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Don Blazys
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Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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 Posted: Tue Mar 09, 2010 6:01 am Post subject: |
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Originally Posted: Sun Feb 21, 2010 3:57 am
If Me/Mp is the electron-proton mass ratio, then:
B(x)-B(x)*a*Me/Mp results in:
_x______w(x)_________B(x)-B(x)*a*Me/Mp____Difference__%Error
10^1___3_______________5_________________ 2_____.666666667
10^2___57______________60________________ 3_____.052631579
10^3___622_____________628_______________ 6_____.009646302
10^4___6,357___________6364_______________7_____.001101148
10^5___63,889__________63,910_____________21____.00032869508
10^6___639,946_________639,963____________17____.00002656474
10^7___6,402,325_______6,402,362___________37____.00000577915
10^8___64,032,121______64,032,274__________153___.00000238943
10^9___640,349,979_____640,350,098_________119___.00000018584
10^10__6,403,587,409___6,403,587,495________86____.00000001343
10^11__64,036,148,166__64,036,148,539_______373___.00000000582
10^12__---------------------_ 640,362,350,541______----____--------------
10^13__---------------------_ 6,403,626,241,270____-----____--------------
Now, the above function that results in the above astonishingly accurate
approximations can be expressed as:
.64036275065348*x - .40011254844227*x^(1/2),
where the numbers .64036275065348 and .40011254844227 can be
called either the "Polygonal number constants" or the "Blazys constants".
However, that does not change the fact that this same exact function
can also be expressed as:
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))-
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))*a*u^(-1)
where a=137.03599908451^(-1)
can be called the "fine structure constant"
and u=1836.152672471880
can be called the "proton to electron mass ratio".
Personally, I find this interesting.
Anybody who thinks that this is not interesting should find
a thread that they do find interesting, and post there.
That's just common sense!
Only fools waste their time reading and posting
on topics that they do not find interesting.
Don. |
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JeffJo
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Joined: 10 Mar 2009
Posts: 1019
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| Posted: Tue Mar 09, 2010 10:47 am Post subject: |
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| Don Blazys wrote: | Now, the above function that results in the above astonishingly accurate approximations can be expressed as:
.64036275065348*x - .40011254844227*x^(1/2),
where the numbers .64036275065348 and .40011254844227 can be called either the "Polygonal number constants" or the "Blazys constants".
However, that does not change the fact that this same exact function can also be expressed as:
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))-
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))*a*u^(-1)
where a=137.03599908451^(-1) can be called the "fine structure constant" and u=1836.152672471880 can be called the "proton to electron mass ratio". |
What hasn't changed, is that the numbers .64036275065348 and .40011254844227 were not chosen because they are necessarily the most accurate coefficients for your function. They were calculated from those expressions for no apparent reason. This is backwards from the way science should be approached. And a clear violation of common sense, which says you draw conclusions from evidence, rather than fit the evidence to the conclusion you want to reach as you are doing.
+++++
[Edit]
Here is a better approach. We know that W(X)~C*X-sqrt(C*X)/2. As X->infinity, the sqrt term becomes negligible realyive to the rest. So J(X)=lim(W(X)/X,X->infinity) is the constant we want. The problem is, to estimate it. We can also estimate C(X) in the full formula directly, by using the quadratic formula.
Here it is:
| Code: | N=Log(X) W J(N) J(N)/J(N-1) C(N) C(N)/C(N-1)
1 3 0.300000000 0.400000000
2 57 0.570000000 1.90000000 0.609019862 1.5225496558
3 622 0.622000000 1.09122807 0.634595590 1.0419948998
4 6,357 0.635700000 1.02202572 0.639699059 1.0080420809
5 63,889 0.638890000 1.00501809 0.640155064 1.0007128428
6 639,946 0.639946000 1.00165287 0.640346108 1.0002984337
7 6,402,325 0.640232500 1.00044769 0.640359027 1.0000201741
8 64,032,121 0.640321210 1.00013856 0.640361221 1.0000034273
9 640,349,979 0.640349979 1.00004493 0.640362632 1.0000022025
10 6,403,587,409 0.640358741 1.00001368 0.640362742 1.0000001723
11 64,036,148,166 0.640361482 1.00000428 0.640362747 1.0000000076 |
You can test how an estimate is converging by taking the ratio of consecutive estimates, as in the 4th and 7th columns above. The fractional part of this ration fits into a nice pattern proportional to sqrt(X), which is hardly surprising. If we continue using the last proportionality constant, J converges to 0.640362749 (which is as much precision I care to attribute here).
The estimate for C(N) is also converging, but with no recognizable pattern. But we might assume that the rest of the coefficients combined will not excede the last one; so using that last one again, C converges to at most 0.640362752. Since we expect that to be high, the previous estimate looks pretty good. Finally, using the J we choose in the counting function yields:
| Code: | N=log(X) W(X) B1(x) Err BJ(X) Err
1 3 5 2 5 2
2 57 60 3 60 3
3 622 628 6 628 6
4 6,357 6,364 7 6,364 7
5 63,889 63,910 21 63,910 21
6 639,946 639,963 17 639,963 17
7 6,402,325 6,402,362 37 6,402,362 37
8 64,032,121 64,032,274 153 64,032,274 153
9 640,349,979 640,350,098 119 640,350,096 117
10 6,403,587,409 6,403,587,495 86 6,403,587,479 70
11 64,036,148,166 64,036,148,539 373 64,036,148,373 207
12 640,362,350,541 640,362,348,887
13 6,403,626,241,268 6,403,626,224,731 |
Here, B1(X) is Don Blazys' second attempt at the function, which is very contrived; and BJ(X) is the first one, but using my constant J. Notes:- BJ(N) does slightly better than B1(N).
- If we use Robert's last estimates for W(10^12) and W(10^13), BJ(N) does much better than B1(N).
- But I don't believe in judging the accuracy based on estimates that are, in part, based on what you are judging the accuracy of. It's silly. So I left them out.
- I corrected one of Don's calculations. I really don't care which was correct, but doing so it made Don's function look better.
- I won't post a "%Error" like Don did because (1) it wasn't in percent, it was a fractional error, and (2) It is meaningless. It goes down more because what you are estimating is going up, than because of your estimation.
- Both of these functions have become erratic predictors around N>8, which could mean nothing. Or it could mean the counting function is wrong. Or it could mean that these high-precision calculations are not right.
- The expression Don has claimed for the constant c=(1-(e^-1)((a*pi+1)^1) is not corect.
- The (1-a/u) correction makes it better, but still not right.
- Better accuracy is obtained by using a correct coefficient in Don's original function, than by using the contrived correction.
- Despite the ad hominem attacks, I do not find this topic interesting. But I do feel the need to discredit the faulty science being foisted on the readers of this list.
[Editing again to get the tables to display, since the preview lied to me]
Last edited by JeffJo on Tue Mar 09, 2010 2:23 pm; edited 4 times in total |
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hogshead
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Joined: 30 Aug 2006
Posts: 577
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| Posted: Tue Mar 09, 2010 12:04 pm Post subject: |
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Don said: | Quote: | Anybody who thinks that this is not interesting should find
a thread that they do find interesting, and post there.
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Just because someone doesn't find a certain aspect of a thread interesting doesn't mean that there might be some other aspect that interests him.
I don't think dis-inviting your critics to the discussion is the best way to get to the truth.
Don, don't you think that any constant could be approximately described in terms of other unrelated constants? |
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ZombiePriest
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Joined: 21 Feb 2010
Posts: 40
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| Posted: Tue Mar 09, 2010 12:12 pm Post subject: |
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So how does the number 23 feature in all this? I'm convinced that it's in there somewhere.
I agree that it is interesting that a dimensionless number takes on a whole new dimension, but this does not seem to teach us anything about polynomials, geometry or maths. Except that there's a constant out there that tells us about the forces between electrons and protons and coincidentally if you chose a large enough polynomial number and perform some hocus pocus numerology you tend to get an error percentage of next to nothing.
This in itself is a remarkable coincidence so perhaps it is worth investigating further for that fact alone, though the maths is far beyond me at this stage. I am curious about the results and what their signifiance is - also how it relates to reality - so good luck! |
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Don Blazys
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Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Wed Mar 10, 2010 7:30 am Post subject: |
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To: JeffJo,
Quoting JeffJo:
| Quote: | | What hasn't changed, is that the numbers .64036275065348 and .40011254844227 were not chosen because they are necessarily the most accurate coefficients for your function. |
They are the most accurate coefficients for my function, period!
Any theory is only as good as it can predict empirical results,
and my function, using those exact same coefficients,
predicted the empirical data that Donk calculated
to a degree of accuracy comparable to that of
approximating the Earths population to within 50 people!
Quoting JeffJo: | Quote: | | This is backwards from the way science should be approached. And a clear violation of common sense, |
Here's how science works young man.
After a sufficient amount of data has been gathered,
theories are put forth and tested...and that's exactly
what happened in this thread!
I put forth the theory that the function involving the
two dimensionless quantities of elementary physics:
B(x)-B(x)*a*u^-1=
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))-
(x-(a*Pi*e+e)^(-1)*x-(1/2)*sqrt(x-(a*Pi*e+e)^(-1)*x))*a*u^(-1) ,
or alternately:
B(x)-B(x)*a*u^-1=
.64036275065348*x - .40011254844227*x^(1/2),
would predict how many polygonal numbers of rank>2
there are under a given number x.
That theory was tested by Donk,
and was demonstrated to be correct!
The result of that test:
__x_________w(x)______B(x)-B(x)*a*u^-1___Difference__%Error
10^11__64,036,148,166__64,036,148,539_______373___.00000000582
confirmed that my theory is true!
Further confirmation will require that coders calculate w(10^12),
and given peoples curiosity, that will happen soon enough...
but with the above data, we can now solve for "a" in my function
and calculate that the fine structure constant is slightly greater than:
137.036062463^-1, which differs from the actual value of the FSC, which is:
137.035999085^-1, by a % of error that is only: -.000000462494238181.
Quoting JeffJo:
| Quote: |
J converges to 0.640362749
C converges to at most 0.640362752
w(10^12)= 640,362,348,887
w(10^12)=6,403,626,224,731 |
My coefficient .64036275065348 is right in between your J and C.
How convenient!
Also, according to your calculations,
my function B(x)-B(x)*a*u^-1
would require that a=137.036026^-1
That's very close to the FSC !
However, my theory requires a=137.035999085^-1
Thus, we must now ask Marilyn to make a phone call to some college or
university that has sufficient computing power to determine w(x) to
x=10^12 and x=10^13. Otherwise, this mystery will remain a mystery.
Quoting JeffJo: | Quote: | | I do not find this topic interesting. |
Well, to the rest of us, you seem downright obsessed with this topic!
Quoting JeffJo: | Quote: | | I do feel the need to discredit the faulty science being foisted on the readers of this list. |
Apparently, you are convinced that the "readers of this list" are
unable to think for themselves and require "saving" from that
"big bad wolf" Don Blazys! Really, you are such a hero!
However, I'm not "foisting" anything on anybody.
This is just a theory that was, and is being tested.
It has already passed one very important test,
and the only possible way to "discredit" it is to give it another.
For that we need a computer powerfull enough to determine w(10^12).
Those who are critical of this theory should "ASK MARILYN"
to use her influence as a columnist to get to the truth of this matter.
Those who are not critical should also "ASK MARILYN" to do that!
Anything short of that is just a waste of time.
To everyone who reads this, PLEASE...WHEN YOU FINISH READING,
SEND MARILYN AN E-MAIL ASKING HER TO SETTLE THIS MATTER!
Don. |
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Don Blazys
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Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Wed Mar 10, 2010 8:02 am Post subject: |
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To: ZombiePriest:
Quoting ZombiePriest: | Quote: | | So how does the number 23 feature in all this? |
Actually, every positive integer >2
is either a polygonal number of rank>2
or a polygonal number of rank 2.
Thus , the function x-B(x)-B(x)*a*u^-1
tells us how many polygonal numbers of rank 2
there are less than a given number x.
23 is a polygonal number of rank 2.
It has all kinds of interesting properties,
but this is a function that applies to all
positive integers >2, either as the approximation of
the set of polygonals of rank >2, or its complement.
Quoting ZombiePriest: | Quote: | | This in itself is a remarkable coincidence so perhaps it is worth investigating further for that fact alone... I am curious about the results and what their signifiance is - also how it relates to reality - so good luck! |
Thanks...  stay tuned!
Don. |
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Don Blazys
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Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Wed Mar 10, 2010 8:30 am Post subject: |
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To Hogshead:
Quoting Hogshead: | Quote: | | I don't think dis-inviting your critics to the discussion is the best way to get to the truth |
.
If the critic provides constructive criticism... then that's okay,
but if the critic simply harangues and muddies up the thread,
well, that's different.
Quoting Hogshead: | Quote: | | Don, don't you think that any constant could be approximately described in terms of other unrelated constants? |
Only to a point. Every constant is and must be unique,
but that wouldn't be the case if it were possible to so describe
any constant to a degree of accuracy that approaches infinity.
Also, such approximations almost never go beyond 3 or 4 digits,
so the 7 digit approximation of the FSC that is implied here is rare indeed.
This function uses only four constants, and they just "happen to be"
the two most important mathematical constants,
and the two most important physical constants.
Thus, this "coincidence" deserves further inverstigation
and any "critic" who tries to thwart and impede this honest
search for the truth will be uninvited.
The jury is still out, and will remain out until w(x) has been determined
to at least x=10^12 and perhaps even x=10^13.
Don.
Last edited by Don Blazys on Thu Mar 11, 2010 1:52 am; edited 2 times in total |
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JeffJo
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Joined: 10 Mar 2009
Posts: 1019
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| Posted: Wed Mar 10, 2010 9:40 am Post subject: |
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| Don Blazys wrote: | Quoting JeffJo:
| Quote: | | What hasn't changed, is that the numbers .64036275065348 and .40011254844227 were not chosen because they are necessarily the most accurate coefficients for your function. |
They are the most accurate coefficients for my function, period! |
Since I found a more accurate set (my J, in your original formula), no they aren't.
| Quote: | | Any theory is only as good as it can predict empirical results, and my function, using those exact same coefficients, predicted the empirical data that Donk calculated to a degree of accuracy comparable to that of approximating the Earths population to within 50 people! |
- You have no theory, you have a conjecture.
- You did not predict anything, you fit your coefficiants to the data after it was found. That proves absolutely nothing.
- Donk's results are not empirical data. If correct, they are the actual values, based of scientific theory. The constants I calculated from Donk's data are empirical.
- It is not amazing - in fact, it can be expected - that you can get this degree of accuracy if you try enough dimensionless constants in enough different combinations when you fit your conjectures to existing data, as you have done.
| Quote: | | I put forth the theory that the function involving the two dimensionless quantities of elementary physics: |
You put forth a conjecture. And as I have repeatedly said, it is meaningless unless you have theories to back up why the dimensionless quantities of elementary physics are related this way.
| Quote: | | However, my theory requires a=137.035999085^-1 |
Your apparently-correct conjecture about the formula "requires" (and that is the wrong word) a constant around 0.64...whatever. Your absurd conjecture about the form of that constant "requires" nothing, unless you have a reason for it to be there. The empirical values I used were better. |
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robert 46
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Joined: 18 Jun 2007
Posts: 1200
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| Posted: Wed Mar 10, 2010 1:48 pm Post subject: |
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Calculating a new projection of w(x) to 10^20, I get a "c" close to Don's modified "c" and much closer to JeffJo's, and a smaller difference which does not go negative until 10^20. However, this is entirely contingent on getting the exact w(x) for the extended range to confirm because my method is very stylized to a first approximation.
| Code: |
10^20 proj. c=0.640362749200832756806961203683 d=0.25
x w(x) Me: B(x)=((c*x)^0.5-d)^2=
0.64036274920083*x-0.40011334306694*x^0.5
Don: B(x)=0.64036275065348*x-0.40011254844227*x^0.5
10^01 3 5 Me 2 Don 5
10^02 57 60 3 60
10^03 622 627 5 628
10^04 6357 6363 6 6364
10^05 63889 63909 20 63910
10^06 639946 639962 16 639963
10^07 6402325 6402362 37 6402362
10^08 64032121 64032273 152 64032274
10^09 640349979 640350096 117 640350098
10^10 6403587409 6403587480 71 6403587495
10^11 64036148166 64036148393 227 64036148539
New w(x) projection can have cumulative errors
12 640362348368 640362349087 719
Don 640362350541 2173
13 6403626224466 6403626226738 2272
Don 6403626241270 16804
14 64036270911767 64036270918949 7182 1.1215e-8%
15 640362736525473 640362736548137 22664 3.5392e-9%
16 6403627451925812 6403627451996993 71181 1.1115e-9%
17 64036274793336150 64036274793556327 220177 3.4383e-10%
18 640362748800072316 640362748800719413 647097 1.0105e-10%
19 6403627490741503411 6403627490743058081 1554670 2.4277e-11%`
20 64036274916082142250 64036274916082142250 0 0 %
proj. w(x) old new old-new
10^12 640362357070 640362348368 8702
10^13 6403626301352 6403626224466 76886
My previous projections for w(10^12) and w(10^13) appear to have been too high.
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Interval, c=
09-10, 0.64036279308256413820600614015348
10-11, 0.64036274919577461010703035810577
11-12, 0.64036274919923682886172155070800
12-13, 0.64036274920120138100322749426044
13-14, 0.64036274920090069952061219210571
14-15, 0.64036274920090499181953768636223
15-16, 0.64036274920090464640446214680386
16-17, 0.64036274920090468133015417893125
17-18, 0.64036274920090465700536517390538
18-19, 0.64036274920090465678836848025334
19-20, 0.64036274920090465649018966009506 |
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Don Blazys
Intellectual
Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Thu Mar 11, 2010 5:07 am Post subject: |
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To: JeffJo,
Quoting Jeffjo: | Quote: | | You did not predict anything, you fit your coefficiants to the data after it was found. |
No, it is you who is the "Johnny Come Lately",
making your results fit the facts (and poorly I might add)
long after the facts are already in!
I, on the other hand, introduced my function B(x)-B(x)*a*Me/Mp
a week in advance of Donks exact count of w(10^11).
Here is the post where I introduce the function B(x)-B(x)*a*Me/Mp,
which is a direct consequence of the function B(x):
| Quote: |
Posted: Sun Feb 21, 2010 3:57 am Post subject: Calculating the Fine Structure Constant.
--------------------------------------------------------------------------------
If Me/Mp is the electron-proton mass ratio, then:
B(x)-B(x)*a*Me/Mp results in:
_x______w(x)_________B(x)-B(x)*a*Me/Mp____Difference__%Error
10^1___3_______________5_________________ 2_____.666666667
10^2___57______________60________________ 3_____.052631579
10^3___622_____________628_______________ 6_____.009646302
10^4___6,357___________6364_______________7_____.001101148
10^5___63,889__________63,910_____________21____.00032869508
10^6___639,946_________639,963____________17____.00002656474
10^7___6,402,325_______6,402,362___________37____.00000577915
10^8___64,032,121______64,032,274__________153___.00000238943
10^9___640,349,979_____640,350,098_________119___.00000018584
10^10__6,403,587,409___6,403,587,495________86____.00000001343
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Note that there is no w(x) or B(x)-B(x)*a*Me/Mp for x=10^11.
Also note the date: (Feb. 21, 2010).
Donk posted his count of w(10^11) exactly 1 week later,
on Sun. Feb. 28, in the Hypography Science Forum.
Comparing Donks count of w(10^11) to B(10^11)-B(10^11)*a*Me/Mp,
we have:
10^11__64,036,148,166___64,036,148,539_____373___.00000000582.
This outrageously good prediction is a matter of record.
Anyone can scroll back to Feb. 21, and Feb. 28 and see for themselves!
Your attempts to obfuscate facts will not work on my thread!
Quoting JeffJo: | Quote: | | Donk's results are not empirical data. |
The word "empirical" means:
"Based on observation rather than theory or principle."
Donks results are clearly based on observation.
He simply programmed his computer and observed the results.
Thus, Donks results are "empirical".
Quoting JeffJo: | Quote: | | The constants I calculated from Donk's data are empirical. |
No!
The constants that you calculated are simply wrong
and are based on "uneducated guesses"!
Thus, they are just plain silly,
and will not even be accurate past x=10^13.
Quoting JeffJo: | Quote: | | It is not amazing - in fact, it can be expected - that you can get this degree of accuracy if you try enough dimensionless constants in enough different combinations when you fit your conjectures to existing data, as you have done. |
Well, for one thing, I'm a working man and I don't have the time to
"try enough dimensionless constants" as you suggest.
However, since you are so certain that "it can be expected",
then perhaps you can provide us with an example!
After all, if my function, which involves only the
two most important dimensionless constants is "contrived",
then surely an intellectual juggernaut such as yourself
should be able to "contrive" an even more accurate function
using as many dimensionless constants and operations as you please!
Quoting JeffJo: | Quote: | | You have no theory, you have a conjecture. |
A theory is a hypothesis or conjecture that has been tested,
and as we all know, my function B(x)-B(x)*a*Me/Mp has been tested.
Moreover, I also have a lower bound prime counting function
that is far more accurate than Li(x) which also requires those constants!
Thus, I have every right to call it a theory,
since both "a" and "u" appear to be necessary
in other "super accurate" approximation functions.
Don. |
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Don Blazys
Intellectual
Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Thu Mar 11, 2010 6:18 am Post subject: |
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To: Robert 46:
Quoting Robert 46: | Quote: | | However, this is entirely contingent on getting the exact w(x) for the extended range to confirm because my method is very stylized to a first approximation |
.
Again, if every reader of this thread were to "ASK MARILYN"
to get involved, then the "soap opera" will end,
and the truth will be known.
Don. |
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JeffJo
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Joined: 10 Mar 2009
Posts: 1019
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| Posted: Thu Mar 11, 2010 9:11 am Post subject: |
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| Don Blazys wrote: | Quoting Jeffjo: | Quote: | | You did not predict anything, you fit your coefficiants to the data after it was found. |
No, it is you who is the "Johnny Come Lately", making your results fit the facts (and poorly I might add) long after the facts are already in!
I, on the other hand, introduced my function B(x)-B(x)*a*Me/Mp a week in advance of Donks exact count of w(10^11). |
Right - you fit that function to the data for W(x) up to x=10^10. You did not predict. And since the "error" for the only new datum does not fit in any pattern that was established? Even if it is smaller, it does not support your assertion that you have a better estimator. One datum cannot prove anything.
| Quote: | Quoting JeffJo: | Quote: | | Donk's results are not empirical data. |
The word "empirical" means:
"Based on observation rather than theory or principle." Donks results are clearly based on observation. He simply programmed his computer and observed the results.
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By that argument, all data is empirical. The real meaning of that definition is that information is based on what can only be observed, not calculated directly from theory or principle. Donk may have obeserved the results, but those results were based on a calculation directly out of the theory of polygonal numbers.
But it is nice of you to demonstrate so clearly how you will twist definitions so that it looks like you are right.
| Quote: | Quoting JeffJo: | Quote: | | It is not amazing - in fact, it can be expected - that you can get this degree of accuracy if you try enough dimensionless constants in enough different combinations when you fit your conjectures to existing data, as you have done. |
Well, for one thing, I'm a working man and I don't have the time to
"try enough dimensionless constants" as you suggest. |
But you claim - and seem to have - an unusual talent for finding them without experimentation. The form of your conjecture seems to work - w(x) ~= c*x - sqrt(c*x)/2. The correction you added merely demonstrates that you did not get the "c"right. You tried to adjust the form, but better accuracy is obtained by adjusting the constant away from your absurd conjecture. |
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Don Blazys
Intellectual
Joined: 20 Feb 2008
Posts: 335
Location: La Crescenta Ca.
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| Posted: Fri Mar 12, 2010 7:45 am Post subject: Calculating the Fine Structure Constant. |
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To: JeffJo,
Quoting JeffJo: | Quote: | | You fit that function to the data for W(x) up to x=10^10. You did not predict. |
I fit that function to the data for w(10^10),
which in turn, allowed me to predict W(10^11).
Moreover, that "fitting" was not "contrived".
It was already clear that the % of error was approaching some constant,
and since my lower bound prime counting function involves both "a" and "u",
I was able ts surmise that the value being approached is indeed a*u^-1.
In other words, (and unlike yourself and Robert 46),
I was not entirely "clueless".
Also, keep in mind that if it were not for the presence of "a" in B(x),
the constant "u" would never have surfaced as it did.
Thus, the function B(x)-B(x)*a*u^-1 is a logical consequence and
extention of the function B(x).
Quoting JeffJo: | Quote: | | Better accuracy is obtained by adjusting the constant away from your absurd conjecture. |
My conjecture is not "absurd". I have a reasonable suspicion that
many "super accurate" counting functions that approximate
sufficiently random or erratic sequences also involve both "a" and "u".
Also, since "Pi" is the limit of how many sides a polygon can have
and "e" is the limit associated with various growth functions,
it should be expected that both "Pi" and "e" would be involved in
counting functions for various classes of polygonal numbers.
However, if we eliminate both "a" and "u" from my function,
then we must also eliminate both "pi" and "e",
which leaves us with two "new" and "poorly understood" constants.
"Pi" and "e" are "mathematical constants often approximated in nature".
"a" and "u" are also "mathematical constants often approximated in nature".
I see no reason why that shouldn't be the case!
You, Robert 45 and I have invested a lot of time studying this function,
and we now have three different projections for w(10^12) and w(10^13).
However, since our projections are not that far apart,
we may have wait for results as high as w(10^14)
before we know which one of us is right.
Thus, we need to focus our efforts on w(x).
Join me in petitioning Marilyn so that she can use her influence
to get some college or university computer dept. to determine
higher values of w(x).
That goes for every reader who is curious and wants to know the truth.
Don. |
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JeffJo
Intellectual
Joined: 10 Mar 2009
Posts: 1019
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| Posted: Fri Mar 12, 2010 8:12 am Post subject: Re: Calculating the Fine Structure Constant. |
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| Don Blazys wrote: | I fit that function to the data for w(10^10),
which in turn, allowed me to predict W(10^11).
Moreover, that "fitting" was not "contrived". |
Then why have you not told us, after repeatedly being asked, why the form is as it is? What is the theroy behind it that makes in "not 'contrived'.?" Because if your only reason is "See how close it is," then that means it is "contrived". That's what "contrived" means. It means you forced to result to fit what you wanted to be fit.
| Quote: | | It was already clear that the % of error was approaching some constant, |
No, the "% of error" was going down, in almost direct proportion to 1/x. The proves nothing by itself, because W(x) is almost in direct proportion to x, and you were getting the "% of error" by dividing actual error - which was oscillating randomly - by w(x).
And you never actually calculated a percentage. Why shoud we beleive anything you speculate about, when you can't even understand what a percentage is, and when it is (or is not, as in this case) a meaningful measurement?
| Quote: | | and since my lower bound prime counting function involves both "a" and "u", |
It did not include "u" until after this process you are claiming justifies the "u." You contrived to put the "u" in, and one datum cannot say anything about the veracity of that contrivance.
| Quote: | | I was not entirely "clueless". |
You seem to be entirely cluelss about what our criticism is.
| Quote: | Quoting JeffJo: | Quote: | | Better accuracy is obtained by adjusting the constant away from your absurd conjecture. |
My conjecture is not "absurd". |
Absurd: "utterly or obviously senseless, illogical, or untrue; contrary to all reason or common sense; laughably foolish or false." I won't claim "untrue" because, just like you, I have no proof it is true or not. But it is utterly senseless, illogical, and contrary to all reason BECAUSE YOU HAVE PROVIDED NO REASON IT IS THERE OTHER THAN "SEE HOW CLOSE IT GETS." And it isn't just the inclusion of these constants we object to, it is the form they take. That is what is contrived.
| Quote: | | However, if we eliminate both "a" and "u" from my function, then we must also eliminate both "pi" and "e", which leaves us with two "new" and "poorly understood" constants. |
No, it means you are left with an empirically-determined constant that is not a known function of anything. Which is all you have.
| Quote: | Join me in petitioning Marilyn so that she can use her influence to get some college or university computer dept. to determine
higher values of w(x). |
Why do you think she has this influence? Why should she care? To do that, she needs a reason to suspect it is right other than "see how close it gets." |
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robert 46
Intellectual
Joined: 18 Jun 2007
Posts: 1200
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| Posted: Fri Mar 12, 2010 11:15 am Post subject: Re: Calculating the Fine Structure Constant. |
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| Don Blazys wrote: | You, Robert 46 and I have invested a lot of time studying this function, and we now have three different projections for w(10^12) and w(10^13).
However, since our projections are not that far apart, we may have wait for results as high as w(10^14) before we know which one of us is right.
Thus, we need to focus our efforts on w(x). |
I've rewritten the program for Turbo Pascal 5.5, and it calculates w(10^9) correctly in 13 1/3 minutes- proving the concept- but crashes due to long int overflows at higher x. If I can get the 8 byte signed int comp type to work I should be able to calculate to higher x.
| Quote: | | Join me in petitioning Marilyn so that she can use her influence to get some college or university computer dept. to determine higher values of w(x). |
Marilyn,
Are you willing to be involved?
Robert |
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