if these images are truly scientific, then the unexplained screams out to be explained.
eVeritas: News for the Faculty and Staff of the University of Miami, reports that a 3D Exhibition on Shroud of Turin Visits Campus April 14:
UM’s Catholic Campus Ministry, along with the Franciscans of Mary, Missionaries of Gratitude, will present the 3D-hologram exhibit, “The Holy Shroud—the Burial Cloth of Christ,” and a lecture by its creator at 8 p.m. on Monday, April 14, on the University Center Patio.
At the event, which is open to students, faculty, and staff, Dutch scientist Petrus Soons will present his scientific research on the images of Christ on the shroud.
For more information on Soons and the history and creation of the Holy Shroud of Turin in 3D, visit http://shroud3d.com/. For more information on the event, please contact Michelle Ducker at michelle@ucatholic.org or Lourdes Wolf Marenus at lwolf@miami.edu.
As some of you know, I certainly have real reservations about Petrus Soons’ 3D work., that statement being the title of a posting from November 2012 in which I wrote what follows (below the line).
Bernardo Galmarini, “the 3D expert that produced the conversion from 2D to 3D,” writes on the shroud3d site [which is Petrus Soons’ site]:
I thought at first, that in this more scientific conversion, the hidden information in the Shroud (3D information in the gray-scale), would be a nuisance or obstacle to produce a human representation of the face, and that I would have to struggle continuously against this. Strangely enough, this hidden scientific information in the Shroud became the key and the basis for this work, reducing my artistic work to only softening the “holes” and deformities (caused surely by the passing of time) and the adapting to what this scientific version commands you to do: filling in and normalizing the “holes” or “dead areas” in the hidden information of the linen. For example: the areas without information in the forehead have been corrected following the surrounding gray-scale with coherent information and with a normal human forehead in mind. This process was helped by the fact, that the central zone of the forehead and the bony structure of the orbits contain very coherent information and that of course was taken as a guideline.
That statement lacks needed clarity. There are certainly holes and deformities. Why is not clear in most cases. It seems completely unjustified to speculate that these are caused by the passing of time. Without knowing how the image was formed, without knowing much about how the shroud was stored or displayed over many centuries, we shouldn’t make such guesses.
Exactly what are the holes and deformities? They have not been detailed on the website. The bloodstains certainly are a problem and to make adjustments for these is perhaps warranted. But what about other deformities? How is the problem of banding addressed? Banding, a variegated background pattern to the cloth, perhaps the result of how the thread of the cloth was bleached and having nothing to do with the passing of time, is certainly the single biggest deformity that exists. It gets peculiar treatment in this new 3D work. The left side of the face (our right) has been partially retouched to minimize the effect. The other side of the face is shaped as though there was no banding but the banding remains. Pictured here is an estimate of the banding in the area of the face.
At the bottom of the beard and the lower areas of the hair, darker areas that are not the result of banding are strikingly evident. These relatively dark areas don’t recede towards the background as expected for grayscale plotting. (You can’t see this without 3D glasses. Don’t even try.) What is the rationale for this obviously apparent artistic adjustment? Moreover, hair above the forehead pompadours frontward without grayscale tones to support it. This hair and facial hair treatment seems artistic.
The entire head and shoulders seem to be completely detached from the background. You can, with 3D glasses on, move your own head ever so slightly and see detached movement. (Again, you can’t see this without 3D glasses.) Galmarini speaks of “hidden scientific information,” presumably but not explicitly the grayscale. I can’t find any data in support of this phenomenon. It seems as though an artificial outline has been introduced around the human form. There does not seem to be any such outline on the Shroud. In fact, researchers, over the years, have noted this lack of outline because it is something that an artist, had an artist created the Shroud, would have certainly included. Interestingly, the areas of the lower neck and upper shoulders, though darker than the background, don’t recede into the background and don’t show detached movement. Most amazingly, the lower part of a prominent water stain above the face is now worn in the hair like a miniature yarmulke while the upper part of the stain adorns the background. This, to my way of thinking, strongly suggests the use of false outlines. What other reason can there be other than to enhance the 3D effect?
The most surprising thing is that the grayscale tones that to the untrained eye look like highlights and shadows, but that in fact become the basis for plotting three-dimensionality, remain in place in the plotted image. If you plot a three-dimensional object from the grayscale density you should have something that looks like a stone statue. Whatever highlights and shadows seem to exist in any resulting computerized virtual-reality image should only be from artificially introduced light placed at a calculated angle and distance in the virtual world. This is what the VP8 Analyzer does and what other software packages such as POV-Ray do. But in the anaglyph in question, it looks as though the original image was stretched like a thin film over the calculated shape. Original highlights, shadows and even herringbone twill patterns are there.
I’m willing to be convinced that I am wrong, that the anaglyph in question is scientific. I would actually like this. If this were so we would have something that is truly amazing. Clarity is needed, however. Specifics are required. I would like to see how much of this conversion to 3D is reproducible in a scientific sense and how much is "only softening the ‘holes’ and deformities."
In order to claim that the 3D images on this site are scientific the steps and procedures must be reproducible by others, at least in theory. Documentation is needed.
- We should know the software or algorithm used to plot the image including any variables or settings used.
- The terminology “hidden scientific information” should be clarified. It is essential to understand how plotting software uses this data.
- Expose higher resolution images for examination if the work was done in higher resolution. While this image may be 800 pixels wide, the resolution is no better than 72 ppi. Ordinary books carry pictures at four times the number of pixels per inch.
- We should be able to see, in anaglyph form for comparison, the unadjusted, scientifically plotted part of the project so that we can judge for ourselves just how much of the final product is by way of adjustment.
- All adjustments made should be explained and justified.
It bothers me to think that these images will be used, as the pastor suggests, in presentations to show the 3D characteristics of the Shroud. These images are certainly being displayed in churches, in exhibits and on the internet without the qualification that this is art and not science. If that is so, it is most unfortunate.
On the other hand, if these images are truly scientific, then the unexplained screams out to be explained.
Don’t get me wrong. There is 3D data in the Shroud’s images. It is the most important quality for knowing that these are not images formed by reflected light as a painter would envision or a camera would capture a human form. The 3D data is a quality that must be accounted for in any hypothesis attempting to explain how the images were formed, be it miraculously, naturally, by fakery or even as honest art. Indeed, this quality, treated scientifically without various forms of electronic manipulation, sooner or later, may suggest how the images were formed.
Scientifically interpreting gray scale into 3D data means thinking of an underlying image formation mechanism and a shroud body configuration. These points should be explicitly mentioned.
I congratulate Dr. Dan Porter for exposing his doubts on Bernardo Galmarini’s work , his approach was made in a truly scientific way as an expert in this field he is.
Neverheless as he pointed out, there is 3D information embedded in Shroud image that enabled Dr. Petrus Soons to achieve such a remarquable result I mean the Hologram of the Man of the Shroud,
Curiously,the «two halves of the body» are like bas reliefs with same apparent imperfections in anatomical proportions I mean the head seems to be too small relative to trunk dimension, the right forearm is «too long» etc, there is a missing middle slice of the body about 18 cm? in correspondence to the distance between the front an dorsal head images on the Shroud.
If the Hologram was an «artistic» artwork shouldn’t those imperfections be suppressed?
Could the same result be obtained from any other image even with some artistic additions I mean from regular phptographs, paintings , phptographs from statues bas reliefs etc.?
I guess the answer is straightforward NO!
I had the privilege to wach the Hologram of the Man of the Shroud in Museo Della Sindone in Turin and it had been a very touching experience, no matter if a little artistic skill was blended with science.
Dr. Petrus Soons has given the Shroud World an amazing gift and we should recognize this and give value to his work and commitment to Shroud studies..
regards
Antero de Frias Moreira
(Centro Português de Sindonologia)
Dr Soons’ images, like those of Ray Downing, are intriguing and encourage speculation about the man depicted on the Shroud, whether or not it is derived from Jesus himself or an artistic imagination. However, the Shroud is not a hologram, in any of the various senses of the word.
It is true that a partial three dimensional form (either material, such as Jackson’s cardboard layers, or virtual, as a digital database in a computer) can be constructed from the image on the shroud, and that holograms can be made from three dimensional forms, but that does not mean that the two dimensional image is a hologram, and more than any other two dimensional image is a hologram.
Soons’ holograms are not derived from the image on the Shroud, but from Bernardo Galmarini’s digital three dimensional form of that image. And that requires a great deal more explanation than is given on Soons’ website. It seems to be a truism that the intensity of the image at any one place appears to be inversely related to a distance between a body and a shroud. However the nature of this inverse relationship is far from obvious, and depends on the position of the body, the position of the shroud, and precisely what is meant by the ‘distance between the two’ (vertical, perpendicular to the cloth, perpendicular to the body, the shortest distance between a point on the body and a point on the cloth, or vice versa). Having established that, one must then determine whether the intensity/distance relationship is linear, exponential, quadratic or something else. These factors are not part of the shroud and must be inferred by the ‘sculptor’ based, I’m afraid, on what he thinks the final form should look like, not on any objective data on the image itself.
It would be interesting to give a sculptor an ordinary full face photograph of someone, and ask them to produce a three dimensional face from it. How wildly inaccurate would it be? And then make a hologram of it. Would it be recognisable?
However, the Shroud is not a hologram, in any of the various senses of the word.
Hugh, I know that those are artificial holograms based on Enrie, but Petrus Soons deeply disagree with you:
http://shroud3d.com/home-page/introduction-holographic-observations-in-the-shroud-image-holographic-theory
All these observations pointed to the fact that there is a great probability, that apart from the 3D-distance information in the gray-scale of the image there could also be holographic information hidden in the Shroud.
If it confirms (Shroud photographs from multiple angles desirable), then… good bye sceptics!
He does disagree, doesn’t he? And he’s wrong, until he demonstrates otherwise. A hologram is not a subjective feeling about something.
Let us not forget a dummy.
A peer-reviewed paper would have helped.
Why so categorically state that Dr. Petrus Soons is wrong?
Who’s the expert in holography?
It can be read in Dr. Petrus Soons website that theoretical physicist Dr. Sue Benson also considered the possibility that the Shroud image could be an hologram and no matter what skeptics claim on this blog it’s a FACT (not a guess or a wish…) that the only image that could be processed from photographs to obtain an HOLOGRAM was the Shroud Image.
Despite there is still no peer reviewed paper on this issue as Louis suggested ,no Holograms can be obtained from regular photographs. and that is a fact.
regards
Antero de Frias Moreira
(Centro Português de Sindonologia)
There are many types of holograms, and there are varying ways of classifying them. We can divide them into two types: reflection holograms and transmission holograms.
A. The reflection hologram
The reflection hologram, in which a truly three-dimensional image is seen near its surface, is the most common type shown in galleries. The hologram is illuminated by a “spot” of white
incandescent light, held at a specific angle and distance and located on the viewer’s side of the hologram. Thus, the image consists of light reflected by the hologram. Recently, these
holograms have been made and displayed in color—their images optically indistinguishable
from the original objects. If a mirror is the object, the holographic image of the mirror reflects
white light; if a diamond is the object, the holographic image of the diamond is seen to
“sparkle.”
Although mass-produced holograms such as the eagle on the VISA card are viewed with
reflected light, they are actually transmission holograms “mirrorized” with a layer of aluminum
on the back.
B. Transmission holograms
The typical transmission hologram is viewed with laser light, usually of the same type used to
make the recording. This light is directed from behind the hologram and the image is transmitted to the observer’s side. The virtual image can be very sharp and deep. For example, through a small hologram, a full-size room with people in it can be seen as if the hologram were a window. If this hologram is broken into small pieces (to be less wasteful, the hologram can be covered by a piece of paper with a hole in it), one can still see the entire scene through each piece. Depending on the location of the piece (hole), a different perspective is observed. Furthermore, if an undiverged laser beam is directed backward (relative to the direction of the reference beam) through the hologram, a real image can be projected onto a screen located at the original position of the object.
small semi-transparent object is illuminated by a light source. The object scatters the light
and creates a second wave which superposes on the recording medium with the reference wave originating from the source.
Of course, the idea of a holography is to encode the phase information into intensity variation. In an amplitude hologram, the phase information is recorded as transmission variation (optical density variation). When the Silver-Halide lm is exposed to light and developed, the grains of silver halides are changed into metallic silver and the transmittance of the lm is altered. The amplitude transmittance ~t(x; y) = t0 I(x; y)T varies spatially the same way as the exposure intensity. But, in a phase hologram, the phase information is recorded as index variation. Thus the amplitude transmittance has magnitude equals to 1 and a varying phase ~t(x; y) = ei(x;y).
Irrespective, we could not presume a scorch to not have similar qualities.
Thank you, David. The Shroud is not a hologram. Nor is it a fact (or FACT) that it is the only image from which a hologram can be derived. Other images have not been tried and found wanting – they have never been tried at all. Any X-ray will produce an equally good or better 3D image, from which an equally good or better hologram could be derived. So could Garlaschelli’s image of the shroud, or one of those produced by the photographic techniques.
If your curiosity was piqued, here are the subdivisions of holographic photography:
“120° Integral Stereogram (Multiplex)
A type of white light transmission hologram which is formed by recording multiple
photographs onto a single hologram. The resulting image usually only provides horizontal
parallax, and often provides the effect of an animated three dimensional image. 120°
integral stereograms are not complete cylinders
360° Integral Stereogram (Multiplex)
A type of white light transmission hologram which is formed by recording multiple
photographs onto a single hologram. the resulting image usually only provides horizontal
parallax, and often provides the effect of an animated three dimensional image. 360°
integral stereograms are complete cylinders, and are often mounted on a motor-driven base
which allows them to rotate at a constant speed.
Computer Generated Stereogram
Hologram produced from multiple 2-d perspective recordings of computer-generated
images. Images can be analog, animated, reduced or enlarged. This is an alternative to the
analog hologram process, in which the subject is imaged directly onto the film with a laser
exposure.
Dichromated Gelatin (reflection)
Dichromated Gelatin (DCG) is a chemical-gelatin mix that produces very bright images in a
golden-yellow color. The images have the least range of depth, but they are viewable in
normal room light without special spotlights.
Embossed Mylar Foil (white light transmission)
Holograms stamped on foil in large numbers, from a transmission hologram master, and
often used in applications where high security is desired. Embossed holograms are
transmission holograms with a mirror. The holographic information is transferred from light
sensitive glass plates to nickel embossing shims. The holographic images are “printed” by
stamping the interference pattern onto plastic and then backing the images with a light
reflecting foil. The resulting hologram can be duplicated millions of times for a few cents
apiece.
Holographic Stereogram
Hologram produced from movie footage of a rotating subject. Images can be computer
generated, animated, reduced or enlarged, or photographed on site. This is an alternative to
the original hologram process, in which the subject is imaged directly onto the film with a
laser exposure.
Embossed holograms
Embossed holograms are used in the security industry because they are difficult to
counterfeit.
Laser Transmission
A type of hologram which is constructed by causing the object beam and reference beam to
interfere from the same side of the holographic film or plate. In order to view the
reconstructed image, semi-coherent filtered light or very coherent laser light is transmitted to
the viewer through the hologram. Other types of holograms use a laser transmission
hologram as the master, from which copies are made. This is the earliest type of hologram
developed by Leith and Upatniks in 1962. Transmission holograms are lit from the rear (like
a photographic transparency) and bend light as it passes through the hologram to your eyes
to form the image.Rainbow Holograms
See “White Light Transmission Holograms.”
Reflection Holograms
Reflection Holograms are lit from the front, reflecting the light to you as you view it, like a
painting or photograph hung on a wall. Different film emulsions produce images with
different characteristics. (Silver Halide, Dichromated Gelatin, Photo Polymer)
White Light Transmission Holograms
White light transmission holograms are illuminated with incandescent light (white light) and
produce images that contain the rainbow spectrum of colors. The colors change as the
viewer moves up and down and are often called “rainbow” holograms. Holographers have
developed considerable control over the colors displayed in this type hologram to produce
images in a specific color or in near full, natural color. Transmission holograms are lit from
the rear (like a photographic transparency) and bend light as it passes through the hologram to your eyes to form the image.”
To Dr. David Bowman
I praise your comments on holograms and I’ll read them carefully.
I guess you’re an expert on holography so I’d like to put some questions.
If you had to give an advice on Dr. Petrus Soons hologram of the Man of the Shroud and alleged holographic properties of the Shroud image what would be your straightforward answer?
Accordingly to the criteria you mentioned on making holograms would it be possible to obtain an Hologram from a image impressed on a linen sheet like the image of the Man of the Shroud and would the same result be achieved with the Garlaschelli’s Shroud?
I apologize for adressing you this way but I guess your opinion will be welcome to most people who comment on this wonderful blog
regards
Antero de Frias Moreira
(Centro Português de Sindonologia)
1) Well, Soons image seems to be on-axis, and, the biggest challenge of the on-axis holography are the twin-images: a conjugate image locating right in front of the true image. Instead of sending the reference beam and object beam in line, it has been proposed that separating and sending them at diff erent angles. However, to separate the beam was difficult in practice at that time, when the best coherent source was the high pressure mercury lamp, with coherent length of only about 0.1mm. The first o ff-axis hologram worked until two men, Leith and Upatnieks, came up an optical trick: to choose one line of the mercury lamp and send it to a grating. Two di fferent orders of the light after the grating are used as the reference and object beam, which are automatically propagating at di fferent angles.
With this off -axis hologram it is possible to detect the object wave without being
disturbed by the reference beam which propagates along another direction. Off -axis holography requires the use of a laser for coherence requirement.
Soons should give us the off-axis conjugate image.
2) The fundamental di fference between a transmission hologram and a refection hologram lies in the direction of the interference fringes that are recored inside the photosensitive emulsion. In a transmission hologram, the reference wave and object wave entering
the emulsion from the same side produce interference fringes in planes that are perpendicular to the plane of the emulsion; while in a reflection hologram, the reference wave and object wave entering the emulsion from di fferent sides produce interference fringes in planes that are parallel to the plane of the emulsion. Observation of the image in a transmission hologram requires the same reference beam that exposed it, and viewing through the plate; while in a reflection hologram, a spot light or sunlight is good enough and the image is observed by viewing the reflection from the plate.
We should anticipate Garlaschelli’s Shroud to then, obligingly, to give quality results in the diffracted interference fringes in planes that are perpendicular to the emulsion plane. This phenomenon may happen in X-rays, photographic techniques as well.
P.S. The hyperboloidal surfaces inside the thin emulsion layer of holographic film, approach flat planes and are perpendicular to the film surface, like venetian blinds in the “open” position. However, because of the inherent characteristics of this family of hyperboloid “mirrors”, each successive reflection will have a precise phase shift of 2p because the optical path is increased by precisely the distance of one wavelength. All the reflected waves are precisely in phase and, therefore, add in amplitude, resulting in a strongest possible wave front representing the object beam. Thus, we may anticipate the phenomenon in other Shroud images like Garlaschelli’s.
The problem is not how you treat the 3D data (into a hologram, a bronze or a 3D printer), but how you generate these data.
It seems “the 3D information was extracted by means of gray scale mapping (also called displacement mapping) by Galmarini in Argentina”, VP8 style, no more.
If you want to ascertain potential “holographic” qualities within X-rays or photographs for instance, I’ll give you a short “lesson”. The low cost of equipment makes it possible for many of the following exercises to be performed as “homework.”
All the experiments require the use of a laser and chemicals for processing the holograms.
and duly observe all safety rules concerning lasers and chemicals.
Generally, the developer and bleach solutions are mixed by the instructor. Since the photochemistry of holography is an ongoing research, it will change as improvements are found. Thus, no particular regime is discussed here. Use according to the detailed instructions that accompany each processing kit provided by the manufacturer.
Similarly, the holographic plate or film used will change with time. Use them in accordance with the instructions of the supplier. The exposure time and the appropriate processing scheme are also provided.
Equipment and facilities
Holograms are made in darkened areas free from drafts, vibration, and noise. Because of the relatively low sensitivity of the recording material, sufficient light is allowed so that one can see comfortably after dark adaptation. To achieve this, use a 25-watt green light bulb in a lamp. Place the lamp under the table, cover it with aluminum foil to adjust the light, and direct it toward the floor. Do not allow direct light to shine on the holography system or on the developing station.
If the room has windows, cover them with black plastic sheets. Enough light can leak through to allow minimum vision after dark adaptation. In case of doubt, leave a holographic plate on a table and expose it to the ambient light for ten minutes. Develop it. If it turns dark, there is too much light.
Flowing tap water is desirable but not necessary. A large tray of clean water can be used to rinse the developed hologram. White trays are desirable because they allow continual inspection. An alternative is to use glass trays resting on white paper.
Make sure all fire codes are observed.
A. Reflection hologram
Equipment requirement: Darkened room with green safe-light, sturdy table or counter, optical table supported by “lazy balls,” mounted diode laser system, object on platform with three-point support, shutter, processing trays with chemicals, and holographic plates.
Figure 10-15—shown earlier—indicates the setup for making a “one-beam reflection hologram,” sometimes called a Lippmann (Nobel Prize in physics, 1908) or Denisyuk hologram.
Procedure
A. Choose a solid object that looks bright when illuminated with laser light and whose size is not bigger than the hologram to be made. Mount (hot glue) it on a small platform made of wood or sheet metal (15 cm × 15 cm) with three round-head short screws underneath (to prevent rocking). Mount the laser on a stand about 25 cm high and direct the light down at 45° at the object, with the light spreading horizontally. The distance between the laser and the object is about 40 cm. Now turn on the safe light and turn off the room light.
B. After the laser has been warmed up for at least five minutes, block the light from reaching the object using a self-standing black cardboard. (We will call this the shutter.)
C. Lean a holoplate directly on the object, with the sticky side touching it. Wait at least 10 seconds.
D. Lift the shutter, but still blocking the light, for 2 seconds, to allow any vibration to subside. Then lift the shutter away completely to allow the light to pass through the holoplate. The exposure is usually about 5 seconds. (Consult the instructions that accompany the plates.) Then block the light again.
E. Develop the hologram according to instructions from the manufacturer.
After the hologram is dried, view it with a spot light such as a pen light, projector, or direct sunlight. Optional: Spray paint the sticky side (emulsion side) with a flat (or “antique”) black paint to provide a darker background and greatly improve the visibility of the image.
B. Transmission holograms
1. Without a mirror
Equipment requirement: Same as for the “reflection hologram” in section A. above. In addition, a stand-alone plate holder is needed. Make one exactly the same way as the object platform described above. Instead of the object, install two long (12 cm) screws on top with a separation less than the width of the holoplate to be used. Paint the screws a diffused black color.
Procedure
A. Set up the system as shown in Figure 10-19. The diode laser is mounted 5 cm above the optical table with the beam spreading horizontally. One side of the beam illuminates the object or objects, and the other side serves as reference beam.
Figure 10-19 The simplest configuration for making a transmission hologram
B. Block the beam with the shutter, turn off the room light, and, on the stand-alone plate holder, lean a holoplate vertically against the black screws with the sticky side facing the object(s). Wait 10 seconds.
C. Lift the shutter and expose for about 30 seconds. Note: If there is a draft across your system, the long exposure time of 30 seconds requires you to put a large box over the entire system during the exposure.
D. Develop and dry as before.
E. This hologram must be viewed with laser light. To do so, lean the finished hologram back on the black screws the same way as during exposure. Cover or remove the objects and look through the hologram toward the location of the objects. A virtual image can be seen as if the object is still there.
F. To observe the real image:
− Relocate the finished hologram in the position where it was exposed.
− Remove the object and, in its place, position a vertical white screen (cardboard) facing the hologram.
− Darken the room and direct a collimated laser beam through the center of the hologram in a direction that is 180° from the original reference beam, i.e., back toward the location of the diode laser used for making the hologram.
All light paths are now reversed and a two-dimensional image is projected onto the screen. Move the laser beam to different locations of the hologram and observe the changing perspectives of the image.
As must be said, this is a mere synopsis. I have not presented every facet.
Regards,
David Bowman
Hmm… in the posting there were a few images therein. They must not have registered, sorry.
To Anoxie
Are you meaning that a «gray scale mapping» was produced from the Shroud image by Bernardo Galmarini and from it a 3D image of the Man of the Shroud was achieved , and the Hologram was produced from treating those 3D data?
My interpretation of Dr. Petrus Soons explanation fits that.
If this is true then the crux is can we get accurate gray scale mapping from images other than Shroud image to «build anatomically near perfect 3D images» ?
regards
Antero de Frias Moreira
( Centro Português de Sindonologia)
P.S. I thank Dr.David Bowman for his technical explanation on Holograms
Yes, at least the basic step seems to be “gray scale mapping” if one reads shroud3d.com. Then there must have been several “procedures” to get “anatomically near perfect 3D images”, which are great, but not scientific.
Let’s think of the fuzzy borders and local resolution variations, they’ve disappeared in the final image.
Theoretically, if you consider a high map, you assume one point on the shroud corresponds to one point on the body. This is right for contact points but not for distant points, which explains why this approach is basically flawed.
Dr. Soons’ work hs such promise and is very interesting.