Tuesday, April 01, 2014

Recent News and There are No Irrational Numbers / Or The Fallacy of The Elegant Solution ( ! )

Monday, March 31, 2014 5:28:43 PM

Recent UnCategorized Thoughts

i normally have a strong & Benign respect for all Life Forms, Helping Spiders out of The Bathtub, Catching Mice in The Building & Relocating them several blocks from here, Thanking The Souls of The Animals that i eat, Expressing Reverence for The Miracle of Flies, Ants, Bees & Dung Beetles; But Recently, & by recently i mean, in The last few months; i’ve been discovering tiny little flying bugs in my room. My Room is remarkably bug free; Few Spiders, No Ants or Cockroaches, Rare Tiny Beetles or LadyBugs. So it’s kind of Anomalous that these Little Flying Bugs, which i think may be something like Gnats, are Extremely Annoying. Part of The Annoyance is that they appear so infrequently. If their were swarms of them; i could determine where they were coming from & vacuum them up, But as it is; They suddenly appear once or twice a day, & then only right in front of me, usually right in my face, possibly attracted by The Carbon Dioxide that i’m expelling.

So i’ve been ‘Clapping’ them !

i feel very guilty about this; But they are very irritating !


i like to imagine that each of these little bugs has a guardian Angel that is supposed to be taking care of them, or directing them towards The ‘Best Solution’ for their Life at that moment, which includes being Clapped when The Time for them in Ripe ( ! )

: - - - - - - - - - - - - - - - : o

It may be too late ( ? ) to Interject a Prediction on The Lost Malaysian Airliner, but i don’t think it’s going to be found anytime soon. But about 6 months from now, The Mystery will be Solved ! It will be discovered that it made a controlled Landing in The Water near an Island somewheres & Either A Passenger or Something on The Plane ( Big Secret ) was removed at that time.

All of The Passengers were probably killed, but some The Children may have been sold into Slavery. But when They do turn up, The reason for The HighJacking will be completely forgotten.

: - - - - - - - - - - - - - - - : o 

i’ve recently come to believe something crazy.

i believe a lot of Crazy Things, but this one may take The Pie.

i’ve come to believe that there are No Irrational Numbers.

An Irrational Number is one like π or e.

An Ordinary Number like one fourth ¼ is digitally represented as .25 .

Point Two Five. And then it Ends.

A number like One Third is Digitally .333 with The 3’s going on forever. This is a Transcendental Number, but Not an Irrational Number. It’s ‘Reasonable’ because it can be Algebraically Defined in a Simple Way with Whole Numbers.

π ( pi ) can Not.

π results from The Division of The Circumference of a Circle, The Line around The Edge, by The Diameter; The Line through The Middle of The Circle. The Radius is Half way through, from The Center to The Edge. The Diameter is from one Edge to The Opposite Edge.

If you measure The Parameter & Diameter Very Carefully; The Resulting Division ( p/d ) will give you 3.1415 or so.

Very Careful Measurements might yield an answer of 3.1415926, but that’s stretching it. That is; You can only get a good answer to only a few digital places.

Nevertheless; Mathematicians believe that they ‘know’ The Value of π to Many Billions of Digit Places !!!

The Irrational Part of π is that these digits to The Right go on & on forever, to Infinity, & they are Non-Periodical. That is; They don’t Repeat. They keep changing in a Chaotic, Seemingly Random Manner. They’re Not Random, because each time to Calculate The Value of π, you’ll get The Same Answer again & again.


The Problem that i have with these Irrational Numbers, & there’s a lot of them. Another is The Square Root of 2. ( √2 )

The Proof that’s Offered that The Square Root of 2 is Irrational is kind of Famous, Dating back to The Greek Philosophers.

The Problem with this Proof is that it’s a lot like The Zeno Paradoxes, in that it goes out to prove something Crazy, Does this; Then leaps to The Conclusion that The Square Root of 2 Must be Irrational, or More Specifically, A Number Like No Other. A Number that is Both Odd & Even or Neither Odd or Even.

That’s The Premise of The Proof; If The Square Root of 2 is ‘Rational’, then The Numerator & Denominator of This Rational Fraction must be Both Odd or Odd & Even, But Not Both Even. If they were Both Even, then The Fraction could be Reduced. What We’re looking for is The Smallest Rational Fraction for The Square Root of Two.

The Proof is a Little Algebraicy, But Suffice to Say; It goes something like this:


Lettuce assume that a/b = √2

For this a/b to be The Simplest Terms

Both a or b may Not be Even or Divisible by a Common Factor

√2 = 1.4142…

√2 = a/b               : a = 7  b = 5 : a/b = 1.4

            a & b are Wildly Approximated

            So that we can see how The Algebraics are Working ( ? )

2 = a2 / b2             : 2 = 72 / 52 = 1.96

a2 = 2 · b2             : 72 = 2 · 52 : 49 = 50

Given then that b2 is 52 = 25

And 25 x 2 is 50; An Even Number; Force to be Even by Multiplication by 2

Then a2 is an Even Number

Our Approximations make a2 = 49

But if a2 were 50 : a = 7.0710

But we’re also asserting that a is axiomatically a Whole Number

So that if This were to work out so that a2 were to be a Whole Number

& (a would also be a Whole Number,

Then (a would be Necessarily Even,

Since any Odd Number Squared is Odd.

e.g.; 32 = 9

- - -

Let us then Arbitrarily Replace (a with 2·k ( or 2k )

k would then be 3.5

But this to ‘Work Out’; k would have to be a Whole Number

- -

Returning to :

2 = a2 / b2             : 2 = 72 / 52 = 1.96

2 = (2k)2 / b2        : 2 = (2 · 3.5)2 / 52 = 1.96

(2k)2 = 4 · k2

2 = 4 · k2 / b2       : 2 = 4 · 3.52 / 52 = 1.96

2 · b2 = 4 · k2        : 2 · 52 = 4 · 3.52 : 50 = 49

b2 = 2 · k2             : 52 = 2 · 3.52 : 25 = 24.5

Which Means that b2  must be Even by The Same Logic Expressed above ( 2 · x ) must be an Even Number.

Now both a & b are Even according to this Juggling Act,

But this all Assumes that a & b Start out as Whole Numbers;

And all The Permutations that they Endure allow their SubDivisions to Remain Whole Numbers too.

Which They don’t.

Even if you were to somehow allow that these Conditionals were Met;

The Jiggery Pokery here is Only Asserting that (a or (b is Not Odd or Even. It is somehow insisting that (a or (b are Outside The Realm of Whole Numbers.

It seems far more Reasonable to assume that this ‘Argument’ is A Paradox of The Zeno Type; And that while it seems Reasonable; It tacitly asserts things that it shouldn’t.

e.g.: That If a2 is a Whole Even Number; (a must be a Whole Number as Well. It was assumed that (a was a Whole Number at The Beginning of The Argument; But then Craziness set in.

- - -

On a More Obvious Level; Doesn’t this Argument Structure assert that all Square Roots are Irrational; Which is Clearly Wrong.

√36 = 6

- - -

√9 = 3

√9 = a/b               : a = 3  b = 1 : a/b = 3

9 = a9 / b9             : 9 = 39 / 19 = 19683


So; There are already some problems with this Structure;

Which Strongly Suggests that it’s a Form of Jiggery Pokery.

The Presumed Strength of this Proof is that it’s The Irrefutable Logic of The Structure that Proves that √2 is Irrational,

But this easily shows that it’s some Crazy ‘Special Case’ that applies only to this one Application.

That is Not The Way Mathematics is supposed to work.

: - - - - - - - - - - - - - - - : o

Another way of looking at this is;

If we’re going to allow that there are Irrational Fractional Numbers,

Why Not Irrational Whole Numbers !

Just take a number like π & take The Decimal Point out;

3.1415… becomes 31415…

Or you can Reverse it to …51413

What are these ?

If you have two such Irrational Whole Numbers;




Which is ‘Bigger’ ?

In The Inverted Form; you can tell if it’s Odd or Even, but that’s about all.

It seems to me that they would all be Equivalent with Infinity,

But also; Be Uniquely Defined Individual Values ( ! ) ?

Or is that Crazy.

By Thinking about Irrational Whole Numbers for a few Moments,

You should come to The Realization that they’re ‘Silly’.

- - -

Lettuce consider one other thing for a moment, in a slight digression.

There is ( i imagine ) something called ‘The Mathematical Reality’

& ‘The Mathematical Realm’.

The Difference between these two is that The Mathematical Reality is Consistent with itself, & Does Not Allow Paradoxes to Exist or Such NonSense as Kurt Gödel’s Proofs that Mathematics is Incomplete. The Mathematical Reality is Complete, Although, Portions of it may be Illusive.

But; The Other thing; The Mathematical Realm is The Alice in Wonderfalls, or The Australian DreamTime of Star Trek ( OS ). It is Timothy Leary’s World of Arithmancy. Anything Goes.

So that; Irrational Whole Numbers can Exist in The Mathematical Realm, but Not The Mathematical Reality.

Irrational Whole Numbers are Not Mathematically Real.

& then; Neither are Irrational Fractional Numbers.

- - -

i got started on this ‘Kick’ after reading a little on Cantor’s Proof for UnCountable Infinities & Realized that his Argument was Pure Jiggery Pokery.

This also Brings up a New Neologism : The Fallacy of The Elegant Solution.

The Fallacy of The Elegant Solution simply States that there are Some Problems in Mathematics, Physics, Economics, Biology, Art or Music; In which there is No Elegant Solution to a Given Problem.

The Fallacy Occurs when The Mathematician or Whatever believes that there Must Be an Elegant Solution, & when they are Sufficiently Frustrated from Trying too Hard, they Make on Up.

They Allow Jiggery Pokery to take over.

They Create an Elegant Solution that Doesn’t Exist.

- - -


There are all these Wondrous Paradoxes in Mathematics & Philosophy, which everyone loves to discuss & Argue over—

But The Crazy Bit is; There Exists another Class of these Jiggery Pokery Arguments that are just as Bogus; But they’ve somehow been ‘Accepted’ into The Mathematical Reality, Where they Do Not Belong.

Irrational Numbers are Just One of Those things that Don’t Belong in The Mathematical Reality.

- -

i don’t think that most Mathematicians make a Distinction between The Mathematical Reality & The Mathematical Realm. They Believe that any Crazy thing that they can Do with Numbers is ‘Real’ & even far more ‘Dangerous’ than that; They often believe that any Mathematic ’Truth’ has some ‘Correspondence’ with The Physical World; Which allows them to Really, Genuinely Believe that they can Prove or Disprove The Existence of all sorts of Silly things like Time Travel, Warp Drive, String Theory, ESP, Dark Matter, Worm Holes or The Gematria.


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