Wednesday, February 27, 2008

top tibba


Today I helped to lead a trip to the top of Top Tibba, a local hill. In spite of all of the musings that ensue, I managed to have a peaceful walk. I even came home with three more rocks for the Redwood Cottage Rock Garden. I also took a picture of some mountain top flowers that were dusty and wilted looking but perhaps in their prime.

We pointed out some ripply rocks that are fossilized remains of a pre-historic beach. Geologists figure the Himalayas are products of a collision between two continental plates, and the rock that has been thrust so high was once a beach of northern India. In geological contexts, these ideas are all discussed as though they were sound conclusions from solid evidence, but the mathematician in me cringes at the muddy waters of this proof. Not that I doubt the point, but that I loathe the argument.

Now I in my ignorance might assume, upon finding a rock that looked like a beach, that since the rock was about as far from a beach as ever a rock was, maybe there were other ways for rocks to become rippled. Maybe the beachy appearance was misleading. I might ponder whether or not sand would fossilize without losing its ripples, but I would not conclude that the ripples constituted irrefutable evidence that the particular rock was once a beach. Assuming such a thing implies that there is no other possible process that would result in such a formation, and I would feel naive to assume that.

The geologists' response, while accepting an idea that is superficially far-fetched (a rock moving from a non-existent ocean to a mountain top), rejects an idea that is scientifically cautious, that maybe within the vast plentitude of what we do not know there lies an arrangement of forces besides water which could produce such a visual effect.

I do not particularly doubt this theory, much less do I have a better idea, but the brand of logic that seems to tie together our understanding of geology makes me grateful to have chosen mathematics.

As long as I have the can of worms opened, I have wondered about academic attacks on creationism. Science has a foundation of organizing knowledge that can be observed, measured and replicated entirely within the physical realm. This excludes the considerations of any interactions, if ever they have occurred, between this world and a supernatural one. My question is this: If there is a supernatural world and if it has ever interacted with our natural world, would our Science do a sufficient job of interpreting such an interaction? Upon interacting with the natural world, does a supernatural force not become natural? Or even worse, does the natural world not become supernatural?

At one point mathematics, which was once only concerned with real numbers, was unable to deal with certain problems. When complex numbers arrived, they provided an articulation of something not altogether different, but more complete. The complex numbers include the real numbers, it was found. The world had been dealing in special cases, and it was no wonder there were unanswered questions. While most people may never go beyond using real numbers in math, the pesky truth remains that they are simple cases of complex numbers, and they always have been. There are questions which are asked in terms of real numbers, but can only be answered using complex numbers.

Wednesday, February 20, 2008

example of reductio ad absurdum

I am occasionally asked about the meaning of the title of this blog. Reductio ad absurdum is the name given to a particular method of proof that works toward a statement which 'reduces to an absurdity'. It is a conniving brand of proof that is reason enough for anyone to appreciate logic. We prove that a statement is true by demonstrating that it cannot be false.

A textbook example (too literally) of reductio ad absurdum or 'proof by contradiction' is found in a proof that √2 is irrational. To prove directly that there is no whole number ratio equal to √2 would involve a thorough investigation of an infinite number of fractions. This would be time consuming, to say the least. Instead, we will assume that we are wrong and prove the impossibility of that sad state of affairs.

So here we go.

Assume toward a contradiction that √2 is a rational number. Then there exist two integers p and q such that √2 = p/q. Furthermore, Without Loss Of Generalization (WLOG), we can demand that p/q is a fraction in reduced form, so that p and q have no common factors. Now:

√2 = p / q
2 = p² / q²
2q² = p²


This means that is even, which in turn means that p is even. If p is even, then it has a factor of 2 and has two factors of 2. Therefore p² = 4k² for some integer k. This gives us:

2q² = 4k²
q² = 2k²


Therefore is even, which in turn means that q is even. Recall that p is also even, as we demonstrated above. But p and q cannot both be even because we said that they have no common factors. Therefore, we have reached a contradiction, and we must conclude (since our algebra was sound) that our initial assumption was impossible, namely that √2 is a rational number. Therefore √2 is an irrational number. End of Proof.

Ah... I enjoy that every time.

Tuesday, February 19, 2008

presidents of the united states of america

Today the guys on the Freakonomics blog pointed out that only one American president had a first name without an accented first syllable. I figured it out, but I also tried to think of all of the presidents. I only came up with 39. I used to know 42 or 41, however many there were when I learned the list. I'm not even sure who's missing at this point. I almost included Steven Tyler and George Harrison. I had Hubert Humphrey on the list because of the stupid metrodome. But 39, that's a pretty good show. Back at the Burchell homeschool, we got a penny for every president that we could list in order and I knew them all.

My dad only had to learn Jefferson Davis.

Thursday, February 14, 2008

ascii nickel

It's supposed to look like this...




                                  ..;;iiiittttjjttttii;;........                                    
                              ..ttLLGGGGffttjjjjttttttjjjjtt;;....                                  
                          ..iiLLLLjjffffiiiiffttLLjjiiiiiiiiffjjii....                              
                        ;;LLttii;;iiiittttiiiittttffLLGGiiii;;iiLLLL;;..                            
                    ..iiGGii..ii;;iiiittiittiiiiiittffffGGtt;;;;;;ffDDii..                          
                    iiDD;;;;..;;ttttiittiittttiiiittttffDDEE;;,,;;;;ffKKtt..                        
                  iiKKii..,,..iiii;;ii;;iittttttttttjjjjffGGLL::....;;LLWWtt..                      
                ..DDff..;;ii;;ii::,,;;;;iiiittttttjjffttjjLLDDtt..iiii;;KKWWii..                    
                LLLL;;;;ii;;;;;;,,;;;;;;ii;;ttttffffttttttLLGGKK..iiiiiiiiWWDD;;                    
              ;;DD;;;;ii;;;;;;;;,,;;;;iiiiiiiijjffffffttttLLGGWWii..iiiiiiGG##jj..                  
              LLtt::ii;;....ii::;;,,;;;;iiiittttLLLLLLttttttGGKKGG;;;;iiiiii##KK;;                  
            ..LL..iiii;;::::;;;;,,,,;;;;ii;;ttiiDDLLtttt;;iittLL##ii;;iiii;;WW##tt..                
            ii;;;;iiff  ..;;..ii..;;;;;;ii;;iiiiDDLLiiii;;ttLLEE##tt;;;;ii;;DD##GG..                
            tt..iiGG::....ii..;;;;;;;;;;;;;;iiiiDDLLiiiiiiffGGWWKKiiii;;ii..tt##KK;;                
            ff;;GGtt..,,  tt..;;;;,,;;iiii;;iittGGLLttffLLGGKKDDjjLLii;;;;,,ii##WWii                
            GGttii..;;..  ff::;;..;;iiiitt..iiiittGGffLLEEffEE;;;;EEtt;;::..;;WW##tt                
            GGjjii..ii..,,ff..::;;iiiiiitt..;;iiffttttffGGWWKKiiiiLLDD..;;....WW##tt                
            GGff,,..ii..iiii,,..::iiiiii;;..;;jjjjiiiiffGG##DDttiiffKK;;..  ..WW##jj                
            GGff..;;;;..LL..;;;;..;;iiii..;;ttLLiiiiiiffGGKKEE..jjLLKKjj..  ..WW##tt                
            LLff..ii..iiGG..::......;;;;;;;;LL;;iittttttLLKKLLffKKLLKKff..  ;;####ii                
            LLjj..;;  LLii;;..;;......;;;;iitt;;ttLLttiiGGGGGGffDDKKii::..  tt##WW;;                
            jjtt....;;GGttjj  ......;;ii;;iitt;;ttffttttLLDDGGttDDKK;;..    LL##KK..                
            ;;ii;;..LLtt;;;;  ....;;ii....iiGG;;iijjffLLGGKKjjGGKKGG....    KK##LL                  
            ..ffiittttiiii;;  ....;;ii,,;;ttLLttiittjjLLGGttjjGGKKtt      iiWW##ii                  
              ttLLii;;iiii;;  ....,,;;  ..;;ttDDiiiiffffffffGGGGGG..      GG##KK..                  
              ..LLjjii;;;;....::;;,,;;;;..;;ttDDttttjjttffLLLLDDff      ;;WW##tt                    
                iiGGii,,....,,iiiiii,,ii  ::ttEEttffDDttLLttLLKKii      GG##KK..                    
                  LLtt......,,;;;;;;iiiiii;;;;KKffLLKK;;;;tttttt      tt##WWii                      
                  ..ii;;;;..;;iiii;;tt,,jj  iiGGffLLKK....;;....    ;;WW##ff..                      
                    ..;;..::;;iiiiii;;..jj;;..GGttffEE........    iiKK##LL..                        
                      ..,,..;;;;;;;;..;;iitt,,ttttjjLL          iiKK##LL..                          
                        ............  ,,;;;;..;;;;LLii      ..ttKKKKtt..                            
                            ..::........;;......;;;;;;  ..iiDDWWLL,,                                
                              ....;;................iittGGDDff;;                                    
                                    ....;;;;;;;;;;iiiiii::..          



I made this with one of my photos using this webpage: http://www.degraeve.com/img2txt.php

Tuesday, February 12, 2008

up to code

My parents are in Wisconsin, relishing the process of finishing their basement to include some more useful space. There are restrictions that prohibit bedrooms with a limited amount of natural light. Basements do not traditionally have large windows, so the necessary changes would involve removing the land which surrounds the house until the basement was actually no longer a basement, at which time other codes would mandate the installation of a sub-basement.

At least they do not have to comply with Indian building standards.

In India, the hot water pipes must circumnavigate the outside of the house three times from the water heater to the kitchen faucet. This assists with global warming.

The outside doors must be too big to shut for six months and too small to remain shut for the other six. This encourages air circulation. Additionally, no inside door shall have a knob that allows the door to be simply "closed". Rather, each side of the door should have a bolt, and it must not stay closed without the bolt. This develops a deep sense of patience/defeat in a person who gets to walk through three rooms to go to the other door of the bathroom after I realize it is locked from the other side.

In Mussoorie, we enjoy the pure solitude of a national forest of some sort. Besides only being able to chop down trees in the dead of night, we are not allowed to build any new structure except directly onto the foundation of a previous building. If your house is made of sticks and tarps, this law usually slides a bit. If you 'know a guy', the construction codes seem to be somewhat negotiable.

The chimney should be carefully routed to fill the attic with smoke. This gives the rats lung cancer, and they die quickly within 83 generations.

If a wood stove is being installed in a classroom, the stove should be placed adjacent to a window and the chimney should be routed out of the window as directly as is convenient without thinking, in order to avoid Major Improvements to the Room Through Heating (MIRTH). This allows the infrared radiation (a.k.a. heat) to escape harmlessly without thawing my toes. Careful removal of the window pane is forbidden, as its structural integrity has been compromised. The window pane must be bashed out with a chunk of wood, and the shards are to be left on the window ledge as an example to others.

Each electrical outlet must be fitted with a Safely Unsafe Plastic Device of Untimely Death by Electrocution (SUPDUDE) which covers the holes except when the outlet is in use. These jam by design and annually drive millions of frenzied but previously rational adults to stick foreign objects inside an electrical outlet. To plug in an Indian extension cord for example, you must stick a pencil or screwdriver into the grounding hole of an outlet in order to slide the plastic guard away from the holes. The pencil does not need to be removed, since the extension cord is not grounded. Also, the extension cord is just two wires.

Yeah, those Americans should be glad they don't have all of our rules to follow.

Tuesday, February 5, 2008

obligatory bob dylan

I suspect that everyone who writes and fancies themselves to be a lethargic intellectual is at some time driven to applaud or criticize Bob Dylan, mostly because he writes and fancies himself to be a lethargic intellectual, and he manages to make a living with it. The rest of us split our days either mustering ourselves to a respectable job (because we are actually lethargic intellectuals) or slinking awkwardly from it in a way that shows we are mostly math teacher and not very much lethargic intellectual. At the end of the day, it is very difficult to distinguish a brooding genius from a sulking nerd.

Anyway, here is mine. Bob Dylan had a lot of really lousy music, and his writing was almost as bad as his voice at times. However, those 465ish songs listed at http://www.bobdylan.com/songs/index.html (some were not written by him and others were re-released habitually) are peppered with brilliance, and being the sunshiny optimist that I am, I will focus on those. Why? Because it is my blog, and having a blog is all about subjecting people to your literary whims, even if they are only echos of lame observations forty years old. This list only involves a few different albums, and it omits a handful of songs which are more obviously worth a listen.

A few Bob Dylan songs that might be better than what you are listening to right now:

Shelter From the Storm. The first time one listens to it, it seems to contain a beautiful or tragic story of some sort, and that's about as far as it gets. The unfinished thoughts and hazy imagery epitomize the poetic ambiguity that was Bob Dylan. A better Bob Dylan fan than myself would know which woman was being discussed and who the one-eyed undertaker is and all that. A better art appreciator than myself would tell me that the song is about someone or something in my own life and that I am really Bob Dylan. That's deep. But it's a great song. Do I understand your question, man, is it hopeless and forlorn?

Lily, Rosemary, and the Jack of Hearts. This is a ballad like a Sherlock Holmes story. I think that it would make a smashing music video with rustling silks and curling smoke and subtle distrust in eyes. But his bodyguards and silver cane were no match for the Jack of Hearts.

Black Diamond Bay. This song is a snapshot of drama cut short, evoking National Geographic images of fear itself entombed in Pompeii. In a few short verses, Dylan efficiently and ruthlessly developes a handful of tragic characters.
Her passport shows a face
From another time and place
She looks nothin' like that


Romance in Durango. This one is cheesy, but I like it.
No llores, mi querida
Dios nos vigila


Desolation Row. If you are a confused college student, this one makes you feel like you really understand life, but then you may realize that profundity and incoherence are not the same thing. Or you may not.
Now you would not think to look at him
But he was famous long ago
For playing the electric violin
On Desolation Row


Honorable Mentions:
Idiot Wind, Sad Eyed Lady of the Lowlands, Standing in the Doorway, Boots of Spanish Leather.

So go to it.

Sunday, February 3, 2008

missing the super bowl

I am supposed to be grading a quiz right now. Two quizzes, in fact. Instead I am just sitting here listening to Jimmy Stewart on an old radio show. Most of the jokes, being about 1953 current events, are rather beyond my appreciation. It is nice background music, though.

Joie and Annie are away for a couple of days, so I have to keep Will alive and get myself to school all by myself. I will miss the Super Bowl, since it starts at 4:30 AM on a school morning. I can hardly wait till Super Bowl XLV, which I intend to watch from a comfortable chair with a plate full of food somewhere in the land of the free and the home of the brave. The Packers will probably be bad again by then, but I will watch it anyway.

At this point I stopped to imagine the worst case scenario for my re-introduction to the Super Bowl in America. It would certainly involve Dolphins vs. Vikings, with a commentary by Troy Aikman. I would probably have to sit on the floor the whole time, and the only food at the party would be stale pretzels and flat warm Grape Jolly Good soda. The commercials would all star Carrot Top and they would all be about cars. The game would end with a 5-3 Vikings victory after a safety in the fourth overtime. Even then I would enjoy every minute of it.