Consequences

Our actions have consequences. When we're being careful, we choose our actions so they'll have the best possible consquences. Most commonly what this means is that we try to change the world so it satisfies our desires more. But our actions don't just change the world, they change our selves. We often divide our activities into two phases, e.g. rehearsal and performance. The purpose of rehearsal is to refine our capabilities. Performance is when apply those capabilities to create an aesthetic experience for an audience, for example. But this division is just a rough cut. All of our actions change who we are at the same time that they change the world.

This division of experience into self and world is problematic. An athlete might consider their own body to be a component of the world. One's actual self might be perhaps the rational component of mind, something constant underlying even one's shifting mental capabilities. One of the essential insights of the Buddhist tradition is that the search for this constant underlying component of the self is futile. And yet this framework of thinking, e.g. "I will do this," seems practically unavoidable. If we want to use a conceptual framework of self and world, how can we think about this without getting distracted by illusions?

Organizational behavior is a doorway to a different perspective. It is not just individual human beings who act. All kinds of organizations act: political, military, industrial, academic, religious, etc. At a planetary scale, all of humanity acts. A basic principle of systems theory is that analysis starts with a clear definition of the system to be analyzed: what is part of the system, and what is not. A complementary axiom is in easy reach: the self is what is not in the system. The key point here is that the division of experience into self and world is like establishing a coordinate system or a frame of reference. It has no ontological foundation but is a practical step to allow conceptual elaboration for solving specific problems.

In organizational situations, it is commonly understood that actions both change the world and also change the self, i.e. change the organization engaged in the action. Teams develop cohesion by working together.

That what we are is a dynamic pattern that is constantly being shaped by our actions and experiences, that an important factor in choosing our actions is how those choices will reshape who we are... this perspective seems easier to achieve when we feel safe and secure. When things are good, we are happy to train ourselves to make them even better. When things are difficult, our entire focuse is on fixing problems with the world so we have no desire or opportunity to train ourselves. People do train themselves to be able to respond to difficult situations, though mostly that is to make themselves more capable of making whatever necessary changes to the world. But sometimes people do understand that shaping the world to meet their desires is not going to go very far, and they need to shape their own expectations. Aging gracefully can include such adjustments. What an older person can do is not the same as what a younger person can do. There is a lot less frustration in playing the hand you've been dealt.

At the planetary scale, the growing human population and the growing levels of consumption are driving us up against ecological limits, mostly prominently due to climate change but many other problems are accelerating too, such as aquifer depletion and ocean desertification. The reflex response is to demand that the world change in order to let us preserve our way of life. But of course our way of life is always changing and will continue to change as a consequence of our actions. However one chooses to partition the situation, it is always a dance between self and world. Our habits change, our understandings change, our values change. This dynamism is both a challenge and an opportunity. If our response to our discomfort is to become ever more stubborn and insensitive, we can certainly ramp up the level of mutual frustration to a catastrophic breaking point. But if we can respond to discomfort with care and flexibility, then we can discover tender joys in the most suprising places.

What Is To Be Done?

We are constantly faced with decisions about what to do, at every scale. Oranges are on sale: how many should I buy? Fossil fuels are creating climate havoc: should we switch to nuclear fission power?

In the simplest situation, one can foresee with sufficient accuracy the results of each alternative action, and choose the one with the most positive result. This formula outlines some major dimensions of a decision-making situation. One needs a set of alternative actions from which to choose; one needs to understand the results of each possible action; one needs to evaluate each of these possible results.

Commonly enough it is not possible to predict accurately the results of actions. We must decide in the face of uncertainty. We might have a pretty good idea about the probilities of the possible results of each possible action. For example, in a card game, we can calculate quite accurately the probabilities for each combination of cards we might draw from a well-shuffled deck. When developing a financial plan for living in retirement, actuarial tables can give reasonable estimates for survival to whatever age. Comparing the uncertain results of various possible actions is quite difficult. Given a choice between one action whose result is a certain $1, against another action whose result is $0 with probability 99% and $100 with probability 1%.... the expected value for each action is the same, $1. Whether to buy a raffle ticket for $1, that is a choice where expected return is not going to sufficient information to make a decision.

Many real world situations do not permit probability calculations with any realistic promise of accuracy. Probabilities are applicable in situations that repeat. Of course situations never repeat exactly, but a large number of situations can be similar enough so that the outcomes of each possible action can be tabulated to provide guidance for what to do when the situation occurs yet again. But sometimes situations don't repeat with any reasonable similarity. What's the probability that Donald Trump will be elected President in 2024? Of course one can assign this whatever probability seems appropriate, but there is no way to check this number against the facts. In situations like this, one can look at the set of plausible outcomes of each possible action. An action might turn out well, or might turn out badly. How well? How badly? Comparing these sets of plausible outcomes is not simple or mechanical, but that's what's required for deciding on what action to take.

Sometimes a decision involves a significant action that takes place essentially at a single point of time. For example, if I am considering a major purchase, at some point I have to signal my decision to complete the transaction. But oftentimes what is called for is an ongoing series of actions. There is deciding what to cook for dinner tonight, and then there is deciding on my diet, on my pattern of meal selection. I don't have to plan out my meals for the rest of my life; I can decide on meals more or less on the spot, depending on my schedule, my activities, the availability and prices of various food items, etc. In a game like chess, there is no way to plan out the full sequence of moves one should make in order to win. Each move must take into account the preceding moves of one's opponent, which cannot be predicted with anything like sufficient accuracy. One can, however, potentially decide on a strategy. A plan is a sequence of actions. A strategy is like a table of possible situations that might arise in the future and what action to take in each situation. Market orders versus limit orders in the stock market would be an example. A market order is the decision to buy or sell some number of shares. A limit order is conditional: whether any shares are bought or sold depends on the market price. A market order is a plan, a limit order is a strategy.

Deciding on a strategy can be very difficult. It can be impractical or impossible to tabulate all the possible situations that can arise in the future. And when one encounters a situation in the future, one might choose a quite different action than whatever had seemed the wisest back when one was contemplating future possibilities. Our understanding of actions and outcomes evolves: we are always learning, or at least we can be learning. So an effective strategy for action is one that enhances the quality of one's future decisions, by providing opportunites for learning along the way, and leaving open as wide a range of possible actions in the future as possible.

We should not be planning to imprison ourselves; we should be planning to liberate ourselves.

Fission Power

Evidence continues to mount that fossil fuel combustion is causing climate havoc. Floods and droughts, damage to cities and farms: it is becoming clear to more and more people that we need to wean ourselves off fossil fuels somehow. This is, however, an enormous challenge. We humans live very large on the earth nowadays, in our combinations of large populations and comfortable lifestyles. We consume energy globally at a rate of about 20 TeraWatts. We cook, heat our homes, drive our cars, run our factories... energy is fundamental to our modern way of life. Most of this energy comes from fossil fuels: coal, petroleum, and methane. To avoid enormous difficulties from any total change to our way of life, we need to substitute non-fossil sources to continue to provide energy at the required scale. Maybe in the future we will develop new sources, but in the next few decades at least we will need to rely on existing technology. Renewable sources such as solar, wind, and hydro are already in widespread use. Energy storage systems can help bridge the gap between fluctuating supply and fluctuating demand. But how to scale up renewable sources to meet the requirements of our modern society remains a daunting challenge. Nuclear fission is another existing technology that already provides steady reliable power at large scale. It is an very real option on the table for addressing climate change.

When your credit card bill is due and your checking account is empty, it is tempting to pay one credit card bill by borrowing from a different credit card. The general temptation is to solve short term problems by creating even larger long term problems. It's not an entirely invalid approach, but it's definitely smart to go down that road with eyes wide open. If we do choose to ramp nuclear power up by the factor of about 25x that would be needed to meet our energy needs, how might that move fit into a longer term strategy?

The long term strategy for modern society is rather cloudy but still worth considering. There is not going to be any kind of consensus possible, but that shouldn't stop a person from thinking about it. Some of the main options:

• The world is due to end quite soon, so a long term strategy has no application.
• We cannot have any idea about the future. Long term planning is an absurd pretense.
• Technology will continue to advance at an ever more astounding pace. Any problems we create now will easily be fixed by the people of the future with their capabilities that will be almost miraculous by our present standards.
• Maybe after a few thousand more years of expanding population and increasing comfort, humanity will start to bump up against actual planetary limits, but there is no point in worrying about that now.
• We are clearly hitting real planetary limits already. But it takes time for us to shift our various systems, such as agriculture, to more sustainable patterns. We cannot continue to consume energy at today's rate, but we need a few decades to shift. The immediate dangers of climate change mean that we need to shift to non-fossil sources sooner than we can reduce our energy consumption. Nuclear power can provide a bridge from today's unsustainable way of living to a future sustainability.

It's worth thinking through what nuclear power would look like under these various scenarios. To ramp up nuclear power by 25x over the next decade or two is already a daunting prospect. If energy consumption continues to double every 50 years or so... what this would mean exactly in terms of uranium mining, waste management, fuel transport, etc. - I don't have answers, but it would be worth exploring such possibilities.

To flesh out such visions of how nuclear power could be scaled up in the future, perhaps the baseline assumption might be that everything goes according to plan. But effective engineering requires us to think about what might go wrong. If we are considering the option of walking down a tightrope to get to our destination, we'd be wise to understand how high off the ground that rope is!

Some of the unpleasant surprises worth considering:

• Natural disasters such as earthquakes can cause radioactive material to escape containment.
• Safe management of nuclear material can require a somewhat advanced level of industrial capabilities to make available the necessary equipment and materials. Even with scaled up nuclear power, other factors could cause our industrial capabilities to be significantly reduced.
• All kinds of human bungling are not just possible but unavoidable. People are not perfect - not even close to perfect.
• It's not just that people make mistakes. People will quite deliberately act to benefit themselves at whatever cost to others. It may be possible to build a very safe reactor, but it will cheaper to build one that is less safe.
• People are always involved in conflicts at every scale. Nuclear technology can be weaponized in any number of ways. Of course we have very many nuclear explosive devices already built and ready for action. But the more we have fissile material circulating and the machinery for refining it etc., the easier it will be to build more explosive devices.

  Weaponization is not limited to nuclear explosives. Depleted uranium is already in widespread use in various types of bullets and other projectiles, just because of its metallurgical properties. Easy availability of radioactive materials will make them attractive for all sorts of uses. Various sorts of dirty bombs, conventional explosives coupled with radiactive shrapnel, are also straightforward possibilities. We have seen in the Ukraine where Russian troops occupied nuclear power facilities, because Ukrainian forces would not likely attack them there because of the risk of releasing radiative materials into the environment.

• Nuclear technology can be a source of conflict. A nation might be developing nuclear technology for entirely peaceful purposes, but this unavoidably also increases their ability to build nuclear weapons. Their enemies will be motivated to attack and destroy their nuclear facilities, to cut off that nuclear capability.

It's also important to think about how we should evaluate consequences. We could just decide that it is too difficult to wean ourselves off fossil fuels, and just accept the ensuing climate change. We could cut our energy consumption dramatically to avoid climate change, and just accept the ensuing disruptions to our way of life. Or, if we decide to scale up nuclear power and some of the possible negative consequences arise, how bad could they be? Nowadays I see folks arguing that nuclear war wouldn't be so bad. Perhaps any cost short of human extinction should be considered acceptable. Even if ramping up nuclear power leads to human extinction... well, humans will surely go extinct sooner or later anyway, and if nuclear power improves our lives before that point, maybe it is a worthwhile bargain.

Understanding the various risks is very difficult. Many of the numbers involved are simply unknown, especially when the time scales involve many thousands of years. But there are also more complicated sources of uncertainty. Government inspectors will help prevent dangerous cost-cutting in nuclear facilities, but then government inspectors are themselves corruptible too. Nuclear advocates will point out that there have been no documented fatalities due to plutonium toxicity. But of course the people that handle plutonium employ many safety measures. Is plutonium safe because we know how dangerous it is? It's a bit like how the Mutually Assured Destruction provided by nuclear weapons has made the world a safer place, in some sense or other.

How can we decide what to do, in a game with such high stakes, with such high uncertainty, faced with such paradoxical logic? At least if we can get some common understanding of the predicament, that might be a start!

Steady Growth

There is a notion around that humanity requires steady growth to be healthy and happy. Steady growth clearly cannot continue for long on a finite planet. So there is another related notion around, that interplanetary colonization is required for humanity to be healthy and happy. Even the solar system is finite of course, so interstellar colonization is a natural next step. Why not intergalactic?!

But there are other physical limits that will constrain growth. Of course it could be that we will discover that our notions about physical limits are not accurate. But then our notions about the need for growth could be wrong, too. Any and all of our ideas could be wrong, but still, we're thinking beings; if we expect to succeed with interstellar colonization, we'd better hone the precision of our thinking!

One of the most fundamental physical limits in our theories today is the speed of light. Perhaps we'll find a way to colonize other galaxies, but it will take us a very long time to get to any of them!

Steady growth generally means exponential growth. Over a generation, the growth in whatever segment of the population will grow in proportion to the size of that segment. If health and happiness is to be equitably distributed, and if health and happiness requires growth, then growth will be exponential.

Physics comes in because humans, whatever else they might be, are also physical objects. The disciples of Ray Kurzweil might quibble: perhaps humans, in essence, are actually information. But even information requires some minimal physical substrate to be stored and processed! In any case, I am certainly not proposing that the specific numbers of my back-of-envelope calculations here should be taken with any seriousness. My point here is that steady growth will eventually bump up against the physical limit of the speed of light. I invite everyone to run the numbers as they see fit.

Suppose humanity's domain is some large sphere, centered on the earth presumably, and stretching out through interstellar space toward the distant galaxies. Since humanity is steadily growing, its domain is also growing. If humanity is growing exponentially, the volume of its domain will also be growing exponentially. Of course humanity can grow, to some extent, while in some fixed domain. That's what we've been doing on earth so far.

What exactly the carrying capacity of earth is, that's difficult to say. But, again, there are physical limits. The earth's mass is about 10^13 times the total mass of humanity. If the population grows at a steady 1% per year, then in about 3000 years, the total mass of humanity will exceed the total mass of the planet earth. Obviously we will run into serious trouble long before that; it is difficult to predict the exact course of our battle against limits to growth. The point of my quick calculations here is that they set some quite hard bounds. If humanity is to continue to grow at a steady 1%, certainly before 3000 years have gone by, we will need to be well down the road of interplanetary colonization.

It's easy to run similar numbers for the solar system. In less than 5000 years, the steadily growing mass of humanity will exceed the total mass of the solar system. Probably we will not find a way to digest the sun, so we will need to be colonizing distant stars well before then.

So let's say that we have spread out in the galaxy out to some radius R. If humanity is growing at 1% per year, the volume of its domain must also be growing at 1% per year, and then the radius will need to grow at 0.3% per year. Once that radius hits 300 light years, that steady growth will require the radius to grow more than one light year per year, i.e. faster than the speed of light!

So a reasonable bound on steady growth of 1% per year is that the domain of humanity will hit a hard physical limit at radius 300 light years. That's a volume of about 3 x 10^61 cm. Given the rough density of galactic matter, the total mass in that volume would be about 3 x 10^40 grams. A human weighs about 10^5 grams, so that would be a maximum population of about 3 x 10^35... assuming humans have incorporated all material into their bodies! Today's population is about 10^10, so that's a population growth of a factor of 3 x 10^25. At a steady 1% growth rate, we'll hit the speed of light in about 6000 years.

Of course these rough calculations involve many very unrealistic assumptions. There is no way that humanity will absorb into their bodies the entire mass of galactic matter inside a sphere of radius 300 light years. But even if they could, we'd hit the speed of light in 6000 years, given a steady 1% growth rate. 6000 years is already not an absurdly long time - it's roughly our historical horizon. Absurdly generous assumptions about the success of humanity's battle against the limits to growth already run into limits that are not absurdly far away.

Non-Euclidean Science

Maybe I should call it non-Aristotelean, or non-Platonic, but the exact name isn't the point. Euclid built geometry up from postulates; Aristotle explained motion as objects returning to their natural state; Plato portrayed experience as the shadow play of forms in an ideal realm. In each case, a complex field of phenomena is explained as the outgrowth of some simple essential foundation. Perhaps I should call my proposal non-foundational science. But I am not proposing any kind of freed-floating science. I am proposing a science that is founded on reality, on the vast tangled web of lived experience. Science is an extract, like resin extracted from the sap of a tree. There is a lot more to a tree than such resin. The tree itself is embedded in soil and climate, in an ecological web, flying pollinators and mycorrhizal fungi. The simple essence emerges from the whole, rather than the whole emerging from the simple essence.

Science as a quest for an inner key that explains everything - such science takes us on a quest into ever more remote realms. It distances us from experiencing what is right at hand. Of course, building and launching the James Webb infrared telescope surely involved considerable attention to experiences right at hand - precision torquing of many bolts, etc. Galaxies and quarks are not objects of direct experience, but neither are they disconnected from direct experience. What I am proposing is no neglect of any corner of the world. I am suggesting a shift in how we understand the way all the bits and pieces fit together.

Non-Euclidean geometry provides an excellent analogy. The surface of a sphere, such as the surface of the earth, is a perfect concrete instance. Euclidean geometry is plane geometry, the geometry of a flat surface. At the scale of a few square miles, the earth is extremely close to a flat surface, and can be mapped onto a flat sheet of paper with great precision. But as the area to be mapped increases to include a significant fraction of the earth's surface, inevitably distortions arise. There is no perfect flat map of the earth.

The impossibility of perfection does not mean that we just give up and produce fantastic maps that have lost any connection with the lived experience of moving around on the earth. The value of a map is exactly in how it relates to such lived experience. Whether a map is good or not, that depends on how the map is to be used. A map that is good for navigation will typically not be a good map for estimating agricultural productivity.

Pure science is science that neglects its relationship to its use. Applied science is science that orients itself to its use. The classical scientific attitude is that applied science grows out of pure science. I am proposing that a healthier approach to science is to see pure science growing out of applied science. Applied science connects to the vast complexity of lived experience. Refining our ideas requires chopping out local regions to be precisely mapped. This always involves distortion and omission: the inevitable price of precision. It's like taking a photograph: a fast shutter speed can reduce blurring from movement, but requires opening the aperture which increases blurring from less depth of field.

Our scientific quest for ultimate theories is like the old searches for the alchemical philosopher's stone or the healer's panacea, a medicine to cure all diseases. Good science requires following the clues wherever they lead, but it also requires a perspective on the actual situation so that one doesn't chase clues just for the sake of the chasing. Good science is science that is engaged with the lived reality of an actual situation.

Double Helices

Here is an image of a torus with a square lattice drawn on it. This lattice is formed by the intersections of two helices drawn on the torus. There are many ways to draw such helices on a torus, and the lattice pattern emerges from the combination of two such helices. This kind of double helix square lattice on a torus is a broad family of geometric shapes.

This kind of geometric shape can be used in music several ways. It can serve as a model for the time evolution of a piece of music. It can also serve as a model for the harmonic relationships between the pitches used in music. Since music is, in large part, a relationship between time and pitch, a piece of music can be modeled as a relationship between two different toruses, a torus of time and a torus of pitch. Of course most music won't fit this model very well or at all. But it can serve as a blueprint for creating music.

Musical time as a helical path on a torus... maybe it's because I have been thinking this way for decades, but it seems quite natural. Of course a piece of music often has more of an arc structure, a beginning, a middle, and an end. But often within that large arc, whole stretches are largely repetitive, where the end of each repetition joins smoothly with the beginning of the next. If the repetitions were exactly the same, this would simply be a circle. But perhaps the words of verses change or other details, so each repetition is slightly different than the last repetition. To bring the last repetition close to the first repetition is of course a more arbitrary choice, but not a very wild one. I hope this makes sense of the notion of musical time as a helical path on a torus.

The idea of pitches being related harmonically in a way similar to a helical lattice on a torus... this is hardly a new idea in the world of music theory. There are many ways to use this kind of geometric shape to represent harmonic relationships. The circle of fifths is the most basic. Major thirds are another fundamental relationship between pairs of pitches. These two intervals then create a mesh of relationships that can be laid out on a torus:

Here the green line traces the circle of fifths. There are four red loops, representing the circles of major thirds.

This torus of harmonic relationships can be drawn for alternate tunings. The different topologies generated display the different musical possibilities of these alternate tunings. One important alternate tuning divides octaves into 19 equal steps instead of the usual 12. The torus of harmonic relationships for 19edo looks like:

The green loop here again represents the circle of fifths. What's more interesting is that major thirds no longer divide up the pitches into separate loops. Instead there is one large loop traversed by major thirds.

With these two toruses and their helical lattices, the harmonic structure of a piece of music can now be mapped out. For the most part, one would expect phrases that are closely related in musical time to be closely related harmonically. There might be abrupt transitions, but they make sense in this approach in the context of surrounding smooth relationships.

The simplest non-trivial mapping uses a loop on the pitch torus, some path through the lattice that returns back to the starting point. This loop is then traversed in musical time. It could be that each repetition traverses the loop. Or perhaps the repetitions don't move much internally, but each repetition moves slightly relative to the previous repetition, so the harmonic loop is traversed over the course of the whole piece.

Algebraic topology is the mathematical discipline where these sorts of smooth mappings are enumerated. Mapping a torus onto a torus is a rather elementary problem in algebraic topology... but there is still a rich variety of possibilities to be explored musically!

Another feature of alternate tunings is that additional basic harmonic relationships can be introduced. Exactly what makes pitches sound harmonically close, that is an endless topic of study and debate. But one fundamental notion with a long history is that frequency ratios very close to a simple rational ratio, that's the basis of close harmonic relationships. An octave is a frequency ratio of 2:1. A perfect fifth is a frequency ratio of 3:2. A major third is a frequency ratio of 5:4. In conventional music, these basic intervals are the foundation of harmony.

One natural step in extending music into wider worlds is to introduce yet another basic interval, governed by the frequency ratio 7:4. This extra relationship makes the torus of harmonic relationships much more difficult to draw... it's not anything that could physically exist in our three dimensional world. But of course mathematically it is nothing very complicated to manage. A tuning that can represent this new interval quite accurately, along with the more conventional intervals, is 171edo, the tuning that divides octaves up into 171 equal steps.

An instrument with so many notes would be physically unwieldy. But with a software synthesizer and algorithmic composition, it is not so hard to build a piece of music based on a mapping of this more complex torus onto a torus of musical time:

Double Helices

Sliding Schismas

For some years now I have been exploring music and tuning, through algorithmic composition. I have a computer program that I tweak, to change tuning systems, scales, etc. How much of the tweaking that I do is actually reflected in the output, in any perceptible way? That's a question worth examining!

Here is a set of musical pieces. The only thing I changed in the software from one piece to the next is that I changed the seed for the random number generator. The random numbers it generates control very many choices in the execution of the program, so these pieces will vary quite a bit. But the primary choice in question is the harmonic movement involved, the key changes. Some of the pieces don't have any movement at all. Others have a progression that is six steps long. Some of the pieces move along the progression in the forward order, other move in the reverse order.

So the question here is: can you divide these pieces into three groups, one group with no key changes, another group that moves in one direction, and a final group that moves in the opposite direction. Can I tell the difference? (The names of the pieces are the seeds I used to initialize the random number generator for each piece.)

• 7000
• 7001
• 7002
• 7003
• 7004
• 7005
• 7006
• 7007

These pieces all use the 53edo tuning system, where octaves are divided into 53 equal steps rather than the conventional 12. These pieces all work with a schisma[17] scale, where 17 notes are selected in each octave out of the full set of 53. In the pieces with no key changes, the scale is constant throughout the piece. In the other pieces, the key changes in a regular pattern, shifting every measure. With six key changes, the scale returns to the starting scale.

Each row in this picture shows which notes are in the scale in one of the keys. In the pieces with key changes, from one measure to the next the scale will shift to the next row up or down in the diagram; in some pieces the key changes move up in the diagram, in other pieces the key changes move down. I repeated the sequence three times in the diagram, and also extended the scale a bit beyond an octave, just to make clear that the pattern continues smoothly through time and up and down the pitch space.

One could play the pieces with no key changes on a piano reasonably accurately. There are five pairs of notes that are very close togther, just one step apart of the 53 per octave. These would correpond to spit keys on a deluxe piano, a slightly sharp version of a note and a slightly flat version. Thinking of the split note as just two versions of a single note, then there are twelve coarse notes per octave, very close to a conventional piano.

The sequence of key changes in the other pieces involve two different shifts in the scale. Moving along the sequence in one direction, the scale shifts five times by a minor third, and once by a minor sixth. Moving in the other direction, the shifts are the inversions, i.e. five major sixths and one major third. In the 53edo tuning system, this combination of key changes brings the scale back to its starting point.

When the scale is shifted by a minor third, the new position of the scale include eight of the notes of the scale before the shift. The shift by a minor sixth has a similar amount of overlap. This overlap allows for good continuity of musical phrases across the shift.

Listen to the pieces above: some have key shifts, and some don't. Can you tell the difference?