The number that knows more about math than you do: and other strange things

Sithdarth · 04-14-2009, 11:47 PM

So I learned earlier today about this number usually called omega but that also goes by the name of Chaitin's constant. The definition of this number is rather complicated but its properties are generally well definable. The first is that there are actually an infinite number of values for omega because there are that many ways to define it. Omega always lies somewhere between 0 and 1, is irrational and impossible to compute. The really neat thing is that if we could find even one of the Omegas we would then be able to use it to prove every mathematical conjecture we could ever construct either true or false. That is to say that all the information there is and ever will be about math is contained in the totally random digits of omega.

I read about this number in a book about quantum computing. It turns out that quantum computing is both a lot simpler and a lot stranger than I used to think. For example, you can get an answer from a quantum computer without actually running the computer. Its called counter factual computing and while intriguing makes my head explode. It also appears that quantum computers can at the same time be finished running a program and not finished running a program.

I just thought I'd share some of the mind blowing things I learned today and get opinions on them and/or find out what completely out there things you guys might have come across at some point.

BitVyper · 04-15-2009, 12:26 AM

I was very interested until I saw the words "Super Omega." Now all I can picture is a golden-haired mathmatician doing battle with the most powerful unsolved problem in number theory. OMEGAAAAAAAAMEEEEEEEEEEEHAAAAAAAAAA!!!!

Seriously though; that's pretty interesting. Thanks for sharing.

Kim · 04-15-2009, 12:27 AM

Ironically, after finding the number the first thing it disproves is itself.

Sithdarth · 04-15-2009, 12:33 AM

Well yes you could never actually find the number itself but if you could find the first 80 million digits in binary like with Pi then we could prove the correctness of any mathematical conjecture that you could construct with less than 80 million bits. I'd wager that's about enough to encompass anything we'd really bother to want to ask it.

Corel · 04-15-2009, 11:18 AM

Not mind blowing, but certainly interesting is the application of Systems Theory to a variety of very different disciplines.

One application of this I do enjoy is thinking about Political systems in terms of their cause and effects to the system as a whole, which can be quite fascinating, as then you get into the Philosophical point of view of "What makes a good society?". Which in turn makes you try to map a system to some sort of idea you've formed.

Vault Of Thrones · 04-15-2009, 03:30 PM

That constant is quite neat. I also find it quite interesting how quite often surprisingly mundane can take longer to calculate than the universe has been around. Computability is an interesting subject.

Quantum computers are also an interesting subject. If (or when) quantum computers become mainstream all current cryptographic practices are essentially worthless, though the solutions that quantum computers would provide are also quite amazing. Mostly though, I just want to know what practical application of entanglement means for my internet speed.

Azisien · 04-15-2009, 03:43 PM

Fascinating, but the logical questions follow: firstly, can the LHC generate it? And secondly, can we make a weapon out of it somehow?

04-14-2009, 11:47 PM	#1
Sithdarth Friendly Neighborhood Quantum Hobo Join Date: Mar 2004 Location: Outside the M-brane look'n in Posts: 5,403	The number that knows more about math than you do: and other strange things So I learned earlier today about this number usually called omega but that also goes by the name of Chaitin's constant. The definition of this number is rather complicated but its properties are generally well definable. The first is that there are actually an infinite number of values for omega because there are that many ways to define it. Omega always lies somewhere between 0 and 1, is irrational and impossible to compute. The really neat thing is that if we could find even one of the Omegas we would then be able to use it to prove every mathematical conjecture we could ever construct either true or false. That is to say that all the information there is and ever will be about math is contained in the totally random digits of omega. I read about this number in a book about quantum computing. It turns out that quantum computing is both a lot simpler and a lot stranger than I used to think. For example, you can get an answer from a quantum computer without actually running the computer. Its called counter factual computing and while intriguing makes my head explode. It also appears that quantum computers can at the same time be finished running a program and not finished running a program. I just thought I'd share some of the mind blowing things I learned today and get opinions on them and/or find out what completely out there things you guys might have come across at some point.

04-15-2009, 12:26 AM	#2
BitVyper History's Strongest Dilettante Join Date: Mar 2004 Location: Arcadia Posts: 6,662	I was very interested until I saw the words "Super Omega." Now all I can picture is a golden-haired mathmatician doing battle with the most powerful unsolved problem in number theory. OMEGAAAAAAAAMEEEEEEEEEEEHAAAAAAAAAA!!!! Seriously though; that's pretty interesting. Thanks for sharing. __________________ "There are worlds out there where the sky is burning, and the sea is asleep, and the rivers dream. People made of smoke and cities made of song. Somewhere there's danger, somewhere there's injustice, somewhere else the tea's getting cold. Come on, Ace; we've got work to do!" Awesome art be here.

04-15-2009, 12:27 AM	#3
Kim adorable Join Date: Sep 2007 Posts: 12,950	Ironically, after finding the number the first thing it disproves is itself. __________________ this post is about how to successfully H the Kimmy

04-15-2009, 03:30 PM	#6
Vault Of Thrones A Threat to the District Join Date: Sep 2007 Location: /dev/null Posts: 444	That constant is quite neat. I also find it quite interesting how quite often surprisingly mundane can take longer to calculate than the universe has been around. Computability is an interesting subject. Quantum computers are also an interesting subject. If (or when) quantum computers become mainstream all current cryptographic practices are essentially worthless, though the solutions that quantum computers would provide are also quite amazing. Mostly though, I just want to know what practical application of entanglement means for my internet speed. __________________ Twitter!

04-15-2009, 12:33 AM	#4
Sithdarth Friendly Neighborhood Quantum Hobo Join Date: Mar 2004 Location: Outside the M-brane look'n in Posts: 5,403	Well yes you could never actually find the number itself but if you could find the first 80 million digits in binary like with Pi then we could prove the correctness of any mathematical conjecture that you could construct with less than 80 million bits. I'd wager that's about enough to encompass anything we'd really bother to want to ask it.

04-15-2009, 11:18 AM	#5
Corel Welcome, to Paedogeddon! Join Date: Nov 2008 Posts: 1,015	Not mind blowing, but certainly interesting is the application of Systems Theory to a variety of very different disciplines. One application of this I do enjoy is thinking about Political systems in terms of their cause and effects to the system as a whole, which can be quite fascinating, as then you get into the Philosophical point of view of "What makes a good society?". Which in turn makes you try to map a system to some sort of idea you've formed.

04-15-2009, 03:43 PM	#7
Azisien wat Join Date: Jan 2005 Posts: 7,177	Fascinating, but the logical questions follow: firstly, can the LHC generate it? And secondly, can we make a weapon out of it somehow?