—————
Principal Values:

Multiples of Pi/2 locate both nodes and antinodes of the sin() and cos() functions.  Multiples of Tau/2 do not.

The second derivatives of the sin() and cos() functions for multiples of Pi/2 locate both inflexion points and extrema.  With multiples of Tau/2, they locate extrema of the cos() function and nodes of the sin() function, but they do not locate nodes of the cos() function or extrema of the sin() function.

In short, Pi/2 locates nodes, antinodes, and inflexion points, which are at values which have always, for good reason, been called Principal Values of the sin() and cos() functions.  The substitution of Tau/4 does not in any way improve upon the present scheme for identifying these values.

—————
Function Values:

The series expansions for calculation of the sin() and cos() functions of an argument x given in radian measure are as follows:

sin x = sum{i=0,1,2,…}((((-1)^(i))/((2i+1)!))((x)^(2i+1)))

cos x = sum{i=0,1,2,…}((((-1)^(i))/((2i)!))((x)^(2i)))

We note that in summation of the series we must exponentiate the argument x to either the power 2i or 2i+1 in forming successive terms of each series.  Since the argument x, under the “Tau proposal”, would have to be subject to measurement using some other-than-radian measure, a different series expansion would be needed to provide the correct numeric value for any given argument (unless everyone, every time they want to evaluate a sine or cosine, happily agrees to divide their number by two before substituting it as the argument x in either of these equations).

If I was Bob, I’d rush right out and get a patent on all of the algorithms I could think of which can be used to quickly calculate such a series, because if Mr. Hartl intends to force computer and microprocessor manufacturers to provide FPU support for it, the patent race might leave Bob behind.

Abramowitz and Stegun do not provide a simplified series expansion for one suitable as a math unit approximation function; and one can only surmise that Mr. Hartl has friends at Texas Instruments, Intel, AMD, or Motorola, who are right on top of the production line for chips that provide the new tausin(), taucos(), and tautan() functions right on their output pins.

The fact that using Tau doesn’t excite me any isn’t all that big of a deal.  But the idea that some people are worse than pushy when it comes to getting what they want, and the idea that they are willing to foist an un-needed “simplification” onto everyone who uses a computer just to make money for them is actually a very big deal; and I object to it strongly.

So, what about the value of “the angle” itself, knowing the value of the sin() function, for instance? Of course, there’s a well-known series expansion which produces the numeric value, in radian measure, of an angle, given the sine of that angle as a function argument:

arcsin(x) = sum{i=0…}((((x)^(2i+1))/(2i+1))(prod{j=1..i}((2j-1)/(2j))))

This series isn’t going to return a value normalized to Tau, so everyone must happily agree to multiply their function return by 2, or go out looking for Mr. Hartl’s new CPU/FPU combination and pay up front for it.  All these afficiondos really need is to multiply or divide the value returned by a floating-point calculation circuit by 2 to get their Tau-normalized value; and in so doing they may be able to avoid a patent infringement case when they use a design for the circuitry containing significant design or invention which someone else already patented and which returns a value normalized to radian measure.  Who knows?  People have thought of all sorts of absurd schemes to “get around” patent protection measures.  Is that what this hullabaloo is all about?

—————
Fourier methods:

For non-periodic functions, we can use half-range expansions, either by reflecting the function about the origin to create an odd function, or about the y-axis to create an even function.  In both cases, the period is twice the range of definition (between 0 and L or between -L and 0) of the function; and since the range denoted by Tau is synonymous with the period, half of its range is outside the range of definition of the function we are seeking to expand.

For periodic functions, the obvious simplification from the argument (2*Pi*t*n/L) to (w*t*n) leads to a simpler form for the Fourier series expansions, and if W = 2*Pi/L = Tau/L, we have done nothing but hide the irrational number Pi (and its equally irrational double, Tau) without introducing any other obvious simplification.

—————
Physical methods:

The Planck constant divided by 2*Pi, called h-bar, appears in many calculations in modern physics; and substituting Tau for 2*Pi would oblige us to divide Planck’s constant by Tau instead.  But this doesn’t do anything to solve the basic problem, which is that the Planck constant alone lacks a commonly accepted and used measurement system to support it; and that even though h-bar works well enough in the SI system of units, there always exists a renormalization problem when applying equations which are supposed to be correct as-is.  The use of Tau does not in any way solve this problem, because the use of h-bar is wrong to begin with; although that fact goes almost unrecognized. And, short of changing from the SI system to some other completely unified system–  which the standards organizations haven’t discovered, yet  –the accepted values of the Planck time, length, and volume will not have values which are reconcilable with h rather than h-bar.

Whether Bob Palais intends to substitute 1/Tau for the factor of 1/2Pi appearing in the equations for uncertainty, or to relegate integer- and half-integer- spin factors to the garbage heap, I have no idea.  There are, however, a significant number of university classrooms in which the question has been raised as to why the factor of 1/2Pi cannot be dispensed with in the calculation of integrals involving expectation values for particle position or momentum; and the most common answer is that both the number e and the value 2Pi will pop up here and there just because of the methods you are using, so there’s nothing you can do about it even if you should deliberately try to get rid of them.

The big thing now is “hash code”.  Instead of having ‘strands’ of code like noodles you’ve got mashed chunks of mixed code scooped out of The_Continuum_Of_All_Context and deposited in lumps in your modules.  That’s better, they say,  because you get a greater variety of flavor in every byte.

If they don’t want that anymore, why do they still want computer keyboards, or text entry boxes where you can type in a name, address, or other string data?  Why do they pretend they still want textual computer languages, when what they really want is a uniform iconic ‘language’ representation which is (arguably) understandable by everyone?

The fact is, they don’t want keyboards either, but aren’t bold enough to reveal the depth of their hostility toward us because right today if they said that, we’d put them in a rubber room somewhere.

But tomorrow they’ll have a little barcode that does everything the keyboard used to do; and that’s what they are working for and developing all of their new and more “advanced” GUI models for.  So they can replace your name and identity with something you’ll never understand or figure out no matter how long you live.  And if you don’t become a reflection of it, they’ll jail you and forget about you.

No doubt you’ll disbelieve this, and go right on humoring the insane and letting them dictate the course of development no matter how far they debilitate the functionality of textual language and its accompanying compiler or interpreter interfaces.  All these tyrants need is a method of generating more hypnotic and suggestive imagery that will undermine your concepts and defray their cohesiveness so that they can hold your intellect suspended by a fine thread of speculative involvement in the notion that somehow your hopes and dreams will materialize out of a forest of icons.

You’ve already lost your reason, because you, just like this attendee, will go to lectures hosted by idiots and lap it all up just to feel like you’re part of the ‘in’ crowd.  That’s more important to you and all of your peers than anything the ‘common man’ says or does; and the lecturer knows it:  He built his career on it.

• God probably gave us noses so we’d have something to blow besides money.

• Sometimes it seems like it takes all day to get nothing done.  [?]

• The PDA which Jeff gave me has a nice auto-completion feature.  The word ‘outgoing’ was in the dictionary, but the word ‘ingoing’ isn’t.  Maybe that’s because there aren’t as many ‘ingoing’ people.
• When people ask, "How’d you get to be so smart?" you ought to wonder why they thought you were born stupid.  I get suspicious when they ask that.  It sounds like one of those ‘Knock, knock’ jokes that inevitably brings some kind of smart-aleck response with it.  I’ve often been tempted to reply, "How’d you get to be such a smart-aleck?"
• April snowers bring May plowers.  { ‘snowers’ pronounced like ‘schnausers’ }

• You don’t want to get married by accident, or because of one.

- Glenn Merritt

And if this isn’t enough for you, try
Reinverting Gofernment

Person 1 dialog is in normal typeface.  Person 2 dialog is italicized.  Here are a couple of examples…

Knock, knock.
Who’s there?
Who.
Who, who?
What are ya?  An owl?

Knock, knock.
Who’s there?
Didge.
Didge, who?
Did I what?

Here’s a short list of these puns that I came up with a while back.  Only the person 1 responses are given.

Boo!  /  What’re ya cryin’ for?
Hutch!  /  Need a hanky?
Who.  /  What are ya?  An owl?
Say:  /  Who.
Havoc.  /  Not since Santiago.
One at.  /  a-three, a-four, …
Tyersh.  /  No thanks.  I’ll tie it myself.
Goog.  /  Quit that baby-talk!
Didge.  /  Did I what?
No, he’s not!  /  [no response]

I can’t guess how many of these you might have heard before, although at the time I came up with them, I’d never heard them before.
Well, it’s one more thing to ’round out’ the content of the Internet, you know!

Why excuse television?  It’s said to have a duty to accurately reflect reality, and society.  So don’t expect to find yourself there.

They look in this mirror at all of the violence, perverse sexuality, and other polluted imagery, and they don’t see themselves there:  They see someone else.

And they can’t wait to go out somewhere so they can harass him.

Separation of Church and State:   The situation where you pray to God and pay your taxes to the devil.

Policy:  Taking a battle-axe to everybody around, when all it would take to fix the problem would be to take a sword and run one guy through.

Media:  They call it media, when there’s nothing medial about it; just the extremal and uni-directional instead.

Monarchy:  A state governed by black-and-white television.

Stupidity:  The notion that you have a license to be obnoxious.

Bourgeois-de-vivre:  The laughter of fools late at night in Lock Haven’s old Fallon Hotel.

Hyperassociative lexiconitis:  A tetanus-like disorder of the cerebral cortex symptomatologically accompanying the form of repetitive electromotion disorder which affects dendritic morphology and development after sustained exposure to hypertext.  See:  hyperlexia, cortico-URLative dermatoma, carcinolexis.

Congratulationarianism:  The one thing the Repugilisticans and the Demographicats have in common.

Gatesean:  Maximal program-memory-model order-of-magnitude; i.e., "…tiny, small, compact, large, huge, giant, gigantic, megalithic, colossal, gargantuan, behemoth, sumo-sized, Gatesean…"

Enemies, modern:  Although the Medes and the Persians may not like us much, they are not our worst enemies.  Our worst enemies are the Medias and the Perversions.

Masochism:  Inflicting gratuitous self-punishment; for example, using aspartame.

…to be continued

]]> http://cqvis.wordpress.com/2008/12/23/definitions/feed/ 0 gamerritt http://cqvis.wordpress.com/2008/12/04/may-29th-blog-lost-not-found/ http://cqvis.wordpress.com/2008/12/04/may-29th-blog-lost-not-found/#comments Thu, 04 Dec 2008 19:29:52 +0000 Greater Meridian http://cqvis.wordpress.com/2008/12/04/may-29th-blog-lost-not-found ]]>