Answers From LaRouche


Q:
How can we discover what are the false axioms?
                              
  - from December 27, 2023 Lima Cadre School

Question: Hello Mr. LaRouche and Helga. My question is the following: What can the youth do, in order to save his nation? And how can we discover what are the false axioms, that we have been taught, in order to correct them, so we don't fail in our leadership?

I, also, have always had this question, about what is Renaissance literature? I would like to know if, in your country, and in other countries, there are writers, who have been developing Renaissance literature? If there are those, can you cite some names, and their works?

LaRouche: What I'll do on this question of axioms: What I've done is, I've laid out this program, and the program was actually, sort of jumped out of my mouth at certain points, when people were asking me questions, but it wasn't accidental, for that reason. I was simply saying things, which as a result of much cumulative experience, impelled me to give those answers on those occasions. No, the question was asked some years ago, as to what a youth movement should do for education. We're talking about youth, who were leaving universities, which were worthless, essentially, at that time; and saying, "What can we do for an education? If the universities are no good, where do we go? What do we do?"

So, I said, we start with Gauss' fundamental theorem of algebra, 1799, Latin edition, in which he denounces the errors of Euler and Lagrange, on the question of the so-called "Cardan problem." And, that we start from there. Gauss's discovery is a typification, it's a point of confrontation in the history of physics and mathematics; it's a typification of the issue of a mathematics, which is simply a kind of soup, that is, that you assume that you can calculate everything by some universal mathematics, which is not true. Because this assumes that there is no such thing as a true, universal physical principle, in the universe. So therefore, Gauss shows that a Cartesian system, or an empiricist Cartesian system, of the type described by Newton, associated with Newton; described by Euler, described by Lagrange, by LaPlace, by Cauchy, and so forth--that this, is junk. It does not correspond to reality.

What we are forced to do, therefore, is to look at--as Plato did, in his notion of powers. You look at several very elementary examples, which we referred to, I'll just identify them. You have, for example: the definition of the comma, by Pythagoras; the comma is not a mathematical entity. The comma is defined, as the fact that, in the singing voice, which is good singing voice, starts to sing a scale up and down, there will be certain differences. Now, if you take a monochord, that is a vibrating string, made tight-- as one string on some kind of a musical stringed instrument--and you put beside it, a measuring stick. Now, you get a human being to sing a scale up and down, in a mode, up and down. Now, you mark the place at which the pitch lies, on the monochord that the person is singing, you note the differences--up and down. These differences as become known as the concept of the comma--a generic concept, which is not a simple mathematical magnitude, in the sense of arithmetic. But, is a physical magnitude, which exists independent of measurement, but which can be measured, in that sense.

So, that's one question. Then, you have the question of the line: How can you construct a line, exactly the double the length of a given line, without going outside that line? You can't do it. They'll say, "Yeah, I can double a line. I can use a compass, and I can double a line." "Ahh! But you're going outside the line to do it, aren't you?" So, within the line, you can not--when you go outside the line, what are you doing? You are creating a surface. Now, a surface is not a line. So therefore, you're cheating! Intellectually you're cheating; it's a fraud. You can not double a line, except by what? Except by going to a higher power. The concept of a surface is a higher power. How can you double a square? Well, there's a way to do that, but you have to do the same thing: You have to go outside the square. And, you get to another concept, a general concept, of a series of doubling of squares. This is also a notion of a power. Then, you say, "Well, how can you double a cube?" Which is the famous Delian [?] problem, which is addressed by the student of the follower of Pythagoras, Archytas, in his discussions with Plato; and he's become a central figure of all Greek mathematics, and Greek thought: How can you double a cube by construction? Well, you can't, ordinarily, but there is a solution for it. These involve powers.

Then, you get a measurement, which is done, again, by another Greek mathematician, Theaetetus: How many sides can a regular solid have? By construction. And you come up with the Five Platonic Solids, as a result of that.

So, these all measure powers. That is, the mind goes, from not inside a mathematics, to calculate arithmetically, but by powers. And we find that everything we know, physically, is a discovery of some power, in nature. Some power, the mind understands. And, this becomes then--these powers become actual powers, in the sense that Leibniz uses the term "powers," or "Kraft," in describing a physical economy: Is that, by increasing the power, to work, we're able to increase the power of mankind, in and over nature.

So, we come with this idea of powers. And therefore, we have a mathematics of powers, which is what Gauss demonstrates, by his proof of the so-called "complex domain," in opposition to Lagrange, and Euler, and so forth. We say, "Well, all right, the powers of mankind's existence, and the improvement of mankind's population, his conditions of life as a species, is based on the discovery and application of these powers. These increased powers, in and over nature." Ah! Well then, we have a history of science, don't we? If these powers represent science, then the transmission of these discoveries, from one generation or one culture to another, represents the transmission of the power of mankind to exist: That is the history of science. And thus, the history of man, and the history of nations, the history of cultures, becomes the determination of the way in which societies accumulate and utilize these powers.

So, that view of history, that view of "What do we mean by a power?" "What do we mean by a discovery?" "What do we mean by an idea?" The other aspect, of course, which is related to this, is the question of Plato's Cave. Now, naïve people, who are not educated, who are ignorant, say, that "I believe, and I know, what I've seen and smelled, tasted, and so forth, with my senses." Those are ignorant people. They have not risen, intellectually, above the level of the monkey, or the higher ape, at best. What's the difference? Well, as Plato says, in using the allegory of the Cave, is that our senses, really, are nothing but part of our living, mortal organism. They do not know what is going on outside our skin; they react to being tickled, by what is going on, inside and outside our skin. But, so therefore, that is not reality. What our senses tell us, is only the shadow, of the reality, which causes the tickling.

Now, when we discover these powers, and are able to prove the efficiency of these powers, then we have reached ideas, which are ideas of the reality, which exist outside our skin. We now know the "tickler," as opposed to the "tickle." Therefore, we look at science as these kinds of ideas, knowing the objects which we can not see, taste, hear, smell, or touch. The objects which cause the shadows, the tickles, which our senses see--or think they see. So, these are ideas: scientific ideas; ideas of history; ideas of man. This is the nature of culture. This is what education should be. Anything contrary to that is false.

So therefore, man, in a sense, is immortal. Why? He's mortal. He's mortal, in terms of the senses. But, man as a mortal being, through the power of ideas, is able to discover principles, which exist outside the skin: the principles, which cause the shadows, which we call "sense-perception."

By transmitting those ideas, from one generation to another, from one culture to another, we, in a sense, become immortal beings. Because now, in our mortal life, we are living in a place in space-time, in which we are being acted upon by things outside that space-time interval, from the past, for example, and from the future. And we are acting on the past and the future. So we have a sense of the simultaneity of eternity. So therefore, we have a moral sense of ourselves, that we are living for what is, in one sense, a short time, mortal time, in life. But, we are acting on the past and the future. And therefore, what we think is moral, what is important, is how we act, on the past and the future. What is our effect, on the outcome of the past? And the future?

When we have that kind of sense, we have a completely different view.

Now, we talk about literature today. Well, mostly it's garbage. Contemporary writers are mostly garbage. They don't have the education that conforms to what I just described. They don't know what this is all about. You have people who write "poetry"; they don't know anything about poetry! Modern poets are worthless. Modern writers, as I know them are generally worthless, in terms of artistic value. Modern music is generally worthless. Modern art is worthless. Most of the 20th Century was an artistic catastrophe! Maybe there were a few people, who tried to maintain the tradition of artistic work, from an earlier period, but as a cultural period, the 20th Century was a global catastrophe. And, the 21st Century hasn't been much of an improvement on that either.

So, don't look for it. Don't look for "relevant" modern art. Or "relevant" culture. It doesn't exist. There are things from the past, which are great examples, for their time, of the cultural achievements of true Classical art. Going back, you can still see a statue from the Classical Greek, in which you see, not tombstone art, but you're seeing a sculpture of a body caught in mid-motion; which conforms with the catenary principle of motion, of universal least action.

So, those are the things to look at. Great art, we'll have to create. But, great art is nothing more nor less than the application of the same principles which were used by the great creative artists of the past. It's a communication of ideas. And, based on things like irony and metaphor, and so forth. And, there is great art, but it's from the past, so far. And, most of what's being taught in universities, today, as art, or taught about the great art of the past, is mostly a waste of time. But, if you want great art, we're going to have to create it. If you want to revive a great artistic tradition, you're going to have to do it.

-30-

Paid for by LaRouche in 2004

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