The power of hidden assumptions

Way back in high school, in 1987 or 1988, I was introduced to the equation for angular magnification (as by a magnifying glass), that being m_θ = 25cm/f (where 25cm is the standard "near point" and f is the focal length of the lens). The explanation was kinda handwaved, and I didn't really get it, but I didn't need to get it in order to use the equation.

Yesterday, I finally ran into a homework question that required understanding the derivation, and I had to figure it out during class (the textbook being almost no help at all) so I could explain it to my students, oops. Turns out there's two very important assumptions that tend to get hidden or glossed over: you don't leave the object in the same place (i.e. you look at it as close as you can without the lens, then put the lens in place and MOVE THE OBJECT until you get a clear image), and the lens has to be right up in your eye so that the angular size of the object and the image are the same. Even our multiple-teaching-award-winning distinguished professor who's helping teach this class got tripped up on the second assumption.

Ah, Bank of America, you magnificent bastards

Two pieces of mail from Bank of America today.

Envelope 1. Notice that the fees for things like cash advances (including cash advance checks) are increasing to 4% of transaction with a minimum of $10, and foreign transaction fees are increasing to 3% (I accidentally used my BoA card to pay for my room in Canada, fortunately got reimbursed for the transaction fee by the school).

Envelope 2. A pile of cash advance checks promising a low APR on cash advances.

Implication: QUICK! Use all these cash advance checks before they cost $10 each to use!

Comics for April 29, 2009

( Nothing of note, lots of older stuff; Other Media: Ms. Marvel action figures )

   Dave Van Domelen, "Kree = YUMMY!" - Galacta, Marvel Assistant-Sized Spectacular #2 (of 2)