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# Divine Proportions

#### timothy posted more than 8 years ago | from the thought-you-said-mathematical-erotica dept.

192

David Halprin writes with a review of a new (and mighty odd sounding) mathematics book: "In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research in specialised areas, so when a friend e-mailed me the link to this book, I was so excited after reading the author's hype, that I ordered a pre-publication copy. My expectations have not been met, unfortunately, hence my analysis precipitated this review." Read on for Halprin's idiosyncractic take on Norman John Wildberger's Divine Proportions: Rational Trigonometry to Universal Geometry.

There are various ways to approach Norman's so-called "Rational Trigonometry" and/or "Universal Geometry." I have examined it from various perspectives and it does not live up to Norman's claims, whichever standpoint, that I have taken.

DEFINITIONS

Firstly, the definitions, given in the Introduction:-

quadrance = (distance)2 = (x2 2 - x1 2) + (y2 2 - y1 2)

N.B.When one has an equation to solve, (say it is a quadratic), one expects two solutions and deals with them accordingly. If, however, in order to solve an equation, that has a square root sign within it, then one has to square both sides of the equation at some time and this doubles the number of solutions. These extra solutions are regarded as inadmissible, despite their potential interest and possible geometric interpretation. (See worked example later.)

Here is a point of view which suffices to reject this book on its own merit, whether or not there are any other objections, although many other readers will already know of many other disapprovals to mine.

Let's consider someone proposing new variables in some geometric enterprise. This happened in Plane Geometry (for instance), post Descartes, when some bright sparks came up with Polar Coordinates, Pedal Coordinates, Contrapedal Coordinates, Bipolar Coordinates, Parabolic Coordinates, Elliptic Coordinates, Tangential Polar Coordinates, Cesaro Intrinsic Coordinates, Whewell Intrinsic Coordinates and Euler Intrinsic Coordinates, etc.

There are three essential steps to any such proposal:

1. The defining of these coordinates — either in words, with a geometrical description, or in clear mathematical symbology.
2. The relationship of these new coordinates with some other planar coordinate system. This amounts to a mathematical statement of a coordinate transformation. (e.g. From Cartesian to Polar and/or Polar to Cartesian.) Once this is so done, then one can transform any previously-found equations to the new symbology, and hence arrive at a new taxonomy for plane curves, or a new way of stating the conditions for two lines to be parallel, perpendicular or concurrent, or for points to be collinear or not, etc.
3. The demonstration how this new system can be a better system for certain types of problems, perhaps with some limitations in special cases, but not denying their right to be subsumed into mathematical texts, curricula, etc.(e.g. Curve-sketching made easier for plane curves, which are expressed in the new coordinate system, if it is to be preferred in selected examples.) Other pre-existing coordinate systems have shortcuts to finding such things as asymptotes, cusps, asymptotic circles, poles, points of inflection, maxima and minima etc., so the reader would expect to see similar findings by Wildberger.

This third step, in my humble opinion, is where Norman comes undone, and then some!

viz.1) Wildberger cites many plane curves and their concomitant equations in his new coordinate system, in Appendix A, (pages 279-286), but his diagrams have been drawn using software that is dependent on standard polar equations, which are then converted by the software to Cartesian form for plotting. In no way is his "Rational Polar Equation" suitable for being implemented by the software employed. Certainly, any programmer worth his salt could devise a not-so-easy and/or complicated routine to transform Rational Polar Equations back to the regular form, but that is no pat-on-the-back for Wildberger, rather it shows the counter-intuitive and flawed reason for using that coordinate framework.

viz.2) Wildberger's five laws are merely standard trigonometrical identities disguised by his new symbology, showing no advantage over the original forms. See table in Appendix.

He cites a triangle problem in his first chapter on page 14. He then gives a so-called "Classical Solution" in 5 equation lines, using a trig. table via a calculator, for part of this method.

Then, in the next page, he gives his so-called "Rational Solution", which requires three diagrams and 8 or 9 equation lines, and this is a flawed solution, to which he seems oblivious, and does not own to it therefore.

Anyone with a modicum of mathematical sense, who tackles this triangle problem, knows the following:-

The usual properties of arithmetic with respect to commutativity, associativity and distributivity also apply equally to common algebra.

When one has an equation to solve (say it is a quadratic), one expects two solutions and deals with them accordingly. However, in order to solve an equation that has a square root sign within it, one has to square both sides of the equation at some time, and this doubles the number of solutions. These extra solutions are regarded as inadmissible, despite their potential interest and possible geometric interpretation.

Viz. The worked example for the rational method for the triangle on page 15 accepts the inadmissible solution as though it is acceptable, whereas the better solution method is the classical method used properly, without recourse to trig tables, and in only four equation lines.

PROBLEM

A triangle ABC has sides a = 5, b = 4 and c = 6.

A st. line from C to AB, (length d), cuts AB at D,

where angle BCD = 45 degrees. What is the length d = CD?

MY SOLUTION

cos B = 3/4 sin B = 7/4, BDC = 180 - (45 + B)

sin BDC = sin (45 + B) = sin 45.cos B + cos 45.sin B

sin(45 + B) = (3/4 + 7/4)/2 = (3 + 7)/(42)

d = 5 sin B/sin BDC = 57/4 x (42)/(3 + 7) x (3 - 7)/(3 - 7)

= 52(37 - 7)/2 = 3.313693059

So, in this first instance, Rational Geometry does NOT provide anything worthwhile, contrary to Norman's hype.

In chapter two, Norman introduces a dissertation on Fields, as though this is an important factor for understanding and using Rational Geometry, despite the fact that up to a student's age of 17, schools don't find it necessary to introduce into his/her brain any Field lessons together with geometry and trigonometry.

Don't forget that his advocacy is to replace classical geometry and trigonometry, (especially lines and angles), at school level. He doesn't suggest retaining it and using his methods as a adjunct and/or complement, especially since some of those guys and gals will become architects, surveyors etc. etc.

Were the academic institutions which set college and university curricula, to take Wildberger at his word, by eliminating regular trigonometry and geometry and replacing it with his concepts, it would be the downfall of current mathematical knowledge and standards for years to come. What's more, the damage would take years from which to recover; an almost irreparable predicament in education.

c.f. Cuisenaire of yesteryear.

However, you don't have to read between the lines to see on page 21 that Wildberger excludes 'characteristic two fields.' Although I am not versed in Field Theory, I opine that such an exclusion does not apply to classical geometry and/or trigonometry, otherwise he would have said so. So, he is already implicitly confessing, to a failure of Rational Geometry in the global sense.

I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on.

Wildberger then goes into proportions using the a:b = c:d symbology, as though it has more merit than the usual a/b = c/d, like we have in the Sine Rule, say. Warum? Wherefore?

On page 9, he states, without proof, the equation for the spread between two lines. From standard trig, one can easily calculate the angle between two lines, and when one squares the sine of that angle one has his equation without recourse to rational geometry. Now if one subtracts this expression from 1, one obtains the square of the cosine of the angle between these two lines. Naturally if one starts with these two terms and adds them one can see why they sum to unity, which he states on page 27 as Fibonacci's Identity.

A rose by any other name is still a rose, I believe; Pythagarose?

Then Wildberger presents variants of this, all of which are obtained with simple college algebra and are further diversions. Then he waffles on about the possibility of a denominator being zero and its implications. WOW.

(See table in Appendix).

Then, we have linear equations and their solutions using determinants as though it is a revelation. WOW WOW!

At this point, why not reinvent the wheel?

Remember, this book is not aimed at secondary students; such a lower level of presentation is promised in an intended future publication. So, why does he tell us cognoscenti' so much that, obviously, we would know before picking up his book?

Is he just filling up the pages, due to lack of the Step 3 material, so we are drooling to obtain an implied revelation or other especially informative disclosure?

N.B. We mustn't hold our breath, so as to avoid cyanosis!

So now, on page 31, we have Polynomial Functions and Zeros. Wildberger examines an example in F19, but does not explain why on earth that has any significance in curve sketching. After all, we expect our graph to be plottable in a Cartesian Framework in the usual field of numbers, which we, and our computer plotting software, always use by default.

Page 32 teaches us how to solve quadratic equations by completing the square. This is so deep, that I hope the reader's gray matter can cope, especially since he/she is, presumably, at tertiary level!

Now to chapter 3 starting on page 35: Cartesian Coordinate geometry. On page 40, he makes a special reference to the conditions of perpendicularity of two lines. This is easily calculated since the product of their gradients must be -1. However, he stresses "that this is the single most important definition in all geometry, it colours the entire subject." Then he follows this up by naming this "blue geometry."

So mind-boggling WOW WOW WOW! He then promises that other colours will appear. I can hardly wait. I hope the new colours match the colour scheme in my study.

Summarily, there has been nothing from Step 3 to illustrate a finding in Rational Geometry, that gives it an edge, at least. He is just making statements, that are already well-known in geometry and trigonometry, and he is an associate professor in mathematics, who should be able to do a lot better than that. I opine that he doffed his professorial hat and replaced it with a dunce's hat in order to write such pretentious garbage.

One must address one's audience, or write to one's intended readership, at a consistently-appropriate level. In matters of a so-called "New Mathematics," he must demonstrate actual advantages, and not attempt to hoodwink us, as he did in the earlier problem on Pg.14 and its badly worked out, so-called "Classical Solution".

If one searches the web, there appears to be no academic interest in "Rational Geometry" by the diasporic mathematical fraternity.

Especially, I had hoped to find that his fellow mathematicians at UNSW would have had something worthwhile to say, and thereby prove me to be an innumerate imbecile for daring to criticise "Divine Proportions."

Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid.

CONCLUSION

In its present format, a better title would be:-

"LE GRAND PURPORTISSIMENT"

This book, overall, is a misrepresentation of the facts. It purports to be what it is not. The promotional literature on the author's web site is descriptive, but more of the author's dream for a mathematical breakthrough than an actual innovation.

If finances were no concern, I would suggest a complete re-presentation of all his original findings under a new title, that states, in effect, that this is a new coordinate framework, that, from time to time, has occasional advantage over the Cartesian Coordinate system, comparable to the other planar frameworks, stated on the first page of this review.

So mote it be. Amen.

APPENDIX

 RATIONAL TRIGONOMETRY LAWS ANALOGOUS LAWS IN TRIGONOMETRY 1. Triple Quad Formula for collinearity of three points Triangular area degenerated to zero. 2. Pythagoras' Theorem for right triangles Pythagoras' Theorem 3. Spread Law for any triangle Sine Rule 4. Cross law for any triangle Cosine Rule 5. Triple Spread Formula for any triangle (Quadrea) 16 x (Area)2

Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

cancel ×

### Karma whoring (5, Informative)

#### UbuntuDupe (970646) | more than 8 years ago | (#15936825)

Slashdotters vetted this before [slashdot.org]

### The answer to the question (0)

#### Anonymous Coward | more than 8 years ago | (#15937364)

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

### OT: Wikipedia down, what happened? (-1, Offtopic)

#### phoenix321 (734987) | more than 8 years ago | (#15936837)

Wikipedia is down ATM with no explanation other than technical difficulties. All subdomains are affected, too.

irc://irc.freenode.net/wikipedia [irc] is the primary source of information right now and there are circulating rumors Cogent cut them off because of a DMCA complaint.

### mod parent troll (0)

#### Anonymous Coward | more than 8 years ago | (#15936885)

wikipedia is fine.

### Re:mod parent troll (0)

#### phoenix321 (734987) | more than 8 years ago | (#15936895)

Nah, it's back up since five minutes and still not writable, so cut me some slack, okay? http://www.thewritingpot.com/wikistatus/ [thewritingpot.com]

### Re:mod parent troll (3, Funny)

#### neonprimetime (528653) | more than 8 years ago | (#15936920)

so cut me some slack, okay?

Those who spend their day monitoring the status of wiki shall receive no slack.

### Re:OT: Wikipedia down, what happened? (1)

#### andrewman327 (635952) | more than 8 years ago | (#15936896)

Wikipedia: Rational Geometry [wikipedia.org] . I do not see any problems.

### Re:OT: Wikipedia down, what happened? (1)

#### Phreakiture (547094) | more than 8 years ago | (#15936913)

Wikipedia is down ATM with no explanation other than technical difficulties. All subdomains are affected, too.

Ten minutes have passed since you posted that, and I am seeing Wikipedia just fine.

### Re:OT: Wikipedia down, what happened? (1)

#### Eudial (590661) | more than 8 years ago | (#15936995)

Ten minutes have passed since you posted that, and I am seeing Wikipedia just fine.

I experienced problems with wikipedia today as well, so I guess it was just bad timing posting it just before wikipedia was up again...

### Re:OT: Wikipedia down, what happened? (1)

#### phoenix321 (734987) | more than 8 years ago | (#15937007)

Yes, and I hang my head in shame.

It was down before I left my workplace today and wasn't up when I logged in at home again, more than two hours later. It's back up right now, write access is slow but possible. Let's see what Wikinews is saying about that...

### The Proportions. (0)

#### Anonymous Coward | more than 8 years ago | (#15936865)

She had a set of divine proportions that could cause cardiac arrest in a Yeti.

For all I know, Slashdot's populace may be affected too.

### Re:The Proportions. (1)

#### PCM2 (4486) | more than 8 years ago | (#15937486)

She had a set of divine proportions that could cause cardiac arrest in a Yeti.

A Bulwer-Lytton candidate [bulwer-lytton.com] to be proud of!

### I'm not that Smart! (5, Funny)

#### neonprimetime (528653) | more than 8 years ago | (#15936867)

In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research in specialised areas

Polemic [wikipedia.org]
Tertiary [wikipedia.org]
Concomitant [wiktionary.org]

### Re:I'm not that Smart! (4, Funny)

#### Keith Russell (4440) | more than 8 years ago | (#15936947)

Does the Architect know his thesaurus is missing?

### Re:I'm not that Smart! (5, Funny)

#### Rude Turnip (49495) | more than 8 years ago | (#15936972)

I, too, found this book to be shallow and pedantic.

### Re:I'm not that Smart! (1, Funny)

#### Anonymous Coward | more than 8 years ago | (#15937523)

Hmm, yes, shallow and pedantic.

### I'm not that funny either... (3, Funny)

#### Chaffar (670874) | more than 8 years ago | (#15936975)

A rose by any other name is still a rose, I believe; Pythagarose?

There's also the recurring WOW WOW WOW's which I believe delightfully attempts to break the morose ambiance that prevails throughout the maelstrom of words that the author has deemed fit to call a critique of Wildberger's latest publication.

### Re:I'm not that Smart! (-1, Troll)

#### Anonymous Coward | more than 8 years ago | (#15937201)

Those are not unusual or difficult words. Perhaps you should try reading more, and more widely than /.

### Re:I'm not that Smart! (1)

#### pVoid (607584) | more than 8 years ago | (#15937345)

Btw, it's "Tut mir leid". not "mit".
Some people just try too hard...

### Re:I'm not that Smart! (3, Funny)

#### Ed Avis (5917) | more than 8 years ago | (#15937450)

I like that review... it starts off reasonable, and gets increasingly Time Cube [timecube.com] as it goes on.

### This is all (1)

#### jugglerjon (559269) | more than 8 years ago | (#15936868)

Intuitively obvious. At least that's what my college professiors would say when lecturing.

### Re:This is all (1)

#### creimer (824291) | more than 8 years ago | (#15936958)

Still greek to me, man. Got any hash for sale?

### All I could think about... (1, Funny)

#### Anonymous Coward | more than 8 years ago | (#15936877)

Mathematician 1+1 = 2
Scientist 1+1 is around 2
Accountant 1+1 = any thing your want

### Re:All I could think about... (3, Funny)

#### Red Herring (47817) | more than 8 years ago | (#15937467)

Engineer: 2+2=5, for large values of 2

#### andrewman327 (635952) | more than 8 years ago | (#15936879)

It is too bad that these new ideas are so poorly implemented and described. The ideas seem appealing at first glance, but they ultimately do not survive close scruntiny.

Sometimes it seems that the only really new ideas being tossed around (outside of lab research and the like) in science are from Wolfram in his book, A New Kind of Science [slashdot.org] . (I do not include creationism in this category because it is not new, so spare me the flames regardless of how you feel about it.) Scientists are great at empirically testing this and that theory but they often have problems altering their own perceptions on existing and accepted information.

I agree with the review that this form of geometry should never supplant the status quo:

Don't forget that his advocacy is to replace classical geometry and trigonometry, (especially lines and angles), at school level. He doesn't suggest retaining it and using his methods as a adjunct and/or complement, especially since some of those guys and gals will become architects, surveyors etc. etc. Were the academic institutions which set college and university curricula, to take Wildberger at his word, by eliminating regular trigonometry and geometry and replacing it with his concepts, it would be the downfall of current mathematical knowledge and standards for years to come. What's more, the damage would take years from which to recover; an almost irreparable predicament in education.

#### eln (21727) | more than 8 years ago | (#15936988)

I do not include creationism in this category because it is not new

It also isn't science.

#### Anonymous Coward | more than 8 years ago | (#15937073)

".. a rare blend of monster raving egomania and utter
batshit insanity"

Cosma Rohilla Shalizi on S.Wolfram, A new kind of science

http://cscs.umich.edu/~crshalizi/reviews/wolfram/ [umich.edu]

#### kfg (145172) | more than 8 years ago | (#15937087)

Scientists are great at empirically testing this and that theory but they often have problems altering their own perceptions on existing and accepted information.

That is the very reason that "scientists" is plural. The flip side of that, however is that scientists are always coming up with new ideas, because that's what they're supposed to do.

Sometimes they do this in the same manner that legislators come up with new laws because that's what they're supposed to do, because it has become a publish or perish world. It doesn't matter what you publish, just the quantity of publication; and how often you and your buddies cite each other to drive up your stats.

KFG

### Re: Too bad (2, Interesting)

#### Wolfbone (668810) | more than 8 years ago | (#15937157)

"Sometimes it seems that the only really new ideas being tossed around (outside of lab research and the like) in science are from Wolfram in his book, A New Kind of Science."

Really new? No. Tossed around? Oh yes ;-)

" In ANKS Wolfram says that "the core of this book can be viewed as introducing a major gener- alization of mathematics" (p. 7). In this he is entirely mistaken, but there are at least two ways in which he has benefited mathematics: he has helped to popularize a relatively little-known mathematical area (CA theory), and he has unwittingly provided several highly instructive examples of the pitfalls of trying to dispense with mathematical rigor."

http://www.ams.org/notices/200302/fea-gray.pdf#sea rch=%22In%20ANKS%20Wolfram%20says%20that%22 [ams.org]

### A New Kind of Science (was Re:Too bad) (4, Insightful)

#### Anonymous Coward | more than 8 years ago | (#15937257)

Sometimes it seems that the only really new ideas being tossed around (outside of lab research and the like) in science are from Wolfram in his book, A New Kind of Science.
I'm still trying to figure out if this was meant to be tongue-in-cheek or not, given the context. A New Kind of Science is a self-published, non-peer-reviewed, 2000-page testament to the sort of hubris that can only afflict mathematical prodigies who lack meaningful human contact at the age when normal people experience social development.

Wolfram performs an over-analysis of a very narrow subset of cellular automata while claiming to have invented the field, that 'mainstream science' refuses to look at this incredible discovery, and that his 'new kind of science' based on recursion and cellular automata will change the world, although he has no idea how.

It reads like something written after reading Godel, Escher, Bach, smoking pot, and thinking, "I'm thinking about thinking. Now I'm thinking about thinking about thinking. Now I'm....whoa, I wonder what that looks like on graph paper?"

From the reviewer's not-so-clear description, it appears this book falls into a similar category.

### Wolfram (1)

#### pinkuff (878101) | more than 8 years ago | (#15937278)

I slogged through the 1000+ pages of the tome three years ago - I remember all my friends were making fun of me because of the size of the book. While some of that stuff is interesting, anybody who claims he's invented a New Kind of Science is a raging lunatic. The way the book is filled with self promotion is a testimony to this, all the more sad because Stephen Wolfram's curriculum is impressive and he might (I'm not equipped to understand) be a genius

### Postscript: I am ... (0)

#### Anonymous Coward | more than 8 years ago | (#15936899)

In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research in specialised areas

PS. I am not a crackpot.

### geesh (4, Insightful)

#### bunions (970377) | more than 8 years ago | (#15936937)

Lay off the thesaurus, you're gonna put your eye out. I'm not sure who that overwrought prose is supposed to impress, but it makes me take an instant dislike to the author.

"I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on."

yes, thanks for providing an explanation for your $10 college words, otherwise we plebs might not have understood you. Also, what's up with the German and French from out of nowhere? I'm all for using them when there is no easy english equivalent, but what the hell, "Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid." Those are just extra words. ### Re:geesh (5, Funny) #### spun (1352) | more than 8 years ago | (#15937088) You need the Pretentious Geek/English translator. Here, let me help: "I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on." "I have to confess that I'm really smart. Smarter than you. In fact, you're pretty damn dumb. So dumb that I have to explain what prestidigitator and legerdemain mean. A prestidigitator does not mean someone who spanks the monkey, and legerdemain does not mean a type of beer. They mean you are dumb." "Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid." "Not only am I very smart, I know more languages than you, proving I am a cultered man of the world. And implying that you are a redneck hick. So suck it, hick, I'm going to go prestidigitate my legerdemain." Hope that helps get you started. If you want to learn more Pretentious Geek, please first stick a broomstick up your ass and tilt your nose upwards at a 45 degree angle, it helps the learning process. ### Re:geesh (3, Informative) #### bunions (970377) | more than 8 years ago | (#15937146) well, no, I speak German, sorta. And Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid translates into, roughly, "such a shame, nothing, nothing, zero, Woe is me, I'm afraid not." He's not saying anything different in German than he's already said in English. It's stupid. also, it's 'es tut mir leid, but I'm not picky. ### Re:geesh (3, Insightful) #### friedo (112163) | more than 8 years ago | (#15937268) You need the Pretentious Geek/English translator. Here, let me help: Pretentious, yes, but not Geek. Geeks strive for well-defined, unambiguous terms, rational organization of subject matter, and language that accomplishes exactly as much as is necessary, and no more. Geek writing is efficient. The OP's analysis is excellent, but frought with writing that goes beyond pretentious. It's just bad. Disorganized, rambling, semi-coherent and full of useless jumbles of letters that communicate nothing. ### Re:geesh (2, Funny) #### H0p313ss (811249) | more than 8 years ago | (#15937458) The OP's analysis is excellent, but frought with writing that goes beyond pretentious. It's just bad. Disorganized, rambling, semi-coherent and full of useless jumbles of letters that communicate nothing. So... somewhat above average for Slashdot then? ### Re:geesh (3, Funny) #### tr0p (728557) | more than 8 years ago | (#15937103) Also, what's up with the German and French from out of nowhere? I'm all for using them when there is no easy english equivalent, but what the hell, "Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid." Those are just extra words. Easy to explain: Legerdemain (sleight of hand). It amplifies the prestidigitator (magician) author's drama induced authority. ### Re:geesh (4, Insightful) #### SatanicPuppy (611928) | more than 8 years ago | (#15937118) Nothing like one mathematician being snarky about another mathematician. Frankly they both bored the shit out of me after about 5 seconds. Why is it that math is always rendered this way? I've met interesting and articulate mathematicians before, so I know they exist...Are they not allowed to write textbooks? Or at least write reviews about textbooks? I was pushed into a near-hatred of math by hordes of pretentious math prodigys that had zero use for any student who didn't start off with what they felt was obvious knowledge. The text book talks down to you, the professor talks down to you, and god forbid you ask for a practical example! I'm not a math genius, but I'm damn good at practical math. The only way I managed to pass calculus the first time was because I happened to be taking it at the same time as a physics course, and I could figure it out where I could see an application in physics. For calc II I shopped around, trying to find a decent book with dismal results. Ended up dropping the class, and shopping for a decent professor the next semester. Math is cool, but goddamn, the way it's taught is awful and jackasses like this reviewer and the joker who wrote the book he's reviewing are a prime reason why. ### Re:geesh (2, Insightful) #### bunions (970377) | more than 8 years ago | (#15937194) Sounds like someone had a string of shitty math teachers. I feel the same way about linux. The symptoms you describe exist in every field, from math to literary critisism to welding to surfing. ### Re:geesh (1) #### SatanicPuppy (611928) | more than 8 years ago | (#15937474) Broadly true, though I actually learned to weld from reading a book about it, and the book kicked ass. People who weld aren't usually brimming with hubris, though literary criticism is not just brimming, but overflowing with it. Math is just as bad, and the thing is (unlike literary criticism), it shouldn't be! If you're doing theoretical math, you shouldn't need to be walking around trying to convince people what a big brain you have...you're doing theoretical math. Now if you're doing lit crit, you gotta talk it up, or people might just think you're an asshole. So while I'd expect to have to sift a lot of garbage while reading a book of literary criticism, I really resent having to do the same for a book of math. Math is simple, elegant, and objective, and it should be presented that way...preferably with a few concrete applications for people like me who like that crap. ### Re:geesh (1) #### bunions (970377) | more than 8 years ago | (#15937521) I'd be happy to recommend a bunch of kickass math books. Pretty much anything on Springer-Verlag with a yellow cover will fit the bill. ;) ### Re:geesh (1) #### Tyger (126248) | more than 8 years ago | (#15937499) My geometry text book was written by a smartass. It hasthe strangest off the wall analogies in it. ### Re:geesh (1) #### Wolfbone (668810) | more than 8 years ago | (#15937560) "Nothing like one mathematician being snarky about another mathematician." Only one of the protagonists here appears to be a mathematician. ### Re:geesh (0, Redundant) #### Threni (635302) | more than 8 years ago | (#15937162) >I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense >that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the >audience members, thereby lessening their attention on what's really going on." > >yes, thanks for providing an explanation for your$10 college words, otherwise we plebs might not
>have understood you.

I couldn't have put it better myself.

### Re:geesh (0)

#### Anonymous Coward | more than 8 years ago | (#15937189)

Es tut mit leid.
In his attempt to sound clever, he turns himself into a douchebag. It's Es tut mir leid. (ger.: I am sorry.)

I am sorry that a thesaur'ed review is accepted at all. It makes the author sounds like a junior high school student trying to bolster his report.

F, for effort.

### Re:geesh (0)

#### Anonymous Coward | more than 8 years ago | (#15937260)

"I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on."

Actually, I was insulted by the fact that he thought I'd not know what "prestidigitator" and "legerdemain" meant.

Also, what's up with the German and French from out of nowhere? I'm all for using them when there is no easy english equivalent, but what the hell, "Alas and alack, niente, gar nichts, zilch. Woe is me. Es tut mit leid." Those are just extra words.

I'm not 100% sure but I think those are examples of words which mean the same things. Which is what he's saying the book actually boils down to: a fancy way of saying something but which adds nothing to what was already known. Anyway, it's certainly a joke of the sort mathematicians seem to like.

### Re:geesh (0)

#### Anonymous Coward | more than 8 years ago | (#15937263)

The author of the review would do well to read Politics and the English Language [mtholyoke.edu] by George Orwell.

### meh (1)

#### krilli (303497) | more than 8 years ago | (#15937483)

Maybe he just likes funny words. I like funny words, and funny letters. J is the funniest letter of the alphabet. Why the huff?

### Re:geesh (1)

#### french_user (996372) | more than 8 years ago | (#15937548)

My little brother who doesn't speak english understood the article. Unnecessary french you said ?

#### exp(pi*sqrt(163)) (613870) | more than 8 years ago | (#15936997)

...the content of this book here [blogspot.com] . The core idea is sound and it looks like it has application to computer graphics.

### My idiosyncratic take (5, Insightful)

#### Junky191 (549088) | more than 8 years ago | (#15937008)

I believe this is the most pretentiously-worded article blurb that has ever been seen on Slashdot.

### Two words (0)

#### Anonymous Coward | more than 8 years ago | (#15937057)

Pompous...windbag...

### Re:My idiosyncratic take (1)

#### kfg (145172) | more than 8 years ago | (#15937288)

I believe this is the most pretentiously-worded article blurb that has ever been seen on Slashdot.

Oooooooo, sounds like a challenge to me, excuse me, provocation (dare).

KFG

### Re:My idiosyncratic take (1)

#### Angostura (703910) | more than 8 years ago | (#15937404)

I feel compelled to quote Disraeli: The review was clearly written by "a sophistical rhetorician, inebriated with the exuberance of his own verbosity, and gifted with an egotistical imagination that can at all times command an interminable and inconsistent series of arguments to malign an opponent and to glorify himself. "

Except of course, the reviewer's prose is so baroque it is impossible to tell whether is arguments are actually inconsistent.

### WTF? (1)

#### bfields (66644) | more than 8 years ago | (#15937009)

Has Archimedes Plutonium taken over Slashdot?

### Re:WTF? (1)

#### Tackhead (54550) | more than 8 years ago | (#15937039)

> Has Archimedes Plutonium taken over Slashdot?

SINUSOIDAL FUNCTIONS on a CARTESIAN PLANE?

(No, wait, that was ROBERT Mc ELWAINE! :)

### El Sucko (5, Insightful)

#### dcollins (135727) | more than 8 years ago | (#15937040)

This review freakin' sucks.

I have an M.A. in Mathematics. I've read some of the "Rational Trigonometry" online before, and yes, it is pretty oddball and has its weakness and can be criticized.

But this review is borederline psychotic. It is poorly written, full of ad hominem attacks, lots of made-up grammar and word usage, wierd random abbreviations... it's scatterbrained, repetitive, and unnecessarily hostile.

There is a critical review to be written about "Rational Trigonometry", but this isn't it. I may not like our current government, but I'm still not going to listen to some incoherent homeless guy raving about it on the street.

### Re:El Sucko (2, Funny)

#### EatHam (597465) | more than 8 years ago | (#15937197)

I'm still not going to listen to some incoherent homeless guy raving about it on the street.

And you don't have to, there are plenty of them on /.

### Re:El Sucko (1)

#### Wolfbone (668810) | more than 8 years ago | (#15937246)

Agreed. Wildberger's manner is off-putting and the idea of replacing trigonometry with his rational trigonometry in high schools seems eccentric but for starters a trigonometry valid in a general field is interesting and this review just stinks.

### Re:El Sucko (0)

#### Anonymous Coward | more than 8 years ago | (#15937275)

"Wierd" is a new one to me.

### Re:El Sucko (0)

#### Anonymous Coward | more than 8 years ago | (#15937446)

It is poorly written, full of ad hominem attacks, lots of made-up grammar and word usage, wierd random abbreviations...
That and his *very first* formula is wrong, it should be (x1-x2)^2+(y1-y2)^2.

### Re:El Sucko (2, Insightful)

#### RackinFrackin (152232) | more than 8 years ago | (#15937490)

It is poorly written, full of ad hominem attacks, lots of made-up grammar and word usage, wierd random abbreviations... it's scatterbrained, repetitive, and unnecessarily hostile.

Not to mention imprecise. In two instances the reviewer says

in order to solve an equation that has a square root sign within it, one has to square both sides of the equation at some time, and this doubles the number of solutions.

which is not true in all cases. Two examples are

\sqrt(x) = x, which has two solutions before and after squaring both sides, and

\sqrt(x)=10, which has one solution before and after.

### Missing Options! (0)

#### Anonymous Coward | more than 8 years ago | (#15937065)

The most obvious Divine Proportions are: 36x24x36.

Oh wait: this is /.

In that case: Trigonometry is sexy!

### Re:Missing Options! (1)

#### Impy the Impiuos Imp (442658) | more than 8 years ago | (#15937284)

> The most obvious Divine Proportions are: 36x24x36.

That would be an odd-shaped palm. WTH are you talking about?

### Save yourself some money by buying the book here! (0)

#### Anonymous Coward | more than 8 years ago | (#15937077)

Save yourself some money by buying the book here: Divine Proportions [amazon.com] . And if you use the "secret" A9.com discount [amazon.com] , you can save an extra 1.57%!

### Poor reading, or poor writing? (1)

#### dthmtluncrn (993273) | more than 8 years ago | (#15937120)

When I first read the posting (in my mind anyways) the name of the book was purported to be: "In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics..." In my opinion this would have been a much more entertaining title. Along the lines of the full Dr. Strangelove [imdb.com] title.

### New obligatory quote... (4, Funny)

#### jpellino (202698) | more than 8 years ago | (#15937129)

"In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research in specialised areas"

"Ya hurt yer what?"

### Sorry, but... (0)

#### Anonymous Coward | more than 8 years ago | (#15937133)

I seem to have wandered onto a site for snobby, elitist mathematicians who write like pretentious twits, when I was really trying to get to a tech news site. Do you happen to know the way to slashdot [slashdot.org] ?

### Re:Sorry, but... (1)

#### Impy the Impiuos Imp (442658) | more than 8 years ago | (#15937295)

Seriously, he could have shown the one example he counters with his own "way", to compare and contrast. Also, don't most solutions involving trig, where you solve in reverse for an angle, offer infinite solutions, all +/- 180 or 360 or something? If so, how does he select his "correct, one" solution?

### Sack the reviewer (1)

#### postbigbang (761081) | more than 8 years ago | (#15937134)

It's tough enough to get people interested in geometry and trig than to bloody some poor prof's attempt at unifying disciplines. It's nice that his review must demonstrate his various vocabularies and distainful lack of surprises..... yet conveying information about the actual content of the book is betrayed while the reviewer stands up and barks like a dog for a pet. Look! I killed this helpless little thing. Aren't I a good boy? Gotta bone.

The review, for its content, is perhaps as useless as the book he's trying to describe-- it doesn't get beyond a sense of hopelessness. If hopelessness is the message then it should be stated, not a long sewn-together set of moans and oh-gawd-is-he-awful's.

There are some of us that get it. Others don't get it. He's obviously not the audience-- and his barbs at perceived accuracy shows how unbending Halprin is. Yes, math demands accuracy and rules, yet understanding trig, linear geometry, and other non-algebraic disciplines isn't a droll matter of lumping proofs after proof.

### Philosophically/Ideologically driven blather (4, Interesting)

#### Coryoth (254751) | more than 8 years ago | (#15937137)

The author (of the book) is, to my mind, tending dramatically toward the loopy side. Take, for instance, this piece he wrote [unsw.edu.au] . It starts out as an interested discussion into some issues in the philosophy of mathematics, so skip down to the middle or closer to the end to read what has, by that point, devolved into an unmitigated rant from a finitist of the worst kind. Questioning the foundations of mathematics is not new, nor is questioning whether we wish to admit the concept of a "completed infinity" as compared to conceptions of "potential infinity", however even the Intuitionist school, hell even Brouwer himself (who was certainly not a man interested in compromise) would be rather appalled by the extremes here. Intuitionist mathematics has developed into a respectable field, with things like nonstandard analysis proving to provide interesting alternative constructions of real numbers and analysis. I can't see how Wilderberger's philosphy will lead anywhere.

Wilderberger's stance - that there is simply a finite "biggest number" and we shouldn't use or allow anything "bigger", and the resulting implications for irrational numbers - is just baffling. I'm guessing it is the extreme (and from what I can tell surprisingly uninformed) finitist philosophy that drives his Rational Geometry (he needs to somehow eliminate non-commensurable/irrational quantities from geometry lest they interfere with his fear of the infinite) - to him the superiority of Rational Geometry is presumably clear, in that it aligns with his extremist philosophy. The problem is that his philosophy seems, at best, half baked. He seems like a mathematician who took an interest in philosophy but couldn't be bothered seriously reading or considering any of the vast amounts of material on philosophy of mathematics. That is to say, he is, in many ways, little better than this lunatic ("Cubehead") [graveyardofthegods.com] who is hell bent of redefining mathematics to fit with the pronouncements of his idol, Gene Ray (creator of Time Cube), regardless of how shaky the grounding philosophy may be.

### Re:Philosophically/Ideologically driven blather (1)

#### nonlnear (893672) | more than 8 years ago | (#15937383)

That article of Wildberger's was hilarious! What's more entertaining than:
Perhaps you believe that even though you cannot write down numbers bigger than w, you can still abstractly contemplate them! This is a metaphysical claim. What does a number bigger than w mean, if there is nothing that it counts, and it can't even be written down? Believing you can visualize' an all-seeing Leprechaun or an unstoppable mouse in your mind, by some melange of images, descriptive phrases and vague feelings, does not mean they exist.
Thank you for the entertainment. That article was better than a good BOFH episode.

### hmmm and I thought this... (1)

#### glitch23 (557124) | more than 8 years ago | (#15937161)

what a book talking about the Divine Proportion as in the number Phi. I'm nearing the end of a book called the Golden Ratio that mentions various names for phi (golden ratio, divine proportion, and there are others). It seems the reviewed book is way too reliant upon mathematics to be fun reading. This book might about the same Divine Proportion but I didn't see anything speciying so in the review.

### It's Friday (5, Funny)

#### papasui (567265) | more than 8 years ago | (#15937175)

I'm usually too lazy to read the article but holy shit I'm not reading the review either.

### A very odd mathematician (2, Informative)

#### ortholattice (175065) | more than 8 years ago | (#15937221)

The author, Norman Wildberger, is one strange mathematician. I could hardly believe his rant against set theory [unsw.edu.au] , which borderlines on crankish or at the very minimum appallingly uninformed. For example, he calls the ZF (Zermelo-Fraenkel) axioms a "sorry list of assertions" - "these statements are awash with difficulties. What is a property? What is a parameter? What is a function? What is a family of sets? Where is the explanation of what all the symbols mean, if indeed they have any meaning? How many further assumptions are hidden behind the syntax and logical conventions assumed by these postulates?" In fact, these axioms are very precisely defined, and rank among mankind's greatest achievements.

(For the uninformed, consult Wikipedia [wikipedia.org] . For a very precise breakdown of these axioms translated to primitve symbols - Wikipedia still includes some higher-level defined symbols that Wildberger objects to because he can't seem to understand them - see the metamath version [metamath.org] . In other words, there is nothing fuzzy or ambiguous about these axioms.)

His set theory rant created quite a furor on Usenet, here [google.com] and here [google.com] .

### I assume you meant... (1)

#### rolfwind (528248) | more than 8 years ago | (#15937223)

Es tut mit leid./blockquote

Es tut mir leid.

### Compensating for something? (4, Informative)

#### Nereus (733242) | more than 8 years ago | (#15937227)

Using long words doesn't make you look any smarter in the same way driving a flashy car doesn't make your dick look any bigger.

Now you tell me.

### Re:Compensating for something? (2, Funny)

#### rolyatknarf (973068) | more than 8 years ago | (#15937310)

But driving a very tiny car might make your dick look bigger.

### Re:Compensating for something? (1)

#### Impy the Impiuos Imp (442658) | more than 8 years ago | (#15937314)

Yeah!

I've known a few guys who thought they were pretty smart, but you've got being right down to an art. You think you're a genius-you drive me up the wall. You're a regular original, a know-it-all. Oh-oo-oh, you think you're special. Oh-oo-oh, you think you're something else...Okay, so you're a rocket scientist.

That don't impress me much. So you got the brain but have you got the touch? Now don't get me wrong, yeah I think you're alright, but that won't keep me warm in the middle of the night.

### Re:Compensating for something? (1)

#### geekoid (135745) | more than 8 years ago | (#15937390)

But having your car built half size would make your dick look HUGH!

### His "Solution" isn't even math (0)

#### Anonymous Coward | more than 8 years ago | (#15937231)

MY SOLUTION

cos B = 3/4 sin B = 7/4, BDC = 180 - (45 + B)

sin BDC = sin (45 + B) = sin 45.cos B + cos 45.sin B

sin(45 + B) = (3/4 + 7/4)/2 = (3 + 7)/(42)

d = 5 sin B/sin BDC = 57/4 x (42)/(3 + 7) x (3 - 7)/(3 - 7)

= 52(37 - 7)/2 = 3.313693059

I don't know what this is supposed to be, but it's not math. The only parts that make sense are "BDC = 180 - (45 + B)" and the line following that. Sin B can't possibly be 7/4, which is greater than 1. And 4 * 2 = 8 not 42. The last three lines are complete jibberish.

### Re:His "Solution" isn't even math (1)

#### svnt (697929) | more than 8 years ago | (#15937501)

Giving the reviewer the benefit of the doubt and assuming he's working in metric or some other alien measurement system (joke!), all you have to do is look at his answer to determine how off-base he is. I'm assuming (since I can't see it) that the triangle ABC is named by its three vertices, A, B, and C.

If you have a triangle where the shortest side is 4, no line from any of the vertices to anywhere on the opposite line could possibly be less than 4. Anybody else see a different answer?

### There are a lot of math crackpots out there... (3, Interesting)

#### exp(pi*sqrt(163)) (613870) | more than 8 years ago | (#15937232)

...99% of whose [wikipedia.org] writings [crank.net] would make a 5 year old's grasp of number theory seem advanced. People who have proved FLT (the easy way), that 0.999... recurring is less than 1, that there are countably many reals and so on. But the author of Divine Proportions is one of those unusual crackpots who's obsessed with an idea but hasn't allowed that to completely compromise their mathematics. These people don't deserve to be beaten down along with the others. I think that having no review of this book would have been better than this review.

### Reviewer's equations aren't even right! (1, Informative)

#### Anonymous Coward | more than 8 years ago | (#15937236)

distance**2 is not x2**2 - x1**2 + y2**2 - y1**2

It is (x1-x2)**2 + (y2-y1)**2

### Sign me up! (1)

#### Plaid Phantom (818438) | more than 8 years ago | (#15937237)

If this sort of attack on each other's work is the basis for modern Mathematical debate, sign me up! This is hilarious!

### Didn't bother to read it (5, Funny)

#### Versalis (29051) | more than 8 years ago | (#15937241)

In my humble opinion, we have an unjustified polemic in the world of mathematics, yet again. My background is tertiary level mathematics and concomitant research

#1 - Humble my ass

#2 - Such excessive sesquipedalianism is an immediate flag that the writer is writing not to inform or help. He's just masturbating his brain in public.

#3 - Humble my ass

### OK, stepping way out on a limb here... (2, Insightful)

#### ursabear (818651) | more than 8 years ago | (#15937267)

Hoping said limb does not break...

A few up-front things:
IANAMathematician;
I appreciate the reviewer's efforts to thoroughly discuss the reviewer's point of view;
I don't mind acknowledging that I'm not as smart as the vast population of Slashdot, but I like math even though I'm not top-notch;
I love to learn stuff, and like to read Slashdot articles/comments that are out of my field, and way over my head;

With the above said...
I don't mind looking up unfamiliar terms that appear in an article or in a review (I like learning) - when the words are concerned with the subject matter at hand. I do mind when I read something that attempts to completely fill up my "new word of the day" calendar (for the next millennium). Why? Because I'm interested in understanding the subject and the review, not in how many new non-topic-related words and phrases that can be crammed into a paragraph.

Lastly, a good review, IMVHO, is one that does not chastise, scold, or belittle the matter of review.

### Distance (0)

#### Anonymous Coward | more than 8 years ago | (#15937274)

"quadrance = (distance)2 = (x2 2 - x1 2) + (y2 2 - y1 2)"

is he being polemic?

### How about a more qualified reviewer? (3, Insightful)

#### nonlnear (893672) | more than 8 years ago | (#15937353)

From the review:
However, you don't have to read between the lines to see on page 21 that Wildberger excludes 'characteristic two fields.' Although I am not versed in Field Theory, I opine that such an exclusion does not apply to classical geometry and/or trigonometry, otherwise he would have said so. So, he is already implicitly confessing, to a failure of Rational Geometry in the global sense.
However, you do have to have the slightest clue what you are talking about if you are going to call the author on the "characteristic two" exclusion.

Wildberger may be a little "out there" (alright, he's completely nuts), but this point is not one you can fault him for. There are a LOT of results which exclude fields of characteristic two. It's not a big deal. In fact, it's commendable that Wildberger has explored the ramifications of his framework in any fields with non-zero characteristic, as the "normal" pedestrian conceptualizations of geometry don't apply.

It would have been nice if /. could have posted a review by somebody who is actually qualified to critique the book. And no, I am not such a person, but I know a couple people who are.

### Review is an obvious troll (2, Informative)

#### Anonymous Coward | more than 8 years ago | (#15937354)

The obvious mistake in the distance formula and the interpretation of the "fields of characteristic 2" exception are intended to rile up people who *are* familiar with these things.

### Re:Review is an obvious troll (0)

#### Anonymous Coward | more than 8 years ago | (#15937559)

And now I too must know, WHAT was the WORD??

### AMAZING! (1)

#### savage1r (856578) | more than 8 years ago | (#15937432)

I was SO BORED by the intro to this article that I practically peed my pants when I realized that there was actually more and that by reading said article it would be possible to put me in a coma within seconds!

### "Mighty odd-sounding?" (3, Informative)

#### complexmath (449417) | more than 8 years ago | (#15937452)

The Divine Proportion is one of the most well-known geometric properties. Here is a link to the wiki page for the uninformed: http://en.wikipedia.org/wiki/Golden_ratio [wikipedia.org]

### "what's really going on" (1)

#### PCM2 (4486) | more than 8 years ago | (#15937468)

I have to confess that I look upon his sojourn into Field Theory as a diversion in the same sense that a prestidigitator (magician), in his field of legerdemain (sleight of hand), distracts the audience members, thereby lessening their attention on what's really going on.

Like using big words to disguise a blatant troll, perhaps?

### Seriously... (0)

#### Anonymous Coward | more than 8 years ago | (#15937494)

The effects of this on constants which are congruent is marginal. In fact, the vast majority of differential mathematice relies soley on equations with multiple correct answers.

So I wonder why this was posted anyhow, it was vetted before, and it brings nothing new to Elaxalgesic Congruence Theory nor General Number Theory.

It's really just another impromptu disparaging of Dianetics.

### /. is math notation for divide and multiply (1)

#### dbdweeb (598548) | more than 8 years ago | (#15937516)

What's all this math? I thought /. was a reference to *nix stuff.

# Slashdot: News for Nerds

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