How to travel in time: Expansion and contraction of possibilities space

As you may know, November 12 is a very important date. It will forever be the iconic date people will think of when they think of time travel. In all seriousness, it should be November 5th, but V for Vendetta went back in time and stole that date before Back to the Future could really claim it. November 5th was the day Marty went back in time and November 12th was the day he came "back to the future." Not only is this one of the best movies of all time, it is also one of the greatest discussions on Time Travel Philosophy.Today's blog post is dedicated to this topic.

Traveling in time is of course impossible. At least any useful time travel. Special relativity says that if you go really fast then return to your planet you will have aged much faster than your Earthling peers. This is about as interesting as it gets. This is just a nuisance and, to my knowledge, is not very useful. Using special relativity you can do tricks with time so that it moves at a different rate than other times, but there is no way to actually go back in time according to modern science (that I'm aware of).

While this is sad, you may have read my post explaining the Banksian Sphere, which challenges humanity to adopt new ways of thinking. This suggests that we may be able to discover time travel if we simply go at it from a completely different direction than simple scientists would. This means that time travel may still be possible using alternate dimensions or other methods, but we just haven't discovered it yet. That being said, we can continue our one sided philosophical discussion.

I think that deja vus are really cool. I love it when I get one because for a minute you feel like you have the superpower of predicting the future. It feels like sometime a long time ago you predicted that this situation would happen. I would claim (using my Banksian Sphere (B.S.) methodology) that you never predicted the future and that it is also not just a mind trick. But rather, it is the extreme deformation of possibilities of reality, allowing one part of the universe to come near to the universe at some time in the past. If you have an infinite dimensional "possibilities space" with infinite possibilities of outcomes for the universe traveling along a single time axis, then it would be possible for a certain point in the "possibilities space" to line up with the same point at a time in the past. This would be possible if the timeline loops back so it's close to where it was before or if the possibilities space expands an contracts throughout time.

I would tend to believe the expansion and contraction theory. If the possibilities space expands and contracts, then it means that it would take more or less effort to go from one point to another. For instance, in this part of the universe (Denver, CO, USA, Earth, Milky Way...mmm milky way) it is very easy for me to fill up my water bottle and drink clean water. A few thousand years ago, it was much more difficult to go from point one (sitting in my chair) to point two (sitting in my chair drinking clean water). These two points in possibilities space have come closer to each other over time. Contrarily, it was much easier to find a record player at the store 40 years ago than it is today. The two points of not having a record player and having a record player have gotten farther apart.

You can see that the naturalness of going from one point to another in possibilities space is not necessarily constant (and not necessarily varying either). I don't currently have any evidence that time loops back on itself, but I'd be interested in hearing theories on that. So if you believe my scientifically flawed argument for the expansion and contraction of possibilities space, then you can easily deduce the possibility of time travel. If a possibility line expands so much that it actually spreads back to the same possibility at a different time, then it may be possible to travel in time.

I hope this inspires all you peeps to figure out how to travel in time.

I wouldn't believe me if I were you. I'm starting to feel ashamed of my weird ideas that should be a disgrace to science.

How to Prevent Footinmouth Disease

Some people reminisce about high school. But when I think about high school I think, High school? Really? Are you serious? High school was the lamest 4 years of my life. My school had Senior Superlatives, which are things like Prettiest Smile, Most Athletic, Most Flirtatious, etc. Well I actually was one of the winners of these "awards." Well if I was popular enough to get an award, then why was high school so lame? I should tell you what the award was. Although I was once ashamed of it, I am now proud to say that I won the senior class "Super Shy" award. Pretty cool huh? For someone who was insecure about my quietness at the time, this was like giving an award for "Most Stupid" or "Most Socially Awkward."

I was in all the advanced classes, so all the people that actually cared enough to vote about who was most popular knew who I was. I was the quiet guy who was good at math and never talked to anyone but Justin. They all knew my name and they all knew I was the quietest kid in class, so they voted me in. My sister won the same award 2 years prior and I always thought extremely highly of her and thought she was pretty popular and not actually quiet, so I ended up not being incredibly bothered by winning that award.

Actually, I'm now kind of proud when I get to tell people I won that award. My perspective on being quiet has changed completely. I was once ashamed of my quietness, but now I'm usually very glad I'm quiet.

Most people assume that quietness is because the person is shy. They think that quiet people have something to say, but just don't have the courage to speak up about it. Perhaps they're afraid of being judged or are overly judgmental of their own ability to formulate thoughts. Shyness is certainly a common reason for being quiet, but is very often not the only reason for being quiet.

Another very common reason for being quiet is simply not having anything to say. There's not much to say about this. This is usually the reason I don't say anything, because I just don't have anything to say. I'm interested in listening to the person talking or I don't feel like silence is as awkward as most people feel. Sometimes there is just nothing to say.

Slow thinking is another reason people are quiet. We were having a discussion at a small group meeting about something philosophical. There was no reading ahead of time. It was just an impromptu discussion. My friend noticed that I hadn't said much and asked me what I was thinking because it looked like I was thinking about something. Well, I was thinking about something, but I was honestly just having a hard time keeping up with the conversation. They were jumping from one topic to the next before I had enough time to come up with my own thought on the subject. It's a lot easier for me to come up with thoughts when I've had time.That's why I like writing and it's also why I can talk about plenty of things when I've spent plenty of time preparing.

The last reason that I'll mention is when people don't talk because they are secretively judging everyone and are being mean by not talking. This is a high school concept. By "high school" I mean stupid. It's extremely rare that this is the case. Shy people are not necessarily that person you should worry about burning down the building. Yes, sometimes the quiet ones are the ones who "burn down the building," but most quiet people are perfectly nice people with good intentions, just like the talkative ones.

Do you know someone who claims their mouth is so big they can fit both their feet in it? I do. I know a few people like that. I feel sorry for them. I have certainly put my foot in my mouth plenty of times, but it's not too common of an occurrence because I usually think about what I say before saying it. This is one of the best benefits of being quiet. Usually quiet people just have the natural tendency to think about what they will say before saying it, thus implementing the "speech filter" before speaking...not right while your toe is entering your mouth. This is a benefit, but it's also not. It's not because I am often so good at using my speech filter before speaking that I'm also really good at letting people see only what I want them to see. Nothing slips out, just the good stuff that make me look like I'm a better, wiser person than I actually am. This is a problem.

Also, people who talk all the time are annoying. You may know someone like this. I know a couple. I'd like to hear one of their opinions on why they talk so much, because my ideas on why they talk are probably wrong. I usually tend to believe that they just like to hear themselves talk or that they think their opinion is more legitimate than another's. Not talking is a great way to avoid annoying people...usually.

Sometimes quiet people are annoying too, though. They (when I say they I mean we) have lots of awkward silences. It takes them too long to think of things to say in a one-on-one conversation to completely avoid silences. We often aren't bothered by silence at all.

I remember riding in a car with a friend who I was thought was quiet, but found out she wasn't. The first hint that she wasn't was when we were in the car riding back from ice skating and she said something like, "I feel weird that we aren't talking." Alarms went off in my head. What? Quiet people don't mind silence. You're an impostor! I thought we had quietness in common, but you aren't truly a quiet person. You just haven't gotten used to the new group you're a part of yet. My suspicions were later confirmed. She wasn't a deep down quiet person, just a temporary one. Even though quiet people don't mind silence, I fully understand the awkwardness of it. Quiet people just know how to embrace the awkwardness.

That is all. Maybe you understand quietness better.

Pacing

Back when I stayed in Alaska all summer I would go hiking pretty often. I'd try to do one or two hikes every week and I developed my philosophy/strategy for hiking. I thought about how to make hiking more enjoyable, because I would sometimes have hikes that were fun and other times it was really difficult and just not fun. I figured out how to make hiking fun.

When you're hiking with other people one of the most frustrating things ever is making sure you go their pace. I've heard that it's also one of the hardest parts of mountaineering (which is just like hiking...only much, much more epic, painful, and difficult). I realized that I started to enjoy hiking much more when I went my own pace and didn't worry about how fast the other person went. On steep climbs I started counting my steps and having a goal of how many steps I would take before taking a 10 second break. I would take pretty small steps and would be going pretty slow, but I had more endurance. And I was much more comfortable giving myself personal goals instead of comparing myself with the people I was hiking with.

I remember hiking a 14er in the middle of the night with other Mines students, and close to the top of Quandry it's a pretty tough climb. I started doing my walk 100 steps, take a 10s break, keep going method. People passed me and some of them I eventually caught up with and beat them to the summit. Other people passed me and I never caught up to them. This shows that they are definitely more intense than me, but I was happy with the hike and had a really good time. I felt good about being able to pace myself and being content with my own speed.

When I was in high school I ran track a couple years. Pacing, however, was not my thing. I ran the 100m, long jump, and triple jump. None of which require endurance or pacing of any kind. For the 100m you just try to get a good start and then go all out to the finish line. The sad part was when I tried the 200 for the first time. I got 100m into the race and found myself only able to run (not sprint) to the finish line like the rest of the guys. It was mildly humiliating. I don't even want to imagine what would have happened if I did the 400, 800, 1600, etc. So it's safe to say that pacing and endurance are things that are pretty new to me.

One of the challenges of my ride next summer will be pacing and coordinating my pacing with my friends who will be coming with me. I'm reading a blog about a lady who rode from the Atlantic Ocean to the Pacific Ocean, raising money for cancer. She did it by herself and sometimes mentions the good and bad things about doing it by herself. One day she passed by a swimming pool on a ridiculously hot day, but didn't have the guts to jump the fence so she could jump in it. I think that going with other people will be helpful for creating more peer pressure for doing stupid but fun things like that. On the same day she witnessed a couple that was biking the opposite way. The husband was flying up the hill and his wife was like a half mile back, walking her bike, feeling the pressure of her husband wanting to go much faster than she could. This doesn't sound like fun.

To solve the cooperative pacing issue, my idea is to have the slowest person set the pace. This depends on the faster guys being nice and not giving too much pressure to go faster. This way we can all stick together and have a good time. We'll be able to encourage each other and tell each other about stupid ideas we have.

Pacing will be an issue we'll have to deal with, but as long as we are honest about it, it won't be a big problem. Communication solves all kinds of issues.

Staring into Space

I went to a wedding today. It was a great wedding and I'm very happy for them. Unfortunately, I wasn't entirely focused on the wedding the whole time. Now that I've written about several different topics, it's become harder for me to think of new ideas. So whenever I think about things in my daily life, I often think they would be great to write a post on. I'll sit there and dwell on it longer than normal, deciding what kind of things I could say.

Well this time I was staring at things. I believe a slow dance was happening and, not having a date, I was sitting down, staring at the wall or staring at the floor. All the while, I was thoroughly enjoying the stare. Have you ever had a good stare going and somebody stops you and asks what you're looking at. Who care's what I'm looking at! I'm just enjoying staring.

Those of you who have ever enjoyed a good stare, you know what I'm talking about. You find a good spot on the wall and just stare. Your eyes lose focus and it's just so relaxing. You don't want to stop staring, but several things keep you from staring forever. 1. After about 30 seconds, I start realizing that other people are probably noticing that I'm staring and thus think I'm weird, 2. Sometimes the most relaxing place to be staring is directly at a person and that's just awkward, 3. Some people just quit staring because they feel like they should be doing something more productive or social than staring at a wall.

It's probably good we all have our reasons for stopping staring. Things would get weird if everyone stared all the time. It would be almost as bad as if everything in the world, except for yourself, froze in place.

I won't go into the nitty gritty of staring, although there is much to be discussed, but I will explain some of the more interesting aspects to staring. To state my credentials, I'll tell you that I pride myself to be the Banks family champion in staring contests. I can stare for a long time and if you think you can beat me, challenge me and we'll see who the true champion is. Most of my studies on double visioned staring occurred at church when I was younger. I would focus on the pastor and see the man in front of me in double vision. I did all kinds of things during sermons, like making psychedelic images inside my eyes, but I'll save that for later.

The most relaxing stare is when your eyes go out of focus. I think they usually revert to the focus they would go to for looking at a far away object. So if you're in a closed space, likely your stare will result in everything going fuzzy. Everything goes fuzzy because nearby light isn't getting refracted like it should for a good image.

Also, you get double vision in an unfocused stare. I'm hoping that everybody else gets this too, because I have never had a conversation with anyone about double vision you get while staring...Wow it would be weird if nobody had ever noticed that but me...Assuming you all have noticed that before, we can continue our one sided discussion. First, a demo...

Hold your finger up in front of your face and focus on the wall. Don't worry about anyone thinking you're weird. You see two blurry images of your finger and the clear image of the wall. Since your lenses are focusing on a single point in the background, they're refracting the blurred image of your finger to two different spots on your two retinas. Somehow your brain puts together the images from both retinas to make what you see, which in this case is two fingers. You can see through the images of your finger because the other eye has an image of the wall on that part of it's retina.

Something else you should do: Put your two index fingers in front of your face and form an upside down V with them. Focus your eyes on the wall. You will notice that the majority of your two fingers are transparent except for a diamond shape right in the middle of the two images. Now that particular spot on your retinas has an image of something nearby (your fingers) on both retinas. Since there is an image at the same spot on each retina, they come together to form one object. That one object is some combination of your two fingers. Weird huh?

I can't resist it. I have to tell you how to make psychedelic images in your eyes. Close your eyes and cover them up with your hands so it's nice and dark. Now cross your eyes and move them around a whole lot so they feel kind of uncomfortable. Don't give up hope. Push through the pain! Now just sit there and stare into space (keeping your eyes closed and covered). You'll start out by seeing light that was temporarily burned into your retinas, but after a little bit that will go away and you will start to see the crazy stuff. You'll see all kinds of weird spider web designs, chaotic patterns, organized patterns, all kinds of stuff. The image will change some over time and I've found that in order to change the image it helps to cross your eyes and move them around. Sometimes it's hard to get this to work and it may take a good amount of time. But it's kind of interesting. Don't ask me how that one works. And you have permission to think I'm crazy if it doesn't work for you, but I promise that it works for me.

On a more serious note, be careful when you stare. It can, apparently, be a deadly hobby.

One a lighter note, I had never heard of a man named

Mike Tindall before today, but he's apparently a really good starer. The All Blacks staring team is the most recent SCS (Staring championship series) champions, however Tindall claims that he used to beat them all the time at staring contests. He has even had injuries such as torn hamstrings, broken legs, and even broken livers. The article has a typo and accidentally says that he is a rugby player. I've emailed The Independent to inform them of this error. I didn't read the whole article, or even pay much attention to it, but it sounds like staring is considered a pretty intense sport in some countries like the UK.

Song of the Day- Part of my recent Iron and Wine obsession: My Lady's House by Iron and Wine

Contemplating the meaning of Food

Yesterday, while I was cooking dinner, Nanna (The little girl's nickname, whom I live with I live) was not in the best mood. She had steak, potatoes, and green beans for dinner and she didn't want it. She got through the steak and potatoes okay, but it took her a good 15 minutes to eat her green beans. It was really funny because she acted a lot like I used to act.

I used to be picky. Pretty sure I was the pickiest out of all the Banks kids. Believe it or not, I never ate potatoes except for french fries because I thought I didn't like them. I never ate beans because I thought I didn't like them. And, of course, I hated most vegetables, oh and ranch dressing. Looking back, I realize that I could have enjoyed life much more if I wasn't so picky. Perhaps my taste buds changed a little bit, but I don't think they changed that much.

It's hard to tell why I was so picky. It doesn't make much sense at all, because a lot of the food I "disliked" was really good food. I was just afraid to taste new food. Vegetables are a completely different story, because they actually don't taste good (no I don't consider beans and potatoes vegetables). I don't understand why I was picky, but I am no longer picky, for the most part.

Food is awesome. I remember one time we got free food at some band event and I expressed my excitement for the free food to somebody I was next too. He dryly responded by saying, "Yeah, free beer is better than free food, though." Of course, I politely laughed and lied by saying Very True, but inside I was thinking, Really? Food is amazing and there is a reason most people consume more food than they consume alcohol. Because it is satisfying and delicious. (Don't try to contradict me by saying that it's necessary for survival. You know you love it)

If I didn't know better, I would snack on Wheat Thins all day long, every single day. I would also have ice cream or pie or cheese cake for desert after both lunch and dinner every day. Unfortunately I do know better, so I've chosen to eat slightly less addicting things, usually. I really love to be able to eat whenever I want to, but I don't like it when I can't stop eating. Like the several times I ate an entire box of Wheat Thins for dinner... or the several times I ate a carton of ice cream in 2 days, by myself.

No, I eat whenever I want to, but my snacks that I keep at hand are usually things like almonds, cheese, and low sodium Triscuits. These are decent tasting foods, except cheese, which is phenomenal, and they're all moderately healthy. They taste good enough that they satisfy me, but I am able to stop eating them before I eat a meal's worth of calories. All this does not mean I don't have a sixth of a pumpkin pie in my fridge that I bought 2 days ago. It just means that I occasionally have the self-control to not eat that stuff.

When you eat healthy, your stomach is just as happy as if you ate unhealthily, but your taste buds are not quite satisfied. Healthy eating also leads to a happy conscience, knowing that you're taking care of yourself. Unhealthy eating satisfies the belly and the taste buds. And if you do it right, you can ignore the guilt that comes with how poorly you're treating your organs with all that fat, carbs, and salt. It's usually hard to ignore the guilt for long, so in the end, you only satisfy your belly and your taste buds.

Since both healthy eating and unhealthy eating benefit 2 out of three of the categories of happiness, then they are both equally valid as far as being immediately happy goes...But this assumes that the stomach, taste buds, and conscience all carry the same weight for producing happiness. Since both methods of eating satisfy the stomach equally, we need to look closer at the taste buds and the conscience.

Taste buds produce an immediate satisfaction. This is extremely appealing because whenever you go to Woodies, you know that all you have to do is eat a bite of pizza and within milliseconds you will be happy with the taste. Most of us don't especially enjoy waiting for satisfaction, so taste satisfaction has a very strong appeal.

For those of you who get immediate satisfaction out of eating healthy, props. But for us mortals, we don't usually have a very strong satisfaction immediately when we eat something healthy. However, we know that healthy food helps us be healthy and in the long run will likely help us live a better life. Healthy food prevents high blood pressure, heart disease, and all kinds of other things that are no fun to go through. Since these benefits are typically far in the future it takes, foresight, wisdom, and self-control to eat healthy. An alternative method would be to live in a closed community where all people ate was healthy food, so you never would know what unhealthy food was like. My parents attempted doing this for me and my siblings by feeding us fruit for dessert, but we eventually convinced them to give us unhealthy food...Buahaha!

Self-control is a really important ability and is useful in countless situations. The main reason it is so important is because we are constantly faced with the choice of choosing immediate satisfaction or long-term satisfaction. Immediate satisfaction is not always bad (Like when I decided to warm up my cold hands on my bike ride today), but can often be the foolish choice (like food).

Mythbuster Edition: School is better than a regular job

Being a student was all I ever knew from 5 years old to 23 years old. That's 18 years. It was both torture and enlightenment. I now have a job that is very laid back. I work 35 hours a week, everyone in my research group is friends, and I get paid more than I've ever been paid in my life. This life is paradise compared to the past several years.

When I went to school there was always some pressing deadline coming up. I was constantly worried about assignments and tests and had to force myself to neglect my work to have fun. Well it wasn't always forcing myself, but having fun always meant I needed to procrastinate on something.

Now I'm free. My deadlines are strict, but not so difficult to meet that I can't get absolutely everything done before 5:00 every day (4:00 most days). I have time to ride my bike home if I want, cook a nice dinner, watch tv, go shopping, or whatever I want. All this comes with no guilt because enjoyment no longer is coupled with procrastination.

As a student I almost always heard from adults that I should enjoy being a student because a regular job is much worse than school. I started having my suspicions about that a few years ago, probably when I was a junior. School sucked. I was constantly stressed and people could see it on my face when I had the strength to neglect my work and go hang out with people.

Some theories about why people feel like work is worse than school:

1. They had an easy major at an easy school.
2. They are workaholics and don't know how to drop what they're doing at 5:00 and go home.
3. They have an abusive work place that doesn't allow them to work less than or equal to 8 hours a day and don't have the ability or guts to quit their job and find a better one.
4. Work is, by nature, worse than school.

Now, I have an extremely cush job as I explained above, so I can't claim an incredible amount of authority on this matter. I am quite confident, however, that my top three reasons happen all the time and are the main reason why people think school is better than work.

Theoretical Idea of Work
Go to office at 8:00. Work till 12. Take hour lunch. Work from 1 to 5. Go home. Live life.

Work is often some mundane task that nobody would ever be willing to do unless they were paid to do it. This is how the world operates. People get paid to do things that need to be done. Sometimes it's a fun job that you were lucky to get or you are one of the few people who are qualified for it. Sometimes it's a boring job that nobody else wants, but you're willing to do it because it pays the bills.

Unless you have the most enjoyable job ever and have no commitments outside of work, you will usually go home around 5 or 6. This leaves about 4 hours to do non-work related things. This is slightly lame. If I had my druthers I would work 4 hours so I could have 8 hours of non-work related things in the afternoon/evening. But this is apparently the sustainable work-to-nonwork ratio that is necessary for sustaining a "successful" capitalism.

This sounds lame, but you still have that 4 hours in the evening. In school, those 4 hours were reserved for doing homework, guilt-stricken-fun-having, or guilt-stricken-errand-running. In the work world, those 4 hours are reserved for guilt-free-relaxing, guilt-free-errand-running, or guilt-free-fun-having.

Dear stressed student,
Take this not as mocking, but rather as encouragement. If school's got ya down, take hope for a day will come when you can have a job and not live under the constant oppression of homework. Another suggestion could be to take this as an opportunity to stick-it-to-the-man and start worrying less about your grades. I started worrying less about my grades when I became a senior and it made life better.
Sincerely,
Former Student

Dear disgruntled worker,
Take this not as mocking, but rather as encouragement. If work's got ya down, take hope for a day will come when you realize it's not that bad or you will finally have the courage/ability to stop being abused by your work place. Another suggestion could be to take this as an opportunity to stick-it-to-the-man and quit your job. This will create new jobs and will surely boost the economy. ***Evil Laugh***
Sincerely,
Joyful Worker

***Revision-11/4/2010: It was suggested to me, by a friend with a "cardboard box major" (music), that I should add a fifth category. That 5th category would be those people who had a major that was actually really fun and not necessarily easy. This is an important category to include because they are often the people who end up with the boring part time job to complement their minimal income from art, music, theater, etc. They also may be the kind of person that gave up on their field of study because of the low income and thus were forced to have a ridiculously lame job. This situation surely makes up a portion of disgruntled workers who would say that school>work.

Alternate Dimensions

If you are my friend, which these days is defined by whether or not we are "Facebook Friends," then you may have seen this suspicious photo on my "wall" or "muro" if your Facebook is in Spanish like mine.

Here I mention a supposed "Discrete Fourier Transform." If you don't know what a Fourier Transform (FT) is, the most important thing to know is that it's pronounced For-yay. The second most important thing to know is that it's cool and gets all sorts of engineers and scientists excited. If you read my note way back when about shadows and projections, then you saw how nerdy I got about them. Well if you think projections are exciting then you'll think FTs are even more exciting...because, well, they are a kind of projection.

A shadow is a position projection. If you look at your shadow, it gives a half way decent description of the position your body is in. You can at least tell that you're standing. It may be missing some information, but it takes the real position of your body and projects it onto a horizontal plane.

A Fourier Transform is a frequency projection. It takes something with lots of frequencies and projects them onto reciprocal space. This tells you how much of each frequency is in the signal.

If you speak into a microphone, then your voice most likely has several frequencies in it. Try saying "Red Rum" in the same way that creepy kid in The Shining says it. His scratchy voice has lots of frequencies in it. Some low pitches and some high pitches. If you're singing (assuming you're a half-way decent singer), then the majority of the frequencies are sitting at whatever pitch you're singing. If you sing an A, then you could take the FT of your voice and it would tell you that there is a strong signal at a frequency of 440Hz. Unless your voice sounds a lot like a tuning fork, then it will have some other frequencies in it. Mostly random vibrations caused by your throat and mouth and lungs and who knows what else. Hopefully this explains what a FT is well enough.

The reason I get excited about Fourier Transforms (and other transforms) is that it's like exploring a new dimension! I mentioned that a FT projects a signal into Reciprocal Space. Reciprocal space is another set of dimensions where you can walk around, but instead of walking from position to position, you walk from frequency to frequency.

Now, your voice is a one dimensional signal. It just oscillates the paper in the microphone back and forth, so basically between -1 and 1 on a number line. The reciprocal space of a microphone vibrating is just a line. If your friend was singing into the microphone and you were walking around it's reciprocal space you would see it get really bright at whatever frequency she was singing at. All the frequencies would just fall along one line.

Now, if you took a picture of your pet cat, like the stray that my friends at the Den adopted for a day (hopefully she's gone by now), you would have a 2 dimensional signal. Pretend you were feeling artistic and made the photo gray-scale. You could look around the picture and see that some locations are brighter than others. Even though this signal is a picture, you can still think of it as a signal with lots of frequencies. Instead of the vibration of air, the image's frequencies are determined by how the brightness changes as you go across the picture. So if you have a 2 dimensional signal like an image, then you can take a FT of it and it would give you a 2 D reciprocal space that describes the frequencies in your signal.

Well, I was feeling particularly adventurous and did that with that picture of that cat at the top. There's a very pretty gray-scale photo of the cat followed by a painfully boring image that is it's FT in reciprocal space. That's right, ladies and gentlemen, that second picture is what a cat looks like in reciprocal space. I imagine it's pretty hard to tell the difference between a cat and a dog in reciprocal space.

You may say, Holy cow that's boring, but how on earth could you get back to normal space after getting transformed into reciprocal space? All you have to do is have someone take an Inverse Fourier Tranform and you're back in normal space. If you look at the top you see that the Inverse FT photo looks a lot like a possessed cat. The only reason the colors are inverted is because Mathematica wasn't consistent in its conventions. If it did the IFT correctly, it would have returned a normal looking picture of a cat. So you now know how to travel to this ultra-boring reciprocal space and then return back to normal space when we're talking about 1D or 2D. I just think it's pretty crazy that the cat turns into something as boring as that middle picture and it still has the same information that it originally had. P.S. the reason why there's no loss of information in this projection is that a FT takes an infinite number of projections and puts them together.

3D Fourier transforms are also possible. It's just like 1D and 2D only everything isn't infinitely narrow or infinitely flat. One very interesting application of 3D Fourier Transforms is X-ray diffraction, which can be used to shoot x-rays at a grain of salt and verify that it is indeed salt without even having to taste it. Most people in the world would just taste it to find out that it's salt, but engineers and scientists like to make things more difficult than they need to be. So they shoot x-rays at it to figure out its crystal structure. Just like sound and images, you take take a FT of a crystal lattice and it gives you a 3D reciprocal space that also looks like a crystal lattice, just a different structure. If you shoot x-rays at a crystal, then the x-rays diffract off the crystal and spread out in their frequencies. Depending on the crystal structure, different frequencies of x-rays will diffract to different locations. When you detect different frequencies of x-rays at different locations, you're basically measuring something very similar to the crystal lattice's Fourier transform and you're looking at it in reciprocal space. Then if you take the IFT of this diffraction then you can figure out that salt has a crystal structure of face-centered-cubic. (Molecules forming the corners of a bunch of cubes with an extra molecule at the center of each cube face).

You may think this was incredibly boring, but this is basically why engineers and scientists think that Fourier Transforms are so great...Travelling to alternate dimensions.