## Friday, July 05, 2013

### All Purpose Math Rant

Stream of Consciousness Rant on Numbers, Mathematics, Geometry, Alien Intelligence, Quixotic Phenomena, Logic, Jiggery Pokery & The Unexamined Problem of ‘Thinking’— Which is an Illusion, just like Morality, Ghosts, Good Fairies, Infinity & The Fundimental Idea of Proofs.

Are There Numbers ?

There is this idea that numbers don’t really exist, anymore than unicorns really exist. numbers & unicorns only exist as ideas that people have thought up, & without people, or The records that we’ve left behind, numbers & unicorns would cease to exist from The universe.

There is another school of thought that suggests that numbers really do exist, in The same way that The color Red Exist. Even if there were no people to see The color Red, it would continue to exist as a well defined frequency range in The ElectroMagnetic Spectrum.

But what if we were to define another frequency range as The color Lyts.

Lyts                 An Hypothetical ‘Color’ that people can’t see, & exists only as a color in The sense that we’ve defined other colors in this same way. Given that no one has ever seen The color Lyts, what does it mean to say that this ‘color’ exists?

Given this ‘Approach’; Might it be reasonable to assert that numbers exist only as tools for The functionality that we give them, in The same way that we can ‘see’ colors, & without this ability for The color to be ‘Seen’ or a number to be Quantified, Then it wouldn’t exist, except within that context.

Without People; Quantities would continue to exist, but numbers wouldn’t.

An Apple, for example would exist as possessing a quantity of appleness, but it would be senseless to think of it as ‘One’ Apple. This Constraint is a purely human contrivance.

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What allows Mathematicians & Physicists so Much Hubris when using Math to Describe Reality, Is that for most Applications, Pretty Close is Plenty Close Enough.

It doesn't really matter if a Space Probe is only Pretty Close to Where they Want it, It will still return some pretty pictures.

If a Ray-Tracing CGI Image is Only Taken to 4 Levels of Shadowy Reflections, Most Lay Persons will Insist that The Resulting Image is Photographically Perfect.

What is Very Curious about this Last Example is that As Artistic Stylizations Change, So Do The Damp Masses Ability to Perceive The Realness of These Images...! ( ? ) That is; What was Considered Perfect CGI Images 5 years ago, are Now Considered Charmingly Hokey at Best.

It's Extremely Fascinating that Not So Long Ago, People Thought That The Grainy Black & White Images of Early Cinematography were Indistinguishable from Reality...!!!

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i also hate the way much of Quantum Mechanics is interpreted. Especially The Cat in the box, and H- Uncertainty principle. Both are commonly interpreted to mean exactly the opposite of what they were meant to mean. The Cat in the box was not meant to suggest a necessity of multiple universe, it was meant to suggest that those ways that suggested multiple universe was clearly stupid...! / The uncertainly principle merely means that whenever you examine anything, you disturb it in some way, and when the thing you're examining is so small that the thing you're using to examine it, is the same size, you're going to disturb it a Lot. If you can figure out how to examine something with substantially feebler units than the thing you want to look at, then this effect disappears.

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i predict that within 50 years, all of what is now thought of physics, with a tiny core understanding remaining, will be brushed aside.

People in the near future will have abandoned quantum theory, and think of Einstein in the same way that psychologists now regard Freud.

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Is there a true & real correspondence between mathematics & physical reality?

It is my ‘hypothesis’ that mathematics & reality are two very different things, and while mathematics may, and has been used successfully to quantify, label, describe and predict physical systems for some time; all of these examples are very simple ones, and The moment that any mathematical model exceeds a very simple threshold, The predictive power of mathematical simulations breaks down. This is most clearly demonstrated with The so-called ‘Three body problem’ in which three bodies in space are ‘falling’ gravitationally around one another, it is essentially ‘impossible’ to accurately predict where they will be at any set time (x in The future. Obviously; Astronomers and Astrophysicists will vehemently disagree with this and insist that they can launch space craft and get them to far off planets & moons with a very degree of precision. But of course; they neglect to mention that these flights include numerous ‘course corrections’ and still, they are only ‘highly’ accurate. It has been demonstrated with Computer simulations for example that simply changing The precision of The fractional values ( e.g.; 2.38 to 2.38928 ) will radically change The final results. Not that one will be a better prediction, but that one will be completely different from The other. And this holds true for several values with one digit increments. The results will not be slightly better in each case, each will yield a completely different solution. And this is demonstrated most clearly with The increasing number of itinerations.

So.

The point being; What i am saying is that mathematics has -no- correspondence with physical reality. None.

Even in The simplest cases; Such as 1 + 1 = 2, may not be accurately ( truly ) used to model reality. One may argue that we can simply take one apple and another apple and put them into a basket which then contains two apples.

My counterargument would be that each ‘apple’ is actually a entity which contains a ‘vague’ amount of appleness. So that you are actually combining one entity of appleness to a second entity of appleness and The basket now contains a greater quantity of appleness than either of The two apple entities alone.

Of course; That’s not The way we think of apples, but everyone should readily agree that without exception, Any two apples are different, and once you accept that idea of ‘appleness’, each ‘apple’ contains a unique amount of ‘appleness’.

One might argue at this point that i am simply moving The goal posts and that if we were to instead use mathematics to exactly quantify The amount of appleness in each apple, we could exactly define how much appleness each apple consisted of, and thus; know with complete certainty how much appleness The basket contains.

My counter-counter argument to this would be that The ‘idea’ of appleness is ‘undefined’ and is used only to express The uncertainty of appleness. In fact; This argument is merely a prelude to The greater argument that it is ‘inaccurate’ to think of apples as having a quantity of appleness at all. i mean; An actual apple no doubt contains foreign matter and there are different kinds of apples, each one, has a unique chemical signature and so on. And on another level, When does The apple start and stop. We might easily imagine The apple being limited by The Skin covering it, but we can smell apples when they are in The vicinity of our noses, so that one might very convincingly argue that The Apples extend considerably beyound their skins.

And if one were to argue towards The conclusion that there existed A Unit Measurement of Appleness; How might this be quantified? There is certainly no Electron which is unique to Apples, nor is there even an Apple Atom. There are Distinct Molecules which are unique to Apples, but i heard just recently that Humans share 50% ( ± ) our DNA with Bananas. And how many of these molecules unique to apples must we inclusively combine to state that this is An Elemental Apple Unit?

Scientists may argue such points with The same enthusiasm that theologians argue as to how many angels can dance on The head of a pin ( 23 ), But this entirely misses The point.

Which is; Reality is an Holistic Totality.

Mathematics is a digital construct. Mathematics is not something that The humanimal mind discovered. It was something that we created.

When; Someday, we find aliens on other worlds, we will no doubt discover that their systems of ‘counting things’ are very unique and in most cases, completely incomprehensible to us.

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Various Arguments that Confront The Absurdity of The Idea : Infinity

- - | There is another positing that suggests that .999- = 1.

- - | Or that A Circle with a Radius of Infinity has a Delimiting Edge that is Perpendicular to A Line at Zero Degrees ( Directly to The Right of The Center )

- - | Or that Parallel Lines meet at Infinity

- - | Or that a Subset of any Line which contains an Infinite Number of Points, Itself contains an Infinite Number of Points.

These point out that The Way we think about Reality in Quantifiable Values, is just Wrong.

The Word ‘Infinity’ is one of those Letter Collections that don’t mean anything. There’s No Genuine Application of where & how it can be used. Even in The Most Speculative Arguments or Stories that feature every spectral Pooka, Absurd Technological Widget, Incomprehensible Alien Arts Program, Clever Tax Evasion or Advertising Swindle protected by Constitutional Edicts.

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The AlphaBetric Tables for Multiplication & Addition

The Curious Thing About The AlphaBetric Base;

Which is InArguably; A Base 26 Counting System.

Thinking about it this way; The Base Ten System that Humans have universally adopted;

Is really only a Base 9 System!

Using The AlphaBetric Method with The Decimal Counting Digits, You'd have:

0 1 2 3 4 5 6 7 8 9

And then what...?

it would be; 11

But what would 11 mean?

It would be 1 Unit of 9's + 1 Unit of 1's. = 10_d

In The AlphaBetric Counting System,

which does NOT use A Zero as a place holder...

Which; By the Way, i can recall being taught was ABSOLUTELY Necessary to Create a Logical & Consistent Counting System that would extend beyound your fingers & toes... ( ? )

...Allows that after X Y Z...

The Next Number is AA,

Which makes perfect sense as A ( or 1_d ) unit of 26_d's + 1 unit of 1's = 27_d

It has been suggested that The AlphaBetric System DOES in fact include A Zero, which must be Necessary to Represent The Absence of One. ( or n - n ).

Well.

The Quantity of Nothing in The Alphabetric System is Represented by The Null Quanta, which uses a Symbol that is not available on this keyboard.

Curiously; Algebraically; The AlphaBetrical Aliens use '0' to Represent The Totality of Everything, or Infinity.

They also don't recognize our idea of Irrational Numbers.

All the numbers that we think of as Irrational have a distinct and unambiguous place on the number line, and they don't think of them as any different than integers.

Also: The don't use The i.f system.

To represent numbers smaller than A ( 1 ) with Geometrical Graphics that are designed to represent All Quantities, Even those that we consider 'Irrational' and by means of this system, Those quanities are precisely defined & completely unambiguous or incomplete.

They are also a little fuzzy when it comes to Integers.

Although their AlphaBetric System uses Integer Digits,

They don't apply this idea of 'Real' Numbers to Things in The Real World.

If we had a Basket with 6 Apples, We would say that there are Exactly 6 Applies in The Basket.

But AlphaBetricians would say that there is a -Specified- Quantity of Appleness in The Basket, Based on A Universal Measurement of What A Unit of Appleness is.

This Integer Unit of Appleness would never really ( Really ) be applied to Any Apples in The Real World.

It is a purely hypothetical Quantity.

They also Think of What we Call Negative Numbers Differently.

They allow for A Quantity of Debt, But don't measure Temperatures in The Negative, or Think of A Car going Backwards as going -40 miles an hour.

They Also Refute the Idea that humans have of Multiplying by A Negative Amount.

Such as -3 x 3 = -9

( Converting AlphaBetrics to Decimals for Clarity )

They Allow that you Can Mulitple 3 x -3 = -9 though.

But -3 x -3 doesn't make any sense to them at all.

All Arithmatic Functions in The Positive are Exactly Mirrored on The Other Side of The Number Line.

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i have an additional ‘Position’ that ‘Logic is Bunk’.

i have committed several dozen pages, if not hundreds to various approaches to this idea, & i keep trying to refine it to a very simple argument of only a few lines, but it invariably leads to countless digressions !

The Essential Idea is that there is this Framework of ‘Good Thinking’ that we commonly call ‘Being Logical’.

There are several Flavors for this; Propositional & Boolean being The Two Formalized Systems that we’re most familiar with.

Propositional Logic is pretty kooky in a variety of ways: Using a System of Truth Tables which just ‘leave out’ a number of The Tables because there’s just no way that they make any sense at all. It has also been thought that Propositional Logic or The More Curious ‘Fractional’ Propositional Logic, which allows for Values from 0 to 1, Rather than just 0 or 1. It has long been hoped that we would soon be able to apply this Propositional Logic System to Computers, & we would thereafter know with Certainty, Anything & Everything. But. No. The Chief Problem with Propositional Logic is that you have to determine The Initial Truth Values of your Propositions, pretty much by just guessing.

The Other System; Boolean; Is thought to be used in The Architecture of CPUs, but while that may be true ( Wildly Generally ) for The First 8 Bit CPUs, The Ones that Use ’Truth Tables’ with 32 or 64 Bits, or More, have long ago left The Initial Ideas of Propositional Logic far behind. It’s all very amazing, but to call it ‘Logic’ is highly irresponsible. It’s Now just This Does That, Very Quickly & pretty Reliably.

The Kind of Logic that i’m referring to when i say that Logic is Bunk is The ‘Ordinary’ Kind that People use when attempting to ‘Prove’ something in The Real World, or even within The Context of Mathematics or Physics.

A Foundational Premise is that there are ( have been ) numerous Mathematical Arguments or Proofs that Referred to Physical Systems, have later been shown to be very erroneous.

One that comes to mind is The Astronomers attempt to ‘Explain’ The Gaps in The Rings of Saturn Rings. They had a wonderful Logical Proof, & Everyone believed it, Until Closeup Photographs of The Rings exposed The Truth, & there weren’t any Gaps. Not The Big ones at least. They were just Dark Rings.

So.

There’s Conventional Logic that Ostensibly Only Proves True Things.

That is; If used Properly; Conventional Logic can’t be used to Mistakenly Prove False things.

The =Other= Kind of Logic that we’re going to Consider is Called ( here ) : Jiggery Pokery Logic.

This System allows The JP Logician to Prove Anything.

Jiggery Pokery is commonly used by just about everyone, Politicians especially, CEO’s, Religious Nuts, Anyone with an Opinion & Small Children to Provide very Convincing Arguments for Why (x is True.

Many of these Jiggery Pokery Arguments are very good, Very Convincing.

Many Jiggery Pokery Arguments are Presented as Real Logical Arguments.

And now we’re approaching The Problem.

With Real ( Conventional ) Logic; A Bad Argument can Be Shown ( in Theory ) to be Fallacious.

But a Jiggery Pokery Argument Can’t. No Matter how many very convincing attacks are thrown at a Jiggery Pokery Argument; It can easily Adjust itself ( Just as A Real Logical Argument Can & Should ) to Correct Any Discovered Flaws.

But while a Real Logical Argument will Eventually run out of ‘Fixes’; The Jiggery Pokery Argument will Never Run out of Fixes. It can only become very tenuous or Tedious.

How many Mathematical Arguments come immediately to mind that may fall into this Category?

Mathematical or Physical Proofs that go on & on & on for hundreds or thousands of pages— Or when you ask a Mathematician or Physicist to Explain some Crazy Argument or Position of theirs, they fill up a Blackboard with obscure equations, & when you ask them to explain some subset or how The Variables relate to one another, they suddenly lose their patience & start screaming at you.

Even if There Really was a Thing called ‘Real Logic’;

It is Impossible to know when it’s Not Jiggery Pokery.

Thus; Logic is Bunk.

It can never be Trusted.

The Function of Real Logic is to Remove all Doubt about The Truth of (x.

Yet this shows that there will always be a Reasonable Doubt.

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