Monday, December 3, 2012

Gödel's first incompleteness theorem explained using (almost) the most common 1000 English words

The Up Goer 5 Text Editor, based on the xkcd comic Up Goer 5, takes what you write and tells you whether any of the words you used is outside of the most used 1000 words in the English language.  As a challenge to myself, I used the editor to write out an outline of (my understanding of) Gödel's first incompleteness theorem.  I cheated a little bit, using ' ' quotes for some technical language.  Enjoy.

Mr Gödel shows that writing and moving letters around can't tell us everything that is true about numbers (part one):

When I write words, each word is made of letters. So, a group of letters can have a meaning. The same is true when we talk about numbers instead of words, but with numbers, there is only one meaning, and we can use different "letters" to change the meaning. So, if I want to say "one is the same as two," I can write '1=2' (which is not true), and if I want to say "one is not the same as two," I can write '~1=2' (which is true).  If we start by saying obviously true things, like '0=0' ("nothing is the same as nothing") or '0+x=x' ("a thing added to nothing makes the same thing"), we can use letters to say new things, like '(0=0)^(0+x=x)' ("nothing is the same as nothing, AND a thing added to nothing makes the same thing").  But can we find out everything that is true about numbers just by saying some obviously true things and moving letters around to find out other true things?  Mr Gödel showed that the answer is no.

First, I will tell you some things you should know. Many years ago, some people who worked with numbers thought that everything it is possible to know about numbers could be shown by moving letters around. It was shown that, when working with words like "and", "or" and "not", moving letters around was enough to show everything that was true or not true. But what about with harder-to-understand things, like numbers?

Some people who worked with numbers tried to write about numbers by using sets. Mr Russell and Mr Whitehead were two such people. They wrote a book called "[Important things about numbers]" which was very long -- in fact, it took more than three hundred pieces of paper to show that one and one make two.

Mr Gödel had an idea, though. He showed that, when you say something like "one and one make two", the thing you say can be made into a number. All you have to do is give a number to each letter you use, and put each of those numbers to the upper right of a 'prime' number -- that is, a number that can't be written as a number times another number besides one. 
The number of the first letter goes to the upper right of the smallest 'prime' number, the number of the second letter goes to the upper right of the second 'prime' number, and so on.  So, if three is to the upper right of two, then we have two times two times two.  Then the numbers get put together and we write the first number times the second number times the third number, and so on.

Suppose we say "nothing is the same as nothing". This can be written as three letters: '0=0'.

Give '0' the number one, and give '=' the number two. Then Mr Gödel would make a new number: two, times three times three, times five. This is the only way the thing we said can be made into a number, and the number can be changed back into the thing we said.

We can say longer things as well, and still turn the things we say into numbers. We can talk about numbers, or about the things we say about number, or even about the things we say about the things we say about numbers, using the way Mr Gödel shows us. It is important to note that we can talk about things we know about (like one, two, three and so on) but we can also talk about things we don't know about (using letters like 'x' or 'P') as long as we give each letter a number that is not used by any other letter.

Mr Gödel made a number that said " "can't be shown by moving letters when written two times" can't be shown by moving letters when written two times." (This might remind you of the work of Mr Quine). In short, the number says "I can't be shown by moving letters around". The thing the number says must be either true or not true.

If it is true, then the number says something true that can't be shown by moving letters.

If it is not true, then it CAN be shown by moving letters, but this means that moving letters can cause us to believe things that aren't true. This goes against what we first thought, since we started by saying only things that are obviously true.

So, the thing Mr Gödel's number says must be true, even though it can't be shown by moving letters around.

Friday, October 5, 2012

2009 School Project - Duct Tape and the Wealth of Nations (by Sam Sournois)

In English 12 -- the last English class I had to take before graduating high school -- our final project was to create something of our own choosing.  I chose to write a satirical essay on using duct tape to solve the world's problems.  The character who "wrote" the essay was named Sam Sournois, a character I used in more than one school project.  I've corrected two typos, but otherwise, all the text and images in this essay are exactly as they were in 2009.




Introduction

            The world, as it is today, is a deplorable place in which life could be described as nasty, brutish and short.  There are times when one wishes to express one’s anger at said world, perhaps by going on a rampage and murdering his or her friends and/or family.  Truly, there are times when it seems as if our humble planet is plagued by so many social, political and environmental problems that society is hopeless, we are all doomed, and we all might as well live in trees, eating each other alive.
            It is this author’s goal to prove that this is not the case: humanity is not, in fact, doomed by all or any of these problems.  There is, in fact, one simple tool that will surely bring forth a new era to the world, an era of wealth, health and happiness.  Ladies and gentlemen, I write to tell you that that tool is me.  And I propose to the reader that the cure to all these social diseases can be found in drawers and toolboxes the civilized world over.  The solution, of course, is duct tape.
            Now, most of you are probably aware that duct tape can be used to fix a wide variety of problems, ranging from broken eyeglass frames, constructing a large truck out of two smaller trucks, or to quickly reattach severed limbs.  But, I hear you pondering, how can duct tape possibly be used to solve major world problems?  The answers might surprise you.

            Duct tape is inherently an instrument of social change.  In fact, as seen in Fig. 1,  anecdotal evidence shows that duct tape usage in any given society roughly correlates with that society’s quality of life (the one exception being Denmark, which has a high Human Development Index, but where everything is built out of Lego bricks, or so I’m told).  Some economists speculate that this phenomenon only occurs because such countries have the resources to make and purchase duct tape, with their affluence leading to the presence of duct tape, not the other way around.  This author, however, sees through such rhetoric, and concludes without question that duct tape is the cause of these high standards of living.
            Given this information, however, the scientific and political complexes can and must work together to find new, innovative and practical ways to use duct tape to the advantage of humanity at large.  Over the past few years of my life, I have gathered all the information necessary to theorize specific uses for duct tape in solving issues all over the world.  If any readers find themselves captivated by my brilliant ideas, please, write a letter to your local elected official.  Alternatively, if you live in a tyrannical monarchy, a Slavonic feudal state, or a theocratic system, please write a letter to your local king, Tsar, or deity, respectively.

Religious Wars

            Religion has always been central in human conflict, from the greatest crusades and Jihads, to a traditional holiday fistfight over a Furby™ on Christmas Eve.  People and societies make their beliefs a part of their identity, and criticisms of their ideologies are interpreted as personal attacks.  But until everyone in the world learns to worship the one true God (Lord Xenu) the various governments of the world shall have to intervene to solve these problems.
            A survey by the Sournois Institute of Technology shows that 90% of wars, religious or otherwise, are at least tangentally involved with a cute little country called Israel.  Israel might even be considered the Kevin Bacon of modern military conflicts.  The many conflicting groups living in the surrounding area can’t seem to decide exactly to whom this small nation belongs.  I propose that the country of Israel be covered with duct tape, in full.  This will be no small job: Israel is approximately 22,770 square kilometres, and we will require as much duct tape to cover up the nation (Fig. 2).  However, as this will misplace approximately 7,282,000 people, it seems only fair to give them each a few hundred shekels for their trouble.  All in all, this project, including the cost of duct tape, will cost upwards of 9.6 billion dollars, or 36 billion Israeli shekels.  However, once the various factions have decided to get along, the duct tape may be taken off of Israel, and the Israelis may continue with their daily lives.

            But of course, merely preventing the two factions from taking the other side’s land won’t, in itself, end such wars.  The leaders of their respective sides must be put together in a room and given time to work out their differences.  I propose that any two leaders of opposing armies or ideologies be put in a room and taped together with—you guessed it—duct tape, until they are forced into working out their problems peacefully.
           
Starvation and Poverty

            Poverty and starvation are problems that exist all over the world, even in our own back yards.  I mean that literally: my own back yard is home to a small community of homeless individuals.  Sometimes we play Euchre.  It’s great fun, but it serves only to hide the true suffering behind the poverty in the world.
            In many cases, poverty is a matter of not having a house.  For this reason, it is my opinion that new homes be built to accommodate the poor individuals who can’t afford to buy homes on their own resources.  Furthermore, I propose that these homes be insulated with duct tape.
            You may think that this sounds impractical, even absurd.  But bear in mind that duct tape is often used in engineering for its resistance to the elements.  In fact, anecdotal evidence shows that duct tape can withstand temperatures up to 2.3 zillion degrees Kelvin.  This would, indeed, be a large project to undertake: in North America, the average Habitat for Humanity house is approximately 1,000 square feet in floor area, and costs about 60,000 dollars to build.  With the use of duct tape insulation, however, these costs could easily be cut to a mere 59,900 dollars per house, probably.
            But what shall these people eat, you may ask?  Let us consider the facts: Duct Tape is made up of a cotton mesh, coated with a layer of polyethylene coating and smothered with a thick coat of rubber adhesive.  For all this nutritional value, duct tape, when purchased in bulk, can cost less than ten dollars per roll.  Theoretically, duct tape could feed every impoverished person in the world for a lower cost than the United States’ annual military expenses.
            As an added bonus, this boom in the duct tape industry would create many new jobs, from duct tape machinery worker, to duct tape executive.  Perhap someday, you might even become the CEO of the Sournois Tape Company, the fifth largest duct tape manufacturing company in the Inland Northwest and BC Interior.

Global Warming

            The debate is over, and the scientific method is no longer necessary: Global Warming is happening, and it will inevitibly doom us all do complete societal chaos.  We know that global warming will be catastrophic and harmful to humanity, because former vice president of the United States, Al Gore, showed the world some scary-looking graphs that said so.  I, for one, take all my scientific advice from former vice presidents, and have found myself asking in the process of many a scientific study, “What would Dan Quayle do?”
            Many politicians and Green activists all over the world have put together plans to end this climate change by a complete reform of government policies worldwide.  Admittedly, a complete worldwide political revolution is a start, but this author proposes something bigger.
            You’ve probably caught onto my thinking by now, and you probably think that I propose making a duct tape shield around the Earth to protect us from the sun’s rays.  While this is a good idea, it is, both figuratively and literally, a band-aid solution, and might in fact end up exacerbating the greenhouse effect, making the world even more of a fiery Hellhole than Al Gore predicts.  As an alternative, I propose placing a duct tape shield around the sun.
            According to some scientists, the Earth’s temperature will rise approximately six degrees Kelvin over the next one hundred years.  By calculations I performed in my head just now, that’s approximately two percent higher than it is now.  So, logically, the shield around the sun will have to be approximately two percent of the Sun’s total surface area, or 1.2*10^17 metres squared (Fig. 3), in order to counteract the warming here on Earth.  This translates to over 46 quintillion rolls of duct tape, which would cost approximately 690 quintillion dollars, excluding taxes.  This is 10,781 times more than the total amount of money in the entire world.  However, I think it would be completely worth this little bit of extra effort to know that we’ll be safe from any unwanted heat.

            Of course, there will be some speaking out against my plan, claiming that I don’t entirely understand how our climate works, saying that the Solar Duct Tape Shield would be financially impractical, and insisting that if global warming is caused by humans, it could easily be solved by the use of existing alternatives such as solar or hydrogen power.  In response, I say that anyone who supports hydrogen power is clearly working for one of the big hydrogen conglomerates, and must be silenced.
            But how, you ask, will they be silenced?  One word: duct tape.  Anyone who speaks out against our cause, whether or not they have scientific evidence to back up their theses, will be censored with the use of duct tape.  We will spread it over their protest signs, tie them up and tape their mouths shut.  Censorship: it worked for the Soviets, and it can work for us.

Racial Discrimination

            Racial discrimination has been around as long as man has had the ability to distinguish one colour from another.  It has torn apart societies, and become the fountainhead of a multitude of politically incorrect jokes which, while hysterically funny, should not be allowed to continue, and do not accurately represent the zeitgeist of our time (or “zeit”).
            This is an issue that particularly hits home for me.  I, myself, was once denied the opportunity to play the titular character in “Rosa Parks: The Musical” based solely on the colour of my skin.  Although the producers claimed it was because of my age, gender, and complete inability to sing or perform in any skillful way, I could see through their cunning lies.  It’s an incident that still haunts me to this very day.
            Nonetheless, we must look at the problem rationally.  What is the problem?  People judge each other because of their different appearances.  But what is the solution?  Some say the solution is to create an environment of social change in which people of different cultures and ethnicities are celebrated for their differences.  But would this really have a long term effect?  In this author’s opinion, “God no”.  The only viable solution is to eliminate the differences between people by making everyone the same colour: say, the silvery, shiny colour of duct tape?
            Anecdotal evidence shows that, when people look the same, they’re more likely to identify with each other.  And if everybody is covered with duct tape, then everyone will look exactly the same, eliminating any need or desire for racism.  From birth, children will be covered with a layer of thick duct tape.  As they grow up, the duct tape will wear out, but we will learn to get into the habit of recovering our skin with duct tape every day.  It will become a part of our daily routines, like brushing your teeth, showering, or moistening your pet manatee.
            Statistics show that the average body surface area of a human adult is approximately 1.73 square metres.  This means that approximately 4,270,000,000 rolls of duct tape will have to be used to cover the entire human population with duct tape.  However, for sanitary reasons, I recommend adding a new layer of duct tape once a week.  As this would be a compulsory policy, it would cost the governments of the world a total annual cost of 23.4 trillion dollars to supply this duct tape, or approximately 3,600 dollars per person per year.  This will be expensive and will probably crush the economies of developing and newly industrialized countries, as well as permanently damaging the economies of the developed countries.  However, this is a sacrifice I’m willing to make.  And, to those who disagree with me, I ask: why do you like racism so much?  I rest my case.

Conclusion

            In conclusion, it is obvious that duct tape is the solution to all of the world’s major problems.  However, there are skeptics in the world who would go to any length to prove this statement incorrect.  They will claim that the solutions duct tape offers are impractical, costly, physically impossible, and ineffectual.  But I shall take it upon myself to point out that most of these skeptics are “scientists” with “degrees” who deal with “theories” and “experiments”.  These ivory-tower folk have no bearing on what happens in the real world, and as such, cannot be trusted to slow the Duct Tape political movement any more than a doctor should be trusted to practice medicine.  In this author’s opinion, science is far too important to be left to scientists.
            As I sincerely hope I have proven to you by now, the one and only way to ensure that the world does not continue its spiral into doom is for all the governments of the world to get come together, forget their differences, and invest in the Duct Tape solution.  As a society, I believe we’ll find that we can afford to execute this solution, because we can’t afford not to.

About the Author
             Sournois received his PhDs in sociology, economics, and socioeconomics from FreePhDs4All.com.  He is a professor of Applications of Duct Tape 101 at the Sournois Institute of Technology, and the author of the bestselling book, “The World is Doomed and it’s All Your Fault: An Optimistic Guide to Social Change”.  Sam is also an executive at the Sournois Tape Company.  In his spare time, Sam enjoys eating, sleeping, and auditioning for Broadway musicals.

Finally, a video which originally accompanied my presentation of my essay:


Wednesday, September 12, 2012

Vlog 31 - Advice


Saturday, September 8, 2012

Every Major's Terrible (Video)

This video was just posted by the SFU Choir's YouTube channel.  It's based on the xkcd comic, "Every Major's Terrible".



For more information, visit http://www.everymajorsterrible.com/

The song was sung by the SFU Choir, of which I am a member (http://www.sfuchoir.ca/), and written by Randall Munroe (http://www.xkcd.com).  The video was produced by Samantha Derochie (http://www.phlyingwaylstudios.com/)

Sunday, August 19, 2012

Shark Movie Titles

Lately on the Space channel (the Canadian equivalent of the SyFy channel), they've been showing several straight-to-TV monster movies featuring sharks, with such classic names as Sharktopus and Dinoshark (both produced by Roger Corman) -- possibly in celebration of Shark Week 2012.  In light of this, I'd like to present you with 100 Stiflingly Unfunny Shark Movie Titles I came up with.

1. Sharkocalypse
2. Sharknimal
3. Sharky Mark and the Funky Bunch
4. Sharks and Recreation
5. Gnarls Sharkley
6. A Bridge Too Shark
7. Jurassic Shark
8. Alone in the Shark
9. Card Shark
10. My Shark Will Go On
11. I Shark the Sheriff
12. Sharkolepsy
13. Raiders of the Lost Shark
14. Penn and Teller: Bullsh*rk!
15. Sharkopolis
16. The Shawshark Redemption
17. Sharkocalypse 2: The Sharkening
18. Shark as a Whip
19. Three Sharks for Muster Mark
20. Sharktopussy
21. Shark of the Beast
22. Sharktuary
23. Sharknicorn
25. Shark-o-lantern
26. Shark Frost
27. Dr. Sharklove (Or: How I Learned to Stop Worrying and Love the Shark)
28. Shark of Ages
29. Sharkin' 2: Electric Sharkaloo
30. Atlas Sharked
31. Shark and Punishment
32. Shark and Sharkibility
33. Sons of A-shark-y
34. Rattleshark
35. Sharkrantula
36. Predashark
37. Sharks and the Single Girl
38. Sharks, Lies and Video Tape
39. The Sharks Brothers
40. There's Sharking About Mary
41. Shark your Duties
42. Battleshark
43. Sharkeant Bilko
44. Citizen Shark
45. The Silence of the Sharks
46. Shark Place and Boardwalk
47. Sharkz 'n' the Hood
48. Lepreshark
49. Sharka Khan
50. Shellsharked
51. Sharkdemic
52. Shark Like it Hot
53. The Great Sharktator
54. The Disharkerlies
55. The Sharklot
56. Sharkema Paradiso
57. Sharkula
58. Sharkenstein
59. Young Sharkenstein
60. Sharkamite
61. Steamshark
62. Honey, I Shark the Kids
63. A Sharkiful Mind
64. Homer's Odysshark
65. Shark it Forward
66. The Sharksons
67. The Spy who Sharked Me
68. Skeleshark
69. The Sharks and the Hound
70. Creepshark
71. Vertishark
72. Shark by Sharkwest
73. Get Sharky
74. The Usual Sharkspects
75. Sharky Balboa
76. Live Free or Die Shark
77. Persharkolis
78. Shark and Awe
79. Shark-Fu
80. Sharknecdoche New York
81. Finnegans Shark
82. Portrait of the Sharkist as a Young Man
83. Sharkmanteau
84. Journey to the Center of the Shark
85. Sharkfellas
86. Shark & Order
87. Double Sharkardy
88. Whose Shark Is It Anyway?
89. The Shark We Were
90. Sharkago
91. The Unsharkables
92. Miss Sharkon
93. The Resharkimator
94. That Darn Shark
95. The Human Sharkipede
96. The Shark Knight Rises
97. Sharkarama
98. A Shark Day's Night
99. To Kill a Sharkingbird
100. Sharkadeus

Thursday, July 26, 2012

More Ambigrams

Here are some more of those ambigrams, like the one in my last post. I'm getting a lot of practice at this. Here are some that I've done for my friends and family so far (posted with their permission).  They're posted in order from earliest to most recent.

(Garrett Ballendine)
(Maria LeRose)
  
(Emily Koban)
(Paula Jane Hranowski)
(Jason Cooper)
(Justin Chow)

Sunday, July 22, 2012

My First Ambigram

Wednesday, April 18, 2012

Vlog 30 - Nursery Rhymes + Nachos

Saturday, April 7, 2012

Collective Faces

I was pointed by Jason Kottke's blog to a series of Collective Snapshots -- images composed of a bunch of photos of the same landmark, basically taking an "average" of all the pictures. I thought I'd see if I could do something like that myself in Photoshop, but with human faces instead of landmarks. I also tried some with cartoon characters. They're not as impressive as the ones in the link above -- I used a little over 20 pictures for each one -- but I though I'd show them to you:

Louis CK:

Marilyn Monroe:

Albert Einstein:

Homer Simpson:

Donald Duck:

Sonic the Hedgehog:

Wednesday, April 4, 2012

Vlog 29 - My Little Pony

Sunday, April 1, 2012

Vlog 28 - One Word

Wednesday, March 28, 2012

Vlog 27 - History

Saturday, March 24, 2012

The Purpose of Memes

(This started out as a comment on a friend's blog post, but it got too long, so rather than use up space on their blog, I thought I'd post my reply here instead)

A friend of mine wrote a reply to an article attempting to explain the purpose of internet memes (You might want to read those posts, or at least my friend's post). I'm sure everyone and their grandmother has a theory as to why memes exist. Now, I may not be old enough to be a grandmother, but I do have my own theories.

I think memes serve the same purpose as inside jokes, small-talk, and circumcision -- to say "Hey, I'm part of the same group you're part of!" It's like a social codeword to say "You can trust me, I'm one of you". I don't think they're fundamentally different from inside jokes, which have existed for all of human history, except that memes have the advantage of digital technology and speed.

As with any codeword, the more information it contains, the better. Obviously, a picture contains more information than a word. Not so obviously, taking an orthographically correct sentence and putting specific errors into it also gives it more information (e.g. "I can has cheezburger?" contains more information than "May I have a cheeseburger?"). If medieval stonemasons could have carried around pictures of cheeseburger-loving cats as a sign of gregariousness, they would have done so.

And yeah, this gives a context to what you're about to read. I don't agree that there has to be a visual stimulus for this context. Just writing the phrase "Y U NO," "Seems legit" or "The Game" brings up instant connotations to those familiar with them, same with hearing the first few seconds of "Never Gonna Give You Up". It's true that visual icons can pack in the most information with the least effort on the part of the viewer, but at our core, humans are closer to being semantic engines than visual engines.

I suppose you could argue that memes can serve as entertainment in themselves, and many of them start out that way, but they tend to just lose this entertainment value and become symbols in themselves. Maybe I'm alone in this, but I just don't find memes like "X all the Y" and "Y U NO" intrinsically funny. This isn't necessarily a bad thing, as long as they still function as social codewords.

Due to the speed of the internet, memes can spread quickly, but they can also become old quickly -- I was tired of "arrow in the knee" jokes before I had even heard one. As with other codewords, memes get switched around every so often. "All Your Base" seemed like it was going to last forever, but it's a little outdated nowadays, and I suspect that even memes as ubiquitous as the Rage faces and X all the Y will eventually go that way as well.

TL;DR version (another meme!): I think it's true that memes use context to pack a lot of information into a small space, but this is a part of their primary purpose as social "codewords".

Bonus - My Favourite Memes
Seems legit
Conspiracy Keanu
PTSD Clarinet Boy
Horatio from CSI Miami

Links:

Cracked: 7 Memes That Went Viral Before The Internet Existed

The Original Article

My Friend's Reply

Know Your Meme

Friday, March 23, 2012

Ishmael #71: "Kleptomaniac"

 
Creative Commons License
It Seemed Funny at the Time by Ben Buckley is licensed under a Creative Commons Attribution-Noncommercial 2.5 Canada License.