Life on a 4-Dimensional Doughnut

Sometimes a simple idea or assumption can lead to an interesting chain of thoughts. I've just watched an educational prime-time program about maths and they ended the episode with one of these ideas, deducted from the maths they were talking about earlier. The program was about dimensions, in particular the 4th dimension.
Imagine you are playing a computer game on your screen. An interesting feature of these games often is that you can walk off one side of the screen and you appear again on the opposite one, e.g. leaving the screen on the left and appearing again on the right. We normally don't think about this very much and just continue with the game. But what does that mean in terms of surface structure if this virtual, 2-dimensional world? How does the world have to be shaped to allow for that to happen?
An intuitive answer of many people would be that it has to have the shape of a sphere. Let's imagine our small 2D walker would stand on a sphere. He could go in any direction and, by walking straight, would reach the point he started from again from exactly the other side. So far so good. But now, think about distances travelled by our small guy. On a sphere, no matter which direction he chooses, the distance to the point of origin is always the same. How about the distances he has to travel in our 2-dimensional world? Even if we imagine the screen to be square, the distance is different for different starting angles (imagine going through one of the corners to appear on the opposite one). So it can't be a sphere!
Let's shape the 2-dimensional world in order to have the desired features. Think of the screen as a piece of paper of the same size. To be able to get to the bottom end by going "off paper" on the top end, we have to bend the paper to form a cylinder. By connecting top and bottom side we enabled our little walker to go back to his point of origin when walking north or south. Now we have to connect left and right by forming a doughnut shape (or more mathematical: a torus), voila! A never ending world for our little wanderer.
Now what have we done? From the viewpoint of our (still) 2-dimensional wanderer, this is a normal 2-dimensional landscape. He just knows that if he walks straight on in his perfectly flat world, he comes back to where he started. Remember: He never experiences up or down (therefore he never thinks of it as a flat world! What else could there be?).
What we (as 3D people) have done is to shape the 2-dimensional world in the 3rd dimension to a 3-dimensional object to do, what the small guy can only think of as magic.

Now let him walk his new world for a while and think about what the 4th dimension could be. To answer this question we can look at the dimensions we already know. To get from dimension 0 (a dot) to the 1st dimension, we can imagine two dots and connect them. Now I can get from one dot to the other by walking along the 1st dimension, passing many other dots on the way. We can do the same to get from the 1st to the 2nd dimension: Every 1-dimensional object is a line. If we draw two lines (imagine parallel ones for simplicity), we can connect them by drawing other lines in between till we filled the space. All these lines are in a 2-dimensional landscape of 1-dimensional lines. The step to the 3rd dimension is equally easy by connecting 2 planes by other planes. If you need a visual aid, you can watch this movie and stop when your head starts hurting (usually around dimension 6 ;-) ).

Suddenly the step from the 3rd to the 4th dimension is easy: We just take two 3-dimensional objects (e.g. yourself) and connect them by other 3D objects going slowly along a line of objects. Think about that for a while and you will see that this is what we normally refer to as time. Just imagine a red cube and a yellow cube and imagine a line of cubes in between slowly changing colour. We can see that all the time in movies! So a 3D-movie as a whole is just a 4-dimensional object, a dot in the 4th dimension, connecting two sets of 3D objects (start and end set of the movie...and before anybody destroys this nice metaphor in a comment, no cuts are allowed!)

Let's go back to where we started with our walker: Now imagine yourself being the wanderer. You walk through a 3-dimensional space. What would it mean to "walk-off the screen"? The space in which we walk a straight line has to be bent in the 4th dimension. From what we did with the piece of paper, this sounds easy! Then we can walk straight and come back to the place we started from. Remember, you would still be walking in the 3rd dimension just like the 2D guy who never left the 2nd dimension on his journeys. (we neglect that it would take time for us to walk there, therefore also moving in the 4th, just imagine you can walk really fast!). What else does that mean?
Some people think that our universe has a toroidal shape (i.e a gigantic doughnut) in the 4th dimension (whatever that looks like). Since light travels in a straight line, if you look really far into the universe, you should be able to see yourself standing there, looking away! But wait, travel needs time (what we've neglected before)! So e.g. the picture of Proxima Centauri, the closest star to our solar system, is what it looked like 4.3 years ago. What does that mean in a toroidal universe? One of the stars we can see is our own sun from millions of years ago? What happens if you travel there? If we could travel faster than light, could be arrive on our own planet in the past? Does "beaming" somebody from point A to point B just mean to bend our dimension so that these to points touch through the 4th and push the guy a bit?

So many questions, a long post, and just because I watched a program on TV. And so many more questions to think about.....

Quote: National Security

"If you want total security, go to prison. There you're fed, clothed, given medical care and so on. The only thing lacking... is freedom."

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"How far you can go without destroying from within what you are trying to defend from without?"

Dwight D. Eisenhower
34th President of the United States
14.10.1890 - 28.03.1969

A new star in comedy heaven

I'm watching American TV quite often because they have good comedy shows. For a few weeks now I'm following the shows of a new comedian. She is really funny! And the media seem to like her, too! I didn't see a comedian getting more airtime and being more discussed in the news. Her name is Sarah Palin.
In her shows and interviews she pretends to be a running mate for McCain and tries to show American voters the pitfalls in conservative politics. With her excessive standpoint she points out where stupidity, narrow-mindedness and fundamentalist viewpoints could lead, when combined in an influential political person.

If only the majority of Americans would see it that way. Let's come back into the real world. Unfortunately roughly 133791000 Americans (21.10) see it differently. For them, Sarah Palin is no reason to vote against McCain as president. Lately, not a single day passed where I didn't ask myself: Why?
American media and conservative politicians deliberately create a culture of fear which, as a new study suggests, might play into the Republican's hands. But that doesn't explain why conservative voters would vote for somebody who is clearly incapable of running a country.

Let's see which traits Sarah Palin has: She likes hunting, is fundamentalist christian (or close), "hockey-mum" and follows small-town values.
This is not a post against religious views, but is somebody who labelled the war in Iraq a "task that is from God" and wants to teach creationism in biology class able to make decisions on a global scale? Who does God want us to attack next? Iran? Pakistan? I think that history has shown that we don't want one of the biggest military forces on the planet in the hands of a (quasi-)theocratic government.
So what else do we have? I googled for small-town values. I wanted to know what exactly they are, but there seems to be a bit of confusion online. I couldn't find a comprehensive list! What comes to my mind when I'm talking about small-town values is narrow-mindedness, babbitts, often subliminal racism and cronyism.
If I look at that list, Sarah Palin apparently really would bring small-town values to Washington. After all, she managed to put those values to good use as major and governor. "She has pursued vendettas, fired officials who crossed her and sometimes blurred the line between government and personal grievance." (NYT). This often happens on a local scale, but are 8 years of small-town values in the White House not enough? Do we really have to push it to the next level?
Unfortunately, I'm not allowed to vote in the USA. But I really beg the American voters to think before making that cross in 2 weeks. A president doesn't need small town-values, but the ability to solve global problems. A president has to be able to make informed decisions which are not dictated by the oil industry and religious fanatics. Science, almost forgotten as a source of information in the last 8 years, can help there if it is not suppressed by political and/or religious agendas. In a global economy, one of the most important issues is an intelligent foreign policy. And being able to see foreign countries from your porch doesn't improve these abilities. It only means you have a property with a good view.

So to all the "real" Americans: Stop being pro-American and start being pro-intelligence and pro-skepticism. America has lost a lot of credibility the last years. You can make a change!

Quote: Web of Discourses

"The strangest and most wonderful construction in the whole animal world are the amazing, intricate constructions made by the primate, Homo sapiens. Each normal individual of this species makes a self. Out of its brain, it spins a web of words and deeds, and, like the other creatures, it doesn't have to know what it's doing; it just does it. The web protects it, just like the snail's shell, and provides it livelihood, just like the spider's web, and advances its prospects for sex, just like the bowerbird's bower. Unlike a spider, an individual human doesn't just exude its web; more like a beaver, it works hard to gather the materials out of which it builds it's protective fortress. Like a bowerbird, it appropriates many found objects which happen to delight it - or its mate - including many that have been designed by others for other purposes.
[...]
So wonderful is the organisation of a termite colony that it seemed to some observers that each termite colony had to have a soul (Marais, 1937). We now understand that its organisation is simply the result of a million semi-independent little agents, each itself an automaton, doing its thing. So wonderful is the organisation of a human self that to many observers it has seemed that each human being had a soul, too: a benevolent Dictator ruling from Headquarters."

Daniel C. Dennett
(in "Conciousness Explained", 1991)

Speaking English

Traveling was different when I was younger. You decided where to go and then prepared by learning enough of the language to survive the most important everyday situations. I always had a small guide book with me with the most important sentences and was proud, when I was able to order my food without having to open it. Of course I knew English at the time (although admittedly, I was far from fluent), but often the people I spoke to didn't know it or were only as good as I was.
So the natural thing to do was to learn as much native language as possible.

Times have changed.
Living in England has improved my ability to speak English by a lot and suddenly, I expect all people in the world to understand and speak it as well. I became as arrogant as many American or English people when it is about traveling. Having English as the world's language doesn't necessarily mean that everybody is able to speak it. Of course this slowly changes. I recently visited Finland and even in the countryside, almost everybody spoke clear English. But does that mean I don't have to learn foreign languages any more? What am I going to miss?

Language evolved alongside with the culture of an area and therefore can be a mirror which reflects many cultural aspects and differences. The way natives use the language and how it differs from your own can hint to cultural conventions and attitudes. Learning a language shows people that you respect and are interested in their culture and their way of living. In many countries (there are exceptions, e.g. France) people are genuinely pleased when you try to speak to them in their tongue and make an effort, even if it is far from being perfect. They often help and correct you and many times it can be the start of an interesting conversation.

Living in an English-speaking world should not be an excuse for not making the effort. If you really want to experience a country, there is no better way than learning its language and trying to speak to its people. And I know that it's often not possible, because the visit is to short or on short notice (e.g. business meetings). But especially in these situations we should always remember, that we are the guests in this country. We should never expect the natives to understand us if we didn't make the effort. It makes things easier for us if they do, but if there are language barriers, we are the ones who have to apologise

Quotes: George Carlin

"I think it's the duty of the comedian to find out where the line is drawn and cross it deliberately."
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“Inside every cynical person, there is a disappointed idealist”
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"Some national parks have long waiting lists for camping reservations. When you have to wait a year to sleep next to a tree, something is wrong."
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"Think of how stupid the average person is, and realize half of them are stupider than that."
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“I have as much authority as the Pope, I just don't have as many people who believe it.”
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“If it's true that our species is alone in the universe, then I'd have to say the universe aimed rather low and settled for very little”
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(more, more and even more!)

George Carlin

Final Curtain

"Hey, did you hear? George Carlin died!"
"George Carlin? I just saw him yesterday!"
"Yeah.......didn't help! He died anyway!"
Unfortunately this conversation was bound to take place two days ago. George Carlin, one of the greatest stand-up comedians of our time, died of heart failure in Santa Monica, California. And although it is all but impossible to write an obituary for every great person that passes away, I have to write one for him before his friends delete his entry from their address books in 6 weeks.

As George, I don't believe in an almighty, invisible GOD and therefore not in an afterlife, heaven or hell. But I do believe that people live on after their deaths: In the minds and the memories of people who knew them. And nowadays technology can help a little bit as YouTube, Wikipedia and other pages in the internet can act as external memories.
And lucky for us, George left us many there that can help, big time!
I only saw the first video of him on the web a few months ago and hardly ever enjoyed a video that much! Perhaps that's the reason why the news of his death hit me hard. I know that there a no more new shows coming!

Now that he gives less than a shit about the sanctity of life let's see who this comedian was:
His life is well documented on Wikipedia and I don't have to repeat that here, so let's look at his shows!
He said the seven words you can't say and even things no one ever said before. He had a lot of good business ideas worth looking at! He knew, he was ahead of his time, unfortunately only 1.5 hours. He knew we can't save this planet and was asking about the difference between abortion and an omelette.
He was also very efficient! He managed to slash the 10 commandments down to 3 by removing unnecessary redundancy. On the other hand, he was very confused about phrases and words constantly changing!
Google for videos of his shows and you find many more. Whenever I go to YouTube I find new ones that I don't know yet. Take the chance to get to know him and make sure the memory lives on!

Now on the off-chance that there is a heaven and a God, I can only hope this God has more humour than his self-appointed clerical workers down here who didn't get the best of the bargain in Carlin's shows. But anyway, if Carlin really went to heaven, let's go to the topless bar near the airport and bow to the man who said the things many of us should say more often!