Standard crank division by zero thread - Page 11

xilman · 2011-03-10, 16:32

Quote:

Originally Posted by CRGreathouse

The purpose of the fit was to show that, even at the second or third decimal place, Blazys' (second) constant appears to be off.

And the purpose of my computation was to spend relatively little brain power and only a small amount of computation as a gamble that it would be all that was necessary to shoot down Blazys' grandiose claims. There appears to be good evidence that the gamble paid off. Writing and optimizing the code was an intellectual effort comparable to solving a half-way decent crossword puzzle and I view my work as being on a par with doing just that.

I'm now done with the puzzle but if anyone else would like the code, either as an exercise in low-level optimization, or as an excuse to perform some rather mindless computation, they are welcome to it.

Bob is quite right, IMO. Any further work on this problem should be done at a much higher level of mathematical sophistication. Sadly, I don't think the problem worthy of an further investment of my time.

Paul

Don Blazys · 2011-03-11, 11:18

Here's what we have so far:

$\varpi(10^{10})=6,403,587,409$ Relative error= $.00000000172$ $\alpha=1/137.0360172888$

$\varpi(10^{11})=64,036,148,166$ Relative error= $-.00000000598$ $\alpha=1/137.03593392608$

$\varpi(10^{12})=640,362,343,980$ Relative error= $-.00000000156$ $\alpha=1/137.03598213253$

$\varpi(10^{13})=6,403,626,146,905$ Relative error= $.00000000293$ $\alpha=1/137.03603103508$

The relative error seems to be going down slowly, but...
notice that solving for alpha gives us values of the fine structure constant
that fluctuate both above and below the current "best estimate" which is:

$1/137.035999084(51)$

The above four approximations of alpha average out to:

$1/137.03599109564$

which is pretty darn close!

By the way, that last small variation in $\alpha$ translates into
$\varpi(10^{13})$ $=.64036274121717*10^{13}-.40011254313336*\sqrt{10^{13}}$
so the Blazys constants don't really vary that much either!

It's interesting that my approximation function gives us values of
the Fine Structure Constant that vary because the latest findings by
astronomers seem to indicate that the Fine Structure Constant varies
across the universe by about the same amount!

You can read about those findings here:

http://www.science20.com/news_articles/if_

Quoting xilman:

Quote:

We should soon have counts as high as 4e13 and can test Blazys' hypothesis further.

How soon till you post 4e13?

Quoting xilman:

Quote:

If anyone else would like the code... they are welcome to it.

Can you e-mail it to me, or post it here? I would be much obliged.

Quoting xilman:

Quote:

Sadly, I don't think the problem worthy of an further investment of my time.

That's okay, the time you did invest hepled me tremendously,
and I appreciate that very much.
If you want me to credit you for determining $\varpi(10^{13})$ when I publish my findings,
then I would be happy to do that.

Don.

Spherical Cow · 2011-03-11, 21:12

Quote:

Originally Posted by Don Blazys

It's interesting that my approximation function gives us values of
the Fine Structure Constant that vary because the latest findings by
astronomers seem to indicate that the Fine Structure Constant varies
across the universe by about the same amount!

You can read about those findings here:

http://www.science20.com/news_articles/if_

I followed this link, but found nothing on the variation of the fine structure constant. Also did a search on that web site, but turned up nothing. Can you link to the specific article?

Thanks.

Norm

science_man_88 · 2011-03-11, 21:23

Quote:

Originally Posted by Spherical Cow

I followed this link, but found nothing on the variation of the fine structure constant. Also did a search on that web site, but turned up nothing. Can you link to the specific article?

Thanks.

Norm

I think if you search you find:

http://www.science20.com/news_articl...niverse_do_too

xilman · 2011-03-11, 22:23

Quote:

Originally Posted by Don Blazys

Can you e-mail it to me, or post it here? I would be much obliged.

Here you are. AFAIK, this is entirely my coding but has some input from Charles, especially the suggestion to use all 8 bits in each element of a char array for sieving. Charles also provided me with code which segments the array. It is markedly faster than mine when counting up to small limits (where "small" means 1e10 or 1e11 perhaps) but appears to be significantly slower at higher limits. If he wants to post his version, that's for him to decide.

Paul

Spherical Cow · 2011-03-12, 00:16

Quote:

Originally Posted by science_man_88

I think if you search you find:

http://www.science20.com/news_articl...niverse_do_too

Great- thanks for posting that.

Norm

Don Blazys · 2011-03-12, 12:20

Quoting xilman:

Quote:

Here you are. AFAIK, this is entirely my coding but has some input from Charles, especially the suggestion to use all 8 bits in each element of a char array for sieving. Charles also provided me with code which segments the array. It is markedly faster than mine when counting up to small limits (where "small" means 1e10 or 1e11 perhaps) but appears to be significantly slower at higher limits. If he wants to post his version, that's for him to decide.

Paul

Thanks Paul.

CRGreathouse · 2011-03-14, 04:52

Quote:

Originally Posted by Don Blazys

How soon till you post 4e13?

I was calculating it, not Paul (afaik). I've been out of town, but now I'm back. I found
6403626146905 up to 1e13, 12807253029888 up to 2e13, 19210880035763 up to 3e13, 25614507102311 up to 4e13, and 32018134211872 up to 5e13.

science_man_88 · 2011-03-14, 11:27

Quote:

Originally Posted by CRGreathouse

I was calculating it, not Paul (afaik). I've been out of town, but now I'm back. I found
6403626146905 up to 1e13, 12807253029888 up to 2e13, 19210880035763 up to 3e13, 25614507102311 up to 4e13, and 32018134211872 up to 5e13.

blazy for the 4e13 value is off by about 90989 in my calculated value!

xilman · 2011-03-14, 11:40

Quote:

Originally Posted by science_man_88

blazy for the 4e13 value is off by about 90989 in my calculated value!

Can't say I'm surprised. The earlier values were showing hints of a systematic discrepancy.

CRGreathouse · 2011-03-14, 14:10

Quote:

Originally Posted by science_man_88

blazy for the 4e13 value is off by about 90989 in my calculated value!

Thanks for that calculation.

I agree with Paul -- I saw this in the earlier data, though I wasn't sure how far off it would be. (I knew it would be positive and guessed it would be from 50,000 to 100,000.)

I'm not continuing the calculations at the moment. If I get interested in the problem again I have an idea that would probably increase the speed of the program (while keeping its essential linear character). It should be possible to find where the error exceeds a million.

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