# Infinity Just Keeps Growing And Growing And Growing: VIDEO

You think you know infinity? Think again. As mathematician Dennis Wildfogel explains in this TED video, infinity is far larger than you ever imagined. Watch and learn AFTER THE JUMP.

« Straight Guys Protest Chick-Fil-A With Gay Kiss: VIDEO |
Main
| Utah Street Sign Spreads Anti-Gay Hate: VIDEO »

08/09/2012

Trending

« «Straight Guys Protest Chick-Fil-A With Gay Kiss: VIDEO« «
#### Home

#### Page 2

#### Page 3

#### Page 4

Find us on Google+

- Benedict Cumberbatch Attempts Beyonce's 'Crazy in Love' Walk - VIDEO
- Anti-gay Forces Unite to Oppose Houston Mayor Annise Parker and the 'Radical Agenda' of LGBT Equality: VIDEO
- Gay Iconography: Lance Bass' Big Coming Out
- Eric Holder Announces Federal Government Will Recognize Gay Marriages in Six More States
- Ellen Holds Auditions to See Who Can Fill Nick the Gardener's Shoes While He Films 'Magic Mike XXL' - VIDEO
- Former Reagan Aide Calls on Southern States to Secede to Stop the Spread of Gay Rights: AUDIO

- Let Annie Lennox Put Some Soul in Your Saturday Step With 'Georgia on My Mind' - VIDEO
- Rep. Steve King Stands By 'Fabricated' Claim He Said Gays Don't Make it to Heaven: VIDEO
- A Looks at Serbia's Gay Community and the Violent, Anti-LGBT Forces Working Against Them: VIDEO
- Federal Judge Fast-tracks Challenge to South Carolina's Gay Marriage Ban, Could Rule By Nov. 3
- 'Family Circle' Magazine Target Of Backlash After Featuring Gay Couple in 'Modern Life' Column
- Human Rights Watch Documents Abuse Of Gays In Jamaica: VIDEO

- Cobra Starship and Icona Pop Have 'Never Been In Love': VIDEO
- Death Of White Rhino Leaves Only 6 Left In The World
- Lady Gaga Invites Fan to Propose to His Boyfriend Onstage: VIDEO
- Florida Attorney General Pam Bondi Files Motion to Keep Stay on Pro-Marriage Equality Ruling
- Bystanders Stop Drunk Redneck's Anti-gay Attack at Dallas Airport: WATCH
- Towleroad Guide to the Tube #1636

- News: Honey Boo Boo, Christian Bale, Ebola, Twitter Queen, Harry Potter
- At Least 2 Students Injured in Seattle-Area High School Shooting: VIDEO
- Gay Advocacy Group Equality Michigan Receives $3 Million Donation From Co-founder's Estate
- Canadian Councillor's Campaign Signs Vandalized, Sprayed 'Homophobe'
- Coeur d'Alene, Idaho Says For-Profit Wedding Chapel Can Discriminate Against Gay Couples
- Elders React to Nicki Minaj's Anaconda: VIDEO

Sun | Mon | Tue | Wed | Thu | Fri | Sat |
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | |||

5 | 6 | 7 | 8 | 9 | 10 | 11 |

12 | 13 | 14 | 15 | 16 | 17 | 18 |

19 | 20 | 21 | 22 | 23 | 24 | 25 |

26 | 27 | 28 | 29 | 30 | 31 |

I LOVE MATH

Posted by: B | Aug 9, 2012 1:39:55 PM

It's this notion of infinity that makes fundamentalists condemn set theory as un-Biblical. They would like to believe that there is only one infinity: God.

http://boingboing.net/2012/08/07/what-do-christian-fundamentali.html

Posted by: Diogenes Arktos | Aug 9, 2012 1:49:10 PM

Good presentation but somewhat oversimplified regarding Godel and Cohen's statement about the Continuum hypothesis (CH). It's not that one cannot prove or disprove CH at all, but rather, that CH is an example of a logical mathematical statement that can be formulated using only the language of the Zermelo-Frankel axioms (ZF), but cannot be proved or disproved within the mathematical structure those axioms define.

In other words, ZF can be used to state the claim of CH, but is insufficient to prove or disprove that claim. You could postulate a system of mathematics in which CH is true (e.g., ZF+CH), and this would work; or, you could just as easily postulate an alternative system in which CH is false.

This situation is a bit like the discovery of non-Euclidean geometries, in which the parallel postulate is not accepted as axiomatically true.

In fact, Godel's incompleteness theorems have far greater consequences than that related to set-theoretic claims like CH. His work showed that in ANY axiomatic system of mathematics, it is possible to formulate a logical statement within that system that cannot be proved or disproved using those axioms.

Posted by: atomic | Aug 9, 2012 1:55:16 PM

Good presentation but somewhat oversimplified regarding Godel and Cohen's statement about the Continuum hypothesis (CH). It's not that one cannot prove or disprove CH at all, but rather, that CH is an example of a logical mathematical statement that can be formulated using only the language of the Zermelo-Frankel axioms (ZF), but cannot be proved or disproved within the mathematical structure those axioms define.

In other words, ZF can be used to state the claim of CH, but is insufficient to prove or disprove that claim. You could postulate a system of mathematics in which CH is true (e.g., ZF+CH), and this would work; or, you could just as easily postulate an alternative system in which CH is false.

This situation is a bit like the discovery of non-Euclidean geometries, in which the parallel postulate is not accepted as axiomatically true.

In fact, Godel's incompleteness theorems have far greater consequences than that related to set-theoretic claims like CH. His work showed that in ANY axiomatic system of mathematics, it is possible to formulate a logical statement within that system that cannot be proved or disproved using those axioms.

Posted by: atomic | Aug 9, 2012 1:55:16 PM

Um, what Atomic sez.

Posted by: TC | Aug 9, 2012 2:08:43 PM

Something for us nerds to ponder, if we haven't already. Interesting that he didn't go into linear infinities or dimensional infinities or quantum infinities or the other infinities that I can conceptualize but cannot think of a title for them.... I suppose there may be an infinity number of types of infinities :)

Posted by: murraygoround | Aug 9, 2012 2:14:47 PM

Did they include waiting at the DMV?

Posted by: anon | Aug 9, 2012 5:19:04 PM

My head just exploded.

Posted by: RJP | Aug 9, 2012 5:28:33 PM

I love this type of stuff. NERDS ROCK!!!

Posted by: Stan | Aug 9, 2012 7:40:01 PM

@atomic:

Quite so. Perhaps you could also include ordinal numbers, cardinal numbers, and perhaps even V=L ;-)

Seriously, how many others who follow TR have the slightest clue about what we are talking about?

I happen to think that this video, which is embedded in the URL I gave in my earlier post (well worth a read - and follow up with the Mother Jones article in Sources & Resouces), is an excellent, short introduction to two major points about mathematics for its target audience, people with minimal mathematical sophistication. (1) multiple infinities (2) some problems cannot be solved within mathematics. In addition to the fundamentalist issue of more than one infinity a/k/a God, I'm sure that the 'holes' in mathematics are also a problem to a group which believes that everything has a neat, tidy unique solution - theirs.

Posted by: Diogenes Arktos | Aug 10, 2012 8:47:59 AM

@ATOMIC: Well that's it, then! Marry me. OK? I mean, I'd love to have a man who could whisper sweet axioms in my ear while he's parallel-postulating me.

Posted by: jamal49 | Aug 10, 2012 12:18:30 PM

@ATOMIC: Close, but not quite.

Here's what you said: "His work showed that in ANY axiomatic system of mathematics, it is possible to formulate a logical statement within that system that cannot be proved or disproved using those axioms."

Instead, what he showed was that in any FINITE axiomatic system of mathematics *POWERFUL*ENOUGH*TO*MODEL*SIMPLE*ARITHMETIC*, then there will be statements that can be constructed within the system that cannot be proven by the system.

Not all axiomatic systems of mathematics are finite and not all finite systems are powerful enough to model simple arithmetic. For example, Presburger arithmetic is finite (only 5 axioms) and is both complete and consistent, but it only defines addition and thus is not powerful enough to model simple arithmetic.

Tarski's axioms of elementary Euclidean geometry are also consistent, but it isn't powerful enough to model simple arithmetic and thus there is no contradiction of Godel.

As for why he didn't go into other aspects of real analysis (and by "real" I mean the mathematical definition of "real"), he only had about 7 minutes and was trying to explain something complex to people who don't know much math. There simply wasn't time. After all, the way in which Godel's proof regarding the continuum is usually stated as: "Assuming the Continuum Hypothesis is true does not lead to a contradiction." Cohen's work is stated similarly, "Assuming the Continuum Hypothesis is false does not lead to a contradiction."

There's a subtle distinction there that goes to how mathematicians conduct proof. It isn't that they did a direct proof that no such proof exists. Instead, they did an indirect proof that showed there was no way to contradict the claim that it is true. One would think that would be enough since not being able to prove it false seemingly indicates that it must be true...but Cohen showed that just because you can't prove it to be false doesn't mean it actually isn't.

But to get into all of that takes time that you just don't have in the format of a TED Talk. It's supposed to be brief and accessible.

Posted by: Rrhain | Aug 10, 2012 5:44:18 PM

A good introduction to set theory and the concept of Infinity is the 1982 book 'Infinity and the Mind' by Rudy Rucker.

Posted by: Chris McCoy | Aug 13, 2012 6:46:41 PM