What is this phrase supposed to mean, exactly? Would the author of the fine summary please fill us in, because I can't parse it at all. Thanks.

Writing "3dB" is conceptually *exactly* the same as writing "200%".

I just checked the Wikipedia article, and it is totally correct, and agrees 100% with what I stated, as does every physics text that I've ever seen. The definition is what it is, and your assertion that "3dB" is exactly the same as "200%" is simply incorrect.

I don't want to repeat myself or belabor the point, but 3dB represents a 2:1 ratio of power, and a 1.41:1 ratio of voltage. This follows simply and irrefutably from the laws of physics at work, and the underlying mathematical relationship of the quantities being measured, be they field quantities or power quantities.

Remember the basic definitions of the quantities, which is that power is proportional to voltage^2, so it is mathematically impossible for them to change together by the same ratio.

When power changes 2:1, or expressed in dB, 10 * log(2) = 3dB,

Then voltage changes 1.41:1, or expressed in dB, 20 * log(1.41) = 3dB.

I hope that you can see now that your mistaken idea that "3dB==2:1 or 200%" for both voltage and power is impossible, because power is proportional to voltage^2, it is mathematically impossible for them to both vary by 2:1 at the same time.

(Just for posterity, a factor of 2 == 3dB *always*.)

That last point that you made for posterity is not correct, because the definition of dB relates to power ratios, and a 2:1 ratio of power is 3dB, whereas a 2:1 ratio of voltage results in a 4:1 ratio of power and 6dB of change.

So, a factor of 2 is only 3dB when measuring power, because for power dB is defined as: dB = 10 * log(P1/P0),

and 10 * log(2) = 3

But when measuring voltage, a factor of 2 is 6dB, because for voltage ratios, dB is defined as: dB = 20 * log(V1/V0),

and 20 * log(2) = 6

"I have several pieces of fruit, one of which is a banana grown in Ecuador."

It may well be that the second piece of fruit was also grown in Ecuador, just like the first one was, but I simply don't know, so I don't make any statement about its country of origin, nor do I ask you to make any assumption or draw any inference about its country of origin. Therefore, this statement isn't deliberately misleading, because I don't know the country of origin of the second piece of fruit, as it doesn't have a country of origin sticker on it. My statement is totally true and complete to the best of my knowledge, and does not deliberately withold any information.

The way I see it, the fact that I stated that the country of origin of the first piece of fruit is Ecuador does not imply or require that the second piece of fruit is or is not from Ecuador also.

The way I read and analyze the sentence is that it is conveying complete information about just one piece of fruit, and no information at all about the other piece of fruit. I don't think that it's correct to assume any facts or restrictions not explicitly stated.

Likewise, in the original problem, "I have two children, one of whom is a boy born on Tuesday. What is the probability that the other is also a boy?"

The parent may not know what day of the week their other child was born on, for many reasons, such as separation due to war from the pregnant mother before the child was born. The father may have escaped from the conflict with one child, and only know from witnesses that his pregnant wife was captured and gave birth to a child while in a prison camp. The child born in prison may have been born on a Tuesday too, but the father doesn't know, and doesn't say. So his statement is totally true and complete to the best of his knowledge. But we can't assume that his statement says anything at all about the day of birth of the second child, nor use it in our calculation of the probability that he or she is a boy.

You offer the analogy:

I have several pieces of fruit and one of them is a banana

But the statement in the puzzle is: "I have two children, one of whom is a boy born on a Tuesday

Your example sentence is not analagous to the original problem, because the original statement provides two facts about one of the children, whereas your sentence provides only one fact about one of the pieces of fruit, therefore your argument is flawed.

The correct analogy is: "I have several pieces of fruit, one of which is a banana grown in Ecuador."

It is obvious that this statement about one of the pieces of fruit does not make any statements about the nature of the other piece of fruit, and certainly does not preclude the possiblility that the second piece of fruit is also a banana. For example, the second piece of fruit could very easily be a banana grown in Honduras, and nobody would consider the statement about the first piece of fruit to be a lie.