Quantum mechanics cannot be used to explain the mind and consciousness, but it does provide patterns of relationship that give us deeper insight into the teachings of yoga. A key mathematical pattern underlying quantum mechanics is the Fourier transform, which can also be used to account for features of yogic cosmology.
Contents for The Yogic View of Consciousness:
|Intro||Ch 1||Ch 2||Ch 3||Ch 4||Ch 5||Ch 6||Ch7||Ch 8|
|Ch 9||Ch 10||Ch 11||Ch 12||Ch 13||Ch 14||Ch 15||Ch 16||Ch 17|
|Ch 18||Ch 19||Ch 20||Ch 21||Ch 22||Ch 23||Ch 24||Ch 25||Ch 26|
|Ch 27||Ch 28||Ch 29||Ch 30||Ch 31||Ch 32||Ch 33|
The previous chapter considered bindus as akin to diffraction gratings that break white light into orders of rainbows. This was intended to provide a metaphor of how minds within minds within minds project through the bindu, akin to how orders of rainbows project out of a diffraction grating. In this context, quantum mechanics (QM from here out) was brought into the discussion. I stated that QM only seems weird in the context of classical scientific realism but from the yogic perspective is quite natural.
Since QM underlies our present understanding of both light and matter, all this talk of waves, rainbows, light, etc. as analogies for understanding yogic ideas begs the question about the role of QM. Therefore, this chapter, and the next one, will be a digression on why QM is natural in the context of yogic cosmology.
QM began as a theory about light and atoms. However, it rapidly evolved into a new and very general way to think about nature. The shift to this new way of thinking was the dividing line between classical and modern physics.
QM introduced into physics the idea of conjugate variables, or complementary variables, which also are called “duals”. This did not appear out of the blue, but evolved from an older mathematical method widely applied in physics called a Fourier transform. The new way of thinking about nature sees the logic of Fourier transforms playing a fundamental role in the behavior of nature. Part of our goal here is to outline what this means.
Recall that Chapter 8 discussed mathematics as patterns of relationship. The Fourier transform is a pattern of relationship, one of great generality and beauty. It is applied in many domains of science and technology. Examples of technologies based on it include: radios, TVs, cell phones, microscopes, telescopes, and in a certain sense, all of QM. We discussed Taimni’s “broadcast station” idea that greater minds “broadcast” into lesser minds. The theory that underlies how radio and TV stations work is based on Fourier transforms.
Analogies between yogic cosmology and physical phenomena indicate that the pattern of relationship embodied in Fourier transforms is also applicable to the perceptions experienced in the state of samadhi. That is, similar patterns of relationship occur in yoga and QM. It is not that QM can be used to explain yogic cosmology. QM, as a theory of light and matter explains how light and matter work, not how minds works.
I want to be as clear as I can about this: I am not invoking QM to explain anything to do with yoga, the mind, or consciousness. I am saying that QM and yoga share similar underlying patterns of relationship. One of the most important patterns of relationship they share is embodied by Fourier transforms. Thus, the same deep generalities QM reveals about physical nature operate throughout the entirety of Manifestation.
As discussed in Chapter 11, the basic distinction in yogic cosmology is form versus consciousness. It is the form side we are concerned with here. When wave concepts are invoked to explain a given form, somehow or another the pattern of relationship embodied by Fourier transforms is lurking in the picture. QM shows that the pattern of relationship embodied in Fourier transforms occurs in physical phenomena in a deep and ubiquitous fashion.
Analogous patterns can be found in yogic cosmology. Concepts such as the gunas, OM, the functions of the bindu, the types and functions of vrittis all partake of the fundamental pattern of relationship symbolized in Fourier transforms.
One wonders if William Blake realized how literal was his poetry (a shout-out to Andrew Rhodes for reminding me of this verse…):
To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.
When similar patterns operate in different phenomena, this is the expression of “as above, so below”. Although causal interactions occur between the various scales of things, “as above, so below” does not seek to demonstrate such causality. Instead, it seeks to show that analogous patterns of relationship operate at different levels of Manifestation.
The discussion below goes as follows. I will: (1) orient the Reader to learning QM, (2) briefly review superposition, (3) discuss what a Fourier transform is, and (4) show how Fourier transforms sit at the heart of QM. Therefore, the present chapter amounts to a book report about QM. This can’t be helped if we wish to have at least some modicum of depth to the discussion.
Why Quantum Mechanics is Difficult
This section is intended to help orient Readers who have vague ideas about QM. The factors that make QM difficult to understand fall into two categories: (1) legitimate scientific concerns, and (2) other stuff. Let’s briefly consider two examples from each category.
Legitimate Science Concerns
- QM was the culmination of about 300 year’s prior experience in math, physics, and related empirical disciplines (chemistry, astronomy, material science, electricity and magnetism, etc.). To try to learn QM out of the blue without some knowledge of this prior history is unrealistic.
- QM began as two independently formulated theories of atoms. In 1925 Heisenberg and colleagues published their matrix mechanics. In 1926 Schrödinger published his wave equation. Within a few years, these were realized to be two different ways to say the same thing. However, as stated above, something more fundamental occurred when QM came on the scene. QM gave rise to a new way to look at how nature works. This new way of thinking was then applied in a wide variety of diverse physical situations, leading to the explosive growth in our knowledge of physical phenomena during the 20th century and continuing now.
In a sense, the original QM is like the trunk of a tree. The prior knowledge in classical physics and the first two decades of 20th century physics were the roots of the tree. The new stuff to grow out of the original QM is like the many branches of the tree. If one is not aware of this tree-like relation then QM will appear incomprehensible.
The focus here, on conjugate variables in physics, is what Heisenberg et al. very consciously introduced into physics, and represents a clear dividing line between classical and modern physics.
- Whole cottage industries of philosophy, metaphysics, and intellectual speculation have wrapped themselves in the mystique of QM. Unlike what I said above about finding common patterns, these ideas instead try to use QM to explain all manner of fringe topics such as the mind, consciousness, parapsychology, “psi” (psychic powers). Additionally, there are fringe controversies in physics such as the many worlds interpretation, the collapse of the wave packet, and other such ideas. None of these fringe ideas affect the practical application of QM. The fringe physics bleeds into the speculative stuff. Taken together, they are like a big, dark cloud that surrounds and obscures the central scientific kernel of QM. The non-scientific topics range from interesting to stupid (leaning heavily towards the stupid), and they serve mainly to side-track one from understanding the nuts and bolts of QM.
- The last factor is sociological. A good percentage of people enjoy being part of an “in crowd”. They also enjoy a feeling of power and authority and one-upping others. There is a certain degree of obscurity surrounding QM stemming from the expression of such factors by those who use QM in practical ways. Some of the more outspoken of these people get a sense of superiority out of using their “in crowd” language, showing people how smart they are, and other such petty psychological factors. These are the pygmies I have mentioned previously, and they are prone to getting caught up in such nonsense. There is priesthood-like quality to all of this that runs hand in hand with the legitimate science mentioned above. When the practitioners revel in the obscurity and do not have the wherewithal to make things clear to laymen the result is scientism instead of science.
This is hardly a trivial observation. There is an ever-growing polarization between those lay-people who distrust all science, and those who blindly accept it like mindless lackeys. This stems in large measure from people who wish to be priests and others who wish (or do not wish) to follow priests. Let me sum this 4th point up with a quote from van der Leeuw:
“…it frightened away the investigating layman and made him feel that it was his fault, his shortcoming which prevented him from understanding its profound mysteries…. When a thing is clear [one] must be able to say it in simple and intelligible language. If he fails to do so and if many volumes must be written to expound what he might have meant, it is a certain sign that his knowledge was confused. Only imperfect knowledge goes hidden under a load of words.”
van der Leeuw was talking about philosophy in this quote, but the same can be said for any branch of learning, including QM.
One final comment: The science and math discussed below is mainstream and well-known to the relevant professionals. They will, I am afraid, be disappointed at the simplicity of my presentation. I shall indeed attempt to explain QM so that any educated person can follow along. There will be no formulas. I will use graphs and pictures to convey the intuitive essence of the ideas. Nonetheless, I will explain the technical features of QM, not fluffy sensationalism.
I introduced basic wave concepts in Chapter 13. Recall that adding and subtracting waves is called superposition. Figure 1 shows simple examples of adding sine waves to give either constructive or destructive interference:
In the top, the waves line up perfectly peak-to-peak and trough-to-trough (are 100% in phase). When waves are perfectly in phase, they add together to give a new wave that is sum of the height (amplitude) of the original waves. This is called constructive interference.
In the bottom, the two waves are 100% out of phase because the peak of one wave lines up with the trough of the other wave. In this case, one wave acts like the negative of the other wave and they cancel each other out to give no wave at all, which is destructive interference.
Since the phase of the waves can result in something that looks like either addition or subtraction, people use the term “superposition” to refer to performing arithmetic on waves. From the humble beginning shown in Figure 1, waves can superposition in the most complex of ways, giving rise to complex ripple patterns, interference patterns, rainbows, and other phenomena that are familiar to all of us. Figure 2 shows some real-life examples of wave superposition. Superposition of waves is the main idea behind Fourier transforms.
Figure 2: Wave superposition results in complex ripple patterns familiar to all of us. Going clockwise: (1) Wake of a boat interfering with water waves (source), (2) light refracting and interfering with itself to make rainbows, like an oil slick (source), (3) More water waves (source), (4), sand molded by water waves after the tide goes out (source).
Fourier transforms were one of the many important mathematical accomplishments of the great French mathematician Joseph Fourier. Fourier had the amazing insight that any arbitrary squiggle line, no matter how complicated, is the superposition of simple sine and cosine waves. He invented formulas linking the complicated line and the simple waves, and those formulas are now called a Fourier transform. Since this discussion is written for laypeople, we are not going to present the formulas. Instead I’ll describe in words what the formulas do.
You can think of the Fourier transform like a little machine. You feed it an input and it spits an output back to you. It takes a complicated squiggly line as an input and then outputs the simple waves that make up the complicated wave. The simple waves are called component waves. You can also reverse the process. If you superposition the component waves, you get the complicated input wave back.
This is best illustrated by example, so consider Figure 3, taken from the Wikipedia entry on Fourier transforms, that nicely illustrates a Fourier transform in action.
The input wave (red) is called a “square wave”. It can be constructed by superpositioning several sine waves (blue) of different heights (amplitudes) and frequencies. The last panel shows how to express the result of performing a Fourier transform on the red square wave.
The top panel is the input (the red square wave). The bottom panel shows the output. The output consists of the amplitude and frequencies of the component waves. The height of each blue line is the amplitude of one of the simple waves. The position of the blue line from left to right indicates the frequency of each wave: the further to the right, the higher the frequency.
When the input wave depicts something changing in time, the output is the frequency of the component waves. The way people say this is a Fourier transform converts from the time domain to the frequency domain.
Because the output consists of many simple waves, each with its own frequency, people refer to the output as a spectrum. A rainbow is a type of spectrum. However, there are many, many different types of spectra. The Fourier transform is very general because it can output any type of spectrum.
Figure 5 is a real-life example of a Fourier transform operating on human speech (taken from here) that is intended to intuitively illustrate the link between the input time signal and the output frequency spectrum.
When we talk, we make a pressure wave that moves through the air. Since the pressure wave changes with time, it is in the time domain. The top of Figure 5 shows a speech pressure wave changing in time. This should be familiar to anyone who has opened a sound file in an audio editor.
As you know, people’s voices have different pitches, or frequencies. Women generally have higher pitched voices than men, for example. The bottom figure is what happens when you perform a Fourier transform on the pressure wave. As you can see on the bottom graph, you get a series of three peaks at different frequencies of roughly 140, 275, and 425 Hz. These are rather low pitches and it’s a safe bet that this is a man’s voice.
This example illustrates what it means to take a time domain signal, feed it into a Fourier transform, and get an output spectrum in the frequency domain. In this example, the Fourier transform allows us to determine the pitches that make up someone’s voice.
Reciprocal Relationship of the Fourier Transform
There is a special relationship between the input signal and its output spectrum. It can be said like this: if the input is wide, the output is narrow. Alternatively, if the input is narrow, the output is wide. You can see this effect in Figure 5. Notice how wide the time signal on the top is, and how the three frequency peaks are narrower and not as spread out.
Figure 6 is a better example of the wide/narrow relationship. In the first row, the input is narrow and the output is wide. That means a short change in time gets Fourier transformed to a wide frequency spectrum. As you move to the 2nd and 3rd rows, the input gets wider, and the corresponding output, the frequency spectrum, gets narrower.
This is called a “reciprocal” relationship. If one side is one way, the other side is the opposite. If the input is narrow, the output is wide. If the input is wide, the output is narrow. I am stressing this because in QM this effect of the Fourier transform is called the “uncertainty principle”. As you can see, it is simply a consequence of the math pattern provided by Fourier transforms.
The reciprocal relationship between input and output is not magic. It follows directly from the mathematics. This is one disadvantage of not showing the math. If one understands the math, the reciprocal relationship is quite obvious and sensible.
What the Fourier transform gives us is a conjugate relationship between the input variable (time) and the output variable (frequency) (think conjugate = conjugal = marriage = two sides of the same coin). The Fourier transform shows that they are two different ways to look at the same thing. The Wikipedia link on conjugate variables provides a perfectly nice explanation:
“Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals of one another”
Another way to look at it is that the input variable and the output variable mutually determine one another. If you know one of them, the Fourier transform automatically allows you to calculate the other one. This is the meaning of conjugate variables. It is this property that lies at the heart of QM, and whose vast elaboration makes up large swaths of modern physics and mathematics.
To conclude, we can summarize the features of the Fourier transform described above:
- The Fourier transform takes an input and converts it into wave stuff, specifically into a spectrum, by using superposition of waves.
- If one side (input or output) is narrow, the other side will be wide.
- The input and output are two different ways to look at the same thing. They are conjugate variables.
Now that we have an overview of what a Fourier transform is, we can discuss how it is applied in QM.
Here is the main idea: QM introduced the use of conjugate variables into physics. This idea captures all that is seemingly weird about QM, and is what makes QM different from classical physics. Why this idea was introduced into physics is not something I discuss in detail here. You can read about the double slit experiment (which is briefly discussed below), or atomic spectra to see how empirical observations forced these ideas into physics. Nature was simply discovered to behave this way.
In QM the relationship between conjugate pairs is called the “uncertainty principle”. The term makes perfect sense in the context of physics. But it is an unfortunate term because it masks the fact that the conjugate pairs are related by a Fourier transform type relationship. The essence of QM is shown in Figure 7.
Figure 7 shows how the physical properties of position and momentum are conjugate variables related by a Fourier transform (technically they are “operators”, not variables, but that is unimportant for our present scope). Position is on the left and momentum on the right. I am purposely not specifying the thing whose position and momentum is shown because this relationship applies to all physical things.
As Figure 7 shows, either position or momentum can correspond to the wave side of the Fourier transform. If position is a single value, then momentum is on the wave side. If position is on the wave side, then momentum is a single value.
The wave side of the Fourier transform does not mean the thing we are discussing forms a wave. This is a common misconception of QM that light or matter can interchange between being a wave or a particle, commonly called the “wave/particle duality”. This is not the correct way to think about it.
The correct way to think about it is to understand how the Fourier transform pattern is used to measure the number values of each conjugate properties.
One of the properties has a sharper value than the other. In Figure 7 this is depicted by the vertical line on the graph. For the top (orange) it is position, and the bottom (blue) it is momentum. In this example, the value for each is just a single number: f2 for position and f1 for momentum.
Then, the other member of the dual pair automatically takes on a range of possible numerical values. In this example, the possible numerical values fall on the numbers laying on the sine wave. This is why it is called uncertainty in physics, because the possible numerical value for the property can be any number that falls on the sine wave. Which number is it? It could be anyone of them, so there is a high uncertainty about the true value of that number. The wave pattern tells us the possible values of the thing’s properties. It does not mean the thing is a wave.
There is nothing magical about this. It is simply how Fourier transforms work. Fourier transforms provide us a pattern to understand the conjugate properties of things in nature. Conjugate properties are called “non-commuting observables” in the technical lingo of QM.
Thus, QM superimposes the logic of Fourier transforms over nature. What this means is that conjugate pairs, like position and momentum, mutually determine each other. If you know one of them, you automatically know the other. If one is a sharp value, the other will necessarily be capable on taking on a wide range of possible values. That two variables can mutually determine each other by a Fourier transform type relationship is what distinguishes modern physics from classical physics.
Some Implications of Conjugate Variables
Thus, as you can see, there is no physical wave and no physical particle. There is only the Fourier Transform-like relationship between the conjugate properties of the system. QM tells us that we do not know what the thing really is. We cannot visualize atoms or electrons or photons. They neither are physical waves nor are they particles, nor do they interchange between the two. QM humbles us and provides a clear-cut example of the limitations of our minds (remember the “pretend you are a fly” discussion?). We simply cannot visualize these really small things. But we do know that some of the properties of these things are linked as conjugate variables by Fourier transforms.
Realizing that QM describes physical phenomena in terms of conjugate variables makes clear one of the weird counter-intuitive aspects of QM. In classical physics, the mathematical patterns used to describe a thing’s properties like position and momentum do not have any effect on each other. Why should where I am located in space (my position) determine how fast I am moving (my momentum)? In our everyday physical experience, it doesn’t seem like my position determines my momentum. This is a perfect example of Kant’s (and others’) idea that appearances are misleading. It may not seem like this is the case, but the fact is, this is the case.
As Figure 7 illustrates, if you are located at a certain position, then this is “hooked up” to the possible values of momentum (where the possible momentum values are spread in a pattern that looks like a wave). Said simply: position and momentum determine each other. They are no longer independent, as was the case in classical physics. This “linking up” of properties via a Fourier transform is the heart of QM and is absent in classical physics. This linking up of the conjugate variables supersedes all other considerations. Dynamics, force laws, etc. must bend to and accommodate this requirement (such “bending of the knee” is built into Schrödinger’s wave equation).
How come it seems that our position and momentum are not linked up in our everyday experience? Way back when all this stuff was discovered, one of the main leaders in QM, Niels Bohr explained this. He called it the “correspondence principle”.
Bohr’s correspondence principle can be stated like this. For a single atom, or small group of atoms, we will see the effect of conjugate variables (such as having a specific position determining the momentum values). But as we add more and more atoms (or whatever small thing we are considering), we gradually wash out the effects of the conjugate variables.
As human beings we are made of gazillions of atoms. When so many atoms come together to form a human, or rock, or even a grain of sand, the effect of the conjugate variables gets washed out. How do they get washed out? The short answer is: nobody knows for sure. There are two main ideas about the link between the classical and quantum that are accepted by the majority of workers in QM. Bohr formulated his correspondence principle, and there is a more modern idea called quantum decoherence. However, there are those who have doubts and, like little piranhas, are constantly nipping and biting at QM to find the answer.
The correspondence principle is technical and has to do with the math of quantum mechanics, specifically things called quantum numbers. When these are small, we experience the quantum effects. When they become large, the quantum effects become so close together that we can no longer make out the wave-like behavior of physical systems and the changes can be taken as continuous for all practical purposes.
Decoherence is also a technical concept. It can be thought of in simple terms as akin to how a mixture of oil and water separate out when allows to stand undisturbed. The analogy is that “things” whose wave functions are initially hooked together (or mixed) separate out because of influences from the environment. Any system we design (an experimental apparatus, a technology based on QM) is not perfectly closed off from the world. The world impinges on the system and destroys quantum interactions that we may not even know about. The net result is that something that appeared blended together becomes separated.
Again, most people accept these ideas to explain how the classical and quantum are linked. But QM is only about 100 years old. It is still an open question whether or not we have the full picture. The math seems complete, but there are those who refuse to accept the cognitive dissonance this theory brings.
Let’s summarize the main ideas about QM:
- QM is the application of the Fourier transform pattern to physical phenomena.
- As such, QM describes some properties of physical things to be related as conjugate variables, such as position and momentum. In the discussion of Fourier transforms above, we showed time and frequency were conjugate pairs. In physics, frequency is related to energy. Therefore, the time/frequency pair can also be expressed as a time/energy pair. There are many other such pairs too that I am not discussing here.
- The properties symbolized by the conjugate pairs mutually determine each other, and their mutual relationship is given by a Fourier transform. One side will be narrow and the other wide (sometimes you get both sides about the same width, as in the middle example of Figure 6). In physics this is called “uncertainty”, but it is really just a consequence of the pattern of relationship embodied in a Fourier transform.
- Since the Fourier transform is all about waves, then superposition sits at the center of how things behave in nature.
- When things are very small (or relatively simple) we can see the effect of the superposition. In big things made of gazillions of small things, the superposition washes out and things appear to follow the classical laws of physics and appear to be continuous.
Double Slit Experiment
Let’s end this extremely brief, extremely simple discussion looking at the double slit experiment that illustrates the property of conjugate variables shown in Figure 7. Everyone agrees that this experiment captures all the seeming weirdness of QM. From the perspective I am taking here, the double slit experiment simply shows the effect of the fact that position and momentum are conjugate variables, and must be linked by a Fourier transform, which means that one of them will fall on a wave distribution and therefore superposition will make interference patterns.
Here, electrons are allowed to pass one-by-one through a double slit apparatus as shown in Figure 8. The electrons are released very slowly so that they go through the apparatus one at time. You would think the electrons would go through one slit or the other and make just two piles on the detector as shown in Figure 8, panel A. However, the answer you get is shown in panel B: even if the electrons go single file through the detectors, over time an interference pattern builds up on the screen.
I recommend you watch the following movie of this.
You can see in the movie how each electron is detected as a single point on the detector screen. This means that the position is well-defined (the particle is at a specific place on the detector screen). Thus position takes the narrow side of the Fourier transform. Therefore, momentum must fall on the wave side of the Fourier transform. Since the possible momentum values fall on the pattern of a wave, and the electron can have any of these momentum values, you get superposition of the various values of position and momentum. This causes interference fringes to form.
Why The Double Slit Experiment is Weird…To Classical Realists
This result illustrates what is “weird” about quantum mechanics. You can see from the individual dots that something that seems to be an individual particle is hitting the detector. However, if just a single thing passed through the slits, then how to explain the interference pattern?
One possibility is to imagine that the single thing going through the slit interferes with itself. But this would imply the thing was a wave, and goes through both slits at the same time, just like, say, a water wave would. But the thing hits the detector screen at only one place. If it was a wave is should “splash” widely against the screen, but that doesn’t happen. Since this explanation doesn’t work, perhaps we should get desperate and imagine, in a manner we cannot at all visualize, that the electron goes through both slits at the same time.
Figure 8: Double slit experiment. Based on intuition, you expect to get the answer shown in panel A, which is incorrect. Panel B shows that you get an interference pattern, even though the little things pass one-by-one.
In either case, it makes no sense to the typical Western intuition that has been conditioned by some 400 years of classical Western realism. Over the slightly less than 100 years that people have known this is how nature works, the paradox of it has driven many otherwise sane people quite mad by trying to visualize what the little object really is.
To repeat: QM teaches us that the little object is not something we can visualize. Our brains are just not wired to visualize electrons, photons, etc., as objects, just like our brains are not wired to visualize four-dimensional objects.
On the other hand, QM allows us to make precise statements about these little things. Some of the little thing’s properties are linked as conjugate variables by a Fourier transform. When one knows the math, there is nothing mysterious or foggy going on. It is all mathematically precise. If it was foggy and mysterious, we would not be able to harness the little objects to make computers, cell phones, MRI machines, and other stuff.
Results like the double slit experiment are only a mystery if one insists that the little objects are classical objects. Attempting to force this issue has nothing to do with QM, and everything to do with bad and sloppy philosophy. Those who would superimpose a classical world over quantum mechanics are like spoiled brats who think they will get their way if they kick and scream loud and long enough.
The confusion that surrounds QM is highly ironic. It is little more than a form of petty anthropocentrism operating under the naïve supposition that the way our brains are wired to perceive the world contains all the possible ways the world can be. That is an extremely stupid position to take.
It comes back to Weyl’s view of science, math, and the noumena. Math gives us possible patterns of relationship. Science measures stuff and figures which patterns best fit what is measured. In the case of QM, we got what we got. It is a window into the noumena. It does not fit our perceptions of how objects behave in everyday life. So be it. So what if the world is more complicated than our brain can conceptualize? I don’t recall one of Moses’s 10 Commandments saying: “The World Shalt Not Be Abstract”.
The Disease of Interpretation
I want to close with an editorial about science involving an issue that is very acute in QM. The idea that some people like to be members of the priest class goes hand-in-hand with scientism. I’ve written two blog posts (post 1, post 2) on Hermann Weyl’s understanding of the link between math and science. Let’s review his main insight:
“In physics we do not a posteriori describe what actually occurs in analogy to the classification of the plants that actually exist on earth, but instead we apply an a priori construction of the possible, into which the actual is embedded…”
Said simply, it means that people superimpose the patterns of relationships expressed by the various forms of math over how nature behaves. When it works, great. But this is all that is going on: we guess about some relative pattern, and then check it against our experience. When one does exactly this activity, one is doing science.
When one abstracts the picture away from the math, the experiments, and the details of matching them up, and instead seeks to make a belief system out of some relatively arbitrary qualitative interpretation, one is doing scientism. They are two totally different activities. Real scientists are busy doing science. It is those people who have aspirations of belonging to the priest class who do scientism.
Even though I have given a brief and simple overview of QM, the idea was to show how the math pattern of the Fourier transform sits at the beating heart of QM, and how it is interpreted with respect to physical phenomena. That is the meat-and-potatoes of the matter.
If you think it is possible to go beyond the math of QM, you need to turn to philosophy or metaphysics. However, then you find yourself digging for the treasure in the West, where the Yaksha of the “bewildering metaphysics born of Ignorance which we mistake for Jnana” will engulf you. (If you don’t get the reference, read The Parable Of The Poor Man section).
Having outlined the meat and potatoes of introductory level QM, the next chapter will discuss some points of overlap between QM and the yogic view of consciousness.