Imagine if library fines were in geometric progression...

I'd be broke. I always incur library fines. And before I get into the story, I think I've found the reason.

By the way, here's the extracted electron gun from the TV.

Library fines don't increase your sense of urgency to pay up, because the fines accumulate in the terms of an arithmetic progression, e.g. a fine of 10 cents per day late:

$0.10, $0.20, $0.30, $0.40, $0.50, $0.60, $0.70, $0.80, $0.90, ...

Another problem I see with this is that a person who has been late for, say... 90 days (let's suppose it's not past the limit upon which the library assumes you've lost the book) is still being penalized with the same fine as someone who has been late for 1 day. (1) Ethical issue: Without expounding, I'd think it's fairer to penalize the latter less. (2) Pragmatic issue: It'd also discourage people from holding onto their books for eons, like me.

What if instead, library fines were in terms of a geometric progression, e.g. starting from 1 cent with a common ratio of 2? 

$0.01, $0.02, $0.04, $0.08, $0.16, $0.32, $0.64, $1.28, ...

As you can see, we can easily work out that you start paying more starting from the 8th day. For positive integer solutions of n such that 10n-2^(n-1) < 0, n is 8 or greater. What about the sum of terms of a geometric progression?

$0.01, $0.03, $0.07, $0.15, $0.31, $0.63, ...

For positive integer solutions of n such that 10n-(2^n)+1 < 0, n is 6 or greater. So you start paying more starting the 6th day.

 

I see it mitigating the existing problems with the library fine system. It will be more difficult for some people to keep up with their fines - but one may argue, that it will encourage more social responsibility when people borrow their books. After all, how many of you keep the receipts/return date notifications when you've finished borrowing your books? Or how many of you have noticed some of these receipts left, in the middle of a book you've borrowed, by the nth borrower before you? Much will be solved if we value knowing the return deadline (lest we accumulate too much fines) over abandoning the inconvenience (associated with duly keeping that small piece of paper). Technologically, a SMS reminder system might also be useful to get everything to work - though there's no incentive for that because it will cost to implement the system, and it will probably result in lesser fines received.

Of course, this is just a simple model. Ideally, the new model should incur a fine at the end of the first day that is as close to $0.10 as possible, while the difference between the two is kept as close as possible within the first few days (the first 7 days will be a good one). See why? 

People have asked me what's the use of learning all the basic functions and modeling - mathematics as a language is as imaginative as music.

Now, whatever the case, I had been the biggest donor to my high school library (think I wrote this somewhere else before). Even if I extend my loans, I get something like 3 weeks before I have to return each book - which is just not enough for most books. The issue is, I hate waiting 1 week before the returned book gets re-shelved. Then I've to get into momentum for the same book again. Sometimes I can get away with photocopying parts of the book inbetween - but that's another complication that I'll not discuss.

So... I end up paying fines quite often. There was once they introduced a book award for the most avid borrower (think I wrote about this someone else before, too), and my friend brought it up and told me that I should be happy because I'd be receiving it. (I probably paid fines on more items than the number borrowed by the next biggest borrower). Oh, I was upset because I don't like receiving this sort of award! Fast forward to today, I still haven't returned 2 books long since graduation... fortunately, the maximum fine is $5.50 - so it's worth it to keep it for as long as possible instead of photocopying important parts/buying a new book. And I received a letter to remind me of these books - then it crossed my mind that I'd be bankrupt if library fines were in geometric progression.

On another note, I finally uploaded some old pictures of the electron gun project. As you know, the electron gun of the TV I was working on was machine-pressed into the vacuum tube. I had to implode the vacuum tube to get it out. It was quite dangerous, but the imploding process went smoothly... though I had a pretty serious cut from clearing the glass afterward. Another possible danger was that there were toxic phosphors that would become airborne - I did smell an odor when I opened the bag after imploding it, and then again not all phosphors have odors - and I didn't make any proper preparations for this problem - just worked in a well-ventilated area away from home, and did the job asap.

I wrapped it all up and stood behind a pillar (top-right) as I smashed the glass.

This is a very good picture of what goes inside the TV.

The deflector plates are actually a frame built around the sides... school textbooks usually show very long plates, which don't make sense, because the electrons travel very fast and would have to exit the electric field in a short time (thereby requiring short plates), lest they collide with the plates per se. Of course, you can decrease the field and lengthen the plate, but the TV will become bulky. I wasn't too certain what the steel foil (see the pyramid-ish thing with slits in a titanium grey color) - probably for beta shielding.

What remains of the implosion warning, and a few bigger glass shards.

I'm starting to update the particle accelerator write-up again. There are a lot of details I've yet to fill in, if you've read it.

 Mood: Bach, Toccata in C minor, BWV 911