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# Don Blazys

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## Reputation Activity

1. Don Blazys got a reaction from Moontanman in Classics help needed
To:Donk,

Quoting Donk:

No there isn't ! Your sensibilities are perfectly valid and accurate!

A lot of classical music is simply not very memorable,
which is to say, not very inspired.

A lot of it is far too dependent on meaningless,
self indulgent arpeggios, passing phrases and filler patterns.

I would never "train" my mind to remember
things that are, in fact, not memorable.

For all we know, such "training" might even diminish our ability
to distinguish between exquisitely beautiful melody,
such as Schubert's "Ave Maria" and mere "mood music".

A truly great melody is one that sticks in your mind and
makes an emotional impact the very first time you hear it.

I own a fairly large collection of classical music CD's,
but I will never ever hear the entire collection
because I will always fast forward past all the boring parts
and go straight to all the good parts.

Don.
2. Don Blazys got a reaction from Turtle in An Exact Value For The Fine Structure Constant.
To: Jess (Pascal),

I checked out Valery Tsimmerman's site. Very impressive! Please give him my regards.

You see, I finally got a chance to do a little research on periodic tables,
magic numbers, shell theories, the theoretical "island of stability", etc.
and what I found is that both the fine structure constant and
the counting function for polygonal numbers of order > 2
do indeed seem to tie into those things.

For instance,
Quoting Valery Tsimmerman:

Well, our polygonal number counting function shows that 64.036273685156% of all positive integers
are polygonal numbers of order greater than 2, so I wonder if there might be some kind correlation here.
3. Don Blazys got a reaction from JMJones0424 in Dark Energy
Quoting mpc755:

http://aether.lbl.gov/image_all.html

Hmmm... so it appears that in a sense,
the topological properties of the universe
are identical to that of a condom!

Well, now that we all know what the universe "really" looks like,
let's all celebrate!

Don.
4. Don Blazys got a reaction from CraigD in An Exact Value For The Fine Structure Constant.
Quoting CraigD.

Lots of stuff on the web about the FSC at very high energy values. Here's one...

http://physics.nist.gov/cuu/Constants/alpha.html

And here's another...

Don.
5. Don Blazys got a reaction from JMJones0424 in An Exact Value For The Fine Structure Constant.
Well, I hope everyone here had a great Christmas vacation!

I sure did.

Now, I have some more really good news for you!

As you all know, the subject of Polygonal numbers is huge,
and constitutes an extraordinarily important part of number theory.

Thus, every truly smart Hypographer should be overjoyed to learn that "Google searching"
the words polygonal numbers now brings up this counting function on... get this...
the very first page!!!

Isn't that great? Doesn't that make you happy?

Don.
6. Don Blazys got a reaction from IDMclean in An Exact Value For The Fine Structure Constant.
To date, by far the most accurate measurement of the fine-structure constant
(measured at the scale of the electron mass) was made by Gerald Gabrielse
and colleagues from Harvard, Cornell and RIKEN.

Measuring the "magnetic moment" of a single electron in a "quantum cyclotron" and
inserting that value into state of the art QED equations, the value they determined is:

$\alpha^{-1}=137.035999084(51)$,

which means that the fine-structure constant lies somewhere in between:

$\alpha^{-1}=137.035999135$, and

$\alpha^{-1}=137.035999033$.

Now, these values were determined back in 2008, and since then,
no significant improvement in accuracy was ever accomplished,
despite enormous improvements in both the design of the equipment
and the QED equations themselves.

Thus, many scientists now suspect that further refinements in
the value of the fine-structure constant may not even be possible,
and that the last two values represent, for all practical purposes,
the actual lower and upper bounds of the fine-structure constant as
measured at the scale of the electron mass. Even Gabrielse himself
believes that the above values will hold for a long, long time to come.

Given the above facts, it now seems that in order to be correct,
any mathematical expression which results in the fine-structure constant
must not only match the above experimental value exactly, but must also include,
within it's form, some simple way of expressing, with the same degree of absolute accuracy,
those seemingly inherent lower and upper bounds.

which describes a finding that occured right here at Hypography many moons ago.
Well, thanks to a great fellow named Lars Blomberg, (who found it via the OEIS)
we now have values of $\varpi(x)$ to $x=10^{15}$.

This information was crucial in not only greatly improving the "counting function",
but also allowed me to derive these values of the fine-structure constant as well:

$\alpha^{-1}=137.035999084=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(6*\pi^{5}*e^{2}-2*e^{2})}$

$\alpha^{-1}=137.035999135=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(6*\pi^{5}*e^{2}-2*e^{1})}$

$\alpha^{-1}=137.035999033=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(\mu*e^{2}-2*e^{\frac{5}{2}})}$

where $\mu=1836.15267247(80)$ is the "proton to electron mass ratio", and
$A=2.566543832171388844467529...$, is that very special "Blazys Constant"
which generates all of the prime numbers, in sequential order, by the following simple method:

Note that the whole number part is the first prime $2$, and that:

$((2.566543832171388844467529...)/2-1)^{-1}$

is approximately:$(3.530176989721365539402422...)$,

where the whole number part is the second prime $3$, and that:

$((3.530176989721365539402422...)/3-1)^{-1}$

is approximately $(5.658487746849688216649061...)$,

where the whole number part is the third prime $5$, and so on.

(In short, we divide the approximate number by it's whole number part, subtract $1$,
and take the reciprocal of the result to get the next approximate number whose whole number part is the next prime!)

That the fine-structure constant is thus related to the prime numbers was also discovered (independently) by Ke Xiao
who publised his findings in a paper entitled "Dimensionless Constants and Blackbody Radiation Laws" in
The Electronic Journal of Theoretical Physics. (It can be "Googled".)

I will post Lars Blomberg's determinations of $\varpi(x)$ in my next post,
and a revised "polygonal number counting function" in the post after that.

There's more... a lot more... but that's all for now.

It's good to be back.

Don.
7. Don Blazys got a reaction from CraigD in An Exact Value For The Fine Structure Constant.
To date, by far the most accurate measurement of the fine-structure constant
(measured at the scale of the electron mass) was made by Gerald Gabrielse
and colleagues from Harvard, Cornell and RIKEN.

Measuring the "magnetic moment" of a single electron in a "quantum cyclotron" and
inserting that value into state of the art QED equations, the value they determined is:

$\alpha^{-1}=137.035999084(51)$,

which means that the fine-structure constant lies somewhere in between:

$\alpha^{-1}=137.035999135$, and

$\alpha^{-1}=137.035999033$.

Now, these values were determined back in 2008, and since then,
no significant improvement in accuracy was ever accomplished,
despite enormous improvements in both the design of the equipment
and the QED equations themselves.

Thus, many scientists now suspect that further refinements in
the value of the fine-structure constant may not even be possible,
and that the last two values represent, for all practical purposes,
the actual lower and upper bounds of the fine-structure constant as
measured at the scale of the electron mass. Even Gabrielse himself
believes that the above values will hold for a long, long time to come.

Given the above facts, it now seems that in order to be correct,
any mathematical expression which results in the fine-structure constant
must not only match the above experimental value exactly, but must also include,
within it's form, some simple way of expressing, with the same degree of absolute accuracy,
those seemingly inherent lower and upper bounds.

which describes a finding that occured right here at Hypography many moons ago.
Well, thanks to a great fellow named Lars Blomberg, (who found it via the OEIS)
we now have values of $\varpi(x)$ to $x=10^{15}$.

This information was crucial in not only greatly improving the "counting function",
but also allowed me to derive these values of the fine-structure constant as well:

$\alpha^{-1}=137.035999084=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(6*\pi^{5}*e^{2}-2*e^{2})}$

$\alpha^{-1}=137.035999135=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(6*\pi^{5}*e^{2}-2*e^{1})}$

$\alpha^{-1}=137.035999033=(A^{-1}*\pi*e+e)*(\pi^{e}+e^{(\frac{-\pi}{2})})-\frac{1}{(\mu*e^{2}-2*e^{\frac{5}{2}})}$

where $\mu=1836.15267247(80)$ is the "proton to electron mass ratio", and
$A=2.566543832171388844467529...$, is that very special "Blazys Constant"
which generates all of the prime numbers, in sequential order, by the following simple method:

Note that the whole number part is the first prime $2$, and that:

$((2.566543832171388844467529...)/2-1)^{-1}$

is approximately:$(3.530176989721365539402422...)$,

where the whole number part is the second prime $3$, and that:

$((3.530176989721365539402422...)/3-1)^{-1}$

is approximately $(5.658487746849688216649061...)$,

where the whole number part is the third prime $5$, and so on.

(In short, we divide the approximate number by it's whole number part, subtract $1$,
and take the reciprocal of the result to get the next approximate number whose whole number part is the next prime!)

That the fine-structure constant is thus related to the prime numbers was also discovered (independently) by Ke Xiao
who publised his findings in a paper entitled "Dimensionless Constants and Blackbody Radiation Laws" in
The Electronic Journal of Theoretical Physics. (It can be "Googled".)

I will post Lars Blomberg's determinations of $\varpi(x)$ in my next post,
and a revised "polygonal number counting function" in the post after that.

There's more... a lot more... but that's all for now.

It's good to be back.

Don.
8. Don Blazys got a reaction from CraigD in Bamboo As Sound Ammplifier?
The speaker vibrates and that creates sound waves.

Putting the speaker in the bamboo causes the bamboo
to vibrate along with the speaker and that creates
more sound waves.

In effect, the bamboo becomes a part of the speaker
so the speaker is, in that sense, made larger.

then it won't be very loud, and no one will hear it.

However, if it vibrates on a table top,
then it will be much louder, and everyone will hear it.

It's the same principle.

Don
9. Don Blazys got a reaction from CraigD in Fibonacci Sequence In Theoretical Physics
Quoting Qfwfq

No, but the OP was speaking of how the Fibbonacci sequence is ubiquitous in nature,
and that would clearly involve the Golden Ratio as part of it's "generating function".

Quoting Jay-qu
Incomplete perhaps, but not yet proven wrong. Opinions are divided on that,
but you know what they say about opinions... they are like... you know...
everybody's got one! Last I read about it, it is still being worked on.

But the point here is that it is not an uncommon suspicion that things in nature
are patterned according to simple (meaning in principle) mathematical constructs.

The universe may or may not come to an "end" (whatever that means),
but its logical and mathematical underpinnings will go on forever.

Don.
10. Don Blazys got a reaction from CraigD in Fibonacci Sequence In Theoretical Physics

The OP speaks of the golden ratio and the golden ratio is approximated as
the ratio between any two succsessive Fibonacci numbers!

Quoting Jay-qu
It's easy to be "snooty", isn't it?

Don.
11. Don Blazys got a reaction from modest in Figurates Up To 10^13
Just checked it... and......it looks good!!!!!!!!!!!!!!!!
My function predicted it to within 1000.
That's really good!
I'll give you a more detailed report and
update the "FSC tracking post" in an hour or so.

If possible, please post the results
from 1,100,000,000,000 to 1,200,000,000,000.
in increments of 10,000,000,000.

We can then analize the fluctuations in greater detail!

Don.
12. Don Blazys got a reaction from CraigD in Mathematical Consistency
Quoting Nootropic:
It IS an "axiom". It's called the "Identity axiom of multiplication".

Quotingng Nootropic:
Axioms are not provable. They are "self evident".

That depends on what "era" of mathematics you are talking about.
You need to get up to date. In the past, it was about right and wrong.
These days, it's all about "feelings".

Quoting Nootropic:
Why should I do that? Journals are dead. Nobody reads them any more.
The only thing their pages are good for is "toilet paper".

I get a lot more readers right here at Hypography!

Real mathematicians such as Grigory Perelman and myself don't send their work to "journals".
Grigory Perelman felt, as I do, that the the professional math community must pay for their crimes,
so rather than send his ground breaking work to a "journal", he "self published" it on line.

He then greatly embarrassed the professional math community by telling them, in essence,
to stick their fields medal where the sun don't shine, and to take their funny money and go shopping!

My work is even more fundamental than his, and judging by the number of e-mails that I have been getting lately,
it is indeed making an impact! A big one!

And why can't you answer that simple yes or no question in my last post?

Don.
13. Don Blazys got a reaction from modest in Flash-fried Spaghettification
Quoting Modest

Mathematical plausibility is plausibility.

I say, try working out the equations, and if they do work out,
then just toss your idea out there and see if it flies. :)

All of these models and theories have now evolved into
"explanations" that are much stranger than fiction anyway!

Don.
14. Don Blazys got a reaction from Turtle in Figurates Up To 10^13
I will edit and update this post as Phillip 1882's results come in.

The third column shows the predicted values of $\varpi(x)$ based on
the best current physical measurements of $\alpha$ which Wikipedia
gives as being between $137.035999033^{-1}$ and $137.035999135^{-1}$.

Note that by the time we get to $x=10^{13}$, the predicted values of $\varpi(x)$
will vary by about plus or minus 30, whereas at present, they only vary by

The fourth column shows the values that result when we solve for $\alpha$ in:

$B(x)*\left(1-\frac{\alpha}{\mu-2*e}\right)=\left(x-\frac{x}{\alpha*\pi*e+e}-\frac{1}{2}*\sqrt{x-\frac{x}{\alpha*\pi*e+e}}\right)*\left(1-\frac{\alpha}{\mu-2*e}\right)$

Note that the fluctuations are slowly decreasing and that these values of $\alpha$
seem to be converging on some particular value.

_______$x$____________$\varpi(x)$_______$B(x)*\left(1-\frac{\alpha}{\mu-2*e}\right)$________$\alpha$________

100,000,000,000_____64,036,148,166______64,036,147,783_________137.03593392608^-1
200,000,000,000_____128,072,369,864_____128,072,369,683________137.03598372618^-1
300,000,000,000_____192,108,604,710_____192,108,603,778________137.03594625176^-1
400,000,000,000_____256,144,844,029_____256,144,844,185________137.03600571478^-1
500,000,000,000_____320,181,088,566_____320,181,088,626________137.03600111220^-1
600,000,000,000_____384,217,336,898_____384,217,335,932________137.03597169223^-1
700,000,000,000_____448,253,585,852_____448,253,585,409________137.03598831869^-1
800,000,000,000_____512,289,836,587_____512,289,836,605________137.03599946950^-1
900,000,000,000_____576,326,089,252_____576,326,089,206________137.03599821781^-1
1,000,000,000,000___640,362,343,980_____640,362,342,983________137.03598213253^-1
1,100,000,000,000___704,398,597,754_____704,398,597,764________137.03599923616^-1
1,200,000,000,000___768,434,854,386_____768,434,853,414________137.03598530327^-1
1,300,000,000,000___832,471,110,338_____832,471,109,826________137.03599238683^-1
1,400,000,000,000___896,507,366,959_____896,507,366,915________137.03599854497^-1
1,500,000,000,000___???,???,???,???
1,600,000,000,000___???,???,???,???
1,700,000,000,000___???,???,???,???
1,800,000,000,000___???,???,???,???
1,900,000,000,000___???,???,???,???
2,000,000,000,000___???,???,???,???

10,000,000,000,000__?,???,???,???,???___6,403,626,165,690+/-30____???.????????????^-1
15. Don Blazys got a reaction from Tormod in I Need Help Quick Please
This:

http://science.howstuffworks.com/magnet.htm

is a pretty good explanation...

Don
16. Don Blazys got a reaction from modest in I Think My Faraday Cage Is Leaking All Over The Place
Here's some more data.

I put my "Verizon LG" cellphone in two different microwave ovens (a "Sharp" and a "Sanyo")
and in both cases, it didn't lose any bars at all. (Both ovens are grounded.)

Don.
17. Don Blazys got a reaction from Qfwfq in Mathematical Consistency
Quoting Myself:

Quoting Ben:

At $T=1,$ the perfectly true, perfectly defined identity:

$T*a^x= \left(T*a\right)^{\frac{\frac{x*\ln(a)}{\ln(T)}+1}{\frac{\ln(a)}{\ln(T)}+1}}$

demonstrates that multiplying $a^x$ by $1$
(so as to leave $a^x$ "unchanged")
would automatically result in divisions by 0,
and since divisions by 0 are strictly disallowed,
multiplication by 1 must also be strictly disallowed.

Everyone here agrees with that because
this identity is simple, incontrovertible,
and can easily be checked by anyone.

New discoveries in math will require math to change
and at this early stage, most folks are still afraid
because the necessary change is indeed somewhat radical.

However, in time, they will think it through,
and once they get used to the truth,
that fear will naturally just fade away.

Quoting Ben:

Do not ask for whom that axe grinds...
it grinds for thee! ;)

Quoting Ben:

Indeed, you have good ears.
It's what's between those ears
that may be in question here!

Don.
18. Don Blazys got a reaction from CraigD in Mathematical Consistency
You see folks, the identity:

$T*a^x= \left(T*a\right)^{\frac{\frac{x*\ln(a)}{\ln(T)}+1}{\frac{\ln(a)}{\ln(T)}+1}}$

is both embarassing and humiliating to the "math community"
because it conclusively and unequivocally demonstrates
that the concept of a "unit coefficient" is badly flawed
and that the notion of 1 being the "identity element"
relative to multiplication is highly illogical.

The consequences of this are enormous, because the "unit coefficient"
is often applied in calculations and 1 being the "identity element"
for multiplication is universally accepted and cited as an "axiom" !

Who would have thought that ultimately, they must both go the way of
the "luminiferous aether" and "phlogiston".

Meanwhile, those so called "professors of mathematics" in our colleges and universities
will continue to not only teach this gibberish and indoctrinate our young people with this rubbish,
but will undoubtedly add insult to injury by demanding payment for their "services"!

You math majors who are paying thousands of dollars for an education are being taken for suckers.
You are being defrauded, duped and swindled! You are getting fleeced
and the wool is being pulled over your eyes! You should at least get your money back!!!

Don.
19.
The equation 6/3=2 implies the true statement 2*3=6. Therefore, the expression 6/3 is allowed.

Likewise, 0/0=N implies the true statement N*0=0. Therefore, the expression 0/0 is also allowed,

even though it is indeterminate.

However, 6/0=N implies the false statement N*0=6. Therefore, the expression 6/0 is strictly disallowed

because it is both impossible and nonsensical.

Don.
20.
The equation 6/3=2 implies the true statement 2*3=6. Therefore, the expression 6/3 is allowed.

Likewise, 0/0=N implies the true statement N*0=0. Therefore, the expression 0/0 is also allowed,

even though it is indeterminate.

However, 6/0=N implies the false statement N*0=6. Therefore, the expression 6/0 is strictly disallowed

because it is both impossible and nonsensical.

Don.
21. Don Blazys got a reaction from modest in Deficient & Abundant Number Fun
Quoting Turtle:

It's a "special case" of a more general formula.

If $p$ is prime, then the sum of the factors of $p^n$ is:

$\frac{p^n-1}{p-1}$

Don.
22. Don Blazys got a reaction from IDMclean in Calculating The Fine Structure Constant.
The "Fine Structure Constant" is the dimensionless (unitless) "pure number":

$\alpha\approx 137.035999084^{-1}$ .

It is so absolutely basic, fundamental and important to physics,
that its symbol is the very first letter of the Greek alphabet..."alpha",
yet it is so poorly understood, that in almost a century,
all we have managed to determine are those measly twelve digits,
at a cost of perhaps thirty million dollars per digit.

Richard Feynman, one of the three greatest physicists of the twentieth century,
(the other two being Albert Einstein and Stephen Hawking) once wrote about it.

Quoting Richard Feynman:

But what if it was suddenly discovered, (perhaps right here at Hypography)
that this number could be determined not just by physical measurements,
but by logic as well?

What if this number was merely an unavoidable consequence
of some lower or upper bound on some simple mathematical function?

I have my own views on what this "mysterious" number really is,
and I would like to share them with you.

Don.
23. Don Blazys got a reaction from CraigD in Calculating The Fine Structure Constant.
The "Fine Structure Constant" is the dimensionless (unitless) "pure number":

$\alpha\approx 137.035999084^{-1}$ .

It is so absolutely basic, fundamental and important to physics,
that its symbol is the very first letter of the Greek alphabet..."alpha",
yet it is so poorly understood, that in almost a century,
all we have managed to determine are those measly twelve digits,
at a cost of perhaps thirty million dollars per digit.

Richard Feynman, one of the three greatest physicists of the twentieth century,
(the other two being Albert Einstein and Stephen Hawking) once wrote about it.

Quoting Richard Feynman:

But what if it was suddenly discovered, (perhaps right here at Hypography)
that this number could be determined not just by physical measurements,
but by logic as well?

What if this number was merely an unavoidable consequence
of some lower or upper bound on some simple mathematical function?

I have my own views on what this "mysterious" number really is,
and I would like to share them with you.

Don.
24.
Welcome to the club!

This sort of thing really makes me wonder.
Where does instinct end and rational thought or "reasoning" begin?

The other day, while I was at work,
I noticed a rather large garden spider building it's web.
That web was an engineering marvel to say the least!
A perfect "circle within a circle" configuration held together by
perfectly spaced "rays" from the center to the outer perimeter,
and...get this...suspended in the air exactly half way
between two trees twelve feet, eight inches apart!
(I measured it as carefully as I could using a tape measure,
but since the web was also about twelve feet in the air,
I may be off by a few inches or so.
Anyway, I wasn't about to go get a ladder, because the folks I work with
would then have thought that I had really lost my mind!)

We get garden spiders here every spring and summer
and I have seen plenty of webs, but this one was simply astonishing!
Truly, this was the "Michaelangelo of spiders"!
I wanted to congratulate it and shake its "hand"!

I was wondering...how on God's green earth did it do that?
If you and I were that size, we couldn't even dream
of accomplishing such a feat for it would probably take us several years
just to secure the initial thread from one tree to the other!

Instinct? Intelligence? Is there a difference? I wonder!

How did it "know" the "halfway point" between the two trees?
Did it "count it's steps" and divide by two?
Did it "eyeball" the distance? Estimate?
Or perhaps it knew by somehow gauging how far
it's weight caused the initial thread to bend.
A natural sense of trigonometry?
Or maybe it was just luck.

The thing is, all the webs here are
roughly halfway between two trees whose distances vary,
so there must be some kind of intelligence at work here.

I could go on and on with other questions such as:
How did it know it's initial thread was strong enough
to hold its weight at that distance?
Indeed, how did it get it's initial thread from one tree to the other?
(Spiders can't fly or jump that far and the ground below
was filled with grass, weeds, rocks and dead leaves,
so as to make it very difficult to avoid getting it entangled.)

And why did the talents of this particular garden spider,
far exeed those of it's peers?

If "instinct" is analagous to "programming",
and "intelligence" to "creativity",
then there were certainly elements of both in that particular spider.

Don.
25.
The following are reasons for why I am quite certain that
Craig D's "unstated assumption objection" is without foundation.

Quoting Craig D:

First of all, it's not "an attempted proof of Fermat's Last Theorem" but, (with all due humility),
a "possibly valid proof of both the Beal Conjecture and Fermat's Last Theorem".

Now, when Craig D says,
well.., that's where he is wrong!
It's not necessary in step (2) of my proof to make
any assumption whatsoever as to the value of $z$.
Anyone can go to step (2) in my proof and see for themselves that
step (2) allows all kinds of different values for $z$,
and that it is in steps (4) and (5) that the existence of both
logarithms and Pythagorean triples necessitate $z=1$ and $z=2$ respectively.

Step (2) in the proof is not an "assumption on the variables",
but rather a "statement that Pythagorean triples exist."
Basically, Craig D wants us to ignore the fact that Pythagorean triples exist!
He doesn't seem to understand that if we don't allow well known facts,
then we don't allow proofs, mathematics, or for that matter, any science whatsoever!

What Craig D also doesn't seem to understand is that factoring is "standard procedure",
and has absolutely nothing to do with "making an assumption",
but rather with "stating a fact"!

"Websters dictionary" defines the word fact as:
"Anything actually existent. Any statement strictly true; truth; reality."
and the word assumption as:
"A supposition. Something taken for granted but not necessarily true or false."

In fact, if only Craig D went to (Fermat's Last Theorem--from Wolfram Math World),
then he would have discovered that the very first thing we do
when faced with an equation such as:

$a^x+b^y=c^z$ ___________________________(11.1)

or

$a^n+b^n=c^n$ ___________________________(11.2)

is factor !!!!!

For equation (11.2), Wolfram gives:

$\left(c^\frac{n}{2}+b^\frac{n}{2}\right)\left(c^\frac{n}{2}-b^\frac{n}{2}\right)=a^n$

and

$\left(c^\frac{n}{2}+a^\frac{n}{2}\right)\left(c^\frac{n}{2}-a^\frac{n}{2}\right)=b^n$

from which we get:

$\left(a^\frac{n}{2}\right)^2+ \left(b^\frac{n}{2}\right)^2=\left(c^\frac{n}{2}\right)^2$

which is, as we can plainly see, factored in exactly the same way as occurs in my proof!

Factoring in this manner is so common and ubiquitous,
that it is considered "par for the course", and frankly,
I'm surprised that Craig D doesn't seem to know that.
Wolfram, and virtually every book on number theory,
would not be teaching factoring if it resulted in "circular reasoning"!

As I said before, factoring does not, in any way, constitute an "unstated assumption",
and in order for there to actually be any kind of "circular reasoning" whatsoever,
I myself would have to make the assumption that
the exponential variables in (2) are all equal to $2$.
However, as anyone can see, I make no such assumption.
I simply allow the variables to remain variables throughout the proof,
and when it finally does occur that $z=1$ and $z=2$ are required,
that requirement is not my doing,
but an unavoidable consequence of the fact
that both the properties of logarithms and Pythagorean triples exist.

The first question automatically denies both Wile's proof of FLT,
and my proof of both the Beal Conjecture and FLT.
Thus, it is wildly speculative and unrealistically hypothetical.
(Kind of like asking: "If there was known to exist a human that looked exactly like a chicken,
would the choice of having it for dinner instead of having it over for dinner be permitted?")

My answer to that question was not "a wordy yes", but:

Quoting myself:

Since we can't eliminate the notion of logarithms from mathematics,
it must be the case that the question itself is nonsensical, which it clearly is!

The second question:

Quoting Craig D:

Which Craig D took to mean:

Quoting craig D:

As anyone can see, I asserted nothing of the sort!
I clearly said that the Wiles proof, if we accept it, (and thats a big "if"),
is far too contrived and convoluted for most people,
and that the more obvious reason we know that
such a triple can't possibly exist is because of my proof !

In post#4, I demonstrated that Craig D was wrong about the "indeterminate forms"
and explained that he is confusing a factorinzation for an "unstated assumption".

In this post, I direct him to (Fermat's Last Theorem--from Wolfram Math World).
so that he can find out for himself that
a factorization is not an "unstated assumption",
is done all the time, and does not result in "circular reasoning".

My proof has therefore not been logically refuted,
and I have all the faith in the world that Craig D,
along with all the other really smart math enthusiasts here at this wonderfull forum,
will, sooner rather than later,
get to the truth of this most important matter.

Don.
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