1924_02_03 ELEMENTS IN GEOMETRY

[Ani]

Note 2p

 

ELEMENTS IN GEOMETRY

 

Sixteenth lecture delivered by the Master before the Youth Esoteric Class on February 3, 1924 in Sofia.

 

- Only the bright road of Wisdom leads to Truth

- It brings us everlasting joy.

Reflection

We listened to a summary of the essays on the topic of “The Use of Imagination”.

 

For next time I would like you to write on topic#18 “The Basic Elements in Geometry”. This topic is somewhat philosophical. If you were asked about the elements in chemistry you would know them, right?

 

I would like for all of you to make a list of all the topics that you have been given so far in the last three years and I would like you to mark the date on each topic so as to see their order. These topics are like building stones in the construction of a building. In the same way, every subject that your mind dwells on will bring you either benefit or harm in a given situation. You must think but you cannot ignore the laws of thought. If you do not follow its laws, you will think falsely, i.e. in your mind you will follow a wrong path. There are only two ways of thinking: one is thinking in the dark, the other is thinking in the bright light, i.e. in the Light in general. Under the current conditions of Life you cannot be neutral. And if someone says that he can be neutral, he must be a deity. Even deities cannot be neutral. So, everyone who thinks will be in one position or the other or in both but not at the same moment, but one after the other.

 

Now some of you might ask, “Why can’t our minds be occupied with some greater subjects?” Why not, you may occupy yourselves with whatever subjects you like but then many external thoughts will come to your mind uninvited. All kinds of external topics will enter your mind but you must learn to discipline your mind, for that is why you are disciples. Disciplining one’s mind is the greatest skill. The undisciplined mind can be likened to a wild horse that jumps over all hurdles, no matter how big they are; it will jump over them even if they are hills and mountains. If you want to tame it you need to put a bridle on it. Sometimes when this wild horse starts raging, before you know it, he jumps over you and over the mountain, bridle and all, and you are left looking for him left and right. This is why you need to apply yourself to disciplining your mind. A disciplined mind is a great force in Nature. By disciplining one’s mind one also shapes one’s own character. You should not be troubled if there are bad thoughts that cross your mind along with the good thoughts; you should regard this as a necessary phenomenon. You cannot change the order of things: both Good and bad will come in their turn. Good and bad exist in the world for a reason that you do not know but what you should know is that you cannot change the way in which Good and bad are related to you. In order for you to change these relations you need to know the laws of your mind. When you start managing your mind - in a most wisely way, at that - you will start understanding the way Good and bad are related to you. Right now you think that you are very strong and that you can slam the brakes on your mind. But do you know what a catastrophe you could cause inside yourself if you slammed the brakes on your mind? You should gently step on the brakes, instead.

 

On the other hand, you must study the laws of your heart. Some of you complain about their mind, others complain about their heart and the third, about their willpower. There is no reason for you to complain about your mind, heart or willpower for they are very good. Your mind is very good, your heart is very good and your willpower is very good. Your mind and your heart and your willpower are where they should be but the only thing that is in your way is that you have forgotten the rules according to which your mind, heart and willpower operate. So you should keep in mind this: the most important thing the disciples of all esoteric schools must do is discipline their minds. For example, if you could discipline yourself right now in this class you would reach a state of peace and quiet and you would be undisturbed by anything around you as if you were by yourself. I have noticed that for the past few days a young girl from some village has started coming and do you know how well she is able to concentrate! Her mind is peaceful and quiet, her thought is moving smoothly and harmoniously. I ask you this: do you know what it would mean to you if you were to acquire this state of concentration today? You, too, used to have the ability to concentrate once but you have lost it. Now you need to restore it again.

 

Now you think that you have become very bad while earlier you used to be better. It is the opposite: you used to be worse before and have become better now. However, earlier you used to have less Light so you could not see yourself well. Now you can see yourself because you have more light. Therefore, being bad or good depends on the amount of Light that you have. Truly, there is one difference between how you were earlier and what you are now. This difference is the following: once you spent less on eating and drinking, you had fewer relationships with people and had less tests and temptations, while now you have more relationships with people and more temptations: in a word, you are more exposed. Let me give you the following example: take a scientist who talks about morality all the time and look at the way he so diligently mitigates his own mistakes. If he breaks a glass, for example, he right away has the thought to justify and mitigate his mistake. What should he do? If this man had more Light he would objectively recognize the fact and would not try to find a justifying cause. Often you act this way, too. Other times you make this other mistake: when given a topic you say, “This topic is of little importance.” As soon as you say this you make a basic mistake in your mind. Take, for example, the topic I gave you today, “Basic Elements in Geometry”: this is a very difficult subject. What is one of the first elements in geometry? (It is the point.)1 How can you explain philosophically that the point is an important geometric element? Do geometric points occupy any space? (No, they don’t.) How was the straight line formed? (It was formed by the movement of the point.) Here is what I ask you, then: if the point does not occupy any space then how was the straight line formed? How could imaginary points that occupy no space form objective points that do occupy space? Here we come to the scholastic philosophy where we can philosophize without ever reaching a definitive conclusion.

 

And so, the point is the first element in geometry. What is the second element? (It’s the line.) The third element? (The plane.) The fourth element? (The body.) The fifth element? (There are no more than four elements.) I leave it to you now to think further. You will need to consider the concept of element the way it is in geometry, i.e. as something that geometry is based on.

 

 

Diagram 1

 

What does this curvy line on the drawing stand for? (It is a parabola.) This curvy line is formed when you hold your thumb and pointing finger open apart. Tell me, then, what is the difference between a parabola and a hyperbola? (The hyperbola has two branches and the parabola has only one.) Well then, if an object starts from the center of the curvy line on the thumb and keeps moving along this line, how will it be able to come back to the same point? For example, if this object starts from point C it will reach point D. What was the matter of the object like at point C: was it thicker or thinner when the movement started? What forces took effect at point C? Have you followed the process of thinking in your mind? At first, a certain idea sits undefined in your mind, i.e. its boundaries are barely defined, but the more you think the more defined this thought becomes until finally it materializes itself outside of you. Take some inventor as an example: at first a certain idea appears in his mind in the form of a project; all the different wheels and parts of the machine are in action, moving first in his mind, after which he looks for a way to realize this idea externally. If a certain idea that has started in your mind is projected into the physical world but cannot be realized, it comes back. There are many people who suffer from unrealized ideas. The whole danger is in the fact that this energy goes back to its source. (Is this harmful, this going back of the energy to its origin?) It has a harmful effect in most cases. For example, someone wants to graduate from some university but if he cannot do that he develops this inner sadness that he was not able to achieve his idea in reality. This is why all noble ideas need to be realized and be realized not in their finite boundaries but in the human consciousness so that they can give one an impulse or open some room for a new activity. Under these new conditions that you are now, instead of having your mind and intelligence developed in you, you develop sensitivity; however, this is not sensitivity in the sense of mercy, but rather in the sense of personal feelings and pride, thus the energy in the back part of your head becomes very intense. Each one of you thinks that he is the most important person in the world, that he is some kind of a deity. All people think like that and no one wants to recognize the Truth. This is true not only of people but of animals, too. Take a dog as an example: even if you as much as touch its tail, it would jump up, saying, “How dare you touch me, sir? You cannot touch my tail!” This is precisely where you, as disciples, should be very careful, for if you are not careful, you will find yourselves in trouble.

 

And now, all of you, as disciples, study the internal side of Life which comprises all other modern sciences. As you study the science of Life you should keep in mind that if you do not treat other people delicately they will respond with the same; if you like criticizing you will be criticized, as well. You say, “It is all right, he can handle it for he needs to know his faults.” Very well, but someone will say something about you tomorrow and then you object right away, “How come! How dare he talk like that about me?” And how come you dare talk about him? If you talk about others then when they talk about you, too, you should be man enough to say, “Let them talk. I can handle all of it!” And you need to suffer the consequences of your mistake. If a certain fact is true then why don’t you admit it? You say to someone, “You are impatient and rude in your manner; you are not merciful for you do not welcome anyone in your house, etc.” Is all of this not a fact? If it is true, you should admit it and be glad that you have something to work on in yourself. Then there comes the objection, “But I am not all that bad.” This is a different matter. Every one of you should have the courage to recognize how much truth there is in a certain fact, namely, if this fact is seventy-five percent, fifty percent or twenty-five percent true. On the other hand, if a fact is completely false, you can say, “All right, I will think about this.”

 

I am not for that method of discipline where you criticize each other and look for each other’s faults, but I want you to be self-aware of how you are. Some people are quick to boil over. It is good that they boil over for they would be worse off otherwise. But when they boil over they need to know where to channel all this energy. The human body has its own vent, a lid through which this energy can be released. Each of you will open the vent of your heart, mind and will so that the energy during this boiling over can be released. Someone enters his house and starts to shout, throw up his arms, jump and he threatens, “I’m going to do this and I’m going to do that, mark my words”, after which he sits down on his chair and starts working. Many learned people use work to cure their anger. For example, if a scientist is shortchanged by a critic and becomes angry, he would take his ax right away and go split some logs to come[A1]  down. It will be good for us to have a garden at our disposal or a vineyard so that every time someone feels offended or insulted by someone he can take the hoe and apply himself to work. You will take turns doing this. You might say, “This is a funny idea.” Yes, it may be funny, but it is also very pleasurable. It is a pleasurable thing to go to the vineyard to cultivate it and talk to it. Only in this way can we find the true method of discipline.

 

All people encounter hardships in their life. Do not think that it is easy to discipline a person, for there is something unbridled in man. Sometimes you become angry with someone and you say to yourself, “No, I will never speak to this man again!” Then you think for a while and say to yourself, “Why not speak to him? I don’t want him to think that I am like this or like that. I will speak to him!” And so then you think and you think until you calm down. Boiling over is not a bad thing - these are all forces that are at work in man. I would grade with a seven2 someone who boils over. And when I am looking for draft horses, I would take those that kick and bite but can work, too. A horse like that may kick and bite but when you harness it in the cart it will pull it; it does excellent work! They say, “This horse kicks a lot.” Yes, this is the kind of horse that I want for he knows how to work. As for a horse that is very placid on the outside and neither kicks nor bites, it will not do any work and it will not pull the cart when you harness it. It is better if we have, inside of us, a force that will make us work than if we do not have anything inside. Do not complain about the bad that is in you, for it is a great force and a great blessing. I use the word bad in a very broad sense. The boiling over, the anger and all other negative traits in you are all a treasure, a special kind of manure that you need to know where and how to apply. It will bring you certain goods in the future but you need to know how to handle it.

 

When you enter school, some of you think that you will not encounter any temptations down this road. No, the world will not welcome you with wreaths, nor will it carry you in its arms. This may happen some day but not yet. Therefore, the road that you are on is still the Narrow Path. You should know that you will encounter a number of hardships in the physical world and in science and in your own ethics. And then the more you know the bigger your hardships and suffering will be. But what is better: to know and to suffer or not to know but suffer, nevertheless? (It is better to know, of course.)

 

I will give you an exercise that you need to do in the course of seven days (from February 3^rd to February 10^th). This is the exercise: let’s say that your spirit is low on the first day, on Monday. Right away, draw a point, then a straight line and a triangle next to it. Note in your notebook what the weather is outside. You will also note what state of mind has caused you to change. On the second day, on Tuesday you will draw a square on the same piece of paper next to the triangle. Then note again the weather and your state of mind. On the third day, on Wednesday, you will draw in your notebook or on your piece of paper a pentagon next to the square. The pentagon can be in the shape of a house, but it will be even better if it is a right-sided geometrical pentagon. On the fourth day, on Thursday, draw a hexagon; on the fifth day, Friday, a heptagon; on the sixth day, Saturday, an octagon, and on the seventh day, Sunday, a nonagon. Thus in the course of these seven days you will have drawn the following shapes:

 

 

Diagram 2

 

You should know all these shapes. They are symbols that represent living forces in Nature. Nature knows these symbols. First you will call into your mind these shapes, then you will draw them in a book, but you need to draw them very correctly, neatly and beautifully. The shape that you draw during a certain day is the one you should keep in your mind throughout the whole day. No matter what your disposition is, good or bad, you will draw a certain shape every morning. Geometry has an excellent effect on people. Therefore, when one is indisposed in one’s spirit, one should take up geometry or should solve mathematical problems. Mathematics, however, is more abstract; it is easier to begin with geometry and end with mathematics.

 

And so, when you draw a point, you will project it in your mind and will reflect on its meaning. The line, on the other hand, stands for a point in motion. When you reflect on each shape, you will cause it to gradually come to life in you. In this way you will understand the source of your indispositions. I will explain to you where indisposition in man comes from: imagine that the house in which you live is well made and it has nice strong walls. But then let’s say that I or someone else came to the house and took away its roof. This will change the nature of your house for it will leave it flat on top. What do you think will be the effect on you; do you think you will feel peaceful in your house; do you think that the rain will think twice before falling down on you? No, your clothes as well as everything else in your house will be subjected to the rain and will be in danger. Then the state of things in you will change, too; your emotions will change. This same thing happens in your mind: often you lift the roof of your mind; you take off your triangle and then only the square is left which is an open plane and by doing this, your mind is thrown out of balance. What should you do? I say this: put the triangle, the roof of your house, on top of the square; cover it with tiles, put the plaster on the walls, attach sturdy doors and then you can have peace in your spirit. Is this not a philosophy?

 

 

Diagram 3

 

On this drawing is shown only the base of the triangle of a house (ab). This triangle, albeit looking like this, is put in action. It represents a boat that floats on the water. The pole C is the mast on which the sails A are spread. What will become of your boat if you were to remove the middle pole, i.e. its mast? It will sit motionless in the water. The mast stands for a force that can drive the boat; if you take the mast off your boat it will be at the mercy of the elements. And after all of this you say, “Where did all these troubles come from?” I say: you have all these troubles because you threw the mast away into the water. “What should I do then?” As soon as you step ashore, you should put another mast on your boat. The boat is your heart. The mast C is an object of Love. Often you say, “I don’t want to love; all people are bad.” As soon as you say that all people are bad it is like throwing your pole in the water and your boat remains without an object. What can I do? Put the wood in its place; your life should have an object! Your love for one and your love for all is one and the same thing, for it is one and the same law. Some say, “I cannot love everyone.” You don’t have to love everyone. By loving one you can love everyone: this is how this matter is in the Mental world. If the heart loses its object, it loses its triangle above. This is why I tell you this: set the rudder of your boat against the wind, which represents your desires. If you abide by this law of movement, you will easily reach the shore that you are aiming for. And then I will ask you how the roof of your house is doing and how your pentagon is holding up. I will also ask you if your boat’s pole is standing up, if you have a nice chimney on your steam-boat, if your vents are open, if you have enough water, coal, etc. And after all this, when you are quite strong and when you have acquired the necessary presence of mind, you will be in a position to deal with both the modern and the esoteric sciences. If you do not become strong then the fortune that you acquire from this science will not be of any use to you personally, but will cause you greater suffering. I am not saying that suffering is something bad or useless, but what I am saying is that in this world one can pass with less suffering.

 

Now, that you have removed the triangle, what are you going to do with only the square of your house left? When one sells one’s house, one should purchase a vegetable garden to cultivate if one wants to acquire new capital. If that happens one will not need a triangle but one will have a garden to cultivate then. In this case it is better for his house to stay where it is. If you want to have a house, you must love! If you do not want to love you will have a garden. You can choose not to love but then you will have a hoe and you will toil over the soil all day long and you will grow cucumbers, cabbage and other vegetables. Can a cucumber make you uncomfortable or can you make a cucumber uncomfortable? No, you may watch over it and plant it and it will not say a single word of harm to you, it will not rebel against you: you do not need to love it and it does not need to love you.

 

And so, there are various occupations in the world and there are various methods in the Esoteric school. By using some of these methods you can transform a lower energy into a more superior one. And energies must be transformed! If you are indisposed in your spirit, you can transform this indisposition within five, ten, fifteen, twenty minutes. How? Go and dig in your garden for a while! Therefore, you will become a gardener for a few minutes and as you dig you will focus so intensely so as to transform your indisposition into a good disposition. Your thought needs to be so intensive so as to make you sweat. It happens sometimes that, just as you sit, you can focus so intensively that you break out in sweat.

 

All these methods that I give you now will be useful to you in the future. When someone is sick or indisposed in one’s spirit, one can cure oneself through transforming one’s energies. One can use these lines and geometric shapes, and by doing this, one will channel the energy from his brain into his lungs. This energy transformation should be done correctly. Geometric shapes are the connective thread thorough which energies can be transformed. It is difficult to achieve such a thing at once, of course; one needs to do many exercises, many trials. One needs to apply things in practice! Do five or ten exercises so that you can be convinced that my words are true. If you succeed in one exercise, do not stop at that but keep on; you need to do ten, fifteen, twenty, fifty, ninety, ninety-nine exercises before you can acquire positive knowledge that precludes all doubt.

 

Now, I want you to do very well the week-long exercise that I gave you. You will need to take a nice piece of paper and draw the shapes very neatly and correctly with the help of a compass and a ruler. If you draw them just so you can say that you have done it, then this is not geometry, this is only some ostensible geometry. The laws of geometry do not allow for inaccuracy and imprecision.

 

First exercise: put your arms out in front of you, vibrating your wrists. Next open your arms while again vibrating your wrists and make sure you do not lock your elbows. Next put your arms back in front of you and then back to the side moving them as if flying: lift them slightly up and down as if flying. Next put your arms together in front of you, then move them up and down and put them back in front of you; this time increasing the vibration of the wrists. Then move the arms up and down and straight in front of you this time moving only the wrists very fast. The vibration of the wrists is increasing more and more then it is slowed down and then increased again (move your wrists only up and down). Lastly, open your arms, moving only the wrists up and down.

 

What does this movement remind you of? (Of bees airing their hive.)

 

Second exercise: move your arms in front of you one up, the other down, like scales while keeping the elbows slightly bent. Quicken the movement. Move right arm down, left arm up; move them slowly at first then gradually speed up the movement (move only your wrists on both sides of your head[A2] ). Then gradually slow down the movements until they are almost imperceptible. Now can you feel a certain movement around your fingers as if an electric current is passing? Now move your arms out in front of your chest then up, then to the sides and then down, thus making many slow circular motions. Next move your arms in the opposite direction: first out in front of you then down, then to the side, then up and then back in front of your chest, again making many circular motions. Now put your hands in front of your face waving them quickly in a circular motion. Finally, put your arms out in front of you.

 

Secret prayer

 

- Only the bright road of Wisdom leads to Truth

- It brings us everlasting joy.

 

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1 Whenever the disciples in the audience respond to a question posed by the Master throughout the lecture, these comments are transcribed in italics and placed in parentheses.

2 Grading in the Bulgarian educational system uses the numbers 2 through 6: 2 being the lowest, failing grade, and 3 through 6 being passing grades with 6 being the highest one.

 [A1][calm]

 [A2]I can’t see the connection to the head, maybe this should read [hands] – [move only your wrists on both hands].