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Question....Good Question.

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  Question....Good Question. "HGWilson, DSc." <hgw@....> - 2016-08-21 09:19 +1000
    Re: Question....Good Question. benj <benj@nobody.net> - 2016-08-20 21:12 -0400
      Re: Question....Good Question. Tom Roberts <tjroberts137@sbcglobal.net> - 2016-08-20 22:28 -0500
    Re: Question....Good Question. "Paul B. Andersen" <relativity@paulba.no> - 2016-08-21 09:07 +0200
      Re: Question....Good Question. "HGWilson, DSc." <hgw@....> - 2016-08-21 19:28 +1000
        Re: Question....Good Question. "Paul B. Andersen" <relativity@paulba.no> - 2016-08-21 13:31 +0200
          Re: Question....Good Question. "HGWilson, DSc." <hgw@....> - 2016-08-22 07:20 +1000
            Re: Question....Good Question. Rafael Valls Hidalgo-Gato <rvalls162@gmail.com> - 2016-08-22 05:38 -0700
              Re: Question....Good Question. "HGWilson, DSc." <hgw@....> - 2016-08-23 05:46 +1000
                Re: Question....Good Question. Rafael Valls Hidalgo-Gato <rvalls162@gmail.com> - 2016-08-22 14:30 -0700
                  Re: Question....Good Question. "HGW." <hw@....> - 2016-08-23 08:11 +1000
                    Re: Question....Good Question. Gary Harnagel <hitlong@yahoo.com> - 2016-08-22 18:41 -0700
            Re: Question....Good Question. "Paul B. Andersen" <relativity@paulba.no> - 2016-08-22 23:07 +0200
        Re: Question....Good Question. Tom Roberts <tjroberts137@sbcglobal.net> - 2016-08-23 09:35 -0500
      Re: Question....Good Question. Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-08-21 11:48 +0200
        Re: Question....Good Question. "Paul B. Andersen" <relativity@paulba.no> - 2016-08-21 14:05 +0200
        Re: Question....Good Question. "HGWilson, DSc." <hgw@....> - 2016-08-22 07:22 +1000

#390464 — Question....Good Question.

It has been claimed by some people here that because light speed has 
been defined accurately, lengths can be now measured with accuracies 
better than 9 significant figures.

Since the same people claim that light moves at c relative to the 
Earth's ECI frame, rather than to its source, does this not mean that a 
rod standardized at the equator would have a different length depending 
on the direction used in the measuring procedure?

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#390465

On 8/20/2016 7:19 PM, HGWilson, DSc. wrote:
> It has been claimed by some people here that because light speed has
> been defined accurately, lengths can be now measured with accuracies
> better than 9 significant figures.
>
> Since the same people claim that light moves at c relative to the
> Earth's ECI frame, rather than to its source, does this not mean that a
> rod standardized at the equator would have a different length depending
> on the direction used in the measuring procedure?

Actually the opposite is true. The fact that there is no aether drift 
means that using light as a measure of length always works. If that were 
not true, then to use light as a standard you'd have to include the 
velocity and direction of the aether with every measurement.

So it is due to MM that the old meter bar has been replaced with a light 
beam. But it's important to note that the constancy of light is just an 
ASSUMPTION so it can be used for length. In fact MM has been repeated a 
few times and in certain cases small but significant aether drifts have 
been measured. So super accuracy is not quite proved.

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#390470

On 8/20/16 8/20/16   8:12 PM, benj wrote:
> So it is due to MM that the old meter bar has been replaced with a light beam.

Not true. It is because hundreds of measurements in the early 1980s showed that 
the errors due to the old definition were unacceptably large. (The old 
definition was based on light from Kr86, not an artifact.)


> But it's important to note that the constancy of light is just an ASSUMPTION so
> it can be used for length.

It's much more than that, as it is an established experimental fact.


> In fact MM has been repeated a few times and in
> certain cases small but significant aether drifts have been measured. So super
> accuracy is not quite proved.

Not true. There are no believable [#] repetitions of the MMX that have 
SIGNIFICANT deviations from a null result. But many of these were made before 
error analysis was common, and were fooled into thinking they observed aether 
drift (e.g. Miller).

	Note we use the word "significant" with different meanings.
	You apparently mean "large enough to notice", while I use
	it with its specific technical meaning: sufficiently larger
	than the errorbars that the result could not reasonably
	happen by chance.

	[#] For instance, experiments in air which did not take
	pains to ensure temperature stability are not believable.
	Nor are experiments that did not measure their systematic
	errors. Here I mean a standard based on TECHNIQUE,
	independent of result.


Tom Roberts

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#390475

On 21.08.2016 01:19, HGWilson, DSc. wrote:
> It has been claimed by some people here that because light speed has
> been defined accurately, lengths can be now measured with accuracies
> better than 9 significant figures.
>
> Since the same people claim that light moves at c relative to the
> Earth's ECI frame, rather than to its source,

Some ignorant people claim that SR say that light moves at
c relative to the Earth's ECI frame, _rather than to its source_.

It is not a matter of opinion what SR say,
it's a matter of fact.

This is what SR say:
https://paulba.no/div/Is_c_invariant.pdf

And what SR say is experimentally well confirmed:

https://paulba.no/paper/Babcock_Bergman.pdf
https://paulba.no/paper/Alvager_et_al.pdf
https://paulba.no/paper/Beckmann_Mandics.pdf
https://paulba.no/paper/Filippas_Fox.pdf
https://paulba.no/paper/Brecher.pdf


> does this not mean that a
> rod standardized at the equator would have a different length depending
> on the direction used in the measuring procedure?

Yes, that does not mean this.

It is remarkable that some ignorant people are
unable to learn that SR say that the speed of
light is invariant.

Down under logic:
SR say the speed of light in vacuum is invariant.
But my blind faith is that the speed of light
can't be invariant.
Therefore must SR say that the speed of light
is not invariant.

-- 
Paul

https://paulba.no/

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#390479

On 21/08/16 17:07, Paul B. Andersen wrote:
> On 21.08.2016 01:19, HGWilson, DSc. wrote:
>> It has been claimed by some people here that because light speed has
>> been defined accurately, lengths can be now measured with accuracies
>> better than 9 significant figures.
>>
>> Since the same people claim that light moves at c relative to the
>> Earth's ECI frame, rather than to its source,
>
> Some ignorant people claim that SR say that light moves at
> c relative to the Earth's ECI frame, _rather than to its source_.

Here is a quote from Tom Roberts, today: The GPS demonstrates that the 
vacuum speed of light is isotropically c in the ECI frame, which is the 
LOCALLY inertial frame centered on the earth (so it does not rotate with 
the planet, but does orbit the sun with it).

Are you agreeing that Tom sprouts endless bullshit?...or is it you who does?


>
>> does this not mean that a
>> rod standardized at the equator would have a different length depending
>> on the direction used in the measuring procedure?
>
> Yes, that does not mean this.

According to Tom Roberts, you are talking bullshit.

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#390489

On 21.08.2016 11:28, HGWilson, DSc. wrote:
> On 21/08/16 17:07, Paul B. Andersen wrote:
>> On 21.08.2016 01:19, HGWilson, DSc. wrote:
>>> It has been claimed by some people here that because light speed has
>>> been defined accurately, lengths can be now measured with accuracies
>>> better than 9 significant figures.
>>>
>>> Since the same people claim that light moves at c relative to the
>>> Earth's ECI frame, rather than to its source,
>>
>> Some ignorant people claim that SR say that light moves at
>> c relative to the Earth's ECI frame, _rather than to its source_.

The point which some ignorant people may have managed to miss is:

The statement:
  "Since the same people claim that light moves at c relative
   to the Earth's ECI frame, rather than to its source"
suggests that "the same people" claim that the speed of light
is not c relative to its source which is moving in the ECI frame.

But "the same people" don't claim that. They claim:

   The speed of light is isotropic c in the ECI frame,
   _and_ it is isotropic c in the momentarily comoving inertial
   frame of the source.

Or more loosely:

   Light moves at c relative to the Earth's ECI frame,
   AND it moves at c relative to its source.

>> It is not a matter of opinion what SR say,
>> it's a matter of fact.
>>
>> This is what SR say:
>> https://paulba.no/div/Is_c_invariant.pdf
>>
>> And what SR say is experimentally well confirmed:
>>
>> https://paulba.no/paper/Babcock_Bergman.pdf
>> https://paulba.no/paper/Alvager_et_al.pdf
>> https://paulba.no/paper/Beckmann_Mandics.pdf
>> https://paulba.no/paper/Filippas_Fox.pdf
>> https://paulba.no/paper/Brecher.pdf
>>
>
> Here is a quote from Tom Roberts, today: The GPS demonstrates that the
> vacuum speed of light is isotropically c in the ECI frame, which is the
> LOCALLY inertial frame centered on the earth (so it does not rotate with
> the planet, but does orbit the sun with it).

Quite.
The GPS is another ever ongoing experiment which
is confirming that the speed of light is isotropically c
in the ECI frame.

> Are you agreeing that Tom sprouts endless bullshit?...or is it you who
> does?

After 35+ years of operation of the GPS Tom's statement above
is a trivial truth, so what is your point?

>>
>>> does this not mean that a
>>> rod standardized at the equator would have a different length depending
>>> on the direction used in the measuring procedure?
>>
>> Yes, that does not mean this.
>
> According to Tom Roberts, you are talking bullshit.

Good grief. :-D
You are actually claiming that Tom would say
I am talking bullshit when I claim that according
to SR the speed of light in vacuum is invariant!

Congratulation, Ralph.
I think you must have broken some kind of a record.

>>
>> It is remarkable that some ignorant people are
>> unable to learn that SR say that the speed of
>> light is invariant.
>>
>> Down under logic:
>> SR say the speed of light in vacuum is invariant.
>> But my blind faith is that the speed of light
>> can't be invariant.
>> Therefore must SR say that the speed of light
>> is not invariant.
>>


-- 
Paul

https://paulba.no/

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#390515

On 21/08/16 21:31, Paul B. Andersen wrote:
> On 21.08.2016 11:28, HGWilson, DSc. wrote:
>> On 21/08/16 17:07, Paul B. Andersen wrote:
>
>>>> Since the same people claim that light moves at c relative to the
>>>> Earth's ECI frame, rather than to its source,
>>>
>>> Some ignorant people claim that SR say that light moves at
>>> c relative to the Earth's ECI frame, _rather than to its source_.
>
> The point which some ignorant people may have managed to miss is:
>
> The statement:
>   "Since the same people claim that light moves at c relative
>    to the Earth's ECI frame, rather than to its source"
> suggests that "the same people" claim that the speed of light
> is not c relative to its source which is moving in the ECI frame.
>
> But "the same people" don't claim that. They claim:
>
>    The speed of light is isotropic c in the ECI frame,
>    _and_ it is isotropic c in the momentarily comoving inertial
>    frame of the source.
>
> Or more loosely:
>
>    Light moves at c relative to the Earth's ECI frame,
>    AND it moves at c relative to its source.

To an observer at rest in the earth's ECI frame, the light moves at c+v 
relative to the source. (as illustrated in a ring gyro for instance 
where the two beams depart the source at c+v and c-v in the non-rotating 
frame.)
...but the sun's ECI frame, is moving relative to the Earth's...so an 
observer at rest in the Sun's frame will see it depart at c+u.
How does the light know in which of the two frames is it supposed to 
move at c?
If you are now going to say simply that it always moves at c in any 
frame, and that an observer at rest in either the sun's or the Earth's 
ECI frame will see a light pulse departing from its source at the same 
c+x then all that crap about the GPS signals moving at c in the Earth's 
ECI frame is completely irrelevant. There is nothing special about any 
ECI frame.


>> Here is a quote from Tom Roberts, today: The GPS demonstrates that the
>> vacuum speed of light is isotropically c in the ECI frame, which is the
>> LOCALLY inertial frame centered on the earth (so it does not rotate with
>> the planet, but does orbit the sun with it).
>
> Quite.
> The GPS is another ever ongoing experiment which
> is confirming that the speed of light is isotropically c
> in the ECI frame.

That's what Ken Seto says...and you all laugh at him.

>> Are you agreeing that Tom sprouts endless bullshit?...or is it you who
>> does?
>
> After 35+ years of operation of the GPS Tom's statement above
> is a trivial truth, so what is your point?
>
>>>
>>>> does this not mean that a
>>>> rod standardized at the equator would have a different length depending
>>>> on the direction used in the measuring procedure?
>>>
>>> Yes, that does not mean this.
>>
>> According to Tom Roberts, you are talking bullshit.
>
> Good grief. :-D
> You are actually claiming that Tom would say
> I am talking bullshit when I claim that according
> to SR the speed of light in vacuum is invariant!

Light has no 'speed' in vacuum or anything else. All speeds are relative.

> Congratulation, Ralph.

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#390568

El domingo, 21 de agosto de 2016, 17:20:02 (UTC-4), HGWilson, DSc.  escribió:
> On 21/08/16 21:31, Paul B. Andersen wrote:
> > On 21.08.2016 11:28, HGWilson, DSc. wrote:
> >> On 21/08/16 17:07, Paul B. Andersen wrote:
> >
> >>>> Since the same people claim that light moves at c relative to the
> >>>> Earth's ECI frame, rather than to its source,
> >>>
> >>> Some ignorant people claim that SR say that light moves at
> >>> c relative to the Earth's ECI frame, _rather than to its source_.
> >
> > The point which some ignorant people may have managed to miss is:
> >
> > The statement:
> >   "Since the same people claim that light moves at c relative
> >    to the Earth's ECI frame, rather than to its source"
> > suggests that "the same people" claim that the speed of light
> > is not c relative to its source which is moving in the ECI frame.
> >
> > But "the same people" don't claim that. They claim:
> >
> >    The speed of light is isotropic c in the ECI frame,
> >    _and_ it is isotropic c in the momentarily comoving inertial
> >    frame of the source.
> >
> > Or more loosely:
> >
> >    Light moves at c relative to the Earth's ECI frame,
> >    AND it moves at c relative to its source.
> 
> To an observer at rest in the earth's ECI frame, the light moves at c+v 
> relative to the source. (as illustrated in a ring gyro for instance 
> where the two beams depart the source at c+v and c-v in the non-rotating 
> frame.)
> ...but the sun's ECI frame, is moving relative to the Earth's...so an 
> observer at rest in the Sun's frame will see it depart at c+u.
> How does the light know in which of the two frames is it supposed to 
> move at c?

Since the GPS very good operation, isotropic light speed c in the ECI is a well
established experimental fact. Have you any objection to that?

See the following thread in this same group:

Selected list of well established experimental facts by the GPS operation
https://groups.google.com/forum/#!topic/sci.physics.relativity/xMHRGCzFbRM

Please, can you specify from where do you take the "sun's ECI frame" concept
that you are mentioning here? In the context of what theory or conception are 
you using it? Maybe the Ptolemy's one?

> If you are now going to say simply that it always moves at c in any 
> frame, and that an observer at rest in either the sun's or the Earth's 
> ECI frame will see a light pulse departing from its source at the same 
> c+x then all that crap about the GPS signals moving at c in the Earth's 
> ECI frame is completely irrelevant. There is nothing special about any 
> ECI frame.
> 
Who refer to more tan one ECI frame? Maybe you identify "ECI frames" with the
infinite inertial frames of today Special Relativity (SR)?

RVHG (Rafael Valls Hidalgo-Gato)

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#390588

On 22/08/16 22:38, Rafael Valls Hidalgo-Gato wrote:
> El domingo, 21 de agosto de 2016, 17:20:02 (UTC-4), HGWilson, DSc.  escribió:
>> On 21/08/16 21:31, Paul B. Andersen wrote:

>>>     Light moves at c relative to the Earth's ECI frame,
>>>     AND it moves at c relative to its source.
>>
>> To an observer at rest in the earth's ECI frame, the light moves at c+v
>> relative to the source. (as illustrated in a ring gyro for instance
>> where the two beams depart the source at c+v and c-v in the non-rotating
>> frame.)
>> ...but the sun's ECI frame, is moving relative to the Earth's...so an
>> observer at rest in the Sun's frame will see it depart at c+u.
>> How does the light know in which of the two frames is it supposed to
>> move at c?
>
> Since the GPS very good operation, isotropic light speed c in the ECI is a well
> established experimental fact. Have you any objection to that?

Yes. It has nothing to do with the ECI frame. The GPS system works 
simply because all orbiting clocks are in absolute synch and each orbit 
ephemeris is very accurately known.

> See the following thread in this same group:
>
> Selected list of well established experimental facts by the GPS operation
> https://groups.google.com/forum/#!topic/sci.physics.relativity/xMHRGCzFbRM
>
> Please, can you specify from where do you take the "sun's ECI frame" concept
> that you are mentioning here? In the context of what theory or conception are
> you using it? Maybe the Ptolemy's one?

An emitted photon moving at c relative to the earth's ECI frame will not 
move at the same speed as one emitted by the same source at c relative 
to the Sun's ECI frame. That should be obvious.

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#390601

El lunes, 22 de agosto de 2016, 15:46:35 (UTC-4), HGWilson, DSc.  escribió:
> On 22/08/16 22:38, Rafael Valls Hidalgo-Gato wrote:
> > El domingo, 21 de agosto de 2016, 17:20:02 (UTC-4), HGWilson, DSc.  escribió:
> >> On 21/08/16 21:31, Paul B. Andersen wrote:
> 
> >>>     Light moves at c relative to the Earth's ECI frame,
> >>>     AND it moves at c relative to its source.
> >>
> >> To an observer at rest in the earth's ECI frame, the light moves at c+v
> >> relative to the source. (as illustrated in a ring gyro for instance
> >> where the two beams depart the source at c+v and c-v in the non-rotating
> >> frame.)
> >> ...but the sun's ECI frame, is moving relative to the Earth's...so an
> >> observer at rest in the Sun's frame will see it depart at c+u.
> >> How does the light know in which of the two frames is it supposed to
> >> move at c?
> >
> > Since the GPS very good operation, isotropic light speed c in the ECI is a well
> > established experimental fact. Have you any objection to that?
> 
> Yes. It has nothing to do with the ECI frame. The GPS system works 
> simply because all orbiting clocks are in absolute synch and each orbit 
> ephemeris is very accurately known.
> 
> > See the following thread in this same group:
> >
> > Selected list of well established experimental facts by the GPS operation
> > https://groups.google.com/forum/#!topic/sci.physics.relativity/xMHRGCzFbRM
> >
> > Please, can you specify from where do you take the "sun's ECI frame" concept
> > that you are mentioning here? In the context of what theory or conception are
> > you using it? Maybe the Ptolemy's one?
> 
> An emitted photon moving at c relative to the earth's ECI frame will not 
> move at the same speed as one emitted by the same source at c relative 
> to the Sun's ECI frame. That should be obvious.

What is for you "Sun's ECI frame"? What theory (following you) uses that
concept? Maybe the today Special Relativity (SR)? Are you totally unable to 
explain others the meaning of what yourself write?

RVHG (Rafael Valls Hidalgo-Gato)

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#390606

On 23/08/16 07:30, Rafael Valls Hidalgo-Gato wrote:
> El lunes, 22 de agosto de 2016, 15:46:35 (UTC-4), HGWilson, DSc.  escribió:
>> On 22/08/16 22:38, Rafael Valls Hidalgo-Gato wrote:

>>>
>>> Please, can you specify from where do you take the "sun's ECI frame" concept
>>> that you are mentioning here? In the context of what theory or conception are
>>> you using it? Maybe the Ptolemy's one?
>>
>> An emitted photon moving at c relative to the earth's ECI frame will not
>> move at the same speed as one emitted by the same source at c relative
>> to the Sun's ECI frame. That should be obvious.
>
> What is for you "Sun's ECI frame"?

Don't you know the answer to that? Then you should not be posting here..

What theory (following you) uses that
> concept? Maybe the today Special Relativity (SR)? Are you totally unable to
> explain others the meaning of what yourself write?
>
> RVHG (Rafael Valls Hidalgo-Gato)
>


-- 

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#390617

On Monday, August 22, 2016 at 4:11:42 PM UTC-6, HGW. wrote:
>
> On 23/08/16 07:30, Rafael Valls Hidalgo-Gato wrote:
> >
> > El lunes, 22 de agosto de 2016, 15:46:35 (UTC-4), HGWilson, DSc.  escribió:
> > >
> > > An emitted photon moving at c relative to the earth's ECI frame will not
> > > move at the same speed as one emitted by the same source at c relative
> > > to the Sun's ECI frame. That should be obvious.
> >
> > What is for you "Sun's ECI frame"?
> 
> Don't you know the answer to that? Then you should not be posting here..

YOU are the one that shouldn't be posting here.  There is NO such thing
as the "Sun's ECI frame" since "ECI" stands for "Earth-Centered Inertial"

The sun-centered inertial frame is called the heliocentric inertial frame.

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#390599

On 21.08.2016 23:20, HGWilson, DSc. wrote:
> On 21/08/16 21:31, Paul B. Andersen wrote:
>> On 21.08.2016 11:28, HGWilson, DSc. wrote:
>>>
>>> According to Tom Roberts, you are talking bullshit.
>>
>> Good grief. :-D
>> You are actually claiming that Tom would say
>> I am talking bullshit when I claim that according
>> to SR the speed of light in vacuum is invariant!
>
> Light has no 'speed' in vacuum or anything else. All speeds are relative.
>

And that statement proves that Tom would say I am talking bullshit
when I claim that according to SR the speed of light in vacuum
is invariant? :-D

>> Congratulation, Ralph.
>> I think you must have broken some kind of a record.

-- 
Paul

https://paulba.no/

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#390649

On 8/21/16 8/21/16 - 4:28 AM, HGWilson, DSc. wrote:
> According to Tom Roberts, you are talking bullshit.

You are completely and utterly incompetent to ascribe what I say to others. The 
bullshit is YOURS.

Tom Roberts

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#390481

Paul B. Andersen wrote:

> […]
> This is what SR say:

_says_ (third-person singular simple present of “(to) say”), because it is 
*one* item: (the) special (theory of) relativity.  [“(to) say” is used 
figuratively here, meaning “to indicate in a written form”.]

<https://en.wiktionary.org/wiki/say#Verb>

> https://paulba.no/div/Is_c_invariant.pdf

Should be _pseudonym_, not “synonym”.

A *synonym* of an original word is another word that has the same or nearly 
the same meaning as the original word (from Ancient Greek σύν /syn/ “with”, 
ὄνομα /ónoma/ “name”). 

<https://en.wikipedia.org/wiki/Synonym>
<https://en.wiktionary.org/wiki/synonym#English>

A *pseudonym* (*synonym*: alias) is a *name*, different from a person’s or 
group’s real name, assumed for a particular purpose (from Greek ψευδώνυμον 
/pseudṓnymon/, from ψεῦδος /pseûdos/ “lie, falsehood”; and ὄνομα /ónoma/ 
“name”).

<https://en.wikipedia.org/wiki/Pseudonym>
<https://en.wiktionary.org/wiki/pseudonym#English>

There are other linguistic errors in your texts.  I recommend to you that 
you proofread your writings in that regard.  English is not my native 
language, but I am very good at it (like CEFR C1), so I can help you there.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#390491

On 21.08.2016 11:48, Thomas 'PointedEars' Lahn wrote:
> Paul B. Andersen wrote:
>
>> […]
>> This is what SR say:
>
> _says_ (third-person singular simple present of “(to) say”), because it is
> *one* item: (the) special (theory of) relativity.  [“(to) say” is used
> figuratively here, meaning “to indicate in a written form”.]

Yes, I know better.
But I will probably keep doing this error from time to time. :-(

>> https://paulba.no/div/Is_c_invariant.pdf
>
> Should be _pseudonym_, not “synonym”.

This is a typo. I know the difference.
If you look at other papers like:
https://paulba.no/div/RalphsParadox.pdf
you will see that I have got it right.

But thanks for catching it.
It is now corrected.

>
> There are other linguistic errors in your texts.  I recommend to you that
> you proofread your writings in that regard.  English is not my native
> language, but I am very good at it (like CEFR C1), so I can help you there.
>

If you would point out linguistic errors in any
of my papers, I would be much obliged.
But please use email to relativity@paulba.no

-- 
Paul

https://paulba.no/

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#390516

On 21/08/16 19:48, Thomas 'PointedEars' Lahn wrote:
> Paul B. Andersen wrote:
>
>> […]
>> This is what SR say:
>
> _says_ (third-person singular simple present of “(to) say”), because it is
> *one* item: (the) special (theory of) relativity.  [“(to) say” is used
> figuratively here, meaning “to indicate in a written form”.]
>
> <https://en.wiktionary.org/wiki/say#Verb>
>
>> https://paulba.no/div/Is_c_invariant.pdf
>
> Should be _pseudonym_, not “synonym”.

Paul's grammatical errors pale to insignificance compared to those of 
his logic.

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