### Wednesday, June 16, 2004

Another great picture from Allison, who I will write an email to very soon! Also some cool links: Gregory Chaitin's home page, which has interesting discussions of meta-mathematics which I tend to agree with - he states that it will probably be necessary to keep on adding different interesting axioms, just as one would expect with the ensemble. Then there is Robert Munafo's home page which includes an excellent long discussion on very large numbers*. And also Sean Carroll's blog, which he is quite good at updating.

* - Ok, here's my really big number system, which I think I came up with in my first year of college. Recursive exponentiation is key. Define the function n-star-x: n*x = x^(n-1*x), with 1*x = x. Thus 3*3 = 3^3^3 = 3^27 ~ eight trillion. Let alpha = (10^100)*(10^100), i.e. google star google, a rather large number. The next obvious step is beta = alpha*(alpha*(...*(alpha*alpha)))) where ... indicated alpha repititions of the n-star-x function. You can call this beta=alpha**alpha if you like. Thus we have described very large numbers with only a little bit of information - so the next logical step is to state the existence of numbers which are the largest that can be explicitly described in N bits, say gamma = largest finite number describable by beta bits. Amusingly enough, this is the current limit of research according to Robert's webpage - they call them busy-beaver turing programs.

** Also the APOD picture for Wed. was my favorite galaxy M87, although M83 is pretty good too, both the galaxy and the band (also listening to black dog these days). I'd rather like to visit M87 at some point in the future. The weather has also been amusing recently, with thunderstorms pouring rain furiously while the sun can still easily be seen shining, and then stopping on a dime, a soaking deluge becoming a fine mist in 30 seconds.

* - Ok, here's my really big number system, which I think I came up with in my first year of college. Recursive exponentiation is key. Define the function n-star-x: n*x = x^(n-1*x), with 1*x = x. Thus 3*3 = 3^3^3 = 3^27 ~ eight trillion. Let alpha = (10^100)*(10^100), i.e. google star google, a rather large number. The next obvious step is beta = alpha*(alpha*(...*(alpha*alpha)))) where ... indicated alpha repititions of the n-star-x function. You can call this beta=alpha**alpha if you like. Thus we have described very large numbers with only a little bit of information - so the next logical step is to state the existence of numbers which are the largest that can be explicitly described in N bits, say gamma = largest finite number describable by beta bits. Amusingly enough, this is the current limit of research according to Robert's webpage - they call them busy-beaver turing programs.

** Also the APOD picture for Wed. was my favorite galaxy M87, although M83 is pretty good too, both the galaxy and the band (also listening to black dog these days). I'd rather like to visit M87 at some point in the future. The weather has also been amusing recently, with thunderstorms pouring rain furiously while the sun can still easily be seen shining, and then stopping on a dime, a soaking deluge becoming a fine mist in 30 seconds.

Comments:

<< Home

Yes, you do owe me an e-mail! I'm glad you like my pictures. I was planning on taking a road trip to visit you and other relatives but I think I may get my little pilonidal problem fixed instead. I'm sure you can understand. But I'll be up to see you sometime this semester, probably with Ben in tow, and I'll bring a CD with bunch of pictures on it for your entertainment. Oh, and I also read the first part of your ASOR theory. Interesting, interesting idea. Nice way to combine metaphysics and well...regular physics. I sent the link to a friend of mine who was looking into some philosophy classes and told him if he could understand it then he didn't need a philosophy class.

Tell Katie hello and hope everything's going well.

Grandpa's print is gorgeous as well.

Post a Comment
Tell Katie hello and hope everything's going well.

Grandpa's print is gorgeous as well.

<< Home