# Paradoxes

I was reading this article on WIRED.com, and it had me thinking about some paradoxes. Post your favorite ones here.

• Before an object can travel distance D, it must travel distance D/2. To travel D/2, it must travel D/4, and so on. This means the distance D can never be traveled.

What would happen if you are going the speed of light and turned on your headlights?

As I recall things, since you can’t go the speed of light, it’s immaterial. However, even if you’re going 99.9999% the speed of light, you’ll always measure the speed of a beam of light you fire as c. The relativistic time and space effects warp things so that this is the case.

Godel’s Incompleteness theorem always amused me, even if it’s not actually a paradox. It states that any consistent sytem of rules, etc must contain statements that can’t be decided. The classic example from logic being:

This statement is false.

The colloquial version from Mathworld is amusing: “… any formal system that is interesting enough to formulate its own consistency can prove its own consistency if and only if it is inconsistent.”

Heres one for ya.

Your in a space ship, going faster than light traveling away from the earth. You look through a powerful telescope back at people on earth. What would you see? if anything at all? Would it appear that people are moving in reverse? Tricky eh

On a similar note, same scenario, except you look away from the earth. What would you see? Since your traveling faster than the light traveling in the same direction as yourself, you would be catching up to them… so would you be able to see things that are happening behind you? Very Tricky

Remember, according to special relativity, that no matter how fast you go, the speed of light is still c relative to you, same c as observed from our relatively slow point of observation on Earth. So you wouldn’t out running the light reflected from Earth, they would appear anyway.

In the interest of melting a brain or two, please consider “The least integer not nameable in fewer than nineteen syllables.” A phrase that itself has only 18 syllables.

A Ham Sandwich Paradox

Which is better, eternal happiness or a ham sandwich? It would appear that eternal happiness is better, but this is really not so! After all, nothing is better than eternal happiness, and a ham sandwich is certainly better than nothing. Therefore a ham sandwich is better than eternal happiness.

Confused?

Don’t forget about the Doppler effect. As you approach 20% of the speed of light, the blue end of the spectrum will be shifted to appear green; green to orange, orange to red, and red will become invisible, being now infrared. By about 40% of C, only the blue light will still be visible, and it will now appear red. At about 99.996% of C, the formerly visible light will only be able to be detected as microwaves!

But fear not! All will not be blackness. As the formerly visible light fades from view, ultraviolet, x-rays, and eventually gamma rays will come into view as visible light. Now that would be cool: being able to see x-rays with the naked eye just like Superman!

Eh…

Because I’m lazy, I did a Google “paradoxes” search. Here’s a fun one…

Of, course… you can’t have a straight circle…

177,777

Yeah, but if you subsequently call it “the least integer not nameable in fewer than nineteen syllables” then what is it?

I think the novelty would wear off rather quickly in the face of that much hard radiation from the blue-shifted direction, though…

For more on Berry’s paradox look here.