The Yogic View of Consciousness 16: Yoga and Quantum Mechanics I


YVC16 CVR-02Quantum 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

  1. 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.
  2. 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.

Non-scientific stuff

  1. 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.
  2. 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.

Wave Review
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:

1. Interference simpleFigure 1: Constructive and 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.


OLYMPUS DIGITAL CAMERAFigure 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
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.

3. Fourier_transform WikiFigure 3: How a Fourier transform works (this is an animated GIF).


4. FT3Figure 4: Input pattern expressed as an output of simple waves.


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.


5. matlabscriptFigure 5: Fourier transform of a human voice showing the pitches (frequencies) making up the voice.


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.


6. gaussian FTsFigure 6: Narrow input = wide output. Wide input = narrow output.


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.

Conjugate Variables
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:

  1. The Fourier transform takes an input and converts it into wave stuff, specifically into a spectrum, by using superposition of waves.
  2. If one side (input or output) is narrow, the other side will be wide.
  3. 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.

Quantum Mechanics
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.

7. FT pos momentumFigure 7: The skeleton of QM.

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.

QM Summary
Let’s summarize the main ideas about QM:

  1. QM is the application of the Fourier transform pattern to physical phenomena.
  2. 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.
  3. 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.
  4. Since the Fourier transform is all about waves, then superposition sits at the center of how things behave in nature.
  5. 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.


8. DBL SLIT Right & WrongFigure 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
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.


25 thoughts on “The Yogic View of Consciousness 16: Yoga and Quantum Mechanics I

  1. PeterJ

    Drat. I wish I had the brains for this stuff. It all seems very relevant to another of my hobbies, the distribution of the prime numbers, but the details confuse my neuronal network. I still cannot grok how position and momentum can be conjugate variables as opposed to being mutually exclusive variables.

    I liked this one – “Only imperfect knowledge goes hidden under a load of words.”

    • Hi Peter!
      Nice to hear from you and thanks for commenting. Hopefully, my explanation makes it more accessible to you. Like I said above, part of the problem with understanding quantum mechanics is how it is so plugged into the prior 300 year history of physics. As to a link with prime numbers, I don’t know. As far as I am aware (which isn’t too much in the modern sense!), I’ve not heard of such a link. Primes are, in some sense, “mutually exclusive”, but as you noted, this is kind of the opposite of conjugated variables.

      As to van der Leeuw’s quote…yeah, I try to live by this. I’m probably not successful most of the time, but at least I have the ideal in mind when I communicate.

      Again, great to hear from you, Peter!

      Best wishes,

      • PeterJ

        Hi Kasyap. – Yes, you definitely have an advantage.

        I can see that the variables are not simultaneously measurable and have no problem with this, (and it seems to be true for anything that moves), but Don’s post seems to suggest that they vary with each other, and at a quantum level this idea really does leave me behind. Or it did. As I write this I begin to see the idea better.

        The prime numbers came to mind because of the Fourier analysis, since the distribution of the primes is the outcome of a superposition of waves. Also random quantum drums, whatever they are, seem to provide an example of this same superposition in observable micro-physical processes.

        I have no doubt at all that QM has everything to do with consciousness but am not tempted to grapple with it too seriously with no maths in my armoury. I can barely score a game of darts in real time.

      • Hi Peter
        Yes, that was really the main intent of the post was to show that (what are technically called) non-commuting observables are mutually linked mathematically. There is so much focus in popular accounts on the idea of simultaneous precise measurement of say, position and momentum, that it often masks the technical fact that non-commuting observables are mathematically related (by a Fourier transform-like relationship). This puts, I think, a different spin on thinking about QM. Instead of a mysterious “uncertainty principle” (again I don’t want to downplay the importance of this way of thinking for making measurements), you get two properties that were treated as independent in classical physics mutually determining each other in QM. That means, in some sense, the related observables are are not different in a fundamental sense, but are different perspectives on the same thing. Position and momentum are two facets of the same property, in some sense.

        I was talking the other day to some physicists at work about QM and I noticed an interesting thing going on. They had a much different philosophical position than me (theirs seemed implicit too; not a surprise). I have adapted Hermann Weyl’s neo-Kantian idealistic view wholesale: we can’t know what nature is, but we can superimpose math patterns over nature, and thereby at least get some insights. In this view, the math is primary and the science is secondary. But the physicists had the opposite view. To them, the math was just a tool, and they were putting the science as primary. The uncertainty principle, to them, tells us something fundamental about nature, and the math is just a means to an end to acquire this insight. To me, it contrasted what I guess could be called “scientific idealism” versus “scientific realism”. Not classical realism, mind you, but scientific realism, where the understanding of nature is put before the math pattern used to understand nature. To me this seems ass-backwards, but it was very interesting for me to notice this difference in our respective viewpoints.

        Anyway, I am still incubating how I will carry this over to yogic ideas and hopefully it will gel soon and I’ll be posting the next installment.

        Talk to you soon, Peter, and as always, thanks so much for your comments and interest!



      • PeterJ

        “Position and momentum are two facets of the same property, in some sense.”

        I can get that. I would liken it to freewill/determinism dichotomy and Hegel’s idea of the ‘sublation’ of such categories, giving us the two perspectives on one phenomenon that you mention. But I still struggle with the idea that a phenomenon can have variable values for each, such that a little less momentum means a little more position etc. Is this a mathematical artefact or an observed phenomenon? To me a particle should either have a position or not have one. It’s a partial position that I can’t get my head around. Probably just me.

      • Hi Peter
        Since we are trying to explain math stuff in words, you have to be careful with your words. It’s not that “a little less momentum means a little more position”. It is that, as the values momentum can take on becomes a smaller set of possible values, the possible set of values for position grows. The limit is the idea of a delta function. If momentum can only take on one perfectly well-defined value, then position can take on potentially an infinite number of values, where the specific numerical values fall on a wave that extends from minus to plus infinity. When you square the amplitude (height) of the wave in QM, this gives the probability a specific value will be measured. So, the position values falling on the crest of a wave are more likely, and those falling on the trough of the wave are less likely.

        It is no artifact. It was forced on physics by measurements. Originally it came from measuring atomic spectra. This led to a somewhat tortuous path of understanding culminating in Heisenberg’s matrix formalism. The matrix math automatically took into account the conjugate relationships. In matrix math (completely independent of physics), there is a simple, elementary formula that says AB – BA = constant. This means if you multiply matrix A by B it is NOT EQUAL to multiplying B by A. This means that matrix multiplication, in general, does not follow the commutative law: AB = BA. AB = BA is, in general, false for matrices. That is, order of multiplication matters. It was originally observed that the discreet energy transitions in atomic spectra have this property (I won’t elaborate here). This fact of observation was taken into account by Heisenberg’s math scheme. Hence “matrix” mechanics. In physics, the constant in the formula, AB – BA = constant, is h/2*pi, Plank’s constant, h, divided by 2 times pi.

        When Schrodinger made his wave equation, eventually, the link to the Fourier transform idea was realized. The matrix math did not easily lend itself to thinking in terms of waves. In the 1930s I believe it was John von Neumann (of inventing the computer fame) who recognized that Heisenberg and Schrodinger’s math were different ways to say the same thing. Since that time, physicists have “cleaned” things up and now present QM as a series of several postulates or axioms. These axioms have no logical or deductive justification, but are justified solely on the basis that you need them to measure things correctly.

        So, applying these ideas in physics is ALL about accurate measurement. It was FORCED on physics. Plank was the first one to feel this force and he, being a classical realist, did not like it one bit. Same can be said for Einstein and Schrodinger.

        As to observed phenomena, look at the double slit experiment again. What is happening here is that position is being forced to a narrow range of values (because the slit is narrow and limits the positions of the electrons). This causes momentum to spread out into the wave pattern of values, where some momentum values are likely and some not. This is where the interference pattern comes from, even if electrons enter the slits one by one. It is because the electron has a well defined position, and therefore, it’s momentum can take on a wide range of values, which they do, and produce the interference pattern. Again, the interference pattern comes because some momentum values are likely (those on the wave crest) and some unlikely (those on the wave trough).

        So, yes, it is totally observed. The math is required to accurately account for what is observed. Like I said, if we really wish to interpret the math, it is telling us: (1) position and momentum are two faces of the same coin (via the Fourier transform-like relationships used in QM) and (2) that we CANNOT visualize what these little entities really are (because we have no way, even in principle, to guess what momentum a single electron will have). Therefore, any classical realist view cannot be fit to these observations.

        There is one last step to understand why a classical interpretation is ruled out. We are so close, I might as well explain it…briefly! This is called Bell’s inequality, invented by John Bell. Again, people make a big mysterious deal out of it, but it is all just simply math. The idea is this: In probability theory, if you have two independent events A and B, then the probability that both will occur is P(A) x P(B) (Eq. 1). In QM, because you have the formulas for constructive and destructive interference on the wave side, you get a different formula: P(A) x P (B) x (some other stuff) (Eq. 2). The other stuff need not concern us. In the double slit, classically you expect a single electron going through the slit would be independent of the other electrons going through the slit. If that was the case, Eq. 1 should tell you the probability of two electrons going through the slits. However, the answer you actually measure is Eq. 2, which accounts for the wave effects introduced by the conjugate relationship (itself a consequence of using the Fourier transform idea to link the conjugates).

        This is a vast oversimplification, but it makes the general point. Since classical probability is not measured, and quantum-based probability is measured, this rules out a classical interpretation of nature. Again, however, it all follows from the math superimposed over how we observe nature to behave. It is all extremely logical. There is nothing at all mysterious about it. All the hoopla and mystique comes into QM with one simple assumption: the world we perceive with our senses is how the ENTIRE world and everything in it works. Like I said, this assumption is just stupid. QM forces us to accept that really little things cannot be visualized like we perceive the world, just like Einstein’s relativity shows that time and space do not, in every circumstance, behave how we perceive time and space to be.

        If the general public knew math, there would be no opportunity for so many charlatans to make a living off of mystifying quantum mechanics. The charlatans survive solely on people’s ignorance, just as they always have.

        Hopefully that helps explain a bit. Like I said in the article, knowing the history of all this makes a great deal of difference. If you tackle QM by itself, especially without a math and physics background, you are just asking for massive intellectual confusion!

        Best wishes,


      • PeterJ

        Wow. Thanks Don. That was well beyond the call of duty. I do understand a lot of that and I’m not questioning any of it. I’m a big fan of Ulrich Mohrhoff on this topic. But here’s the thing.

        “As to observed phenomena, look at the double slit experiment again. What is happening here is that position is being forced to a narrow range of values (because the slit is narrow and limits the positions of the electrons).”

        At the moment of the observation the electron has a position. Only when we do not observe it does it get fuzzy (or whatever). We can calculate the probability of it being observed here or there, but it seems to me that this would not actually require that it has any partial values for momentum or position before we do. Perhaps it doesn’t exist at all when we’re not looking. We infer its values and our predictions seem to work, but we have not yet made sense of or perhaps even discovered what is actually going on.

        Or that’s what I’ was getting at. It may be utter nonsense. I suppose I’m suggesting that the data doesn’t quite prove that the electron is actually doing everything that the maths predicts that it is, even if it predicts every observation correctly.

        Please don’t feel obliged to say much about this. I’m just exploring.

  2. kashyap vasavada

    Hi PETERJ:
    Like you I also read Don’s blogs with lot of interest. I have couple of advantages though. One is my physics background as a retired physics professor and another is my Hindu background. But admittedly the universe is intriguing to say the least and we are all trying to understand it in our own little ways. Your disbelief about position and momentum being conjugate variables arises if we try to understand quantum mechanics in terms of our everyday life which is strictly classical. Quantum mechanics says that these two conjugate variables are not simultaneously measurable (better than the uncertainty limits) . Period! This is not part of our everyday life and appears counterintuitive to our every day logic! Although I agree with Don that QM may or may not have anything to do with consciousness, the puzzling aspect is similar. I believe concept of divinity is also not understandable in terms of our every day experiences! In that sense they may be similar.

    • Hi Kashyap! Thanks for commenting. I hope I didn’t slay my beginner level explanation of QM too bad! Please feel free to point out mistakes! Best wishes! Don

      • kashyap vasavada

        Hi Don: Overall you have done a very good job of explaining impossibility of simultaneous accurate measurements of conjugate variables. Little nit-picking!! In Fig. 7 you are comparing x and p. There should not be any time t. In top left instead of f2, you want X0. In top right you want Cos(2πp X0 /h). In bottom right you want p 0 instead of f1 and in bottom left you want Cos(2π p 0 X /h) . h is Planck’s constant. In the wave top right it should be h/X0 instead of 1/f2. In bottom left it should be h/ p 0 instead of 1/f1. Rest is fine. Main message is the spread in (expected) measured values of x and p (not any specific values of x and p) which you have shown very well.

      • Hi Kashyap! Once again, thank you so much for the peer review. I’ll make the changes soon when I have the time. Best wishes! -Don

  3. PeterJ

    Sorry Kashyap – I ‘replied’ to Don but actually replied to you, so my reply went backwards in time and arrived before your comment. Only to be expected in a discussion of QM…

  4. kashyap vasavada

    Hi Don: There is something I have been forgetting to mention. There is an *Ashram* in NJ. A very knowledgeable ( American) swami , who was an engineer before he took Sanyas runs that! He has a series of recorded lectures on Yoga sutras etc. Taimni’s book is great, but in case you have time and interest, you might listen to these lectures also. He goes verse by verse in great detail. I am going through them these days, slowly!
    The web site is
    under teachings.
    Let me know what you think of them. Sanskrit with english transliteration can be found on web.
    Best wishes.

    • Hi Kashyap!
      Thanks for the link! I downloaded the first several talks. I listened to the first one and the speaker does sound very interesting. I’ve been neglecting the blog the past couple weeks. We have our big brain ischemia meeting coming up soon, and so have been busy preparing for that. Hopefully I’ll post next installment soon.

      Thanks again for the link, Kashyap!

      Best wishes,


      • kashyap vasavada

        Hi Don: I thought I would add some off topic comments here for further discussion.
        Recently I read some of your articles from archives.
        (1) About “especially for people born into Western cultures, which I consider bad karma on a spiritual level.” I would not worry about this! It is true that karma theory does not really work without the concept of reincarnation. For example, one can ask how a new born baby, who has some terrible disease. could have done something wrong in this life? But no body can choose his/her birth. You already have lot more knowledge and accomplishment in Hindu religion via meditation and studies than lot of born Hindus who just go to temples and participate in rituals!
        (2) One of your readers asked whether Asamprajnata Samadhi and Nirbij Samadhi are same. I am also under the same impression i.e these two words describe the same state. Apparently Taimni thinks otherwise.These are perhaps 2 thousand or more years old concepts. So it is not surprising that there may be some difference of opinion about their meaning. In few weeks I am going to a talk by a Vedantin scholar and I will ask him about this point and let you know.
        (3) I saw your comment on Lubos’ blog on Einstein etc. I did not want to leave a comment about it there. As you know, although Lubos is probably smartest physicist on the blogosphere, he is highly opinionated!! I would say that the last chapter in the book on quantum mechanics is not written yet. In addition to Einstein, some very prominent physicists like Weinberg, T’hooft and others still think that we do not yet know the whole story.These are intriguing questions whose final resolution is not at hand to this day. In any case, no body has any idea of how the theory of quantum gravity will work out. Although Einstein was most likely wrong about EPR argument, EPR and (subsequent) Bell’s theorem and experiments have resulted in tremendous advances. If a quantum computer becomes possible someday we have to thank these developments for it.

      • Hi Kashyap!

        So nice to hear from you! Sorry for the slow down here on the blog. I am preparing for our major international conference coming up the end of this month and just got off a 3 hr/day teaching stint.

        Thanks for the additional comments. Will give brief replies.

        (1) I spend a lot of time thinking about karma and reincarnation. An important aspect of the model I am building here in the Yogic View of Consciousness is that our “normal” waking mind is confined to the surface screen. Somewhere way in the depths of the cave of consciousness (e.g. deep in the unconscious mind) are records of past lives. I have, in my altered states experiences, tapped these in very feeble and incomplete fashions. Reincarnation is not linear in time. Time is not what it appears to our waking consciousness. In some sense, all of our incarnations happen simultaneously. In some even deeper sense, this idea I am trying to express about the mahabindu being like a diffraction grating speaks to this point. All things that exist in manifestation are of the same consciousness. In this sense, everything is a reincarnation of everything else. This is a consequence of the one mahabindu “diffracting” the one consciousness.

        (2) Regarding asamprajmata and nirbija samadhi. Taimni makes the point that the Yoga Sutras are so terse that they would not waste two words for the same concept. This assertion makes very good logical sense. The reason I advocate the definitions I do is because of my lucid dream experiences. I believe I have experienced asamprajnata samadhi here at the vitarka level. In DO_OBE I call this the “void”. I have been there many times. However, I have never experienced nirbija samasdhi, where this is consciousness completely dissociated from everything. Given my very low level experiences with vitarka asamprajnata samadhi, I can imagine what nirbija samadhi could be like, and I think the quote I provided by van Der Leeuw does a good job describing the nirbija state. Anyway, I would be most interested in hearing what you learn from scholars you have access to.

        (3) Thank you for noticing my comment on Lubos’ blog. Yes, he certainly expresses his opinions! I would characterize Lubos as a “quantum purist” or even a “quantum puritan”. His writings have led me to read directly some of the writings of Bohr, Heisenberg, Dirac, Born, and Einstein. In spite of his inflammatory style, it seems to me he is constantly repeating and defending what Bohr, Heisenberg, et al said. However, he is not a reactionary trying to turn the clock backwards, but tries to preserve the progressive nature of quantum mechanics. Based on my readings of the founders of QM, I tend to agree with Lubos that some past and current ideas are reactionary in that they are trying to return to a classical physics.

        The fact that QM and General Relativity cannot be reconciled indicates there is some very deep factor at play, something that has eluded the smartest minds for the past century. In this context, I think Lubos does a useful service by keeping the pure QM in a pure state and not let it get contaminated with speculative or superfluous baggage. I think having a clear view of the most pure form of QM will be important for whoever sees through it to the next stage in physics.

        If I had to bet money on the direction the next stage will unfold, I would go with Kenneth Wilson and his generalization of renormalization. The main reason QM has the form it does (e.g. linear operators) and classical physics has the form it does (e.g. old fashioned differential equations) is because of the respective scales of the phenomena. QM tells us we are too big to know the details at the microscales, yet gives us the ability to account for things at those scales the best we possibly can. That is one direction at least. The other important aspect falls back to mathematics. QM puts the discreet in the focus, whereas GR is the capstone of the continuous view of manifestation. Again, Wilson’s work is a step towards reconciling these opposites. Condensed matter physics deals with seemingly continuous phenomena that we know are made of discreet components. Taking this eternal tension of discreet vs. continuous to the next level, I think, will be a centerpiece of the next stage in physics.

        And to cap it off, I think the idea of mathematical form will take on a new importance. I am very influenced now by Hermann Weyl and his philosophy of science that I have described here on the blog. I would suggest his philosophy is quite alien to modern physics because he puts the mathematical form before the physical phenomena. Weyl was an idealist and believed we could never know, in any substantial sense, the nature of the physical phenomena. Our only handle to get glimpses of it is via the mathematical forms.

        I would suggest that since the revolutions in QM and GR, people have been philosophical realists, and focused on the physical phenomena. They are trying to explain space, time, energy, what have you, under the naive realist assumption that our mind can qualitatively understand these things. Weyl had no such illusions. There is only mathematical forms that we may superimpose over what we observe with more or less accuracy. But what we observe is forever beyond our ken in our ‘normal” waking state. The only way to go beyond is via the yogic methods I am writing about here. And based on the writings of those who have made the deep inner journeys, it seems to reinforce what Weyl understood intuitively: it is all just forms. Forms that can be mathematically described with more or less accuracy.

        Well, Kashyap, so much for “brief”! To summarize: I think Lubos’ position helps keep QM pure. He finds many levels to criticize “mixed” positions that try to extend the original QM. For this moment in history, it seems a prudent approach. It will be of great interest to see if any “beyond the standard model” physics is seen once LHC turns back on at higher energies. If no, then I think that will give great weight to Weyl’s position. If yes, then it will be very exciting for all onlookers.

        I hope I was able to convey my thoughts suitably. I will very much look forward to your reply.

        Best wishes!


      • PeterJ

        Hell Don. You write better comments than I write essays. This is fabulous. I’m going to read it again.

        An idea came up with your mention of surfaces. Have you come across the Bekenstein Bound? I always had a feeling that this has something to do with consciousness.

      • Hi Pete!

        Sorry for the tardy reply. Other things have been keeping me from the blog. Hopefully they will pass soon and I can get back to the YVC essay. Haha – thanks for the kind comments! All I can think to say in reply is “it takes one to know one”! 🙂

        The Bekenstein bound is an interesting idea that lives in a very weird context. I don’t know what to make of it. It contradicts Leibniz speculation that things can be shrunk or enlarged to infinity, or that a finite volume contains an infinity of “stuff”. It derives from trying to mix General Relativity and thermodynamics, so it quite a weird beast. The concept of “time” in thermodynamics is ambiguous because of entropy, and because there is no general theory of thermodynamics that encompasses equilibrium and non-equilibrium cases. On the other hand, the concept of “time” is very precise mathematically in GR. So, one must wonder which of the two theoretical structures is closer to the true nature of time, or if either of them is even in the ballpark!

        Overall I don’t fully accept the idea because, as someone who puts yoga and Hindu thinking before Western thinking, I accept the consciousness and infinity are somehow identical concepts. So, there cannot be any kind of intrinsic limit on consciousness. Perhaps the B-bound says something about the limits of how consciousness can act through the human form, but I don’t think it can say anything about consciousness per se. It’s all very much a part of the hinterlands of speculative mathematics and physics and as such constitutes a bunch of relatively subtle vrittis. But the truth is gotten by silencing vrittis, not playing around with relatively subtle ones. So, I come back to the image of the hamster on its wheel, going round and round very fast, and going nowhere.

        Anyway, hopefully I’ll be more active here soon. It’s great to hear from you, Pete, as always!



  5. kashyap vasavada

    Hi Don: I forgot one thing. As long as we are bragging about Hinduism one can add the following to the 5 points you mentioned in one of the articles!!
    (6) It is interesting to note that the sages somehow realized deep connection between humans and lower forms of animals in agreement with theory of evolution, unlike western religions which regarded human beings as separate form of creation from animals. There is a mythological story of “Dasavatar of Vishnu” (ten avatars of Vishnu) which starts from sea animal fish, then amphibian turtle, then half animal , half human and subsequently human form!

    • Hi Kashyap

      Thanks for adding this about evolution. I did a very brief write up on it in Chapter 9 of YVOC. Look for the section “Darwin was a Monkey“. It basically reiterates what you said, in the context of the yogic concept of pratiprasava, which is the “unfolding” of the more complex patterns back to the simpler patterns performed by yogis when they do samadhi. In fact, I don’t know if you saw this chapter 9: it might be of interest to you because I also discuss the reversible/irreversible debate in physics.

      Thanks, Kashyap!


  6. kashyap vasavada

    Interesting question about Bekenstein Bound and consciousness! Bekenstein bound is well respected in physics context, such as cosmology, black holes, information theory etc. But science knows so little about consciousness that it might be dangerous to try to relate the two. That may be the reason why,Don, a neuroscientist, is interested in Yogic ideas!

    • Hi Kashyap!

      Thanks for commenting! There is a paragraph in the Wikipedia page I linked in my reply to Peter about the “Human Brain”. It says, “If the brain is approximated by a sphere…”. This is rather funny and reminds one of the old joke about approximating a cow by a sphere! Anyway, the brain is certainly not a sphere. In fact, people have measured that the surface area of the cerebral cortex has a fractal dimension over 2. Further, the brain is the most complex physical structure known and presents a series of condensed matter physics problems that are so astounding as to take one’s breath away.

      But in general, you are correct. Yoga provides us an additional direction by which to understand the mind and consciousness and very much complements the physicalist views of Western science.

      Best wishes!


    • I wouldn’t say it was uninteresting, Peter. Some of the smartest physicists are working on this issue right now. It is very interesting in the connection I mentioned with Leibniz, that a finite volume cannot contain an infinity of information. This may be a clear-cut border between physics and speculative philosophy. Logically, there is nothing to stop us positing an infinity of “stuff” in a finite volume, which is what a fractal represents. On the other hand, the B-bound is an extension of well-established theoretical ideas going in a direction that suggests, for scientific purposes, we cannot think in such terms. Thus, we see the age-old problem of the finite vs. infinite under all this.

      • PeterJ

        I’d rather say that there is a border between physics and reality which only philosophy and yoga can span, and it is what I do say in my essay on the Grail quest. It seems to me that many problems in physics would be solved if we put them back in metaphysics where they belong.

        I wonder if the infinite/finite problem might be best addressed via Nagarjuna’s doctrine of two truths/worlds, which allows us to have our cake and eat it.

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