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03-23-2010, 08:14 AM   #796
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QuoteOriginally posted by falconeye Quote
1. Please, get the part about crop factors right. Ken did make no mistake in computing 55/43=1.27 as the rations of diagonals of 645D vs 35mm. Also, crop factors are >1 by definition as being relative to a mount's full image diagonal (i.e., not 0.8). If you must compare to 35mm, call it conversion factor instead.
Ken Rockwell based his sensor comparison on his faulty mathematics.

Comparing diagonals only makes sense when the rectangles in question have the same aspect ratio. i.e. it only makes sense compare diagonals of a 3:2 sensor vs another 3:2 sensor, a 4:3 sensor vs another 4:3 sensor, a 4:3 monitor vs another 4:3 monitor, a 16:9 LCD vs another 16:9 plasma, etc.

It is because when we compare the ratio between linear dimensions, the ratio between the areas is guaranteed to be the square thereof - and when we compare sensor sizes, the fundamental measurement is between area - comparing linearly is only a convenient measure.

16x24 = 384, sqrt(16x16+24x24) ~ 28.8
24x36 = 864, sqrt(24x24+36x36) ~ 43.3

864/384 = 2.25 ~ (43.3/28.8)x(43.3/28.8)

In fact, we don't even need to calculate the areas or even the diagonals to see an FF sensor is 2.25 times the area of an APS-C sensor, because we can measure one side of each sensor and square the quotient: (24/16)*(24/16) = 2.25.

However, this guarantee falls apart the moment we start to compare linear dimensions between shapes that aren't similar, e.g. rectangles with different aspect ratio.

To illustrate this point, imagine someone makes a sensor of size 1mm x 100mm. Its diagonal length is about 100mm (more than double the FF sensor diagonal!!) but its area is only 100mm squared (only a quarter of APS-C sensor area!!)

If you say my example is too imaginary and that nobody will ever make a 1mm x 100mm sensor, how about if somebody makes a 16:9 sensor with size 39mm x 22mm. Now its diagonal is 44.8 mm, slightly but clearly longer than FF's diagonal. However, its area is now 858 mm squared, also slightly but clearly smaller than FF's area.

So in terms of area, the meaningful measurement of light-collecting ability, this 16:9 sensor is smaller than an FF sensor, but with Ken-Rockwell-Logic (TM), it would seem that the 16:9 sensor is larger than an FF sensor.

Demonstrably, Ken either does not know enough photography to understand the photographic reason behind linear dimension comparisons, or maybe he understands, but screwed up his calculations with his sorry high-school-failing mathematics.


Last edited by wolfier; 03-23-2010 at 08:36 AM.
03-23-2010, 08:40 AM   #797
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QuoteOriginally posted by wolfier Quote
Comparing diagonals only makes sense when the rectangles in question have the same aspect ratio.
I am always for critics if it is appropriate. And here, it is inappropriate.

If you compare (a,b) with (a',b'), you got many options for a factor, based on, e.g.:

a*b [surface]
sqrt(a*b) [geometric mean]
sqrt(a^2+b^2) [2-norm aka euclidian norm aka diagonal]
|a|+|b| [1-norm aka mean]
1/(1/|a|+1/|b|) [-1-norm]
...

There is no good or bad choice. Ken took his. To criticise this is childish.

The euclidian norm is a common choice in the photographic industry too because it is the factor which determines optics. One is typically quoting the (linear) factor in diagonal and/or the (square) factor in surface.


P.S.
A 100x1mm sensor with 40MP would be a damned cool thing with 65k pixels in one dimension
(I know what you wanted to say. But the argument only applies as long as you assume a given target aspect ratio)

Last edited by falconeye; 03-23-2010 at 08:55 AM.
03-23-2010, 08:44 AM   #798
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QuoteOriginally posted by wolfier Quote
So in terms of area, the meaningful measurement of light-collecting ability, this 16:9 sensor is smaller than an FF sensor, but with Ken-Rockwell-Logic (TM), it would seem that the 16:9 sensor is larger than an FF sensor.
You make some good points here. In order to have a similar measure to "crop" which applies across different aspect ratios, I suggest that we simply use the square root of the area ratio. With this calculation, 24x36 is "1.3 crop" wrt. 645D (i.e. not 1.27).

Or, if we agree on 24x36 having the value 1, we get APS-C as 1.5-1.6 crop and 645D as 0.77 crop.
03-23-2010, 09:28 AM   #799
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QuoteOriginally posted by falconeye Quote
I am always for critics if it is appropriate. And here, it is inappropriate.

If you compare (a,b) with (a',b'), you got many options for a factor, based on, e.g.:

a*b [surface]
sqrt(a*b) [geometric mean]
sqrt(a^2+b^2) [2-norm aka euclidian norm aka diagonal]
|a|+|b| [1-norm aka mean]
1/(1/|a|+1/|b|) [-1-norm]
...

There is no good or bad choice.

...

The euclidian norm is a common choice in the photographic industry too because it is the factor which determines optics. One is typically quoting the (linear) factor in diagonal and/or the (square) factor in surface.
In this context, he is specifically referring to the "size" of light-collecting sensors, with the intent to compare light collection ability. In this sense, area is the only meaningful measurement. Yes you can compare points on the plane using Geometric, Harmonic, Quadratic Arithmetic means of their Euclidean (or Polar, not that I care...) coordinates, but among these, only the Geometic Mean of the perpendicular dimensions makes sense in this context, because it's directly related to the area.

The diagonal measure can make sense in thousands of other places in the photographic industry - but when we compare light-collecting ability of sensors, it is the wrong measure.

QuoteQuote:
Ken took his. To criticise this is childish.
He took his choice, but not any arbitrary choice is correct and his just happens to be one of the wrong measures.

QuoteQuote:
P.S.
A 100x1mm sensor with 40MP would be a damned cool thing with 65k pixels in one dimension
(I know what you wanted to say. But the argument only applies as long as you assume a given target aspect ratio)
At least we agree that a 100x1mm sensor is cool

03-23-2010, 03:23 PM   #800
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QuoteOriginally posted by wolfier Quote
In this context, he is specifically referring to the "size" of light-collecting sensors, with the intent to compare light collection ability.
If this were the case, I would agree.
Ken writes "the Pentax' 33 x 44mm sensor isn't much bigger than 24 x 36mm; only 27% bigger linearly". And as such, this sentence isn't wrong. I would have put it differently (like you, or using words 'diagonal' or '+30%'). But that's an author's freedom.

I only say so because the majority of Ken's article is so unbelievably BS (like "amateur 3:2 aspect ratio" ) that critics should focus on the really weak parts. 'Nough said.
03-23-2010, 04:06 PM   #801
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KR makes money on hits. It's that simple. He stirs the pot and rake in the advertising as people link to him from all over.

Though I have to say am greatly disappointed that California didn't pass that bill.
03-24-2010, 01:39 AM   #802
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I thought this wasn't the thread for anal maths, falcon.
03-24-2010, 05:13 AM   #803
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QuoteOriginally posted by omega leader Quote
KR makes money on hits. It's that simple. He stirs the pot and rake in the advertising as people link to him from all over.
He responded to my open letter just to get a link in to his site, which my original article avoided. But I am not one to deny the right to reply, even if it is the same line he spins out endlessly. Put all the evidence out there and let people judge for themselves. He makes no money off people reading a page, unless they click an advert.

03-24-2010, 05:16 AM   #804
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QuoteOriginally posted by lithos Quote
I thought this wasn't the thread for anal maths, falcon.
This is all in reaction to post #546, the open letter by rparmar. He improved his letter since (thanks to rparmar!) but wolfier choose to challenge me

lithos, btw I don't like your wording here. I'll ignore it which the ignore function may automate for me.
03-24-2010, 05:22 AM   #805
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QuoteOriginally posted by rparmar Quote
He responded to my open letter
Congratulations!
So, you got your letter delivered

BTW, did you remove the back link? I don't see it in his reply.

The real purpose of crosslinks of course is to be ranked higher in search engines. So, even if none of the readers click a linked ad, he still benefits from the link.
03-24-2010, 06:16 AM   #806
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The link is in his name tag.
Edit: I didn't click it.
03-24-2010, 07:34 AM   #807
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QuoteOriginally posted by lithos Quote
I thought this wasn't the thread for anal maths, falcon.

That sounds like the engineering of a robotics procto exam.

Yikes
03-24-2010, 08:00 AM   #808
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QuoteOriginally posted by falconeye Quote
The real purpose of crosslinks of course is to be ranked higher in search engines. So, even if none of the readers click a linked ad, he still benefits from the link.
This is true. But it still comes to nothing if no-one clicks an ad. Just more disgruntled people hitting his site and getting misinformed.
03-24-2010, 08:55 AM   #809
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QuoteOriginally posted by omega leader Quote
KR makes money on hits. It's that simple. He stirs the pot and rake in the advertising as people link to him from all over.
Yes, that's what it's all about exactly. He even more or less admits on his site that not everything should be taken quite seriously and that he needs the ad revenues to support his growing family. So I really wonder why do we keep on talking about this guy and his "reviews" page after page?
03-24-2010, 09:09 AM   #810
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The problem that I have with Ken Rockwell (and this is a little different from the theme of this thread, but Oh well...) is that he speaks with a lot of confidence, but apparently little knowledge. There was a time when I thought he knew everything. "Ken Rockwell says you don't need to use a tripod, I guess I'll stop using tripods." "Ken Rockwell says that film is as good as digital." Ken Rockwell says that digital is better than film." (still haven't figured out how to reconcile those last two).

Photographers who don't understand the basics can be completely misguided on how to take good photos by reading his site. I really don't care about his reviews of equipment -- they are generally pretty useless, but his articles on how to do things photographically are not helpful and can actually be destructive to good photographic technique.
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