The Golden Ratio 676
raceBannon writes "The book surprised and fascinated me. I thought it was going to be solely about the Golden Ratio. Mario Livio does cover the topic but along the way he throws in some mathematical history and even touches on the idea that math may not be a universal concept spread across the galaxy." Read on for the rest of raceBannon's review.
The Golden Ratio | |
author | Mario Livio |
pages | 320 |
publisher | Broadway |
rating | 7/10 |
reviewer | raceBannon |
ISBN | 0767908155 |
summary | Through telling the tale of the Golden Ratio, Livio explains how this simple ratio pops up in all kinds of physical phenomenon and debunks the idea that the ratio is present in many famous man-made structures and art work. Along the way, he provides historical tidbits regarding some of the well-known and not so well-known mathematicians throughout the ages and he tells the story of some of the more famous and not so famous mathematical advances. Finally, he discusses the possibility that mathematics may represent some kind of global truth that exists throughout the cosmos. |
I have to admit that it is a little spooky to me that this ratio, this irrational number (1.6180339887...), pops up in many varied natural phenomena from how sunflowers grow to the formation of spiral galaxies; not to mention that the Golden Ratio and the Fibonacci Series are related. It makes you want to think that there is a God with a plan.
The Golden Ratio is defined as follows: In a line segment ABC, if the ratio of the length AB to BC is the same as the ratio of AC to AB, then the line has been cut in extreme and mean ratio, or in a Golden Ratio called Phi.
On the flip side, Livio squarely debunks the idea that the Golden Ratio is present in many famous paintings and architecture that has been postulated in previous books. He rightly points out that you can find the Golden Ratio in anything depending on where you decide to place the measuring tape. The idea that the Golden Ratio is such a symbol of universal beauty that it appears by accident in our great man-made buildings and artwork does not carry any weight. I think Livio makes his point.
He also uses the Golden Ratio as a framework to illuminate other historical tidbits about key mathematical figures, guys like Pythagoras and Euclid, who continue to affect the mathematical world to this day. I love this kind of stuff; the historical context of how and why these legends did what they did is very interesting to me. For example, I did not know that Euclid himself did not discover geometry or even make any great new contributions to the field in terms of ways to apply it. What he is famous for is organizing the information into a coherent fashion. He was a teacher of the highest order; so much so that Abraham Lincoln himself used Euclid's texts, unchanged after all those years, to learn the subject back in Lincoln's log cabin days.
The book is not all a philosophical discussion. Livio does use some simple math examples to make his points but it was at a level that I could follow. According to my college professor, I escaped College Calculus by sheer luck. Livio does provide the rigorous math examples in appendices at the end of the book (I did not bother with these).
Finally, Livio takes a shot at the idea that mathematics is a universal concept across the entire universe. To be honest, I have always assumed that it was. After all, I am a Trekkie and this concept goes unstated throughout all four TV series. The idea that mathematics is a human construction and probably holds no water in another civilization that grew up on the other side of the universe makes a lot of sense to me. I have to admit; I need to ponder that one for a while.
I recommend this book. If you like the history of science, your high school algebra class is just a little more than a dark fog in your memory, and you get a charge out of scientific mysteries, you will not be disappointed.
You can purchase The Golden Ratio from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.
I wrote a review.. (Score:-1, Interesting)
A god with a plan? (Score:5, Interesting)
The balance and beauty of nature and all that?
OF COURSE there is a pattern, and things work out. Look at evolution.
You take a puddle in the middle of nowhere.. it has an ecosystem in it with a perfectly balanced population (too many, it dries up, too few, they reproduce...). Would these little creatures say "Oh wow! Look how there is JUST enough water for each of us! There must be a GOD!".... silly, right?
Nature seems balanced in the world, becuase that world produced nature... they are intertwined, infinitely.
Irrational numbers only seem strange because of the way we choose to look at things... the fact that it doesn't reduce to some fraction in our counting system doesn't *mean* anything holy or significant....
The fibonacci series and the golden ratio are related? Sure are.
(The ratio of successive numbers in the fib. series approaches the golden ratio as you go upwards)
But it's not so weird, is it? A sunflower.. the way it grows, it builds on itself.. in a spiral... naturally following this series.
Is it some grand creator that made it that way, or is it just the plain, obvious way for something to grow?
What would be evidence of a creator would be if things did NOT follow what was natural and obvious. If these things did NOT follow the golden ratio and other straight math.. if we could find no explanation for why things had a weird ratio, or weird behavior.. no explanation from the current or possible past enviroment to explain how something evolved.... come to me with that, then we can talk about a creator.
Until then, i'ts just nature.
I rememeber this from... (Score:5, Interesting)
Furniture design (Score:5, Interesting)
universal math? (Score:5, Interesting)
Yes and no. Mathematics is just a way of modelling things abstractly. Even things like counting from one to ten is a model for concrete objects, and provides a way of, say, making sure the number of cows you have today is the same as the number of cows you had yesterday. At the higher level, mathematics lets you model shapes, motion, acceleration, and gravitational collapse of entire stars.
The most common types of mathematics we use include decimal arithmetic (trading with money), algebra (solving for unknown quantities), and geometry (simplifying the world into abstract shapes). Hundreds of other branches of mathematics exist to model different things in different ways, and none of them are "right" -- they all are optimized for particular problem-solving.
With that in mind, I find it inconceivable that advanced civilizations on other planets would not have some kind of mathematics, and at least share the natural numbers with us (not necessarily base ten, though). If all you're doing is raising food for your family, then even arithmetic may be more than you need to bother with. But anything that involves abstract problem-solving, measurement, and/or exchange of goods for trade is going to need some kind of math. The models they use may bear no resemblance to the ones we use, but that doesn't mean it's not math.
Definition FYI (Score:3, Interesting)
The number 1.618..., which is half the sum of one plus the square root of five (1+SQRT(5))/2. This number was known in ancient times, and has many interesting properties in many fields. In Fibonacci series, the higher one goes in the series, the closer the ratio between a number and it's predecessor comes to the Golden Ratio.
From "The Technical Analysis of Stocks, Options & Futures" - William F. Eng
Geez, I never thought my Trading and /. would come together. Then again it is delving into the Uber Math Geek world - lol
Re:Something I learned from Martin Gardner... (Score:5, Interesting)
On a calculator:
1) start with any number
2) press [1/x] [+] [1] [=]
3) GOTO 2
In other words this converges to the golden ratio! It takes a while, so normally you do this when you're bored.
Re:Why wouldn't math be known across the universe? (Score:5, Interesting)
Debunking constants (Score:5, Interesting)
This doesn't sound exactly right.
I think it may be the case that writers have attributed the use of phi in art when there was no such intentional use by the artist.
But the very nature of phi makes it unlikely not to appear in certain contexts.
Same with pi.
The thing I love about math is that it has utterly nothing to do with reality or the universe or anything at all.
Typically, however, physicists make assumptions that match, more or less closely, to what is happening in the real world, so the conclusions from such assumptions match, more or less closely, to what is actually happening in the real world.
But there is no reason why some utterly alien intelligence can't make a set of assumptions that match their reality, which would be utterly alien to us, yet still valid, and still recognizable by mathematicians, if not physicists.
This is the giant flaw at the end of the book Contact, by Carl Sagan. Ellie discovers a message in the constant pi, placed there by an intelligence. If this were a constant of physics, that would imply the existence of some incredibly advanced intelligence that engineered the universe to contain a constant with precisely that value. This is somewhat plausible, and I believe it was Sagan's intent.
But he picked pi, which actually has nothing at all to do with this or any other universe.
What kind of incredibly advanced intelligence can possibly engineer that? I can only think of One.
Pi the movie (Score:5, Interesting)
Not bad (aside from one glaringly obviousl mathematical error). The thing that I mulled over the most was the proposition that a large integer could be a number of fundamental significance. In the movie it was 216 digits long. I had always figured all the really fundamental numbers were irrational. After thinking about it and looking up on the internet it seems there are actually only 6: pi, e, i, 1, 0, and phi (and arguably, -1). And the first five can be directly related with the equation:
e^(pi*i) + 1 = 0
phi is not directly related to the others in such a manner (In the movie the god number is somehow tied to both pi and phi). Although pi and phi both happen to be ratios that are also irrational. But to get back to my original point, the suggestion that any number of a truly fundamental significance besides 0 and 1 would be not only rational but an integer seems improbable.
Re:Why wouldn't math be known across the universe? (Score:5, Interesting)
In a fascinating book, a Hindu scholar and monk, Sri Tirthaji, discovered in the Hindu Veda scriptures the basis for our math system. There he found shortcuts for most all our math work - easy ways to do difficult long divisions in a matter of seconds, quadratic formulas, PI to over 32 digits, the Pythagorean theorem (much before the Greeks), derivatives, calculus.
Our math is actually from the Vedas, and the Arabs got it from them, and then spread it through the Western world. The Vedas are at least several thousand years old.
The book is called Vedic Mathematics or Sixteen Simple Mathematical Formulae from the Vedas [amazon.com] and can be found at amazon or used book stores.
It's one of the major works of genius of science. The first time i read it, it was shocking how advanced it was, and simple! Any division such as 1.748362 / 59487 can be done long handed (pencil and paper) in a minute.
Our math system, how it was discovered or invented, who knows and how far back, is absolutely brilliant.
Re:A god with a plan? (Score:2, Interesting)
Since I'm taking a class on general relativity this semester, I'll weigh in with a quote of Albert Einstein.
In other words, maybe nature is what it is because God created it that way, or maybe it is what it is because it has to be.
also (Score:2, Interesting)
Re:Numbers are numbers (Score:2, Interesting)
For instance 1/3 in base 10 is (.33333333->infinity)
but with a radix of 3 is
Re:Numbers are numbers (Score:1, Interesting)
What you are describing is arithmetic and concepts of numbers, not really mathematics. Also consider that there are tribes out there whose languages only have words for one, two, and many. I am not trying to nitpick, and I agree that you can not go very far without mathematics, but I do not think that mere survival is dependant on mathematics.
Why do we need cardinality? (Score:5, Interesting)
You are assuming that everyone has a concept of cardinality. Realistically, people don't have much of one beyond the number six (yes, there are outlyers for whom eight objects in a group is eight objects not one-two-three-four-five-six-seven-eight objects). If a being had no concept of cardinality, that would make many things more difficult, but many others much easier. This organism would not think of a system as the sum of its parts, but rather as a cohesive whole (or rather the cohesive whole). It is likely that they would be philosophical geniuses compared to us. There are creatures of this type toward the end of Calculating God by Robert J. Sawyer (See your favorite bookseller and/or your local library), and their possible existance is not implausable.
Re:A god with a plan? (Score:5, Interesting)
Assuming God is all powerful, as is the usual definition of God, then God would not need to follow any plan. Things would just be. 1+1=2, 1+2=3, etc until you try to do math with a number that God had not created yet. Then thigns would break down.
Of course, that is the plan - to keep things consistant so they scale and continue to work. x1+1=x2
Once you realize that God is slave to math and rules, then you must comclude that math is more powerful and absolute than God. Therefore your old notion of a traditional God should be superceeded byt the ultimate one - mathematics.
When you pray, you pray that the maths of the universe work out in your favor. Since we mathmatically backtrace events, we know that God has not suspended reality, but you have mathmaticaly evaluated the likely outcomes and calulated the propability of your favored action to be within the realm of mathematical rendering. So you pray. Had it been clear cut you would not have wasted your time.
Math is the CPU in wich the universe runs.
Re:Why wouldn't math be known across the universe? (Score:2, Interesting)
Re:Mathematics not universal? (Score:3, Interesting)
A branch of math called group theory models all the possible kinds of symmetry. Any study of symmetry will eventually lead to the same ideas that group theory is based upon. Doesn't that make group theory universal?
Yes, I'm a Platonist when it comes to math.
Re:Debunking constants (Score:3, Interesting)
Aside from conveniently (and fallaciously) proving a negative, the first condition is highly unlikely to be satisfied in any premodern work, and the second condition borders on the absurd. In one case, he takes a discrepancy of less than a quarter inch in a painting measuring more than four feet high as a "disproof" of the use of the Golden Ratio.
In fact, the majority of the book is devoted to such sloppy debunking. The remaining fraction of the text -- which actually touches on real mathematics -- is quite interesting, but comprises perhaps fifty pages at most, and probably could have been condensed into a longish magazine article.
Re:Why wouldn't math be known across the universe? (Score:3, Interesting)
The reason we see in "visible light" is because that is the brightest radiation given off by most stars, especially our nearest one.
If an alien's local star gives off most of its radiation in a slightly different part of the spectrum, still mostly visible light, but let's suppose shifted more towards blue, then the alien's visual systems will be evolved to see that the best.
Re:Pi the movie (Score:5, Interesting)
What about the Monster [wolfram.com]?
This is the largest "simple" group which doesn't fit into any group category. What this means is rather hard to explain in simple terms, but this group has lots of mysterious connections to other maths. The order is 2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 *29 *31*41*47*59*71.
Re:Why wouldn't math be known across the universe? (Score:3, Interesting)
An interesting idea; under what kinds of conditions might it be possible? An electron may be both here and there, but a sheep (to pick a particular object) is either here or there. Technically, I suppose that this sheep in front of me is both here and on the other side of the hill with different probabilities, but the probability for it's being anywhere else is so small that I'm unlikely to observe it in the next several billion years. Postulate some sort of quantum intelligence; it seems to me that one of two things must be true: (a) it occurs on a scale so small that we are unlikely to encounter one another or (b) it has in some fashion managed to extend quantum effects to a scale more like our own. Starting from the latter perspective, they would certainly be alien! Would they exist in some fuzzy quantum state so that they are always both here and there? Can they choose where to be (just as we can "choose" where electrons are in electron-slit experiments by observing them)? Integers would certainly be a strange concept for them -- a fuzzy being postulating that an object be in a single place, not infinitely many? Physics concepts like "speed of light" would also be alien to them, if they could coherently be here at one instant of time (quantum time?) and there at the next instant.
Arguments against postmodern deconstructionists (Score:1, Interesting)
I'm a physicist and I've been ridiculed by my philosophist friends for arguing against this point.
"What else is natural science than a common set of rules for perception" is their answer and I can't answer it. I believe my inability to refute their point is simply because the point they make is so idiotic, but still...
Any advise?
Fibonacci (Score:5, Interesting)
The most interesting part of the book for me was the correlation between Fibonacci and the Golden ratio. As I read it, as you ascend the Fibonacci sequence the ratio between the current number and the one before it converges on the golden ratio. F20 divided by F19 is as near the golden ratio to as many decimal places as any of us have use for, probably.
An interesting "party trick" was also mentioned that I remember vividly. Take any two numbers and add them, then take the new number and the larger of the first two and add them, then take the new sum and the old sum and add, ala Fibonacci. Continue for twenty or so iterations and the 20th number divided by the 19th will be damn close to the golden ratio. This is, I think, because any such construction is a linear multiple of the base Fibonacci set (see prev. paragraph). When you divide, the common multiple falls off and you still get Phi. I thought that was pretty cool.
Re:The Da Vinci Code (Score:5, Interesting)
His university mentor, a Jewish concentration-camp survivor (Soviet, not Nazi), was performing a similar pattern-search using Pi as his data set. This is where the title of the movie comes from.
The plot thickens when a group of Hasidic fanatics who are searching for the name of God by scanning the Torrah for patterns recruit Max to help them, and Max's curiosity, along with his migrane-induced hallucinations, leads him to the blurry line between number theory and numberology.
It's probably one of my favorite movies of the last 10 years.
Re:Mathematics not universal? (Score:2, Interesting)
Obviously the laws of the universe are going to be the same, otherwise we wouldn't live in the same universe and we wouldn't be having this discussion. But the modeling might be different, either more efficent or just a different path to get from point A to point C.
Remember that movie Contact where the Vagans sent us a coded message that humans couldn't understand until we put the messages together in 3 dimensional space, instead of on a flat piece of paper.
I think IF there are other sentient species out there then it is possible that their view of the univierse has developed differently then ours, but they still must observe the same universe as ours. They might call gravity a hamburger for all we know, but a rose by any other name smells just as sweet.
So in effect, the mathmatical models may not be universal, but their results will be. I can't imagine being able to master space flight without simple mathmatical concepts like addition. Look at the universe, specifically how biology works and addition is every where.
my 2 cents. -- Jim
Re:Mathematics not universal? (Score:5, Interesting)
You're assuming a relationship between mathematics and the "laws of nature" that isn't there. As Einstein put it, As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality."
Mathematics is as socially constructed as any other form of language. It is based on axioms and defintions, not observation of reality. We select those axioms and definitions in a way to be useful to us, just as we select for those lingustic constructs that are useful. But this selection is based on our desire to communicate with others - it is a social construct. Once upon a time if you asked mathematicians what nubmer, when squared, gave negative one, they'd say there was no such number; now, any bright middle school kids know it's i.
"Reality" is also to a large degree socially constructed, since all can ever speak of is our observations, which are socially conditioned. You see what you expect to see or are trained to see. (You don't see the fnords [mit.edu], or Sombody Else's Problem [wikipedia.org], while the hypothetical planet Vulcan [csicop.org] (the one inside the orbit of Mercury, not Mr. Spock's home) was observed several times, as were Blondlot's N-rays [skepdic.com].) This is why double-blind protocols are used - though if everyone involved has an expectation, that doesn't help.
What we think of as "reality" is just a model that we mostly share. The electron, for example, is not a component of human experience but a component of a model that unifies and predicts many observations. That is a very good and useful model, but it is entirely conceivable that some extra-terrestrial civilization has (or some future human civilization will have) a model that is just as useful but doesn't contain anything like electrons. (Just like Chinese Medicine has a "patterne-thinking" model of the human being that is radically different than and incompatible with the reductionist model, yet is extremely useful.) What would such an electron-free model look like? I can't tell you, I'm too conditioned by the electron model.
Remember: for any set of observations, there are an infinite number of hypothesis to fit them. There's no end to the curves you can plot through any finite set of data points. We see the points and call them a line, but it ain't necessarily so [principiadiscordia.com]. The best we can do is eliminate lines that don't go anywhere near the points.
Re:Why do we need cardinality? (Score:2, Interesting)
Re:Mathematics not universal? (Score:4, Interesting)
However, it would be possible to derive mathematical systems very different from our own. It all depends on what one takes to be fundamental concepts. For example, we define functions in terms of sets, but we could also define sets in terms of functions.
We're not even certain that some of our own axioms are true. For example, the axiom of choice says that given any set of disjoint non-empty sets, there exists a set that contains exactly one element from each set. While most people will say that this seems to be a reasonable statement, if it is true, a number of counterintuitive statements are also true.
None of these things change the universe, only the way the universe is modeled. One might be able to come to some new conclusions and possibly even a few contradictory conclusions using a different form of mathematics, but all in all mathematics effectively is universal since there is no reason a mathematician from earth couldn't learn to understand alien mathematics.
Re:Mathematics not universal? (Score:5, Interesting)
The fundamental question is this: is, or isn't, mathematics an extension of logic? A smart man named Frege (read about him here [st-and.ac.uk]) said, yes, it is. He showed a way to connect formal logic with set theory, which is the basis for mathematics as we know it.
There was only one problem: Russell's Paradox. Bertrand Russell [st-and.ac.uk] showed that, using Frege's axioms that defined set theory, we have a contradiction - Russell's Paradox. And as any student of logic knows, a contradiction can be used to prove anything at all, which means that mathematics as Frege defined it was not viable.
To make a very long and very interesting story short, Russell (with Alfred Whitehead) attempted to create a foundation for mathematics that would not give rise to Russell's paradox - the Principia Mathematica. And everyone thought the world was cool.
Then, in the 1930s, Kurt Godel [st-and.ac.uk] came along and smashed a hole in Russell's approach by showing that, given a sufficiently powerful formal system, one will always find unprovable truths and irrefutible falsehoods. So mathematics was, by that line of reasoning, incomplete.
This leaves the door open to a variety of critiques, the most relevant of which is that it is automatically not universal. After all, how could it be - there are things missing! We can't prove everything that is true, and we can't disprove everything that is false!
Godel's argument tells us that we are unable to describe the universal laws of nature using non-universal and incomplete mathematics. That dosen't make mathematics useless - it just places a limit on what we can or cannot do. For instance, we cannot use deductive mathematics to describe the laws of nature in their entirety, because we know that any effort to be complete is doomed to failure - by Godel's theorems.
Also, there are some specific areas of mathematics that lead to direct examples of non-universal, but nonetheless consistent interpertations of nature. Take, for instance, Euclidean and differential geometry. Euclidean geometry is the geometry of flat planes, whereas differential geometry describes abstract mathematical notions. It was once thought that Euclidean geometry is "sufficient", and that it is the simplest way of representing spacial relationships. However, as it turns out, differential geometry is actually much more simpler when it comes to dealing with, say, the theory of relativity - even though it is not intuitively connected to our perception of the universe.
So in short, we have two different "geometries", each of which can, supposedly, explain spacial representation. Both are valid, but one is much more useful. Neither is universal. And yet, there is no contradiction.
I don't know about anyone else, but I think this stuff is interesting.
Re:Mathematics not universal? (Score:3, Interesting)
The Periodic Table.
The way to start communicating with an alien species is going to start with simple numbers and arithmatic, and then an important sequence will be:
(1,1) (1,2) (2,3) (2,4) (3,6) (3,7) (4,9)
the stable isotopes of Hydrogen, Helium, Lithium, Berylium, and so on up the periodic table.
Once two species share this information, then they can talk about stuff, literally. By adding unstable elements, they can talk about time.
Chris
Re:Mathematics not universal? (Score:5, Interesting)
WRONG.
Let's take 2 valid mathematical system: Classical Mathematics(CM) and Intuitionist Mathematics(IM).
One thing that is provable in one system might not be provable in the other, or could even be wrong.
For example, if we take the mathematical subset of Logic we have Classical Logic(CL) and Intuitionist Logic(IT).
In CL, NOT(NOT(P)) |= P.
It is easy to see why.
Same with A OR NOT(A).
However, for IL, something is only True if and only if it's provable.
So, NOT(NOT(P)) |= P becomes:
If there is no proof that a proof of P is impossible, then P is provable. This is invalid. The absence of a counter-example doesn't prove the fact.
So we see that NOT(NOT(P)) doesn't imply that there is a proof of P.
Same for A or NOT(A), because we cannot assume that it's always possible to either prove A or it's negation.
One of the fundamental differences in the 2 math systems is that, in IM, it requires a constructive proof.
So, in IM, you cannot prove something like that:
Proof
(...)
Case1: A = X then (...)
Case2: A != X then (...)
(...)
This doesn't work, for the same reason as A or NOT A, you need to prove one or another, so you need to prove that A = X or that A != X.
Ok, the point is, these are 2 working, acceptable and valid mathematical systems, but they cannot be swapped, because CM != IM.
So, NO, two math systems CANNOT be translated back and forth. This is but the tip of the iceberg.
Re:I wrote a review.. (Score:3, Interesting)
Funny, because there's not a single pentagram anywhere in Euclid's Elements [clarku.edu]. Care to research your plagiarees a bit further?
Belloc
Re:Mathematics not universal? (Score:4, Interesting)
I personally think, however, that the definition leans towards the "wavelength of light" definition rather than the emotional definition.
Some criticisms of the book (Score:5, Interesting)
First let me highlight one of the really nice points that the author makes (with many well-researched examples in the book). Recently created myths about things long ago can easily be mistaken has ancient stories. It was interesting to learn that the Renaissance fascination in art and architecture was basically a 19th century invention. For me, the most interesting thing about the book is its debunking of similar historical myths, always working to show what grain of truth their might be to them.
One minor gripe I have is in the context of the praise above. While debunking historical myths, the book reinforces the myth that Einstein's theory of Special Relativity was primarily motived by the Michelson-Morley experiments.
For me, the both the most interesting thing and the most disappointing thing about the book is that the history of the Golden Ratio isn't all that interesting. What turns out to be most interesting is the history of the myths about the Golden Ratio.
This is not to say that the Golden Ratio isn't interesting itself. It's relation to fractals, repeated fractions and parallel curves is interesting, but I guess I would have preferred a "happy ending" where it would play something likes its reputed role in psychology/aesthetics. Of course it is hardly the fault of the author that it doesn't have such an ending
Re:Mathematics not universal? (Score:4, Interesting)
There is a sloppy argument in the parent that perception = reality. That is demonstrably false, if one imagines the "impossible box" illusion, for instance. Besides, it doesn't matter: if there is not a reality, we're both insane figments of the reader's imagination, because only the reader is creating reality (hi reader! keep thinking about me for a while!). After all, I know it's not you and you know it's not me...
A more rigorous reading would be that the process of perception creates my personal experience of reality. Well duh. So reality is distinct from the perception model -- I know that the process of perception is imperfect (via repeated and sometimes painful demonstration), and does not in fact create an accurate model of the empirical reality that thwacks me in the nose when I misjudge a softball catch. That the information in the model is incomplete or contradictory is demonstrated whenever you discover an illusion. That there is a reality is demonstrated when it bonks you.
BUT... That we have unique understanding of 'blue' does not practically prevent us from conversing constructively about 'blue' and having high confidence that what I recognize as 'blue' will be recognized by you and any other capable person as 'blue'. To the degree that we are specific about the method of measuring 'blue' it becomes more likely that we can agree. It doesn't matter that your 'blue' is related to 'sour' in your mind, as long as we agree that it is the color of the sky (when the other would label the sky 'blue').
Aside - Edwin Land [wikipedia.org] showed that color perception is largely relative - blue light is always around 470nm but... the perception of the hue of a color depends largely on the relative intensity of other wavelengths also present. He was able to produce full-color images from grey-scale filters in two different-color light sources.
So yes, 'blue' is an advanced concept that would have to be nailed down after months or years of discussion with the BEMs, possibly involving retinex [wikipedia.org] algorithms to 'decide' if a thing is blue or not. There is, however, a 'blue' out there in reality to point at, and however they percieve it, we can explain to them that 'that' is 'blue'. Perception is relative, but reality is objective, for an agreed frame of reference.
A red stoplight indicates that you are not approaching it at a speed sufficiently close to the speed of light, but from the cop's point of view it's still red.
Vedic Math and Indian Math. (Score:3, Interesting)
Vedic 'math' is mostly arithmetic; it's about how to multiply numbers faster (cool method that; helped me throughout most of school) and, like you said, long form division. Even in that, I doubt it was from the Vedas themselves; I remember reading about those 'tricks' (using the term in a broad sense; not a negative connotation) even before I read Tirthaji's book in an old book published in 1936. The book claimed it was a translation of an even earlier Sanskrit book on mathematics (an absolutely fascinating treatise called Leelavati Ganitham); don't quite think it mentioned any Vedic references.
Indian mathematics, OTOH, was mostly from the Medieval Ages, between 5th and 10th centuries CE, when mathematicians such as Bhaskaracharya and, of course, Aryabhatta, wrote their treatises. The reason, apparently, was astronomy and trade; when you are the center of a globalised trade in gems and spices, you want to get your math right.
Quite possible that ancient India knew about calculus, but it's more likely than not that it was a result of a gradual excellence in the sciences, not something that's been left to us automagically by our Vedic ancestors.