qntm's Blog, page 5
October 27, 2013
Citation found
Blog » Red is the color of blood, rubies and strawberries.
Yellow is the color of gold, butter, or ripe lemons.
Green is the color of emeralds, jade, and growing grass.
Blue is the colour of the clear sky and the deep sea.
...
Yellow is the color of gold, butter, or ripe lemons.
Green is the color of emeralds, jade, and growing grass.
Blue is the colour of the clear sky and the deep sea.
...
October 21, 2013
How many infinities are there?
Blog » Is there more than one infinity?
Yes.
Are some infinities larger than others?
Yes.
Is there a largest infinity?
No.
Does that mean that there are infinitely many infinities?
Yes.
So... which infinity is the number of infinities? How many infinities are there?
There are two types of number. There are ordinal numbers and there are cardinal numbers. The finite ordinals and the finite cardinals are exactly the same. The infinite ordinals and the infinite cardinals are different from one another. Which of the two would you like me to settle first?
How many ordinals are there?
There are infinitely many ordinals.
Okay... but which infinity?
"How many" is a tricky concept in set theory when we start dealing with infinite sets. What you're actually trying to ask is:
What is the cardinality of the set of all ordinals?
Answer: There is no set of all ordinals.
The ordinals form a sequence. Each ordinal is defined in terms of all the ordinals that are smaller than it. ...
Yes.
Are some infinities larger than others?
Yes.
Is there a largest infinity?
No.
Does that mean that there are infinitely many infinities?
Yes.
So... which infinity is the number of infinities? How many infinities are there?
There are two types of number. There are ordinal numbers and there are cardinal numbers. The finite ordinals and the finite cardinals are exactly the same. The infinite ordinals and the infinite cardinals are different from one another. Which of the two would you like me to settle first?
How many ordinals are there?
There are infinitely many ordinals.
Okay... but which infinity?
"How many" is a tricky concept in set theory when we start dealing with infinite sets. What you're actually trying to ask is:
What is the cardinality of the set of all ordinals?
Answer: There is no set of all ordinals.
The ordinals form a sequence. Each ordinal is defined in terms of all the ordinals that are smaller than it. ...
September 11, 2013
Hey look, I'm on Drabblecast
Blog » Not me specifically, a thing I wrote.
The thing I wrote was I don't know, Timmy, being God is a big responsibility, a short science fiction story about the very real dangers of hypercomputation.
The thing on Drabblecast is an audio recording of the same! You need to be a subscribing Drabblecast member to listen to it. So, if you are, maybe you already listened to it!
The recording is from a live reading of the story at... well, supposedly, at WorldCon 72, but that hasn't happened yet, so I think it was more likely to have been WorldCon 71 in San Antonio....
The thing I wrote was I don't know, Timmy, being God is a big responsibility, a short science fiction story about the very real dangers of hypercomputation.
The thing on Drabblecast is an audio recording of the same! You need to be a subscribing Drabblecast member to listen to it. So, if you are, maybe you already listened to it!
The recording is from a live reading of the story at... well, supposedly, at WorldCon 72, but that hasn't happened yet, so I think it was more likely to have been WorldCon 71 in San Antonio....
