Here there is a rectangular patch of land with dense trees.
On this day there was strong wind parallel to that pach of land, so there was a section with little wind covered by the trees between two wind corridors.
A number of small birds was there. They were slighlty bigger than the usual little birds we see in urban parks and that I feed at my house balcony. They seemed much more aerodynamic, geared for high speeds and agility.
For more than an hour, I witnessed as those birds were doing laps between the two wind corridors.
They would speed by themselves along the windless part or the circuit and when they reached the wind section after leaving the cover of the trees they would spend a few seconds almost still in the air, sustained by the strong wind, and then they were shot like arrows back to where they came from as they caught the force of the wind.
They were using the wind wall as slingshot and doing round trips for over an hour, occasionally resting in a fence at the other edge of the tree wall.
As there was no obvious benefit from this behavior, I can only conclude that they were doing it as a play, they were enjoying it. They were playing like our kids do.
And that seemed a very interesting thing in itself, compounded by many of its implications.
I felt happy for them. I reminded of some bigger birds I have seen when surfing in the sea, that pierced waves consecutively when they could just fly above them.
The sound is obviously artificial, nevertheless, it very accurately reproduces the amplification of the strings’ sound by the body of the accoustic violin, as well as the players’ movements.
It just seems to dampen the vibrato, but I can be misled by using different strings.
But the main advantage is that I can record regardless of the actual acoustic conditions of the place. It also allows the player to hear himself as if in the audience, which means real-time feedback on performance.
assemblies of cellular composite material at MIT by Kenneth Cheung
In the organization of the future there are only two groups of people: those who create value and those who coach into value creation. In the organization of the future there is no place for “managers” because the psychological mechanism that justifies them is made redundant. The need for a “manager” is a symptom that you need investment in either of those two groups of people. Therefore instead of spending money on proxies you spend on addressing the real needs of your organization. The only investment that makes economic sense is the investment in value creation.
The fact that we separate subjects of scientific study (“management” in this case) and consider them isolated from everything else is a scientific mistake as Descartes himself pointed out in his “Rules for the Direction of the Mind”. Its what PMI terms a “reduccionist approach” to understanding systems. But we compound that error with another one which is to apply the same approach to the application of those principles. That is why we pay people just to “manage” instead of investing in a unified evolving semi-autonomous and lightly-governed value creation structure — the organization of the future.
Jack Dorsey (former CEO of Twitter) recently claimed that he can dismiss all middle managers and have direct access to his workers. He is correct in doing so not exactly because of his argument (based on automation technology) but because of the principle stated above.
Donald Reinertsen in his book “The Principles of Product Development Flow, 2nd Generation Lean Product Development” applies principles from network engineering, manufacturing, the military and others, to the approaches for managing complex systems under variability conditions. It is aligned with the principle stated by Descartes. Its proper science.
This article follows the introduction to the piano for beginners available here.
Lets look at page 1 of Goodman’s book about abstract algebra (version 2.6).
He defines symmetry as an “undetectable motion”.
There are two components to this. One is the motion, or the action, an event or transformation that takes place. This transformation can include the identity transformation if you accept that changing nothing is also an action. The other component is the fact that this transformation changes nothing in the state of the object upon which it acts. The end state is the same as the initial state, therefore you cannot tell that the action took place just by looking at the outcomes. In this sense, a symmetry is doing something while doing nothing. For our purposes here, we generalize the definition to the change and the preservation of any property of the system under study. That is, a symmetry is a change on a property of the system that leaves another property invariant (unchanged). We will naturally be applying the definition to the system of the piano musical notes.
Without needing to objectively define music, we can define at least one of the attributes that distinguishes it from every other sequence of sounds. And that is a presence of a structure, or equivalently, an order. Music is a variation over a structure. For example, the difference between talking and singing is the symmetric structure of the latter. Using symmetries is one way of facilitating the creative process in music.
More specifically, we have two components in the system which can be acted upon by symmetries:
structure, that is, the choice of notes used
function or operation, that is, any relationship that can be established between the elements in the structure (notes)
Something we can therefore establish from the start is that whenever we have a symmetry we have a structure, and vice-versa. These are intermutable concepts. By definition, whenever we have music we have a structure, therefore to talk about music is to talk about symmetries. It is important to have this logical mapping in mind because, as those who are familiar with mathematics already know, we can study any system in place of another that we are inquiring about as long as we can establish a “faithful” relationship between those two systems. In our case here, we address the system of music using the system of symmetries, and due to this we are in fact acting upon and talking about the same exact thing. This also means that it is irrelevant whether a composer actually thought about symmetries while composing (most probably he didn’t).
It is also important to make it clear that a symmetry is not a pattern. A pattern is focused on the outcome, while a symmetry is focused on an action, therefore on the creation. Example of a symmetry: a rotation of a square on the 2D plane by 90 degrees around its center.
We can classify the symmetries we are interested in based on whether the structure or the operation are fixed:
if both are fixed then nothing changes; this is the identity transformation which for our purposes here is not a meaningful symmetry (but it is a necessary member of symmetry groups in mathematics)
if only structure changes, we have a structural symmetry, that is, the same relationship between notes; in this case the action is the structure, that is, the choice of notes, and their relationship is invariant ex: A B C D
if only the operation changes, we have a functional symmetry; in this case the notes do not change and therefore the only allowed operation is the choice of octaves. This is the same note played in different octaves.
if both change, the symmetry can be one of them or both depending on what can be fixed ex: A C B D… which can have as invariant the relationships 2, -1, 2, -1, etc
Because the operation or relationship is relative to a structure, we can start the creative process by a choice of structure. We create or choose a structure that defines an operation such that the pair is a symmetry. In this case structure induces symmetry which in turn induces new structure. And this is the creative process based on the concept of simmetry.
ex 1. create a structure from scratch: A C B D (example for case 4 above)
ex 2. take an existing structure A A B A A C, define a structure over it and create a new symmetric structure 2.1. (A A (B))(A A (C)) —> (A A (B))(A A (C)) + (A A (D)) 2.2. (A (A B A))(A (C —> (A (A B A))(A (C + D C))(A (E F E))
Improving an existing structure and creating a structure which can be improved are of course two different things. Some people struggle with just one of those. Symmetries allow to unlock the capability to create a structure upon which to improve. It is an architecture of general creation.
Different instruments favour different symmetries. This is in essence what makes music different between instruments.
We may start with an objective intention about what we wish to portray in musical language, but until the creation is done there always is a stage of exploration. By defining symmetries and variations of them we can evolve that structure until we find a resonance, that is, a unified structural “soundness”. A resonance in this context is an identity of a system. A system can have different resonances and it should be useful to study their relative properties, namely whether a particular resonance should be considered the unique identity of a system, in which case probably this system would be perfectly described. For our purposes here any resonance suffices in signaling we achieved our desired end — we created a new musical piece.
The difference between a composer in the classical sense and other people is not in the sensibility or imagination but in the knowledge of applicable symmetries. This is what is most impacted and favoured by experience, and therefore it is not determined by innate ability and can be developed. Classical composers had visions and feelings and inclinations just like you do. They knew how to use a musical instrument just like you do. But what you lack that they developed to a high degree is the understanding of the musical symmetries, because those processes codify musical creation itself.
This knowledge is precisely what is neglected by an obssessive focus on performance that is incurred by the totality of acclaimed piano players. Thus ironically, those who pursue a pure understanding of the composers they study, actually miss their essencial quality — the range of symmetric tools and transformations that they developed and that lie at the genesis of all of their creations. This is something that can be reproduced faithfully by anyone, but here also we do not benefit from imitation. There is no point in creating music like someone else used to do. Creation has nothing in common with pure reproduction. Is it a worthy reward to have worked so hard to play a musical instrument just to end up a trained monkey on a craft? Reward yourself by creating instead. That is what is worthy of you. As I explained elsewhere, this “systematic” creative process is in fact the only thing that has ever happened.
As a final remark, I can be somewhat bothered by the instrumentalization of the ideas here developed, namely by artificial replacements of human creativity, but I wish to see it as one more strong argument for the necessity of humans claiming possession of these tools. Otherwise there cannot be a leveled playing field, that is a human playing field. So claim it for yourself.
This is my suggested approach to the Piano for two scenarios:
1) just got a piano but you know nothing about music 2) starting to learn how to play pieces for both hands
I developed this approach after I analysed the bottlenecks in my own learning and how I could make it more efficient. You can expect to spend several weeks in the exercises but it will pay off big time because it will make learning the harder stuff much easier. By the time you start reading the score you will already be able to handle the keys without looking and it will allow to focus on what really matters which is understanding the score.
Just like learning how to drive a car, this is a process of gradual automation, bottom-up.
You can download a powerpoint with the exercises here.
The article about symmetries expands on this introduction into composing music.
Here’s where the comedy begins. Those who most loudly claim their superiority on account of their credentials are often the people who have most carefully avoided the risks that produce greatness. Have they endured years of structured, proper thoughts? Have they ever stood alone with an idea that is un-yielding, that refuses to bend to the consensus? Have they pursued it where it led no matter the consequences? The tragedy is not that such people exist, but that they have been mistaken for people who should be taken seriously. That is what should bother you if you are a free thinker.
The first thing that came to existence should by definition have been single, since it was the outcome of the first change that ever happened. Because it came to existence from nothing, it had to contain the principle of change in itself, since change is an attribute and not an object. Therefore the first thing changed. Once change created quantity, the first system was born. The first system generated new things which in turn generated new systems.
This process still happens today. In fact, it is the only thing that has ever happened. Therefore, still today new things can be generated out of nothing like their own kind. At any moment, a system can be created like no other before it.
This is the fundamental magician principle in the Tarot card No 1.
This music captures that moment when the Genesis change is about to take place. When interacting components are about to create a new system and the Creation takes place again.
Compliments of the Author 