The idea of an automobile has yet to arise. Mathematician Bernhard Riemann, for example, discussed in the 1850s new types of geometries that you would encounter on surfaces curved like a sphere or a saddle instead of the flat plane geometry that we learn in school. Where this becomes interesting is in the notions of beauty in physics. So the answers to your questions aren't nothing x 3, but rather in lines with patenting and making money. Ard: And the beauty is in those variations. All their work, then, is confined to a realm a universe of discourse? David: And then poetic truth is just going to be largely entertainment? I suppose we do discover the answers to our sums etc, but invented the method of finding them.
If it is discovered then we can argue that it is there regardless of human activity. David: And yet the music is the same, the score. Some people say that mathematic is being created and some say that people discovered math. Was mathematic discovered or created. This naturally leads us to ask the question why mathematics is so effective at describing our universe — a question asked many times before by a number of great minds. The language that we use to do this modeling is invented. Later more mathematics was invented to deal with the abstractions of earlier maths, leading to more and more complex abstractions, but the invention of math was done to deal with concrete things, like geometry and trade.
With centuries of use, these symbols may have become modified in an evolutionary manner into the more roundish symbols we scribble today. Music didn't exist, yet music is totally a mathematical construct. Certain topics and categories of mathematics might be created based on the need during the time. Math has no such freedom. And then, of course, as we evolve as a species and we learn more about reality, we pluck more math and more math and more math to do that job. Last but not least, it is possible that our models of how the Universe works are completely wrong.
Physics is a framework invented to generalize what I am perceiving. You could say that poetry and aesthetic delight is right at the top. Remember how irrational numbers petrified the bejesus out of the Pythagoreans? Some of these stories, like the idea of a material object, are hardwired into the human brain. Different geometries can be seen in Figure 3 below. I wonder what the Neanderthal word for lion might have been? Even though numbers like 2 or 4 are invented, they are only names for constants.
As David Deutsch famously said, the fact that we understand the laws of Nature, is pretty much like saying that you land on another planet, and find aliens completely able to speak to you in english. The value of a dollar is measured mathematically. Ard: So would you say…? David: So in some sense they were there woven into the fabric of quantum mechanics, before we even thought of them? Who knows, such a thing might actually be useful. In modern society, there is evidence that 128-bit numbers remain fair game, though the difficulties of enforcing this are notorious. So we discover the world around us, now how do we use and manipulate this world.
In fact, I am not convinced that Euclid himself was entirely happy with his fifth postulate; in his book The Elements the proofs for his first 28 postulates do not make use of it. Mathematical Platonists eagerly point out that elegant fractal patterns are common in nature, and that mathematicians clearly discover rather than invent them. Ok, now that the scene is set, I find it incredibly annoying that you cannot divide by zero. I think the correct answer is basically as you've described. This he was not able to, having to eventually concede that the Cartesian coordinate system was the simplest and most logical way to map physical space. The food just came to it from above, and all it sensed was the flow of currents.
Inventing the symbols and inventing the thing, are not the same. I think these insights are more important, but at a more basic level, you are right, and I can't complain too much. Peter Tyson investigates two millennia of mathematical discovery. An interesting point of view is voiced by mathematician Sir Michael Atiyah, in which he takes into account our brains evolutionary predisposition to make sense of the world around it: If one views the brain in its evolutionary context then the mysterious success of mathematics in the physical sciences is at least partially explained. I see no reason why this same observation should not apply to mathematics also. Well, some things do, and it's It's not remarkable that such a thing is still being discussed. Do you really believe that, or are you just doing that to get a…? There is a middle ground, which might seem like a compromise but I believe provides valuable insights into this topic: mathematics is an intricate combination of inventions and discoveries.
In the film, many different countries are trying to communicate with the aliens and the Chinese had some success using the game of Majong to do so. For a long time these non—Euclidean geometries were treated as non-physical, amusing curiosities. So to my mind, mathematics has evolved in small advances over millennia. But let me ask it a different way. Back to the very basic, mathematics itself did not exist before there was somebody who literally studied mathematics, who worked on mathematics etc. In short, math is kind of like science. Moreover, it makes the thesis more realistic.
Another example of this is imaginary numbers; the square root of minus one. You have the following in your hand: A one-cent piece from 1978 A one-cent piece from 1986 A one-cent piece from 2004 I could have said you have 3 cents. And this is how much of cutting edge engineering is done these days. So it depends on the context. Like I suggested above, I am not sure that mathematics is really all that different from a game.
David: And that the mind is like a garden. So if you want to know what the square root of minus one is, we call it i. You want the most profound kind of truth that you can find. They were there all the time. Similarly, string theorists today often develop the mathematical machinery they need. So I think the ultimate truth is mathematical.