Feedback/Notes

 

Latest Activity

Chris B commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"How are you all managing under Covid threat?"
2 hours ago
Chris B commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"Still no full lockdown here, Joan. Regular health care is at a quarter of its capacity, waiting…"
2 hours ago
Ruth Anthony-Gardner added a discussion to the group Our Climate, Scumpism is Denialism
Thumbnail

Arctic Worries

You may remember that Arctic Sea Ice was dramatically declining until the record low of 2012. The…See More
4 hours ago
Joan Denoo commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"Chris B, Wonderful cartoon of a wolf and some sheep. Right on! I know listening to the talk…"
9 hours ago
Joan Denoo commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"Chris B, I follow the virus numbers for The Netherlands and I am sure the citizens are ready for a…"
12 hours ago
Mrs.B commented on Loren Miller's group Quote Of The Day
"That power needs cutting."
15 hours ago
Mrs.B commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"We watched PBS last night too, Randy. Sounds positive for hopefully removing some carbon, as long…"
15 hours ago
Davy commented on Doone's group Humans of Earth and a Cheat, a Liar, a Fraud, a Bully, a Racist, a Predator, a Con man who is a useful Russian Idiot aka a Man with No Money Named Scump News
"As they say there is only one poll that counts all the others mean nothing."
16 hours ago
Stephen commented on Stephen's group Secularism in the UK and Europe.and the connection between much of the media and the Tory establishment. NEWS
"I Lost 39 Members of My Family in the Holocaust, Jeremy Corbyn is No Antisemite | Andrew Feinstein"
17 hours ago
Loren Miller commented on Loren Miller's group Quote Of The Day
"Many religions now come before us with ingratiating smirks and outspread hands, like an unctuous…"
20 hours ago
Randall Smith commented on Sydni Moser's group Coffee Break without any Mention of that Idiot
"Sick and tired of watching the same old CNN and MSNBC "news", I watched 3 hours of nature…"
20 hours ago
Mrs.B commented on Hope's group Imagine No Organized Religion or at least a Religion without Scump
"Yes, & very frighteningly dangerous."
yesterday
Onyango Makagutu commented on Hope's group Imagine No Organized Religion or at least a Religion without Scump
"Mrs B, i don't think it is something to be comprehended. It is absurd"
yesterday
Mrs.B commented on Hope's group Imagine No Organized Religion or at least a Religion without Scump
"I will never comprehend any of this."
yesterday
Stephen commented on Hope's group Imagine No Organized Religion or at least a Religion without Scump
"A teacher gets beheaded by a Muslim man but the whole Islamic world rages against France for…"
yesterday
Mrs.B commented on Loren Miller's group Quote Of The Day
"Horrid things done in religion's name."
yesterday
Stephen commented on Loren Miller's group Quote Of The Day
"How can it be a bad thing for a worldview to argue (a) that our experience of reality, not myth or…"
yesterday
Chris B commented on Loren Miller's group Quote Of The Day
"Very true and beautiful!"
yesterday
Olivia T. updated their profile
yesterday
Loren Miller commented on Loren Miller's group Quote Of The Day
"Morality is doing right, no matter what you are told. Religion is doing what you are told, no…"
yesterday

We are a worldwide social network of freethinkers, atheists, agnostics and secular humanists.

As a kid, I was fascinated by the number infinity. It is hard for us humans to wrap our minds around the concept of infinity. But mathematics makes it possible of course. And fun. I found this great article on the "Hilbert Hotel", I hope you enjoy it too.

 

May 9, 2010, 5:00 pm

The Hilbert Hotel

Steven Strogatz

Steven Strogatz on math, from basic to baffling.

In late February I received an e-mail message from a reader named Kim Forbes.  Her six-year-old son Ben had asked her a math question she couldn’t answer, and she was hoping I could help:

Today is the 100th day of school. He was very excited and told me everything he knows about the number 100, including that 100 was an even number. He then told me that 101 was an odd number and 1 million was an even number, etc.  He then paused and asked: “Is infinity even or odd?”

I explained that infinity is neither even nor odd.  It’s not a number in the usual sense, and it doesn’t obey the rules of arithmetic.  All sorts of contradictions would follow if it did.  For instance, “if infinity were odd, 2 times infinity would be even.  But both are infinity!  So the whole idea of odd and even does not make sense for infinity.”

Kim replied:

Thank you.  Ben was satisfied with that answer and kind of likes the idea that infinity is big enough to be both odd and even.

Although something got garbled in translation (infinity is neither odd nor even, not both), Ben’s rendering hints at a larger truth.  Infinity can be mind-boggling.
 
Some of its strangest aspects first came to light in the late 1800s, with Georg Cantor’s groundbreaking work on “set theory.”  Cantor was particularly interested in infinite sets of numbers and points, like the set {1, 2, 3, 4,…} of “natural numbers” and the set of points on a line.  He defined a rigorous way to compare different infinite sets and discovered, shockingly, that some infinities are bigger than others.

At the time, Cantor’s theory provoked not just resistance, but outrage.  Henri Poincaré, one of the leading mathematicians of the day, called it a “disease.”  But another giant of the era, David Hilbert, saw it as a lasting contribution and later proclaimed, “No one shall expel us from the Paradise that Cantor has created.”

My goal here is to give you a glimpse of this paradise.  But rather than working directly with sets of numbers or points, let me follow an approach introduced by Hilbert himself.  He vividly conveyed the strangeness and wonder of Cantor’s theory by telling a parable about a grand hotel, now known as the Hilbert Hotel.

It’s always booked solid, yet there’s always a vacancy.

For the Hilbert Hotel doesn’t merely have hundreds of rooms — it has an infinite number of them.  Whenever a new guest arrives, the manager shifts the occupant of room 1 to room 2, room 2 to room 3, and so on.  That frees up room 1 for the newcomer, and accommodates everyone else as well (though inconveniencing them by the move).

Now suppose infinitely many new guests arrive, sweaty and short-tempered.  No problem.  The unflappable manager moves the occupant of room 1 to room 2, room 2 to room 4, room 3 to room 6, and so on.  This doubling trick opens up all the odd-numbered rooms — infinitely many of them — for the new guests.

Later that night, an endless convoy of buses rumbles up to reception.  There are infinitely many buses, and worse still, each one is loaded with an infinity of crabby people demanding that the hotel live up to its motto, “There’s always room at the Hilbert Hotel.”

The manager has faced this challenge before and takes it in stride.

 

Read the rest here.

Views: 58

Replies to This Discussion

Hilbert was a sadist, his hotel's guests are masochists, and the manager is both.

RSS

© 2020   Created by Atheist Universe.   Powered by

Badges  |  Report an Issue  |  Privacy Policy  |  Terms of Service