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A reading from e=mc2 by David Bodanis,
The big question though is why? Why is squaring the velocity of what you measure such an accurate way to describe what happens in nature?
One reason is that the very geometry of our world often produces squared numbers. When you move twice as close toward a reading lamp, the light on the page you're reading doesn't simply get twice as strong. The light's intensity increases four times.
When you're at the outer distance, the light from the lamp is spread over a large area. When you go closer, that same amount of light gets concentrated on a much smaller area.
That's a wonderful explanation David, but we don't live in a 2D world. How would this work in our 3D world?
Well, consider a cube. Now imagine a light source at the center. If you're at 4, what will be the volume?
4 x 4 x 4 = 64 cube
Now move twice as close towards the center. What will be the volume at 2?
2 x 2 x 2 = 8 cube
When you moved from 4 to 2, the volume didn't cut in half. It decreased by a square value. Now you can understand why light's intensity increases by squares.
But my logic can't be correct. Let me show you why.
The sole purpose of the above example was to show you that when you double the distance, you don't double the volume, you square it!
Now move back to 4. Let's double the distance to 8. What will be the volume at 8?
8 x 8 x 8 = 512
8 is double the distance from 4. Is 64 squared equal to 512? No... So do you think that light will increase by a square value? No... So what gives?
I need help
The big question though is why? Why is squaring the velocity of what you measure such an accurate way to describe what happens in nature?
One reason is that the very geometry of our world often produces squared numbers. When you move twice as close toward a reading lamp, the light on the page you're reading doesn't simply get twice as strong. The light's intensity increases four times.
When you're at the outer distance, the light from the lamp is spread over a large area. When you go closer, that same amount of light gets concentrated on a much smaller area.
That's a wonderful explanation David, but we don't live in a 2D world. How would this work in our 3D world?
Well, consider a cube. Now imagine a light source at the center. If you're at 4, what will be the volume?
4 x 4 x 4 = 64 cube
Now move twice as close towards the center. What will be the volume at 2?
2 x 2 x 2 = 8 cube
When you moved from 4 to 2, the volume didn't cut in half. It decreased by a square value. Now you can understand why light's intensity increases by squares.
But my logic can't be correct. Let me show you why.
The sole purpose of the above example was to show you that when you double the distance, you don't double the volume, you square it!
Now move back to 4. Let's double the distance to 8. What will be the volume at 8?
8 x 8 x 8 = 512
8 is double the distance from 4. Is 64 squared equal to 512? No... So do you think that light will increase by a square value? No... So what gives?
I need help