do agree that the standards are wrong in places, maybe in lots of places, but the existence of those standards doesn't take away parental choice and responsibility.
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JimFive

And encourage miscreants to find ways to remotely disable the camera.

I actually agree with your statement, missing camera footage should be treated as destroyed evidence (which, as I understand it, is treated as if it would support the other side). But there is potential for abuse on the other side, also.
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JimFive

Threading helps, too. It is a huge pain to try to follow a conversation on an unthreaded comment system.
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JimFive

I agree with this, I would very much like to be able to use a preferred, threaded client with offline capabilities.
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Jimfive

Post to remove accidental moderation. --- Sorry

How about, instead of asking "Do you have an action plan?" ask, "What is your action plan?" or "Please send me your action plan."

We already do this, that generator is called a compiler. By the time you have specified a design to the same detail as an engineer specifies a bridge you have already written all the code. Engineers specify a design down to every individual bolt. Software specifications do not design down the individual line of code. This is the difference between engineering and programming: in engineering when a design is completed then the object still has to be built, in programming when the design is completed then the program is done.
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JimFive

Seriously? You think that MOST people in your class forgot single-digit multiplications (even as they continued to use them daily) and started counting on their fingers (or drawing dots on paper)? Because that's what "calculate them manually" means, doing it by hand. There are 3 ways to do single digit multiplication: memorize, count, or restate the problem into problems that you have already memorized. Restating requires that you have a sufficient number of the problems memorized for it to work.

The teaching methods I describe are first grade and addition/multiplication using tokens is a perfect example of what those operations actually are and quite helpful in moving from physical manipulation to the symbolic manipulation of arithmetic. If you think that there is more to either of those operations than can be shown by an array of stones on a table then please, enlighten me. That grid of tokens can show commutation, distribution, association, primality, squareness, divisibility, etc. Moving that physical representation to a symbolic system is what arithmetic in lower elementary is about. I submit that knowing the answer to those 45 problems without having to spend time figuring them out every time is useful to the student and everyone who has ever complained about cashiers being unable to make change agrees with me.
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JimFive

So, when you do the problem 7*8 what is your thought process?

You seem to be hung up on the idea of a literal table of math problems, while I think I've been pretty clear that I'm referring to a figurative table that is the collection of 45 single digit problems that make up the basics of symbolic arithmetic manipulation. And, I think it is safe to say that you have a significant number of them memorized.

Sure and what did you think? You certainly didn't think 9+9 is 18 and 18+9 is 27 and 27+9 is 36 and 36+9 is 45 and 45+9 is 54, which is what you get from "an understanding of multiplication" without having any memorized answers. You seem to believe that you haven't memorized these things but if you are not counting on your fingers to add numbers together then you HAVE memorized these things, and you probably memorized them so long ago that you can't remember not knowing them. Certainly, there are tricks that make mental math easier, but those tricks still rely on you having memorized a sufficient set of single digit addition and multiplication problems.

It's not a second. If it's a second then they have enough stuff memorized to do the arithmetic. It seems that you've never worked with a student struggling with basic arithmetic such that it takes them 15-30 seconds to do 15+27, if they do it all without giving up. By that time the teacher is on a different problem and the student is falling further behind.

Using a calculator before you understand how and why multiplication works means that you are likely to never understand. You seem to be under the impression that memorizing of tables is used in place of teaching how the operations work. Children are taught to add using tokens on a desk, dots on a line, and marks on a page, then they are pushed to memorize the single digit answers. Multiplication, similarly, starts with making rectangles of tokens and then moves onto paper before memorization of the answers.

In arithmetic the only thing more basic than single digit addition is the numbers themselves.

The problem with rote learning is not in the memorization of simple arithmetic facts. The problem with rote learning in mathematics comes when you start doing mathematics instead of arithmetic.
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JimFive

You're talking about standardized tests, I'm referring to in classroom tests.

You are being disingenuous. If you know 9x6 without thinking about the answer then you have memorized it, whether you ever filled out a grid with the answers is irrelevant to whether you have memorized the material.

If the teacher is demonstrating a problem, e.g. 6x-27 = 15 and for the next step writes 6x=42 it is surely easier for the student to follow along if they can quickly see that 27+15 = 42 without having to write it out and calculate it.

You can't gain understanding if you fall back on a calculator for basic knowledge. Now, whether you think it is valuable to be able to do long division it is practically impossible if you don't know single digit multiplication. A student who knows the multiplication table will be able to complete a quiz on division while the student who doesn't, won't. I'm not saying that students should never use calculators, I'm saying that learning the basic material is important and until you've learned it a calculator is a hindrance.

As an aside, they don't seem to actually teach it as a table any longer, which is good because learning them as separate facts prevents relying on the patterns of the table format.
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JimFive