Mathematical Paradox

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I think may not have written the problem down correctly, however I have recently discovered that many mathematicians have conjectured that when a complex number axiom is introduced near an infinitesimally close posture to '1', '1' may indeed be reached if mathematical gymnastics and pseudo-rimannian series are introduced.

That is the kind of 'food-for-thought' I attempted to introduce.

So...

At how many hops would the frog reach it then?

The answer is the same as this riddle:

Let's say you are flogging a dead horse with arm motions n units long, but you get tired quickly. So, every time you flog, you only flog half the distance of the previous stroke. After how many flogs does your arm stop?

Are you implying that this tread is a "dead horse" being flogged?

Just kidding!

But more interesting is this: what would be the distance of that last stroke with the whip?

Is the answer

(A)One over infinity. That is: it would be the reciprocal of infinity times N (the length of the original stroke of the whip)?

Or is it:

(B) The Planck Length (the theoretical shortest possible distance for anything in this here universe we live in)?

Good question! It just depends about whether we're (a) talking about a pure mathematical puzzle, or (b) a mathematical puzzle with randomness in measurement, or (c) a physical puzzle.

IMO this is where this particular thread got hung up. That said, I like the idea of the flogging arm asymptoting down into a quivering little vibration. At some point perhaps it would make sound, then radio waves, then maybe light.

Exactly.

Hmmm...

The first part- yes- would have to happen!

Your arm would turn into a tuning fork! It would make nice musical tone!

And it would rise in pitch with each halving of distance.

And guess what.

Since we're doing factors if two (as with the frog) that would mean that your pitch would rise by exactly one octave with each turn! Go from middle C to the next C on the piano, to the next C, and so on.

An octave rise is a doubling of vibration frequency, and an octave drop is a halving.

The sound of your vibrating arm would be suddenly audible in the base range. Then would move up octave steps into the midrange. And then would become a piecing ring in the treble range. And then suddenly you wouldnt be able to hear it all. But dogs could still hear it. Then dogs would no longer be able to hear it, but bats could still hear it. Finally it would go into ultra sound so high pitched that even bats couldnt hear it.

But Im not sure about the second part of you're saying-that sound would become light energy.

Sound is one thing, and electromagnetic radiation is something else. Sound is an object made of molecules and atoms vibrating causing air waves (ie pulse in the molecules in the air). While light/radio is electrons doing stuff that causes ripples in electrical fields.

You're right about light and radio. You'd need to do something with magnets and coils of wire to get to electromagnetic.

I think you should first tell me how the fine tuning of the cosmological constant and the gravitational constant is 'non-sense' and then I will explain how this can be done by using pseudo-Riemannian series and complex value operators. It is a fair deal.

so much dissertation over something so simple.

any axis (axial intersection) that has no volume will never approach a zero point when it's distance from it is divided by 2 no matter how many times.
if the axial point however does have volume, then it is it's negative x-axis value that will intersect the median of zero at a point dictated by it's proximity to the origin.

nothing else is of worthy consideration concerning the question.

The Planck Length is the shortest meaningful distance, not the shortest possible distance.

This is only correct if you constrain yourself to a XeR series.

i do not know what that means. i presume it is where x is an element of a real number series, and if so, then i am constrained by it.

imaginary number systems are simply arbitrary and are used to help resolve indeterminate arguments

but you are the professor, so i will defer to the fact that i am not sufficiently educated to discuss this on more than just a conceptual level.

The system of complex number guarantees that ever finite degree polynomial equation has a solution.

In particular the equation x^2 + 1 =0.

Complex numbers are required in any science or engineering where angular phase or temporal phase is important.

that does not compute (when considered as a response to any other assertion in this thread).
you may have as well have simply said x^2 = -1.
in imaginary numbers where impossible values exist, it is possible to shoe horn anything into a variable (with no real definition but for a symbol) in order to complete the mathematical sentence (eg the mysterious value of -i).


since in reality, there is no such thing as negative 1, it is viewed from reality as being merely a reference point relative to starting point, or a distance from an end point.


in the question the OP proposes, then if the elements are quantifiable (eg length of frog) there will be an answer, but no values have been supplied as to the dimensions of the 2 ordinate entities (the frog's or the end point's), then it is assumed that both those entities are points with no dimension. in that case, there is no other answer than that nothing (no entity of dimension) can be subdivided to zero, so even after an infinite amount of bisection, any value will never be reduced to zero. but of course infinity is just as unreal as is zero.



but all i have gleaned from my personal speculation in what could be described as "the mathematical reality of my world" is not influenced by the history of other people's exploration of such ideas, and so i am academically ignorant.

this was an enjoyable thread...thanks, to all who participated