# real count

#### phillip1882

i would increase the number of generated TM's until i get a stable value for the seventh digit.

#### Maschke

i would increase the number of generated TM's until i get a stable value for the seventh digit.
How do you know what the 7th digit is?

"increase the number of generated TMs?" What does that even mean? I don't think we're making any progress at all here.

#### phillip1882

again. my program generates "random" TM's and then estimates wheter they halt. if you do this for a large enough number of TM's, the most significant bits approach a finite value.

#### Maschke

i would increase the number of generated TM's until i get a stable value for the seventh digit.
I'm making an effort to understand your idea. I haven't read your code nor understood the details of your earlier posts. So when you say "increase the number of generated TMs," that makes no sense to me. Let alone having them converge on a stable value.

If you randomly -- true random or pseudorandom no difference in this argument -- generated a TM, it might or might not halt on various given inputs. It might calculate the square root of 2 or approximate Newtonian gravity in a video game. You are literally generating a random program.

Why on earth should we expect such a sequence of randomly generated TMs to converge, and what does that even mean?

I imagine this is all quite clear in your mind. If you would believe me when I tell you it's totally unclear in mine, but that I desire to understand, perhaps you can take this from the top and make it clear and simple for my little brain and ever shortening attention span.

Thank you.

#### phillip1882

okay. let me give you an example. let's say i wanted to estimate pi, but using probability instead of a pi generating function. i could take a circle of radius 1, put a square around that, and generate random points. if the point landed inside the circle, lets call that success. if outside, a fail. if you generate a large enough number of points, you would get a value that aproaches pi.
i'm doing this with turing machines.
I
f you randomly -- true random or pseudorandom no difference in this argument -- generated a TM, it might or might not halt on various given inputs. It might calculate the square root of 2 or approximate Newtonian gravity in a video game. You are literally generating a random program.
yes exactly. and by estimating whether they halt, i can use the data to approximate chaitins omega.
i admit the estimation is not perfect. there are many TM's that would halt that my program would say don't halt. for example a machine that uses more than 10 million bits of data, or lasts longer than an hour, but on the whole it's fairly accurate.

#### phillip1882

i think this might help.

#### Maschke

i think this might help.
I didn't watch the vid. Numberphile in general is pretty good. Why don't you summarize it.

I'm happy if you're happy, but I really don't see your point. You generate some random TMs (which actually you don't seem to be doing -- you're initializing a random number of states with random values. A TM is a sequence of instructions to control a TM. Perhaps you ought to read up on what a TM is. I think you are generating finite state machines but I haven't spent the time to be sure what you're doing) -- and then concluding that a certain percentage of them appear to halt or not within a bounded number of steps. I don't doubt that you have put some time and energy into your project, but I don't think any of it means what you think it does. But as you are no longer making any claims or assertions related to your initial post, I haven't got much to add.

#### phillip1882

you are generating finite state machines...
yes. but this is a perfectly valid way of viewing a turing machine as far as I'm aware.
and then concluding that a certain percentage of them appear to halt or not within a bounded number of steps.
yes.
my point is if you can approximate chiatins constant, then nothing is outside computability.
I didn't watch the vid. Numberphile in general is pretty good. Why don't you summarize it.
according to the video, any irrational number can be approximated with a fraction, to the desired degree of accuracy.

#### Maschke

yes. but this is a perfectly valid way of viewing a turing machine as far as I'm aware.
No.

my point is if you can approximate chiatins constant, then nothing is outside computability.
As you are repeatedly claiming the opposite of an 83 year old well-known result, the burden is on you to prove that you're right and everyone else is wrong.

according to the video, any irrational number can be approximated with a fraction, to the desired degree of accuracy.
For sure. Which has nothing to do with the claims you are making. In order to approximate a real with a rational, you need to know what real you're approximating. You can't just "approximate" the next bit when you have no idea what that bit is.

I haven't said anything new for a while so it's time for me to let this go. I encourage your enthusiasm for the subject and would recommend some more reading and study.

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#### phillip1882

i've decided to prove it by running the program. several bugs were in my original program, which i took care of.
it should take about 2 months to fully run the program. i haven't looked at the current known bits of chiatins omega.
but will after my program is complete.