[OOC] Myriad Reality

[Zeal]

<Snipped quote by Zeal>

Oh, I'm sorry about that. What song?

@Host

It's called See you again by Whiz Khalifa...the chorus made me cry not whiz's sing/rapping.

[Host]

<Snipped quote by Host>

It's called See you again by Whiz Khalifa...the chorus made me cry not whiz's sing/rapping.

@Zeal

What's it about?

[Zeal]

<Snipped quote by Zeal>

What's it about?

@Host

Someone's passed friend. How they are living happily and how they can't wait to see the passed friend again.

[Host]

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Someone's passed friend. How they are living happily and how they can't wait to see the passed friend again.

@Zeal

Aw. That's sad.

[Zeal]

<Snipped quote by Zeal>

Aw. That's sad.

@Host

Yeah.

[Host]

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Yeah.

@Zeal

Where'd you hear it?

[Zeal]

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Where'd you hear it?

@Host

Radio while I was driving.

[Host]

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Radio while I was driving.

@Zeal

Ah. That whole driving thing.

[Zeal]

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Ah. That whole driving thing.

@Host

Eeyup.

[whizzball1]

Huh. Half of the Presidential candidates are opposed to gay marriage. But only one is vocal about it, and of course it's the candidate from Texas, because Texas is awesome.

Well, except for the fact that it's really hot. But otherwise, it's awesome.

[Host]

<Snipped quote by Host>

Eeyup.

@Zeal

I'm in Spanish, so I'll be in and out.

Huh. Half of the Presidential candidates are opposed to gay marriage. But only one is vocal about it, and of course it's the candidate from Texas, because Texas is awesome.

Well, except for the fact that it's really hot. But otherwise, it's awesome.

@whizzball1

First of all, hot is the best. Second of all, YOU LIVE IN CALIFORNIA. IT'S HOTTER THERE.

Did you read that on today's Prophecy Watch?

[whizzball1]

<Snipped quote by Zeal>

I'm in Spanish, so I'll be in and out.

<Snipped quote by whizzball1>

First of all, hot is the best. Second of all, YOU LIVE IN CALIFORNIA. IT'S HOTTER THERE.

Did you read that on today's Prophecy Watch?

@Host

It was on a news website.

[Host]

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It was on a news website.

@whizzball1

Aw. Subscribe to the newsletter.

[Host]

I almost forgot that Ananke's power isn't pure teleportation.

[Zeal]

I almost forgot that Ananke's power isn't pure teleportation.

@Host

Hm...I wonder when I should introduce my Codex char...

[Host]

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Hm...I wonder when I should introduce my Codex char...

@Zeal

Whenever you want to.

[whizzball1]

Today, my maths book told me about Hilbert's Paradox, and asked me to try and think of a way to fit all the passengers from infinite buses, each having infinite passengers, into a hotel already filled with infinite people. (All those are the natural infinities.) Somehow, I managed to figure out the prime powers solution despite having never heard of it before. That was fun.

[Host]

Today, my maths book told me about Hilbert's Paradox, and asked me to try and think of a way to fit all the passengers from infinite buses, each having infinite passengers, into a hotel already filled with infinite people. (All those are the natural infinities.) Somehow, I managed to figure out the prime powers solution despite having never heard of it before. That was fun.

@whizzball1

Never heard that analogy before.

[whizzball1]

<Snipped quote by whizzball1>

Never heard that analogy before.

@Host

Really? Well, say you had the hotel and it was filled up, as is usually the original setting. But then, in front of the hotel come an infinite number of buses, each with an infinite number of people, all of which need to go into the hotel. And so the hotel manager takes all the people from the hotel and loads them into an empty bus he has. So now you have infinite buses which need to go into the hotel, labelled 1, 2, 3, 4... How does he arrange them so that all the people get a room? (This is a bit of a variation in that the people in the hotel are removed first.)

I initially considered taking the people from bus 1, numbering them, squaring their number, and putting them in the room that was the answer. Then the people from bus 2 would be numbered, their number would be cubed, and that new number would be their room. I thought this pattern might continue to work because no natural number is both a square root and a cube root, except for 1.

Then I tried bus 3, and raised those people's numbers to the fourth power, but I realised that every single fourth power would be a perfect square, because raising a number to the fourth power is the same thing as squaring the number and then squaring that.

So, my thought process moved to trying to figure out a series of numbers that could never be the product of two previous numbers that were used. This was clearly the prime numbers. So, I considered numbering the people in bus 1, squaring their numbers, and assigning them to those rooms. The numbers of the people in bus 2 would be cubed. The numbers of the people in bus 3 would be raised to the fifth power. By this, I realised that none of these powers would ever overlap. No fifth power could be a third power. No 101th power could be a 73rd power. And thus my solution was found. Expressed algorithmically:

For each bus B, take each passenger P, raise P to the power of the Bth prime number, and assign that passenger to the answer. The answer given in the maths book was different, but I went to the Wikipedia page and found that my solution was one of those listed.

[Host]

<Snipped quote by Host>

Really? Well, say you had the hotel and it was filled up, as is usually the original setting. But then, in front of the hotel come an infinite number of buses, each with an infinite number of people, all of which need to go into the hotel. And so the hotel manager takes all the people from the hotel and loads them into an empty bus he has. So now you have infinite buses which need to go into the hotel, labelled 1, 2, 3, 4... How does he arrange them so that all the people get a room? (This is a bit of a variation in that the people in the hotel are removed first.)

I initially considered taking the people from bus 1, numbering them, squaring their number, and putting them in the room that was the answer. Then the people from bus 2 would be numbered, their number would be cubed, and that new number would be their room. I thought this pattern might continue to work because no natural number is both a square root and a cube root, except for 1.

Then I tried bus 3, and raised those people's numbers to the fourth power, but I realised that every single fourth power would be a perfect square, because raising a number to the fourth power is the same thing as squaring the number and then squaring that.

So, my thought process moved to trying to figure out a series of numbers that could never be the product of two previous numbers that were used. This was clearly the prime numbers. So, I considered numbering the people in bus 1, squaring their numbers, and assigning them to those rooms. The numbers of the people in bus 2 would be cubed. The numbers of the people in bus 3 would be raised to the fifth power. By this, I realised that none of these powers would ever overlap. No fifth power could be a third power. No 101th power could be a 73rd power. And thus my solution was found. Expressed algorithmically:

For each bus B, take each passenger P, raise P to the power of the Bth prime number, and assign that passenger to the answer. The answer given in the maths book was different, but I went to the Wikipedia page and found that my solution was one of those listed.

@whizzball1

That situation could be applied in a more mathematical way. That's not realistic.