how far down the rabbit hole should i go?

based on some discussion w/ivan while he was visiting last week, i've got a question for anyone that is reading this:

how technical is too technical?

my initial motivation for this series and topic was to take events and thought processes that i have and make them more manageable for rachel, as well as to incite other people to wrangle or at least think about questions and problems that occupy me.

here comes the rub:

• the questions can be very intriguing, but the real juicy stuff is a little further down
• diving too deeply in the actual solutions or directions that i bring up can easily alienate whole sections of the audience (lol, no one reads this anyways.)
• there are times when i actually don't know that much about the topic space and would have to do a lot of work to actually provide something meaningful besides more questions
• the whole point is to ask more and more questions and then try to reason your way out of holes when someone gets an answer.

let me know-

solving UHAUL

a few of my friends have moved in the past few weeks, and this has sparked an interesting discussion in my head. like any other task, my mind constantly searches for the optimal solution. because of this, i thoroughly enjoy cramming boxes of different shapes and sizes into a UHaul truck, attempting to fit as much as possible in one go. sound like a familiar problem?

enter KNAPSACK. a common cs problem that seems very similar. a brief translation to this problem would be: given my possessions (the items,) and the UHaul truck (my knapsack,) maximize the amount of stuff i can cram into the truck.

however this variation has a few curveballs:

• in KNAPSACK, items are usually just real numbers, here they are objects with a volume.
  
• this means that you could have a subset whose overall size is the largest w/o surpassing the volume of the truck, but you are now confronted with the task of actually finding an orientation of the items in container that actually fits everything.
• not only do you have volume, but i think shape might be a pretty weird variable in the item set.
• you realistically want to value/prioritize which items you must include like your bed or dresser or tv.
• at a certain point, if not all possessions can be fit in the container at the same time, the problem shifts from maximizing usage to minimizing the number of containers needed to consume all items.
  
• you normally are doing things in a pipeline manner, (sorting, packing into boxes, moving boxes into truck.) so you might not have the omniscient view of all items as you start to pack the truck, and ymmv based on when you see certain items. this throws the traditional dynamic programming approach out the window.
  

so we can try to simplify this problem a little bit before trying to solve it:

• confine all items to be rectangular prisms
• maybe even start with 2D (packing rectangles,) which i want to dub PLANTING for maximizing crop sections in the fields.

have you noticed i really enjoy citing cs problems in ALL CAPS?

it's a race

i think i might lose this one, but this is what i am attempting to do:

solve sudoku in the time it takes someone to solve a sudoku.

i'll keep you posted. i've got the brute force rules of the puzzle coded, not there are the more "higher thinking" strategies that need to be taken into account now.

queue distracted mode on the train.

thought for food

so we hosted a second seder this past week and as a part of an icebreaker (that we eventually used at the end of the night) was to write down on a slip of paper the answer to the question:

what does it mean to be free?

there were some serious responses, some light-hearted jests and such. this morning on the train i was recalling them and had a thought.

to me, freedom is having a circle of friends and family such that i do not feel afraid to share my inner geek moments. it amazes me that there are scenarios and environments where curiosity and innovation are discouraged. i'm very fortunate to have been brought up never being hindered, always pushed to see how far i could go with my ideas.

yay.

how many wrongs make a right?

i was chatting with my sister one day about the concept of inner geek moments, and it reminded me about the concept of being wrong repeatedly. we are all familiar with the phrase "two wrongs do not make a right." but i think there is actually a very common scenario to contradict this.
most people studying linguistics know about the concept of "the evolution of a language." i use it all the time when i make up words that strictly aren't a part of english but people listening know exactly what i am talking about. eventually the term or noun becomes used by a larger portion of the population, and in extreme cases will get entered into the OED. more commonly, the word will live on in urban dictionary.

current words looking to make it big:

• smoove

• daese

• spleet

so just think about it children: if you want to make it in the world of literary legitimacy, all you need to do is be wrong long enough and enough supporters thinking you are right.

discrete mountains, continuous functions?

One of the first inner geek moments recorded in the wild occurred in Montserrat Spain. If you are ever in the area and have a daytrip to spare, I highly recommend it. Not only is it a monastery in the mountains of features one of the few idols of a black virgin Mary as well as a fairly nice boys choir, they have a fairly fun set of hiking trails. Somewhere in the middle of things, we're probably deep into the part where we lost the trail and are bopping around in some random monk's digs. My mind starts going, and I remember a little trick from YSP back in Chicago.

The day starts with us reaching the base of the mountain at 10am. We hike up and down the mountain. There are switchbacks and sometimes we pick the wrong trail. It makes no difference what path we take, really. We ultimately get just short of the summit and setup camp for the night. We decide that we want to see the sunrise from the peak so we wake up at 6am the next day and hike to the top, where we relax, have breakfast, snap a picture, and make our way back down the mountain.

Rachel overlooking Montserrat

Continuing back down, we take a similar meandering path. Stop to pose for a picture, detour to escape a bear, we might have even left our camera at the top and had to have backtracked to retrieve it. After a grueling day of hiking, we stop at the gift-shop, buy a lousy t-shirt and then ride the tram back down into the city.

The geeky part of this that you can prove that with 100% certainty that there exists at least one time of day for which you were at the exact same altitude on both halves of the trip. More explicitly, there exists a time t in [00:00-23:59] such that f_0(t) = f_1(t) if f_i are functions of your altitude on the respective days of the hike.

Not convinced? Here are a few more clues:

We know that since we started our trip and ended our trip in the same place, so

f_0(00:00) = f_1(23:59)

We also know that we spent the night up in the mountain, so

f_0(23:59) = f_1(00:00)

The kicker is now that both functions f_0 and f_1 are continuous. There was no spot in time that we magically jumped altitudes, it was hectic, scattered even, but continuous nonetheless. Graphing these two functions on top of each other will show you that there is some value of t for which the two functions intersect. Bingo!

For further coolness, you can apply this same argument to the world and weather. One can easily accept that temperature when graphed out is also continuous. This allows me to say:

There exists at least one place (actually an uncountable number of places) for which the temperature at that location and the exact opposite, going through the center of the earth is the same.

but is it an IGM?

i've been talking to people about inner geek moments, and i keep redefining it's definition. not so much in terms of "what is an IGM?" but more like, "this is definitely not an inner geek moment." i guess IGM is in NP. (heh.)

here are some clarifications: is it 'inner geek' moments, or inner 'geek moments'? i posit that everyone has a concept similar to 'inner geek.' but few have inner 'geek moments' and that is exactly what i am trying to catalog.

a few examples to help illustrate my point:

• having a detailed discussion on continuous functions during dinner does not imply an IGM, this phenomena of geeking out happens often.
• pondering a seemingly implausible statements using theorems about continuous functions while hiking in the mountains in spain could be seen as an inner geek moment.

(how many times will the words inner, geek, and moment appear in this blog?)

i also want to stress that inner geek moments are not restricted to math and computer science although those subjects tend to dominate mine. giving blood one day led me to this fabled question.

and does it feel weird that in a blog, i'm linking to posts in the future?