Image: Tom Beddard
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Overview
Why Math Works
If you shut yourself in a room and devise some abstract mathematics for the sake of sheer intellectual fascination, you might not expect your scribblings to have any relevance to the real world. Your parents would probably bug you about what you were doing with your life. And yet time and again, scientists find that the creations of pure thought match what they discover in nature. Does it mean the world at its deepest levels is somehow mathematical? Does it simply mean that scientists are good at cherry-picking the conceptual tools they need? Mathematicians, physicists, philosophers and others debate that question, as astrophysicist Mario Livio describes in the August issue of Scientific American. Whatever the answer may be, we can still marvel at the beauty of mathematical structures.
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14 Comments
Add CommentJuly 29 2011?
Reply | Report Abuse | Link to thislooks like someone has invented the Time machine..:p
Te caption for the first image makes it sound like there's just one Julia set in the world. In fact, Julia sets are a whole class of fractals associated to different functions. Saying that "the Julia set" is one of the best known fractals is like saying "the prime number" is one of the best known numbers.
Reply | Report Abuse | Link to thisYou were obviously in a hurry to see the next picture. I suggest that you go back and read the caption once more.
Reply | Report Abuse | Link to thisThat we find such mathematically governed objects beautiful is, obviously, evidence that we've evolved to detect and respond to geometrical regularities, and the utility of that response is evident in everything from reproductive fitness to technology. But there's surely more to it than that. Why are there regularities? Exploration of that question has brought us two general possibilities: that regularities are a random feature of a multiverse in which every possible configuration turns up somewhere, or that mathematics is the fundamental stuff of design. To state the latter is not necessarily to embrace theism or even deism, but it is certainly to raise some interesting philosophical possibilities.
Reply | Report Abuse | Link to thisClay Farris Naff
claynaff.com
<3 this
Reply | Report Abuse | Link to thismakes me think of bathsheba.
http://www.bathsheba.com/
A Julia set is never created by intention.It is simply the repetition of the same act,creation of a leaf, a nut,a flower, etc. in the same conditions.
Reply | Report Abuse | Link to thisIts beauty does not belong to it.Its beauty is created by human mind.
TRUTH, that's what mathematics is about. There is an obvious gap between perceived truth and discovered truth, simply because you can only discover what was not perceived before. We have only 5 comparatively weak senses sending us signals and a very powerful brain that synthesizes these signals, to make useful conclusions as to the reality or truth of our environment.
Reply | Report Abuse | Link to thisThat function is what gestalt psychology studies, and obviously sometimes the brain creates very wrong, and always incomplete pictures of that reality. 10 frames a second on a video is all it takes to create the illusion of continuity in a video, for instance. Mathematics is the science of using reason to make accurate predictions about what lies beyond these huge gaps left by human observation and inspection.
On the other hand, computers accurately divide seconds into milli, mircro, nano, pico seconds, using numbers expressed in only ones and zeros. That's the power of mathematics. Using axiomatic mathematics, we can even make conjectures about what life/reality would be like in worlds which don't even exist. Suppose the path of a photon was really curved but appeared straight to us, for example, could we get from point A to point B quicker by travelling some alternate (hyperspace)path, (like a neutrino?) instead of in a line that appeared straight to us?
That is the true power of mathematics, it DISCOVERS realities that lie outside of the periphery of human observation. Our brains have long since outstripped the power of pure conclusions from observation. Science is about the empirical observation of physical phenomena, however minuscule. Math is about making conclusions about not just observable phenomena, but also about what the philosopher Immanuel Kant referred to as the noumena, things as they really are, TRUTH!
Pretty much the same can be said about science, except the axioms emerge as subtle assumptions in our theories. In a paradigm shift, the assumptions can change dramatically.
Reply | Report Abuse | Link to thisThere are sets of various colors in the picture: white, pink, black. Is the black set the Julia set? It is very unlike the handful of Julia sets I have seen. What is the mapping?
Reply | Report Abuse | Link to thisThe Julia set reminds me of the scimitar blade of the Giant Kelp.
Reply | Report Abuse | Link to thisThe slide show link doesn't work for me.
Reply | Report Abuse | Link to thisI suppose being in Australia could be the problem, everything is upside-down here.
The explanation I find satisfying is that mathematics is a game played for fun in the mind where one has a field where one can make any assumptions (axioms) and any rules (but then maintain consistency.) Manipulate these and see what interpretations it can develop.
Reply | Report Abuse | Link to thisIn some cases hand over your interpretations to (experimental) physicists and astronomers and let them find out which axioms and rules seem to fit present or past (or possible future) realities the best. The best is defined as the simplest and most accurately predictive. Consider the errors and try to correct.
Mathematics is "cheap" but the physical experiments and astronomy are now quite expensive
"The slide show link doesn't work for me.
Reply | Report Abuse | Link to thisI suppose being in Australia could be the problem, everything is upside-down here."
The effect is named "Quarky (up down) Lysdexism"
Locked in your room or, in the case of Jean LeRay, a Nazi prison camp.
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