Merry Christmas and a Happy New Year!!

 

So how do you feel about American supercars? Other than the Saleen S7 I never thought much of what America had to offer. But have you seen the new Corvette from Chevrolet? It still looks American enough but it seems this one is here to compete with the big European players. Still no official word for horsepower or a time 0-60 but it is said that the horsepower is at least 620 and 0-60 in the low three seconds. That's quite impressive, at least in my book. More to be seen in the Detroit auto show this January.

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http://jalopnik.com/cars/detroit-auto-show/2009-chevrolet-corvette-zr1-revealed-officially-334923.php

Just the thing to get you into the Christmas spirit, check out these tests about Christmas on Blogthings!

So lets see! The Naughty or Nice test, only for girls, sorry guys! Turns out I have been pretty nice this year, or have lied to most questions

You Were Nice This Year

You Were 35% Naughty, 65% Nice Okay, so you weren't *entirely* nice this year But Santa doesn't expect a modern girl to be perfect You were good enough - and you'll be rewarded for it

You Are Rudolph

Sweet and shy, you tend to be happiest when you're making someone else happy. Why You're Naughty: You sometimes stick that nose where it doesn't belong Why You're Nice: Christmas would be a sad affair without you!

So how should you spend the holidays? Well I know I'm a Christmas freak, didn't need a test to tell me that... Anyway I guess I'll be doing a lot of shopping, baking, wrapping, decorating and all these things over the coming weeks! Already listening to Now That's What I Call Xmas btw!

Your Holiday Personality is Fun

You're all about the celebrating. Whether you're partying hard or singing along to Christmas music, you're totally enjoying the holidays. Make your own Christmas ornaments. Create a holiday mix for all your friends' stockings. Run around your neighborhood late Christmas Eve ringing bells.

Now for the good stuff What will you get this year? It seems I'll be getting money... Not very excited about that, I like unwrapping presents...

You Christmas Stocking Will Be Filled with Money

You've either been really really good this year... Or Santa is trying to pay you off!

Paradoxes are extremely interesting as they seem to challenge our fundamental ideas on how the world works. People have been looking at paradoxes for thousands of years and there is still discussion on some of the oldest paradoxes people have recorded. What makes them so interesting is that most of them are true in a mathematical/logical way but they don't make any sense intuitively. Here are some examples:

Happiness or a ham sandwich?

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.

Smullyan (1), p. 219

I wish to prove to you that there exists a unicorn. To do this it obviously suffices to prove the (possibly) stronger statement that there exists an existing unicorn. (By an existing unicorn I of course mean one that exists.) Surely if there exists an existing unicorn, then there must exist a unicorn. So all I have to do is prove that an existing unicorn exists. Well, there are exactly two possibilities:

(1) An existing unicorn exists.

(2) An existing unicorn does not exist.

Possibility (2) is clearly contradictory: How could an existing unicorn not exist? Just as it is true that a blue unicorn is necessarily blue, an existing unicorn must necessarily be existing.

"Interesting" and "uninteresting" numbers

The question arises: Are there any uninteresting numbers? We can prove that there are none by the following simple steps. If there are dull numbers, then we can divide all numbers into two sets - interesting and dull. In the set of dull numbers there will be only one number that is the smallest. Since it is the smallest uninteresting number it becomes, ipso facto , an interesting number. We must therefore remove it from the dull set and place it in the other. But now there will be another smallest uninteresting number. Repeating this process will make any dull number interesting.

The ship of Theseus

The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

Plutarch, Vita Thesei, 22-23

Proving that 2 = 1

Here is the version offered by Augustus De Morgan: Let x = 1. Then x² = x. So x² - 1 = x -1. Dividing both sides by x -1, we conclude that x + 1 = 1; that is, since x = 1, 2 = 1.

Quine, p.5

Assume that

a = b.    (1)

Multiplying both sides by a,

a² = ab.     (2)

Subtracting b² from both sides,

a² - b² = ab - b² .    (3)

Factorizing both sides,

(a + b)(a - b) = b(a - b).    (4)

Dividing both sides by (a - b),

a + b = b.    (5)

If now we take a = b = 1, we conclude that 2 = 1. Or we can subtract b from both sides and conclude that a, which can be taken as any number, must be equal to zero. Or we can substitute b for a and conclude that any number is double itself. Our result can thus be interpreted in a number of ways, all equally ridiculous.

Northrop, p. 85

The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless. As Northrop goes on to show, the same trick can be used to prove, e.g., that any two unequal numbers are equal, or that all positive whole numbers are equal.

Of course paradoxes are everywhere, you just need to look carefully

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http://www.paradoxes.co.uk/
http://en.wikipedia.org/wiki/List_of_paradoxes