How to understand infinity and hold universal models in your head.

What I want to bring to your attention today is pretty simple, it has to do with being able to picture universal models in your head and being able to picture PI and infinity. This may take a bit of time but I hope to give you the tools you need to do this in about a five minute read.

The first thing I think we all need to do is face reality. We all love to believe that we are these amazing beings with amazing abilities that are just locked away somewhere. We like to pretend that our minds are these amazing computers that we are locked out of for some reason, using only 10% of said brainpower. The truth is that we use 100% of our brain, just not all at once.

We must be reminded that our brains are just an organ made up of nerves, and that modern computers surpass our brains many times over in terms of processing power. Can you get the answer to a math question like 14,325 x 16,153 = ? within a few milliseconds? Well your Ipod can! Can your digital camera track thousands of points of light in the sky at night as it moves around looking at them? Not very well....but you can.

If computers have so much more processing power than us, how are we better? Simple! We are better because our brains have amazingly efficient programming. Our brains are the equivalent of getting Windows 7 running on a Commodore 64, an almost impossible accomplishment.

Using a calculator is not a weakness, its a sign of acknowledgment that you are better off using a tool. In the same way, using computers to make up for the areas we lack is a sign of intelligence, just the same as inventing the wheel was.

So to prove how weak we really are mentally I have a simple game for you to play in your head.

THE GAME:

Picture in your mind a black triangle on a white background, picture the details. Now while maintaining the same level of detail, imagine a second triangle. With the same detail picture 5 triangles in any arrangement while maintaining detail. After you have 5 triangles, try imagining 10 with the same level of detail as the one. If you can reach 10 triangles, increase by another 10 triangles and see how many triangles you can visualize while maintaining the same level of detail as one triangle.

Most people who I have done this to seem to either get to about 10 triangles and tap out, many claim to be able to imagine about 60, and a few liars claim to be able to get a few hundred triangles. (They are ahead of this game)

So what you just ran into, was the limit of the brain's ability to visualize. A modern computer could do this task a million times over anything the smartest human could do, its just the limits of the brain, relax, we all have a hard time here.

If you cheat, you can win, and winning is the goal here when there are no losers. So how do you picture several hundred triangles? You cheat! Arrange triangles into grids of 5x5 if you can, then shrink them into solid black boxes, start stacking boxes in your mind. Now you can have a much higher number of triangles.

What did we just do? We just cheated, but its fine, its the only way we can win. We used what is called LOD rendering.

To quote Wikipedia (In computer graphics, accounting for level of detail involves decreasing the complexity of a 3D object representation as it moves away from the viewer or according other metrics such as object importance, eye-space speed or position. Level of detail techniques increases the efficiency of rendering by decreasing the workload on graphics pipeline stages, usually vertex transformations. The reduced visual quality of the model is often unnoticed because of the small effect on object appearance when distant or moving fast. )

LOD is the answer to everything we need to be able to do such things as model the universe in our heads.

With LOD rendering in our minds we can easily understand abstract things like a true circle, PI, or infinity.

Lets use LOD rendering on infinity as a quick example. I will use a number line.

-(I DON'T CARE) -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +(I DON'T CARE)

Notice how we disregard the rest of the numbers that will go on forever? We simply acknowledge that numbers keep going on and on and on, and just don't worry about maintaining a perfect level of detail all the way out until the numbers start repeating again somewhere down the road.

When you try to work on such things as models of the universe in your head, you must always, always, use LOD to even attempt such a feat.


Now in closing here I do want to add what this means in education, seems unrelated, but I feel this is entirely the answer.

For me, math was next to impossible, I could never grasp the abstract math, then one day I learned how to round numbers and to use rounding to simplify long numbers. Once I had the nifty tool of rounding, things became simple. Sure I didn't have the exact answer, but I didn't need one, I could get in the ballpark.

Infinity is used to keep us down. In school you learn that infinity goes on and on forever. So as a kid you no doubt at one point tried to imagine infinity. One, two, three, a hundred, a thousand, a, million, a billion, a.... and you eventually gave up because those pesky zeros would just keep going and going. You likely felt discouraged by not being able to reach your goal, you were defeated.

When you learned about Pi and tried to visualize it, you might have tried going out a few numbers, or a few hundred, you remembered how infinity was impossible and likely stopped trying to understand Pi. It's ok that you failed, it's not ok for you to feel like a failure.

Later you may have tried to understand the deficit, and likely you gave up because of how many big numbers were used. Any time an astronomical number came up, you gave up because you remembered that you couldn't work with such big numbers. Many people just assume that they are inferior because they cannot think with big numbers and figure that their lack of understanding is their own fault, and not the fault of giant numbers being used to manipulate. Seeing so many defeated people really saddens me. Anyway, that's all I wanted to write. Please feel free to comment/critique.

I find it curious that you and it seems many others didn't naturally pick up on these types of tricks when you were young. I was talented in mathematics and sciences. When the teacher taught, I always visualized the lessons in real time. That's how I process naturally. I found many shortcuts in math to arrive at the answer before anyone else. Was the kid who could ace the test, but not show work. When you said to double the triangles, I automatically "cheated". Isn't that the correct way to do it? I got 216 no problem: 6x6x6.

Oh yeah, when I think of what pi means, I literally take a circle in my mind, draw a line through it horizontally, then straighten the circle out above the smaller one. It's the equivalent sides used to figure the area or volume of a figure. So if you put a circle inside a square, and it perfectly touches on all sides, it will have pi/4 area as compared to the square.

[edit on 26-1-2010 by unityemissions]

reply to post by unityemissions


It's because we are discouraged, it seems so simple once we understand it, but we are cheated into thinking that simplicity is always wrong.

Just imagine what your mind really does. A computer could never compete with our mind.

Our mind solves more complicated equations then any instrument we know of.
Its just that we dont acknowledge everything our mind does. We only focus on.... what ever we focus on. We never acknowledge every detail our mind is commanded to do while we do our thinking.

If you tried to solve the same equations your mind was commanded to solve by your requested actions. Lets say hitting the letter A on the key board. It would probably take you 20 minutes or more with the use of a calculator to figure out how your mind managed to do it mathematically.


Our mind cant cheat. It will do what ever it is told by your command.

I to automatically cheated. I stopped picturing the triangles in a row at 5 and start spawning them in a huge array where I could picture as many as I needed, not all at once but I know they are there if I need to see them, but I guess I could probably picture a 2d 10x10 grid with no problem. Does anyone else kinda find them hard to count?

We automatically try to make things we don't understand complicated, but once we reach a realization or come to realize what we were missing, it immediately becomes very simple and we're shocked at how hard we were making it.

We would have better schools if the education system would realize this and not treat everyone like they think the same.... My wife was in high school before she discovered she was dyslexic and could read backwards faster than forwards. We each use different methods to figuring out the world around us.

I hated algebra and could not comprehend it and even understanding what I do now, it frustrates me to even attempt it. Most of that is probably from my frustration towards the subject but in order to get around that block I think I would have to forget what I've learned and try learning it all over again with fresh insight, but that's nearly impossible to do as it's hard to forget something on purpose...

School still teach as it was 100 years ago the same way, just think if the medical system still worked like a 100 years ago, who would go!

As soon as you said 5 triangles, I arranged them in the shape of a pentagram in my head with the points of the triangle all facing outward. Now instead of 5 triangles I just visualize 1 5-pointed star.