tupp

Look, if you flip the terms of the equation the only thing equivalency will tell you is how to get the same diameter lens with different focal lengths. It's simply a number that relates things to each other and make them comparable.
You are 100% correct in that I think it's not that relevant and as you have shown lens construction or "features" is more important. However the lenses you showed do NOT have the same aperture which is evident in the upper right corner, I would suspect that f4 is the "mean" aperture of the apodization filter which makes sense as you loose light to the darkened edges of the filter. I do like the idea of such a filter and want to try to make one for my 50mm f1.4 that have aperture to "spare" so to speak.

For what the equivalency formula is it holds true, but at the same time you have to understand what it does not do.
 

I still dont understand what you want to prove.
Same lens with focal reducer on smaller sensor will give the same look. 
Different but faster lens will not give you same look but not because of the sensor, but the characteristics of the lens.
Focus fall-off is lens dependant. Helios 44m-4 will give more creamy blur than Zeiss 55 1.8. Panasonic 25 F1.4 will never be as creamy as Carl Zeiss Jenna Tessar 2.8/50. But not because of the sensor size... SLR Magic 25 F0.95 will be smoother than Canon 50 1.8 STM... it's all about lens characteristics.
 

Bravissimo brotha', you can tell a difference between a lens manufactured by Sony and a lens manufactured by Voigtlaender. Sick skillZ!
If he use the same lens with focal reducer you will not see any difference between the two images. I have tried it.

Oblique rays strike the center of the image as well as the corners.  These are aperture dependent and are called marginal rays.  The relationship between f-number and the marginal ray angle is given by f/# = sin(theta), where theta is the marginal ray angle.  So, at f/1 the marginal ray angle is 30 degrees, and so on.
The obliquity of the marginal ray does cause a form of pixel vignetting that perhaps should be called pixel apodization.  The effect is that the edges of bokeh blurs - where the marginal ray obliquity is highest - is darkened relative to the center.  The good news is that this is the definition of "good bokeh".
I think Andrew's two sample images reveal this effect.  I would guess that the bottom image was shot with the faster lens.
 

It is fighting physics.  There are manufacturing limitations when grinding and polishing glass as well as manufacturing limitations as to how perfectly you can align and space each of the elements correctly.  Optical designers only have a limited range of glass types to use.  Eventually tolerances, manufacturing limitations and material availability/costs mean it's a technical and/or economic impossibility to match the performance you get from a simple longer/slower lens on a bigger sensor.  If sensor size didn't make a difference to the image we wouldn't see Arri, Sony, and RED all moving to FF / VV and bigger as their flagship camera systems.  

I use them for stills too.  No complaints here.  My Oly 2.8 pro lens does render a little more detail if one is pixel peeping, but nothing I've noticed to be remarkable compared to 2.8 on the Voights.
Anyway, this is the most EOSHD'y of EOSHD topics.  The great debate among camera nerds.  As if sensor size one way or another really matters to people that actually shoot stuff that gets used for any real purpose.  
I mean, I have footage from my old XH-A1 that rivals most of the footage I shot this year.  I certainly have my own preferences for shooting FF and like it, but ultimately it's not going to make a big difference on what is shot and deliver on a job.*  
Just curious, but aside from something needed in extreme low-light situations, can anyone here provide an example where what they did on M43 or FF would ultimately matter a hulluva lot to the client?
*to the people I usually gig for anyway

Ummmm....

If you look at Nikon lenses the large flange distance means the angle can't be too high simply due to the distance. (ignore the wonky ultra wide angle that had a long element stick in under the mirror).
Sony on the other hand had a huge problem with the a7s giving a red cast with some wide angle lenses.

I'm in that camp, the B85 has swirly cat-eye bokeh wide open - especially when the background is trees/foliage. I much prefer the FE 85. The B135 does the same thing, hate it. The B25 and B18 OTOH are flat out awesome. I have the FE 28 and 85, and sold the Batis 25/85 to get them.
The Huff comparison demonstrates exactly what some make so overly complicated - play the equivalence game with aperture/FL and you get the exact same image across various sensor sizes. Though Huff's fanboy "Olympus has better rendering" with a drill shot is just silly.
FF's advantage over m43 is even with a moderate aperture lens like a 1.8, you get DOF that requires pretty expensive m43 glass. With the cost of top shelf m43 and aps-c bodies hitting $2000, you really have to evaluate the entire system and your needs because the difference in price isn't that much - especially if you're buying f/1.8's in FF-land and faster glass in m43-land.
Used prices also level the playing field quite a bit. I saw an a9 for $2600, a7r3's are dropping to about that level too. Other bodies are far less. If you're shopping Sony, the F/4 zooms have been around awhile and so on.
Cheers
Chris

Ok than If you look the initial provided comparison in A. Read's article, apart of nominal/objective perspective equivalence it is also noticeable (as one poster already noted) that aesthetic impression of depth of field is not the same. Plans in perspective looks closer or further, so in one case there's impression of stronger 3d quality, or a even deeper background in whole. That is result of inner construction qualities of lenses - and that's the one of the reason, between others, why some lenses cost more and being acclaim as more precious. That fact I used as argument in statement that it is note quite correct to compare very high-end and very precise thought-out m43 lens with their cheaper FF contrepairs based only on the mathematically same DoF.
For example, Voigt 17.5 here used in comparison, as also others in the Nokton m43 lines, are extremely precise constructed to be able to provide specific chosen (and of course subtle) distinctive effects. It is as secret receipt of chosen accentuation and inevitable compromised weaknesses - on which distance image is most detailed with smooth back-and-side rollofs or bokeh nuances; which distance-sharpness to sacrifice to achieve wanted strong effects at other favorable distance; on which aperture and why lens get highest sharpness and where (center and peripheral distribution of sharpness); how to play with color shifting and contrast across aperture range; how to render (faster) movements vs static shots etc.  We can appreciate it or not, being exalted or not depends of taste and personally search specific attributes - but it is without doubt that very sophisticated know-how experience and long tested elaboration, as also higher quality glasses, are involved in construction of these lenses - so, are they really pricey or not, it is very disputable. Having opportunities to compare them with actual results of much higher price cine-lenses (apart of more technical traits as level of focus breathing etc) - I'd say that nowadays these voigts are very moderate or even cheap in price.
By reports and tests it looks that the same is applicable to, say, Veydra line, for their chosen and accurately aimed/provided qualities - some relevant testers claim that they are even better than Zeiss Primes, but double or triple cheaper.

I don t get the point, you always can tell which picture is fullframe and which is apsc or mft or whatever.  It s not about the light, it s the look, and this look you can t replicate using faster lenses.

I get the "false-equivalency" argument. 
I shoot M43 all the time.  And, if you look reeeeeely hard enough, I do think you can tell a difference, in aggregate, between M43 and FF.  The telltales of FF shooting can be evident if you know where to look.  For instance,  usually a smoother bokeh and sharper focus with shallow DOF.  A f2 through modern glass on a FF sensor, for example, can look "cleaner" in a way that M43@f.95 does not.  
These advantages, I think, are nit-picky though.  The differences are subtle.  It's often really hard to tell!  And if a skillful someone is shooting m43 with fast glass, you're probably not going to know the difference or pay attention enough to care in the first place.
I'm shooting a doc right now with the Voightlanders on the GH5 and I'd put it up against anything I've shot with my FF Canon equipment.  If you're shooting M43 or FF, your viewer doesn't really care.  Are you a good shooter?  That's what matters.
All that said, and like I've mentioned before, I still prefer to shoot FF on a fast 50mm prime for interviews.  It's just easier to set up a shot 'kuz of space and lighting --and you can really throw the background out of focus with a f1.2.  That forgives a lot of sins in corporate locations/environments.  Hey, I'm a practical guy.  OTOH, when shooting interviews with my M43 gear I tend to use my 42.5mm lens @f1.2 --and the DOF is wildly shallow and intense too.  The flatness of the "portrait" FOV is a nice look unto itself.  One just needs more physical space in the room to make that happen.  Also, you end up farther away from the interview subject, which can impair any intimacy if you're trying to create such a thing. 
My decisions tend to be less about opticals and much more about other considerations.  Freeing your self from the dogmas of "this vs. that" with gear is a big step to make.  I encourage everyone to make it ASAP. 

I think its perfectly legitimate to do that as well but for some reason its really, really wound some of those people up !
I was being a bit loose with that word as in the UK racism law the definition of race also incorporates national origin.
The correct term I should have used of course is dickheadism
 

Honestly I don't care if it's exactly the same camera (or product) as something already existing as long as there's no hiding or misleading people about that fact.
My friend has a few of their monitors, they are exactly the same as some I have (Feelworld and a few other names). The only thing I think is weird about that company is it's misleading/confusing pricing of monitors and the way in which you order them. That being said people can operate as they wish, it's up to you as the consumer whether you purchase it.

Great footage (and music)!  Thanks!  
 
Interesting.  The tests are required every time one starts the camera?
 
1800x1030 works for me.  What's the longest run time you've achieved with that mode?
 
I've heard some good things about the Viltrox focal reducers.  I have the RJ focal reducer for the EOSM with a Nikkor mount, and it was used in a couple of the shots in this test (along with the 18mm-55mm kit lens):
            All of this footage employs the All-I frames video hack in a Magic Lantern build from 2015.  Frame rates were 23.98 fps and 59.94fps (yielding 1280x720 which was scaled up to 1920x1080).  The Flaat 10 picture style was used in all shots with the first shot ungraded, but I gave a touch more snap to the contrast of the rest of the clips.
 
The ISO was set to 800, but noise was prominent in some footage.  So, I'll probably dial the ISO back down to 100 or 200 when possible.
 
The bit rate was boosted to 1.5x, but I got a hiccup (dropped frame or doubled frames) four seconds into one of the shots.  So, regardless of the cause, I will probably back off of that setting and bring the bit rate down to 1.3x in subsequent shoots.
 
A screw-in ND and a polarizer were stacked, so. occasionally, there was slight vignetting.  However, there was some weirdness with the vignetting moving/changing in the middle of shots, which could be attributed to OIS, except that same behavior seemed to appear in the shots with the manual Nikkor 20mm with the RJ focal reducer.   Have to take a closer look at this apparent phenomenon.  Anyone have ideas on the cause?
 
This test was rushed, and I forgot to change the shutter speed from 1/60th to 1/120th in the first 60fps (slo-mo) shot, so that clip looks slightly smeary.
 
I see a little moire/aliasing and a moment of banding, but I think that this imaging quality could work for a lot of situations.

Great. Any application of this for sound recording as well? My understanding is that sound does not work with lossless compressed, right? Perhaps with higher speeds one can record uncompressed with sound.

I've uploaded another video with the SD card hack:
 
@tupp It takes about 3 or 4 minutes to do the two tests before the sd overclock is ready to use, and then the camera runs as normal. You should be able to shoot 1920x1080 in 5x zoom mode without overclocking in 10 bit lossless - you won't get much record time but it's feasible. I can already get nearly continuous shooting in 1800x1030 12 bit lossless movie crop mode.
I did notice it isn't possible to shoot video without the "release shutter without lens" enabled, don't know if it would be possible to get around that with Magic Lantern.
Also, unsure if I mentioned that Viltrox are planning to do a 0.71x focal reducer for EF-M mount - they told me it should be out in the summer. I don't have a bmpcc speedbooster any longer so this should be a cheaper alternative, with the advantage of electronic contacts for EF lenses.

It was full HD.  I think that the sharpness of the lens, combined with the subject distance and the fineness of the wood texture made for a "perfect storm."  However, I have made some more tests, which I will try to post soon, and there was also moire problems with some coarse fabric.
 
 
This is an amazing capability for such an inexpensive camera!  Thanks for sharing!
 
I've got to get some S16 lenses, or try the BMPCC speed booster (if/when the Photodiox M4/3 to EF-M adapter appears).
 
By the way, I tested it, and one can't shoot video with a manual lens while the "Release shutter without lens" is disabled -- so one might have to be careful not to press the shutter button when using the BMPCC speed booster on the EOSM.
 
 
Oh, that's a bummer.  Hope someone finds a way around that.
 
The thing is, I would be happy with just 1920x1080 and less overclocking.

The monitors were sold and I owned one. But mine was an exact replica of a feelworld monitor just rebranded. The owner is a fiery spaniard but I dont see why they couldn't pull it off. Just dont expect any kind of service if you do buy it. 

it's the same cinemartin brand as those suspicious "cheap monitors" that never came to be sold and that were supposed to be rebranded chinese product?

Not as yet but I suspect even on here we'd struggle to match the argument going on about it over at NewsShooter - with the designer no less - where there are accusations of plagiarism, lies and even outright racism with someone claiming because the designer is Spanish it will never get finished on time !
https://www.newsshooter.com/2018/05/09/cinemartin-fran-8k-camera/
Main bone of contention/accusation seems to be that some posters are convinced that Cinemartin are passing this camera off as their own
https://www.ximea.com/en/products-news/pci-express-camera-cmv50000
 

Yes.  I read that, but that makes even less sense than BMD and Panasonic offering only EF mounts (or longer) for their S35 cameras.  What if somebody wants to use a M4/3 lens on the Yongnuo M4/3 camera?  or, what if somebody wants to use a speed booster, tilt-shift adapter, c-mount lens, etc. on the Yongnuo M4/3 camera?
 
All they have to do to easily solve those dilemmas (and probably sell more cameras) is to start with a M4/3 mount and supply the camera with a smart, reinforced M4/3-to-EF adapter... and the camera will still take the Yongnuo lenses.

If one lens seems to work fine and others don't then perhaps it could be a bad connection between the lens and the adapter?  I'd suggest cleaning the lens contacts on the offending lenses, on the adapter and on the camera as well.  
It's quick and easy and worst case is the problem persists but now your lenses are a bit cleaner and you've ruled out a possible source of the issue 

Sneak peek
 

Reminiscent of the Olympus Air or the Sony QX, which are linked in your article along with a couple of other similar concepts from Kodak and DxO.
 
Can't understand why they decided on an EF mount for a M4/3 camera, but it seems like many camera manufacturers wear blinders when it comes to considering any lens mount other than EF.