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Mathematical Paradox

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naturalplastic
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04 May 2016, 6:00 pm

Nine7752 wrote:
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.


Exactly.



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04 May 2016, 6:18 pm

Nine7752 wrote:
Good question! 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.


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.



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05 May 2016, 8:00 am

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


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05 May 2016, 3:38 pm

naturalplastic wrote:
So...

At how many hops would the frog reach it then?


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.


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06 May 2016, 6:20 am

Deltaville wrote:
naturalplastic wrote:
So...

At how many hops would the frog reach it then?


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.



eric76
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09 May 2016, 10:36 pm

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



Deltaville
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20 May 2016, 2:19 am

b9 wrote:
Deltaville wrote:
naturalplastic wrote:
So...

At how many hops would the frog reach it then?


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.


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


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20 May 2016, 6:29 am

Deltaville wrote:
b9 wrote:
Deltaville wrote:
naturalplastic wrote:
So...

At how many hops would the frog reach it then?


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.


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.



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21 May 2016, 10:15 am

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.


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b9
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22 May 2016, 5:51 am

BaalChatzaf wrote:
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.



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31 Aug 2017, 3:05 am

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



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31 Aug 2017, 3:22 am

Deltaville wrote:
Ever heard of this problem?

Let us a assume a frog jumps half a distance to it's destination. Therefore, its jumps would account as: 1/2 the distance + 1/4 the distance + 1/8 the distance and so forth.

Essentially, 1/2n

Would it ever reach its destination? Well I have computed that formula numerous amount of time and mathematically, it always results as impossible to reach.

Or perhaps not...

Some theoretical mathematicians have argued theoretically, after a googleplex of times, the destination would be reach as the resulting step is a positive integer. Infinitely small, yes, but nevertheless a positive integer.

Do the same laws of mathematics still apply when one reaches an enormous, unfathomable value?

Please discuss.


This is a "limit" problem. The answer is, no, the frog never reaches it's destination, but we treat it as if it did.

So how can the frog not reach it's destination? (we are assuming this is only a theoretical problem and the space is not quantized).

Instead of looking at it like the distance the frog travels halves, we can look at it like the destination moves away faster than the fog approaches it, and at each jump the frog takes, the time to reach it's destination increases.

You can also think of it as the path of the frog curving away from the destination.



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31 Aug 2017, 3:44 am

Chronos wrote:
Deltaville wrote:
Ever heard of this problem?

Let us a assume a frog jumps half a distance to it's destination. Therefore, its jumps would account as: 1/2 the distance + 1/4 the distance + 1/8 the distance and so forth.

Essentially, 1/2n

Would it ever reach its destination? Well I have computed that formula numerous amount of time and mathematically, it always results as impossible to reach.

Or perhaps not...

Some theoretical mathematicians have argued theoretically, after a googleplex of times, the destination would be reach as the resulting step is a positive integer. Infinitely small, yes, but nevertheless a positive integer.

Do the same laws of mathematics still apply when one reaches an enormous, unfathomable value?

Please discuss.


This is a "limit" problem. The answer is, no, the frog never reaches it's destination, but we treat it as if it did.

So how can the frog not reach it's destination? (we are assuming this is only a theoretical problem and the space is not quantized).

Instead of looking at it like the distance the frog travels halves, we can look at it like the destination moves away faster than the fog approaches it, and at each jump the frog takes, the time to reach it's destination increases.

You can also think of it as the path of the frog curving away from the destination.


i think that the OP has confused subtraction with division (as stupid as that sounds).

so any number divided by any other number in an endless cycle will never equal zero. that is because zero is not a component of anything.

one may consider a slightly different scenario:

if the smallest element of space is a "point", then because "points" have no length or width or height, they do not exist.
so if space of composed of infinite points, then that must mean that infinity times nothing is infinity.
either that or space does not exist at all and is just a mental illusion.

and say something accelerates to a velocity along a linear path, then because the line is composed of infinite points, then the fact that the object can move at all must mean they have infinite acceleration in a way because the slightest movement the object makes means that they have traveled an infinite amount of points in a less than infinite amount of time.....

yeah great old thread....



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31 Aug 2017, 5:38 am

We don't have infinitesimal units in real numbers, as a result of axioms. I think the theoretical mathematicians in the OP changed some axioms, but that info didn't make the post.

I didn't read every page, but I immediately went to set theory. Build a set that includes the space covered by the frog, and it will be open near the destination, but will not include the destination.


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naturalplastic
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31 Aug 2017, 8:12 am

Yes. "Entertaining" is a good way of putting it.

It got rather heated and personal at certain points. So if you are too new on WP to have seen it before you might enjoy the mud wrestle of reading every page. Lol!



naturalplastic
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31 Aug 2017, 8:23 am

eric76 wrote:
The Planck Length is the shortest meaningful distance, not the shortest possible distance.


Not necessarily.

Some theorize that reality itself is granular (like either an old fashioned analog photograph, or like the pixels in a digital picture) and that the Planck length IS the shortest possible distance. The Planck Length could be the indivisible grains that make up reality.

Further- its been proposed that the length of time it takes light to traverse the Planck Length (force those photons to walk the Planck, me hardies) is the shortest possible length of time (so time is also granular and moves in hiccups).

Or not.

Both the granular, and non granular versions of the universe are put forward as unproven theories.