In the last post I said at a certain point that I would expect a physicist with Goethean leanings and familiar with my work to confront me with an array of arguments and questions. So, let's begin with those.
Taking into consideration your own explanation of how the Newtonian theoretical understanding, when it is combined with your view that in subjective observations R and B are apparently deflected in opposing directions (whilst, at the same time, G is not deflected at all) can account for all combinations of the observable boundary colours, why do you assert that Goethe's theory of colours cannot achieve that goal itself, when in principle it is identical to it. Effectively, can you tell me what difference there is between the idea that B deflects in a direction toward the apex of the prism, R towards the base, and G stays put, and Goethe's proposal that in a subjective prismatic experiments the object under observation is displaced in the direction of the prism's apex, which in the process creates the known boundary colours due to the overlapping of light over darkness at one end and darkness over light at the other?
Yes, I can tell you what differences (for there are more than just one) there are between my Newtonian explanation for those so-called boundary colours and Goethe's. In order to do that let us look at the picture below, which is a copy of the original picture from Goethe's Theory of colours, as we'll read the cited paragraph below it (which is shown in a different font).
Goethe's Figure G.II.2
If we cause the white disk to move, in appearance, entirely from its place, which can be done effectually by prisms, it will be coloured according to the direction in which it apparently moves... If we look at the disk G.II.2.a through a prism, so that it appear moved to G.II.2.b, the outer edge will appear blue and blue-red, according to the law of the figure G.II.1.B, the other edge being yellow, and yellow-red, according to the law of the figure G.II.1.C. For in the first case the white figure is, as it were, extended over the dark boundary, and in the other case the dark boundary is passed over the white figure. The same happens if the disk is, to appearance, moved from G.II.2.a to G.II.2.c, from G.II.2.a to G.II.2.d, and so throughout the circle.
Ignoring for the time being the parts highlighted in red, the first difference between my Newtonian explanation and Goethe's becomes immediately apparent when we compare his picture and verbal explanation with what would be my own graphical depiction and verbal explanation of a similar observation. See below.
Now, the plain reality is that to any physicist who nurtures a belief that Goethe's theory is validly describing the nature of light and colour it should have easily become apparent that his explanation of the experiment depicted in the figure G.II.2 is fatally deficient right from the outset. Can you see why that is in fact the case?
It's all most simple, straightforward and obvious, really. Thus, in effect if Goethe's understanding of this particular prismatic observation were correct, on the one hand the blue area in my diagram should contain the cyan part as well, whilst on the other the yellow area in my picture should contain the red part too. Keeping in mind that our blue Goethe called blue-red, the cyan Goethe called blue and the red he called yellow-red, take a good look at both pictures above, look through your prism at the white circles in both pictures again, think for a while if you still cannot see what I'm talking about, and then, finally, if you're still mystified by what I said in this paragraph please stop reading these pages immediately, for you're not equipped for that task.
Goethe's entire theory of colours rests upon one crucial idea. Which is that in order for any colour to become apparent a source of light viewed through a triangular prism must appear to have been displaced from its original place over a dark boundary. And fundamentally it is precisely here where the entire theory can be shown to categorically fail, as we will demonstrate by the end of this page. To that end we shall now turn our attention to another subjective prismatic experiment from his book.
If we attentively examine these opposite coloured edges, we find that they only appear in the direction of the apparent change of place. A round figure leaves us in some degree uncertain as to this: a quadrangular figure removes all doubt.
The quadrangular figure G.II.3.a, moved in the direction G.II.3.a G.II.3.b, or G.II.3.a G.II.3.d, exhibits no colour on the sides which are parallel with the direction in which it moves: on the other hand, if moved in the direction G.II.3.a G.II.3.c, parallel with its diagonal, all the edges of the figure appear coloured.
Thus, a former position is here confirmed; namely to produce colour, an object must be so displaced that the light edges be apparently carried over a dark surface, the dark edges over a light surface, the figure over its boundary, the boundary over the figure.
Now, having cited this particular experiment in its entirety we shall add to it a couple of paragraphs that will help in making the whole issue clearer. See below.
If we attentively examine these opposite coloured edges, we find that they only appear in the direction of the apparent change of place. A round figure leaves us in some degree uncertain as to this: a quadrangular figure removes all doubt.
The quadrangular figure G.II.3.a, moved in the direction G.II.3.a G.II.3.b, or G.II.3.a G.II.3.d, exhibits no colour on the sides which are parallel with the direction in which it moves: on the other hand, if moved in the direction G.II.3.a G.II.3.c, parallel with its diagonal, all the edges of the figure appear coloured.
Goethe's Figure G.II.3
Thus, a former position is here confirmed; namely to produce colour, an object must be so displaced that the light edges be apparently carried over a dark surface, the dark edges over a light surface, the figure over its boundary, the boundary over the figure.
Now, having cited this particular experiment in its entirety we shall add to it a couple of paragraphs that will help in making the whole issue clearer. See below.
The colour which is outside, or foremost, in the apparent change of an object by refraction, is always the broader, and we will henceforth call this a border: the colour that remains next the outline is the narrower, and this we will call an edge.
If we move a dark boundary towards a light surface, the yellow broader border is foremost, and the narrower yellow-red edge follows close to the outline. If we move a light boundary towards a dark surface, the broader violet (which Goethe had also called blue-red) border is foremost, and the narrower blue edge follows.
And since Goethe's own diagrams are hardly accurate depictions of what the observer truly sees through his prism, below we shall also display a much more accurate rendition of the original picture above.
On the dumbfounding reality that no one's noticed for more than 200 years
Consider the following facts.
Goethe published his Theory of colours in 1810. His book is still in print today, as it has been since its inception. A countless number of people have read it, with the vast majority of those being either professional physicists or philosophers. Thousands of those readers have written thousands of books about it and many of them have made it the principal source of their entire life and fortune. Thousands of physicists have subjected it to a level of scrutiny that is characteristic to most scientists, regardless if they were doing it as disciples or as opponents. Thousands of physicists, philosophers, artists and other kinds of professional people from all around the globe are, as we speak, passionately lobbying either for or against Goethe's theory of colours.
This is the reality that to my mind is so incredibly dumbfounding that in spite of all the best intentions I can muster I still find the entire issue intolerably inexcusable. And now, with all that being said and publicly recorded, let me show you how easily we can establish--beyond the shadow of a doubt--whether Goethe's Theory of colours bears any scientific validity, or not. Stay with me.
Remember my earlier remark that Goethe's entire theory rests upon one quintessential idea: That the colours seen in any prismatic observations are direct consequences of the apparent displacement of an object from its original position that is effected by a prism. And thus, since that is the ideam magnae upon which Goethe's entire theory of colours unconditionally depends (and therefore ultimately either lives or dies) a careful and objective scrutiny of it shall be more than sufficient to show us in the end how we all, as the current living world, should present it to those that will come tomorrow.
I'd love so much to be able to see inside your brain at this point, for no longer than perhaps half an hour or so. The reason I would love that is because upon a first examination about how one could definitively prove either the validity or indeed the invalidity of the ideam magnae one may rather easily find that, if pushed in a corner, one may choose to resort to a number of arguments that could really make the task of a would-be prosecutor, so to speak, very difficult indeed.
Let me give you a concrete example of what I'm trying to say. Consider a physicist with strong Newtonian beliefs who would argue that the ideam magnae is purely a concocted story, towards which Goethe had been inexorably driven by his preconceived beliefs and to which he had also added a known and unavoidable observational fact. By contrast, he would continue, Newton's theory of light and colours has a solid physical basis and it was in the end arrived at by adding to that empirical basis only later some logical inferences, which Newton nonetheless continued for many years to subject to a rigorous experimentation. Then, in the final part of his argumentation he could make use of a diagram similar to the one shown below...
...and then he could begin explaining that the picture above depicts what a subjective observation of the green and white rectangles at 1 would reveal to the observer who's looking through his prism oriented with its apex pointing to the left beginning from an initial distance of about 70-80 cm (2) and then gradually increasing the distance until seeing the image depicted under number 5, when the distance between the point of observation and the screen of his computer's monitor would be approximately 3 m. He could then continue by explaining that there is a good reason for using the green rectangles in addition to the white ones, for it can be proven that in subjective observations objects of that colour do not appear to be in any way deflected--or displaced, if you like--by a prism if they are observed against a black background, which makes them perfect points of reference in prismatic observations of that nature.
To cut a long story short, a Newtonian defender could offer all the arguments I have already discussed in what would be a pretty consistent and compelling presentation about the strong points of Newton's theory of light and colours. For no one in his right mind can deny that there is simply no more persuasive theory out there (which could fully account, as a most pertinent example, for all the colours that are displayed by the white rectangles numbered 2, 3 and 4). Think about that. In earnestness.
Finally, in summing up, a Newtonian defender should point out to the Goethean one the fact that there is, at the very least, one most dubious thing in Goethe's own explanation for the results of a subjective observation. Which is this.
Now, let's make no bones about it, the plain reality is that even if one accepts the ideam magnae right from the outset and as it really is (meaning without any evidence behind it) there should be not a single doubt about the fact that the entire issue not only looks and sounds bad--it also smells bad (meaning it has the typical smell of a blatant lie). Let me tell you why no one should even dare to suggest that what I've said is not in fact a fact.
Take first a look with the naked eye at the white rectangle 1 in the picture above, look at it next through a prism (oriented and from a distance as those specified), verify what you have seen is basically what's shown along the sides of the white rectangle 2, and now start reasoning along with me.
If you believe that Goethe's theory is right, when you look at the white rectangle 1 through a prism do you believe that you see those colours because the prism has literally moved the white rectangle from its place to another place? Do you? At this point I see that a great many of you have suddenly fallen into a kind of silent trance. Now, regardless of what your answer really was let me show you next another picture, and then ask you the same question again.
There are many things which to the majority of human brains appear to be absolutely clear and rather obvious, if they're explained by other brains with apparently more knowledge than theirs. Then, there are other things which to a select minority will suddenly get clearly understood and obvious, when a couple of other brains paint different images of that same thing which they had neither seen nor contemplated until then. There are also some things which to some lone brains out there they far too often appear either clearly wrong when to all others they seem absolutely right, or vice versa, for good measure. And this thing, let me tell you, is without question one of those.
To my mind Goethe's ideam magnae (great idea) is so incredibly naive and silly that in many ways I feel like I'm being bullyingly pushed into a dark corner and insolently spat right on the face '"You can think what you want and you may do what you think, but let me tell you that you can never prove that a prism cannot displace a white object surrounded by a black background from its original position--which in the end means that you will never be able to completely eliminate my idea as a possible cause for the colours seen in prismatic experiments". And, in/as/from a strict and most perverse principle/matter of fact/perspective, that is pretty much true.
But there is always more than one way to skin any particular cat. So let me accept Goethe's ideam magnae without any qualification and ask you to take another look at the picture above. See how much the prism appears to have displaced the relevant part of the metal rod from its true position? That is a big displacement, considering how close it appears to be to that face of the prism. Observe next that the displaced part of the rod is bordered on its vertical sides by the two familiar Y-R (on the right side of the rod) and C-B (on its left side).
Now, at this point I want to ask any Goethean with a solid understanding of the theory of colours if they can provide a sound explanation for the results displayed in the picture above. Especially I'd love to hear how they would link into a consistent explanation the amount of displacement of a refracted object with the widths of its boundary colours, which is a subject Goethe wrote about in his book (albeit, in a very brief and superficial account and a quite vague mode of expression for a writer of his calibre). To my mind it's been clearly obvious for many years now that one of the murkiest parts in both the conventional/Newtonian theory and also in Goethe's is that concerned with the image displacement in prismatic observations. There's also another most interesting fact about that particular issue. That in diametrical contrast to the prevalence of that reality, to my mind that subject was one of the easiest of all to understand, assess, investigate, make sense of and eventually resolve to the extent it uncompromisingly demands from all the other things that come under its scrutiny. This particular subject is very important for a number of reasons, so I will next spend a fair amount of time to discuss its most important attributes and implications.
Many years ago, when I was taking baby steps into the realm of physics and its many territories, I designed my very first experiment in order to verify and determine--once and for all--whether the mainstream theoretical understanding regarding the nature of light in prismatic experiments was true, and therefore correct in assertions. The experiment in question was the one pictured below, and after conducting it I came to my first definitive conclusion. Which was that the conventional theory regarding the behaviour of light in prismatic observations was blatantly and uncompromisingly wrong, and therefore incorrect in all its related assertions.
Can you imagine the reason that had driven me towards what I still believe to this day to have been the right conclusion? In any event, the reason in question was the inevitable consequence of the following line of reasoning. Thus, according to the best of my understanding, if the conventional theory were correct, then instead of the apparent gap that was seemingly created by the prism into the black cardboard held right behind it, in the picture on the left, there should have appeared a black area extending downwards, in the direction of the prism's base. That should have indeed become an observable consequence due to the uncompromising assertion that light rays/photons carry the image along the paths they travel, which are determined by the natures of the media they travel through and from, and which in our case should have been angled in the direction mentioned a moment ago. As in regards to the other picture above, the effect that should have become manifestly evident would have been one of a diametrically opposite nature and extension. I don't think that there's any need of me to say more than that. There is however one other thing that is by far more important than any other conceivably related in some way to our current topic, and that particular thing is certainly worthy of attention, as we'll see in just a moment or two.
There is no doubt whatsoever that the issue of image displacement in prismatic observations is still too hot for the conventional physics to handle, which is a truth that I have known for too many years to even care about these days. Nevertheless, there are quite a few other truths that I have known for a very long time, and let me tell you that about those I've always cared so much that I have dedicated ample time over the years to pay them the attention they deserved and learn how to eventually live with and along them peacefully, serenely, for a little while yet.
About ten years ago I found myself embroiled in some contentious discussions with a number of people who were trying their hardest and best to convince me that I was wrong in basically everything I said. Today, when we appropriately live in the symbolic year for exquisite hindsight, I am in earnestness becoming more aware each day about how and why those many differently coloured events from my past are finally finding their rightful place into my living present. It is a cathartic cliché, but today I don't mind that--for those are, in truthfulness, two words I never used before.
One thing amongst the many I had heard from others is central to the mainstream view concerned with the image displacement in a prism. That particular thing is the ideam magnae at the core of the conventional understanding regarding the topic of image displacement in prismatic observations, and it is encapsulated in the paragraph below.
Although a prism displaces light towards its base, when the refracted light is projected backwards it makes the object appear as though it originated in the opposite direction of this displacement. Consequently, we say that the image created by a prism is displaced towards the apex of the prism. This point is extremely important and worth reiterating: A prism deviates light towards its base and images toward its apex.
And since we know that a picture tells a thousand words, I'll next drop below not one but a couple of them.
We have already seen and heard the fundamental basis--the bedrock, if you like--upon which the entire conventional understanding regarding the nature of image displacement in prismatic observations integrally rests and depends. To all that at this point I'll add the diagram below, which comes from Newton's Opticks. The reason I am showing you this particular picture is to emphasise the astonishing fact that in the matter of image prismatic displacement there has been no change at all in 316 years. Now, upon hearing that one may conclude that the most logical explanation for such a long status quo must be a solid and persuasive indicator that the entire subject of image displacement in prismatic observations is correct. "Nothing happened because there's no need of anything else in that matter" one may declare.
I'd love so much to be able to see inside your brain at this point, for no longer than perhaps half an hour or so. The reason I would love that is because upon a first examination about how one could definitively prove either the validity or indeed the invalidity of the ideam magnae one may rather easily find that, if pushed in a corner, one may choose to resort to a number of arguments that could really make the task of a would-be prosecutor, so to speak, very difficult indeed.
Let me give you a concrete example of what I'm trying to say. Consider a physicist with strong Newtonian beliefs who would argue that the ideam magnae is purely a concocted story, towards which Goethe had been inexorably driven by his preconceived beliefs and to which he had also added a known and unavoidable observational fact. By contrast, he would continue, Newton's theory of light and colours has a solid physical basis and it was in the end arrived at by adding to that empirical basis only later some logical inferences, which Newton nonetheless continued for many years to subject to a rigorous experimentation. Then, in the final part of his argumentation he could make use of a diagram similar to the one shown below...
...and then he could begin explaining that the picture above depicts what a subjective observation of the green and white rectangles at 1 would reveal to the observer who's looking through his prism oriented with its apex pointing to the left beginning from an initial distance of about 70-80 cm (2) and then gradually increasing the distance until seeing the image depicted under number 5, when the distance between the point of observation and the screen of his computer's monitor would be approximately 3 m. He could then continue by explaining that there is a good reason for using the green rectangles in addition to the white ones, for it can be proven that in subjective observations objects of that colour do not appear to be in any way deflected--or displaced, if you like--by a prism if they are observed against a black background, which makes them perfect points of reference in prismatic observations of that nature.
To cut a long story short, a Newtonian defender could offer all the arguments I have already discussed in what would be a pretty consistent and compelling presentation about the strong points of Newton's theory of light and colours. For no one in his right mind can deny that there is simply no more persuasive theory out there (which could fully account, as a most pertinent example, for all the colours that are displayed by the white rectangles numbered 2, 3 and 4). Think about that. In earnestness.
Finally, in summing up, a Newtonian defender should point out to the Goethean one the fact that there is, at the very least, one most dubious thing in Goethe's own explanation for the results of a subjective observation. Which is this.
Now, let's make no bones about it, the plain reality is that even if one accepts the ideam magnae right from the outset and as it really is (meaning without any evidence behind it) there should be not a single doubt about the fact that the entire issue not only looks and sounds bad--it also smells bad (meaning it has the typical smell of a blatant lie). Let me tell you why no one should even dare to suggest that what I've said is not in fact a fact.
Take first a look with the naked eye at the white rectangle 1 in the picture above, look at it next through a prism (oriented and from a distance as those specified), verify what you have seen is basically what's shown along the sides of the white rectangle 2, and now start reasoning along with me.
If you believe that Goethe's theory is right, when you look at the white rectangle 1 through a prism do you believe that you see those colours because the prism has literally moved the white rectangle from its place to another place? Do you? At this point I see that a great many of you have suddenly fallen into a kind of silent trance. Now, regardless of what your answer really was let me show you next another picture, and then ask you the same question again.
There are many things which to the majority of human brains appear to be absolutely clear and rather obvious, if they're explained by other brains with apparently more knowledge than theirs. Then, there are other things which to a select minority will suddenly get clearly understood and obvious, when a couple of other brains paint different images of that same thing which they had neither seen nor contemplated until then. There are also some things which to some lone brains out there they far too often appear either clearly wrong when to all others they seem absolutely right, or vice versa, for good measure. And this thing, let me tell you, is without question one of those.
To my mind Goethe's ideam magnae (great idea) is so incredibly naive and silly that in many ways I feel like I'm being bullyingly pushed into a dark corner and insolently spat right on the face '"You can think what you want and you may do what you think, but let me tell you that you can never prove that a prism cannot displace a white object surrounded by a black background from its original position--which in the end means that you will never be able to completely eliminate my idea as a possible cause for the colours seen in prismatic experiments". And, in/as/from a strict and most perverse principle/matter of fact/perspective, that is pretty much true.
But there is always more than one way to skin any particular cat. So let me accept Goethe's ideam magnae without any qualification and ask you to take another look at the picture above. See how much the prism appears to have displaced the relevant part of the metal rod from its true position? That is a big displacement, considering how close it appears to be to that face of the prism. Observe next that the displaced part of the rod is bordered on its vertical sides by the two familiar Y-R (on the right side of the rod) and C-B (on its left side).
Now, at this point I want to ask any Goethean with a solid understanding of the theory of colours if they can provide a sound explanation for the results displayed in the picture above. Especially I'd love to hear how they would link into a consistent explanation the amount of displacement of a refracted object with the widths of its boundary colours, which is a subject Goethe wrote about in his book (albeit, in a very brief and superficial account and a quite vague mode of expression for a writer of his calibre). To my mind it's been clearly obvious for many years now that one of the murkiest parts in both the conventional/Newtonian theory and also in Goethe's is that concerned with the image displacement in prismatic observations. There's also another most interesting fact about that particular issue. That in diametrical contrast to the prevalence of that reality, to my mind that subject was one of the easiest of all to understand, assess, investigate, make sense of and eventually resolve to the extent it uncompromisingly demands from all the other things that come under its scrutiny. This particular subject is very important for a number of reasons, so I will next spend a fair amount of time to discuss its most important attributes and implications.
Many years ago, when I was taking baby steps into the realm of physics and its many territories, I designed my very first experiment in order to verify and determine--once and for all--whether the mainstream theoretical understanding regarding the nature of light in prismatic experiments was true, and therefore correct in assertions. The experiment in question was the one pictured below, and after conducting it I came to my first definitive conclusion. Which was that the conventional theory regarding the behaviour of light in prismatic observations was blatantly and uncompromisingly wrong, and therefore incorrect in all its related assertions.
Can you imagine the reason that had driven me towards what I still believe to this day to have been the right conclusion? In any event, the reason in question was the inevitable consequence of the following line of reasoning. Thus, according to the best of my understanding, if the conventional theory were correct, then instead of the apparent gap that was seemingly created by the prism into the black cardboard held right behind it, in the picture on the left, there should have appeared a black area extending downwards, in the direction of the prism's base. That should have indeed become an observable consequence due to the uncompromising assertion that light rays/photons carry the image along the paths they travel, which are determined by the natures of the media they travel through and from, and which in our case should have been angled in the direction mentioned a moment ago. As in regards to the other picture above, the effect that should have become manifestly evident would have been one of a diametrically opposite nature and extension. I don't think that there's any need of me to say more than that. There is however one other thing that is by far more important than any other conceivably related in some way to our current topic, and that particular thing is certainly worthy of attention, as we'll see in just a moment or two.
There is no doubt whatsoever that the issue of image displacement in prismatic observations is still too hot for the conventional physics to handle, which is a truth that I have known for too many years to even care about these days. Nevertheless, there are quite a few other truths that I have known for a very long time, and let me tell you that about those I've always cared so much that I have dedicated ample time over the years to pay them the attention they deserved and learn how to eventually live with and along them peacefully, serenely, for a little while yet.
About ten years ago I found myself embroiled in some contentious discussions with a number of people who were trying their hardest and best to convince me that I was wrong in basically everything I said. Today, when we appropriately live in the symbolic year for exquisite hindsight, I am in earnestness becoming more aware each day about how and why those many differently coloured events from my past are finally finding their rightful place into my living present. It is a cathartic cliché, but today I don't mind that--for those are, in truthfulness, two words I never used before.
One thing amongst the many I had heard from others is central to the mainstream view concerned with the image displacement in a prism. That particular thing is the ideam magnae at the core of the conventional understanding regarding the topic of image displacement in prismatic observations, and it is encapsulated in the paragraph below.
And since we know that a picture tells a thousand words, I'll next drop below not one but a couple of them.
I hated the ideam magnae right from the time it came into my world. I hated it, first and foremost, because the message it's proclaiming has always rung inside my ears with a droning semblance of trustworthiness. Which, to my mind, had not one grain of. Then I hated it because in due time I came to realise that for all intents and purposes it was next to impossible to either defend against or to defeat it by using only logical argumentation and by appealing to one's reason. But just hating something bears no fruit and brings no yield. So I stopped doing that, and then gradually managed to extend my outlook and field of vision into the subject I loved................
Anyways, let me start again.
We have already seen and heard the fundamental basis--the bedrock, if you like--upon which the entire conventional understanding regarding the nature of image displacement in prismatic observations integrally rests and depends. To all that at this point I'll add the diagram below, which comes from Newton's Opticks. The reason I am showing you this particular picture is to emphasise the astonishing fact that in the matter of image prismatic displacement there has been no change at all in 316 years. Now, upon hearing that one may conclude that the most logical explanation for such a long status quo must be a solid and persuasive indicator that the entire subject of image displacement in prismatic observations is correct. "Nothing happened because there's no need of anything else in that matter" one may declare.
The sheer reality about that matter however is poignantly different, as I'll show you next.
Armed with a solid understanding of the conventional theory concerned with the nature of image displacement in subjective prismatic observations we proceed to examine the picture below.
It shouldn't take long at all to see that the image displacement in this picture could not have been in any shape or form caused by the spatial orientation of the camera that took the picture. That's assuming that you have read all my pages and understood what I've been talking about. But the reality about that possibility is, more than likely, very unlikely. In view of that I decided that for the rest of this post I will try to link my present work with that of the past (which means that this particular post is going to be rather long, and that it will take quite some time to lay it all down as such).
There are a number of very good reasons behind my saying that it shouldn't take long to conclude that the conventional theory is definitely inadequate to account in a coherent and cohesive manner for the results observed in the subjective experiment pictured above. Before starting in earnest to discuss them though I'd like to point them all out for you and thus give you a chance to try to anticipate on what kind of ground and foundations have my beliefs been built. And I'll do that by using the means shown below.
So, in the upper part of the picture I have highlighted in different colours the parts of the image where the eye of a keen observer should notice visual anomalies, so to speak, which if properly assessed and understood can point out and lead the investigator to some of the most sought-after answers in the field. Nevertheless, in reality things are of course always easier said than done, which means that in order to have any chance of resolving in that way some complex matter one needs much more than just a keen eye and a Ph. D. But let's not waste our time in discussing those kinds of peripheral issues.
I want you to look first at those two-line segments in the picture, and try to think in what way could they be connected. I personally first thought about that little subject many years ago, and I am quiet proud to know that I elucidated fully, on my own, and beyond the shadow of a doubt. Incredibly, I've never ever seen that topic being discussed or mentioned anywhere at all, at any point in time. The subject I'm referring to is the perhaps most obvious prismatic peculiarity. See below.
Why is the base of the prism so clearly on display for the observer's eye when by all known accounts it simply shouldn't, couldn't, wouldn't. Right? Wrong. Obviously. To my mind then it became right from the start imperatively necessary to find out asap via what processes or factors does that particular aspect of the prism become an absolute matter of fact. In the end, I can assure you that the answer to that question turned out to be rather easy to uncover, as you will see in a moment.
The reason behind the fact we are discussing is straightforwardly simple, and you should be able to deduce it (if you don't already know it, that is) as soon as you take a good look at the picture below.
Every conceivable subjective observation through s prism is determined by the interplay of the two active faces of the prism, which due to their particular orientations enables the observer to get a perspective of whatever there may lay along the spatial dimension that is normally forbidden to the naked eye. I'm talking here of course by what we call the third dimension of space--its depth. Thus, in our case the base of the prism becomes visible due to the inclination of the face of the prism, which virtually is a window that is facing at an angle the floor, if you want. And this is also the real reason for which there is a displacement of objects viewed through a prism toward its apex. I'll give you now a few moments to think about that while looking at a beautiful depiction of that process in the picture below.
It certainly is an idea the brain accommodates very comfortably, for when it's analysed by using the common sense as a yardstick it passes all the tests with flying colours. But it's not only satisfactory to that kind of scrutiny. It is also successfully passing the more stringent demands of a scientific investigation. Consider for instance this particular line of investigation. Can the idea put forward here account in some quantitative measure for the observable results of all relevant subjective experiments? The answer is yes. One concrete example could be the one I offered many years ago, which was depicted in the picture below.
I took two 45⁰ prisms (of the size specified on the left) and after placing them as shown in the picture on the right I drew two lines that should indicate the exact amount of displacement the observer would see, if the idea at the centre of the issue was correct. Then in the middle of the picture I placed a diagram that depicted the entire line of reasoning from a geometrical perspective.
My understanding of our current topic of discussion meets all the demands required by what we call a good scientific theory. (That is a realisation I only began to see in the relatively recent times, after many years of a chaotic struggle with things I didn't know and within an inhospitable and unfamiliar environment that I didn't understand.) It is a good theory for a number of reasons, of which the first and foremost is the fact that it is fully verifiable. And that is, as I nowadays understand, the quintessential attribute of a good theory. By contrast the long reigning conventional understanding is far from being a good theoretical view of the phenomenon of image displacement in prismatic observations. That's because, let's be frank about it, it does not offer any direct means for a quantitative verification. (Which, by the way, is the same crucial flaw in Goethe's vision of the colour phenomena.) A simple examination of the textbooks on the matter will immediately reveal that fact. Indeed, when I first started reading the conventional textbooks in physics, I was stunned to see the virtually total absence of mathematics in their presentation of the subject, which is a very rare occurrence, as we know. But if that was the first event that had struck me as highly odd, soon enough a second one I came to learn about proved to have even a more astonishing effect on me.
These two diagrams are official depictions of the conventional understanding and they can be seen in numerous places online. (Check out OptiCampus.com for example.) Nevertheless, the message they are conveying is manifestly--and easily demonstrable--incorrect, wrong, false and untrue. Yet beside myself I have never seen anyone else do it (demonstrate it).
I did it on a few occasions over the years, and in a number of different ways. For instance, the first couple of times I did it by using the experiment depicted in the two images below.
Let me briefly explain what the two pictures are showing. I first drew a line across one face of a prism at exactly halfway, then I began to slowly turn it around and observed how the image of the line was moving at a higher point in the direction of the apex. My argument against the conventional understanding then was that I did not have to adjust the line of sight of the camera (or mine as an observer, for that matter) in order to notice the apparent displacement of line's image, which is clearly evident in the pictures I took. In effect I therefore proved that the observer does not have to place his eye in and along the line of refraction to see the displacement of an image in a prism.
Then on another occasion I used the experiment pictured below.
Taking as point of reference the well-known effect of the total internal reflection of light in a 45⁰ prism, I drew a line across one of the straight faces of such a prism at exactly the halfway mark (as shown in the middle picture above) and upon rotating the prism around I saw that in total contrast to what an observer would have conventionally expected, the image of the line was still displaced in the direction of the apex. And since this yet another observational fact that flies right in the face of the conventional teachings we feel quite entitled to say "There's something rotten in Denmark, my people".
This experiment, when it is combined with its complementary counterpart below, provide the most eloquent evidential example sustaining my understanding about the real causes behind the phenomenon of image displacement in prismatic observations.
On the inclined face of a 45⁰ prism I drew a horizontal line at the halfway point. (Left picture.) Then, without changing my line of sight, I turned the prism around and looked at it with its straight face in front. (Right picture.)
The result of such experiment is that the observer will see the image of the line in the same place, along the middle of the prism. In other words, there is no displacement in this case. An obvious question then arises that demands an unambiguous answer. Why is there no displacement observed in this case when in its counterpart there definitely is one? The conventional understanding simply cannot answer that question. In fact, it fails to provide a consistent explanation for either. The conclusion is clear, straightforward, direct and in the end definitive: The conventional understanding cannot answer that question. According to my understanding, on the other hand, in the first case of this two-fold experiment there is a displacement of the image of the line toward the apex of the prism because the observation is carried out through an inclined 'window', whereas in the second case the observation is conducted through a 'window' that is straight, which really means that it has a spatial orientation running parallelly to the spatial orientation of the observer.
This post is turning out to get much longer than I had anticipated. So, in the interest of everyone concerned, I have decided to conclude it here and continue the presentation of my work in the next post, which will be Part 3 of the titled subject. See you then.
There are a number of very good reasons behind my saying that it shouldn't take long to conclude that the conventional theory is definitely inadequate to account in a coherent and cohesive manner for the results observed in the subjective experiment pictured above. Before starting in earnest to discuss them though I'd like to point them all out for you and thus give you a chance to try to anticipate on what kind of ground and foundations have my beliefs been built. And I'll do that by using the means shown below.
I want you to look first at those two-line segments in the picture, and try to think in what way could they be connected. I personally first thought about that little subject many years ago, and I am quiet proud to know that I elucidated fully, on my own, and beyond the shadow of a doubt. Incredibly, I've never ever seen that topic being discussed or mentioned anywhere at all, at any point in time. The subject I'm referring to is the perhaps most obvious prismatic peculiarity. See below.
Why is the base of the prism so clearly on display for the observer's eye when by all known accounts it simply shouldn't, couldn't, wouldn't. Right? Wrong. Obviously. To my mind then it became right from the start imperatively necessary to find out asap via what processes or factors does that particular aspect of the prism become an absolute matter of fact. In the end, I can assure you that the answer to that question turned out to be rather easy to uncover, as you will see in a moment.
The reason behind the fact we are discussing is straightforwardly simple, and you should be able to deduce it (if you don't already know it, that is) as soon as you take a good look at the picture below.
It certainly is an idea the brain accommodates very comfortably, for when it's analysed by using the common sense as a yardstick it passes all the tests with flying colours. But it's not only satisfactory to that kind of scrutiny. It is also successfully passing the more stringent demands of a scientific investigation. Consider for instance this particular line of investigation. Can the idea put forward here account in some quantitative measure for the observable results of all relevant subjective experiments? The answer is yes. One concrete example could be the one I offered many years ago, which was depicted in the picture below.
I took two 45⁰ prisms (of the size specified on the left) and after placing them as shown in the picture on the right I drew two lines that should indicate the exact amount of displacement the observer would see, if the idea at the centre of the issue was correct. Then in the middle of the picture I placed a diagram that depicted the entire line of reasoning from a geometrical perspective.
My understanding of our current topic of discussion meets all the demands required by what we call a good scientific theory. (That is a realisation I only began to see in the relatively recent times, after many years of a chaotic struggle with things I didn't know and within an inhospitable and unfamiliar environment that I didn't understand.) It is a good theory for a number of reasons, of which the first and foremost is the fact that it is fully verifiable. And that is, as I nowadays understand, the quintessential attribute of a good theory. By contrast the long reigning conventional understanding is far from being a good theoretical view of the phenomenon of image displacement in prismatic observations. That's because, let's be frank about it, it does not offer any direct means for a quantitative verification. (Which, by the way, is the same crucial flaw in Goethe's vision of the colour phenomena.) A simple examination of the textbooks on the matter will immediately reveal that fact. Indeed, when I first started reading the conventional textbooks in physics, I was stunned to see the virtually total absence of mathematics in their presentation of the subject, which is a very rare occurrence, as we know. But if that was the first event that had struck me as highly odd, soon enough a second one I came to learn about proved to have even a more astonishing effect on me.
These two diagrams are official depictions of the conventional understanding and they can be seen in numerous places online. (Check out OptiCampus.com for example.) Nevertheless, the message they are conveying is manifestly--and easily demonstrable--incorrect, wrong, false and untrue. Yet beside myself I have never seen anyone else do it (demonstrate it).
I did it on a few occasions over the years, and in a number of different ways. For instance, the first couple of times I did it by using the experiment depicted in the two images below.
Then on another occasion I used the experiment pictured below.
Taking as point of reference the well-known effect of the total internal reflection of light in a 45⁰ prism, I drew a line across one of the straight faces of such a prism at exactly the halfway mark (as shown in the middle picture above) and upon rotating the prism around I saw that in total contrast to what an observer would have conventionally expected, the image of the line was still displaced in the direction of the apex. And since this yet another observational fact that flies right in the face of the conventional teachings we feel quite entitled to say "There's something rotten in Denmark, my people".
This experiment, when it is combined with its complementary counterpart below, provide the most eloquent evidential example sustaining my understanding about the real causes behind the phenomenon of image displacement in prismatic observations.
The result of such experiment is that the observer will see the image of the line in the same place, along the middle of the prism. In other words, there is no displacement in this case. An obvious question then arises that demands an unambiguous answer. Why is there no displacement observed in this case when in its counterpart there definitely is one? The conventional understanding simply cannot answer that question. In fact, it fails to provide a consistent explanation for either. The conclusion is clear, straightforward, direct and in the end definitive: The conventional understanding cannot answer that question. According to my understanding, on the other hand, in the first case of this two-fold experiment there is a displacement of the image of the line toward the apex of the prism because the observation is carried out through an inclined 'window', whereas in the second case the observation is conducted through a 'window' that is straight, which really means that it has a spatial orientation running parallelly to the spatial orientation of the observer.
This post is turning out to get much longer than I had anticipated. So, in the interest of everyone concerned, I have decided to conclude it here and continue the presentation of my work in the next post, which will be Part 3 of the titled subject. See you then.