Could you explain the problem completley… so i don’t have to look it up… then maybe i can solve it…
It’s not that hard, Xeno claims a man fires an arrow at a tortoise, but before the arrow arrives the tortoise has moved on
Also.
It’s basically a question that tries to resolve the problem of motion and time, if the arrow is aimed at the tortoise and time and space are instants, then according to logic the arrow should never hit it’s target, because as it travels the tortoise is in motion also, and the arrow never meets the point where the tortoise was.
zeno stuff
[tab]you have the amount of time given and then you divide that into an infinite amount of instances you can then claim that each instant is of value zero but to then return and determine the summation of instances you would be multiplying zero times infinity which is indeterminate… the best claim is then that in reality you are dividing the time given by infinite which is not zero finite/inf = .000000000000000000…0000000000000001 so the actual instants have a size. in otherwords infinitesimally small does not mean zero in size…[/tab]
[tab]
One of the conditions of this dichotomy paradox necessarily entails that the arrow will never reach the tortoise:
in dealing solely with distances d/(2^n), and as the opening words explicitly state, one is only contemplating the infinite divisibility of distance travelled BEFORE the entire distance d is travelled - “BEFORE an object can travel a given distance d”.
So if one is concerned about the arrow actually reaching the tortoise, one ought to consider the whole picture and deal also with once an object HAS travelled a given distance d, and even AFTER an object has travelled a distance d.
It doesn’t seem to matter whether the tortoise moves at all, or even if it moves towards the arrow, because the arrow still has to pass through an infinite number of fractions of the distance BEFORE reaching the tortoise, whatever the tortoise is doing. And then on top of that, “the arrow/fletcher’s paradox” says the arrow isn’t even moving…
Are you looking for a solution to the paradox such that the arrow DOES reach the tortoise? Whether we use calculus at all is irrelevant if one of the assumptions is that we’re only dealing with what happens BEFORE distance d is travelled.[/tab]
[tab]You could of also said use a Taylor Maclaurin series or an integral with natural logs such as the half life equation, but yes correct.[/tab]
Ok just cutting and pasting what is written on the wiki is not an answer. 
It’s technically correct though.
Er… I didn’t?
And… ok - it doesn’t feel like I solved anything though, I just picked out and criticised the main assumption.
You also said Abstract was right for saying something else, so what was the answer you were looking for?
The answer both I and Abstract gave, I am not sure what you are trying to say here, that the laws of calculus are wrong or that Zeno is wrong or both.
You are technically correct in what you say, but that is not the answer.
It probably helps to visualise this in terms of a bouncing ball, we know eventually it comes to rest, common sense tells us this, and that time and distance are not exactly halving. Hence Zeno is basically making a logical error of assuming time and distance are exactly halving in his paradox.
Ok so that’s the answer?
It doesn’t seem very satisfying since the point d/2 IS d/2, simply by virtue of the conditions of the paradox: premises are not subject to logical error within the paradox itself. Likewise for t/2 if the paradox is being applied to time rather than distance. Of course in reality, distance d/2 is not covered in t/2 units of time, due to various things such as air resistance, imperfectly flat ground for the tortoise to walk along and thus variable velocity and/or speed, and even concepts of relativity affecting spacetime differently for each object since they are each travelling at relatively different speeds.
But this paradox is a theoretical one, not a real one - as any physical re-enactment of the paradox would easily solve it.
I’m not sure if we’re tabbing anymore on this one, since you seem to have found a satisfying answer and you have even said what you were looking for untabbed? But here is another technically correct solution:
[tab]At a small enough level of magnification, objects are seen to never actually be touching. Two surfaces are always repelled by the tiny repulsive magnetic charges exerted at a sub-atomic level, which gives a particular distance that cannot be closed between two objects. At some point during the d/(2^n) series, the remaining distance that the arrow has left to travel will equal this threshold, beyond which it cannot travel further anyway - at which point it can be said to be touching as much as it ever would, without having fully travelled distance d.
However, if d is simply redefined to take into account this fact, the paradox is restored.[/tab]
The answer to ALL of the Zeno paradoxes is the understanding of simple calculus.
I think you mean an acceptance of simple calculus.
You yourself rightly deny that infinity is defined. So for limits to converge towards a definite answer, this is like saying something finite can result from something infinite.
I forget the outcome of this old thread about whether 0.9(recurring) equalled 1.
A convergent series of 9/10+9/100+9/1000+… would definitely tend towards 1, but for it to equal 1 requires an intuitive leap rather than a strict and rigorous approach taken forever and ever just to never quite get there.
This intuitive leap is necessary for the acceptance of calculus, which is more of a mindset adopted for things like Zeno’s paradox to no longer seem paradoxical, than a solution for it.
Only because you don’t understand the underlying laws of calculus.
Limits are asymptotic they neither denote anything “real” nor are they per se fictions. They are what values can approach but never reach.
en.wikipedia.org/wiki/Taylor_series
Second-order Taylor series approximation (in gray) of a function f(x,y) = e^x\log{(1+y)} around origin.
*Don’t accept the underlying laws of calculus.
Nothing you’ve said gets rid of this problem of infinity in calculus. Asymptotes are just an example of what I was talking about that you need to make an intuitive leap to reach. And then you say they’re approached but never reached, which is just what I said about convergent series never quite getting there if you take a strict and rigorous approach to them forever and ever…
You can’t repeat my argument in order to say it’s wrong. Quoting the wiki-history of the Taylor series doesn’t prove anything either.
It isn’t a problem an axiom is not an issue unless you make it one by semantics and then everyone will just think you are a crank.
The problem is solved and successfully disputed according to all science and maths. The fact that you don’t understand it, is possibly interesting but not a reason to really discuss your ignorance with you.
I am a crank.
This is not the thread to discuss “my” ignorance, no, whether with or without appeals to authority rather than actual arguments. I’ll drop it on the condition that you come up with more lovely puzzles 
I apologise that I know of none.
Sounds like a deal. I will.
cut-the-knot.org/Probability … ulbs.shtml
Tough one this.
and:
Monkeying around
Easier.
I find it hard to believe that no one can remotely guess at both these problems. They’re both intimately related to logic and maths?
Ok clue for both first one parallel advances lead to serial conclusions.
Monks meh this is just straight logic. Not giving a clue to this if you can’t solve it, you’re not a philosopher.
I have some questions about the 2nd problem, and also some guesses (more than one because they depend on the answers to the questions).
[tab]Does the messenger say that at least one monk definitely has the disease, or only that they “may”? If it’s “may,” I do not think any monks would die (assuming the question isn’t looking for an answer like “however many ate the rice”).
If they know that at least one monk has the disease:
Are we counting the day the messenger came as day 1 or day 0? The monks see each other three times a day, so they seen each other either 33 or 30 times depending. And the number of dead monks will be equal to whichever (again, assuming they are told that at least one monk has the disease).
I don’t think this as easy a question as you make it out to be.[/tab]
Still working on the first problem.
I don’t think I’m equipped to think the first problem through on my own, so I’m going to think here in hopes that someone can make something of my ramblings.
[tab]The prisoners can’t count the number of people who have been to the room, because they can only transmit 0 or 1 to the next prisoner. They can, however, count the days that pass, and count themselves prior to going in. The days might be useful, espcially since they know that prior to day 100, they won’t be getting out. Themselves probably isn’t, since they can’t really communicate their prisoner number using a bulb with only two states.
The thing I keep getting caught up on is how to deal with multiple repeat visits. The first repeat visit can be passed along by chaning 0 to 1. But the second repeat visit will break that signal, and any visitor that comes after that won’t be able to tell if it’s been switched and switched back, or if it was never switched in the first place.
I think the best place to start is with a smaller set, say 3 prisoners.
Call the first prisoner to be picked A, and the other two B and C.
After A is picked, either A, B, or C could be picked, and so on ad infinitum.
So we have a tree that looks like this:
A_
/|_______
A_______________________________B____________________________C____
/______________|_/|_/|______
A______________B_______C________A_____________B__CA_B__C
In the tree, only the path that ends in the light blue C or the medium green B would be successful in saying that everyone had been to the room.
One thing to note is that this tree can be traversed recursively. If on the second day, the warden picks A again, it’s exactly the same situation as it was on the first day.
But if the warden picks A on the third day after picking B or C, it isn’t the same as the first day, but the same as the second. Unfortunately, it doesn’t seem like this can be communicated. Just using 0 or 1, we can’t convey which branch of the tree we’re on, because already on the second day there are three possible branches, and only two possible light bulb states.
So we can only convey one thing to one person at a time. That means the answer is going to involve something like the lightbulb communicating “add 1”, or maybe something more veriable like “add today’s number.” The general idea is that each prisoner is keeping his or her own count, and the lightbulb tells him or her to perform some action on that count. Then there’s a rule about turning on the light, something like “turn it on if this is your first visit.” But “add 1” won’t work with “turn it on if this is your first visit”: in the three prisoner case, if it went A, B, C, no matter what happens after that, A’s count would be 0, B’s would be 1 and C’s would be 1. They would never get to three (assuming that’s what they’re getting to, which it probably isn’t but needn’t be).
That what I have so far.[/tab]
Euler’s Equation and the Reality of Nature.
=.
a)
Euler’s Equation as a mathematical reality.
Euler’s identity is "the gold standard for mathematical beauty’.
Euler’s identity is “the most famous formula in all mathematics”.
‘ . . . this equation is the mathematical analogue of Leonardo
da Vinci’s Mona Lisa painting or Michelangelo’s statue of David’
‘It is God’s equation’, ‘our jewel ‘, ‘ It is a mathematical icon’.
. . . . etc.
b)
Euler’s Equation as a physical reality.
"it is absolutely paradoxical; we cannot understand it,
and we don’t know what it means, . . . . .’
‘ Euler’s Equation reaches down into the very depths of existence’
‘ Is Euler’s Equation about fundamental matters?’
‘It would be nice to understand Euler’s Identity as a physical process
using physics.‘
‘ Is it possible to unite Euler’s Identity with physics, quantum physics ?’
==.
My aim is to understand the reality of nature.
Can Euler’s equation explain me something about reality?
To give the answer to this. question I need to bind
Euler’s equation with an object – particle.
Can it be math- point or string- particle or triangle-particle?
No, Euler’s formula has quantity (pi) which says me that
the particle must be only a circle .
Now I want to understand the behavior of circle - particle and
therefore I need to use spatial relativity and quantum theories.
These two theories say me that the reason of circle – particle’s
movement is its own inner impulse (h) or (h*=h/2pi).
a)
Using its own inner impulse (h) circle - particle moves
( as a wheel) in a straight line with constant speed c = 1.
We call such particle - ‘photon’.
From Earth – gravity point of view this speed is maximally.
From Vacuum point of view this speed is minimally.
In this movement quantum of light behave as a corpuscular (no charge).
b)
Using its own inner impulse / intrinsic angular momentum
( h* = h / 2pi ) circle - particle rotates around its axis.
In such movement particle has charge, produce electric waves
( waves property of particle) and its speed ( frequency) is : c>1.
We call such particle - ‘ electron’ and its energy is: E=h*f.
In this way I can understand the reality of nature.
==.
P.S.
’ They would play a greater and greater role in mathematics –
and then, with the advent of quantum mechanics in the twentieth
century, in physics and engineering and any field that deals with
cyclical phenomena such as waves that can be represented by
complex numbers. For a complex number allows you to represent
two processes such as phase and wavelenght simultaneously –
and a complex exponential allows you to map a straight line
onto a circle in a complex plane.’
/ Book: The great equations. Chapter four.
The gold standard for mathematical beauty.
Euler’s equation. Page 104. /
Euler’s e-iPi+1=0 is an amazing equation, not in-and-of itself,
but because it sharply points to our utter ignorance of the
simplest mathematical and scientific fundamentals.
The equation means that in flat Euclidean space, e and Pi happen
to have their particular values to satisfy any equation that relates
their mathematical constructs. In curved space, e and Pi vary.
/ Rasulkhozha S. Sharafiddinov . /
===…
P.S.
Love is the gravity of the soul.
/ by Abstract /
=.
There is gravity attraction in the universe.
And there is love attraction in the world.
Physicists say that the gravity attraction power
is the smallest power.
Then, maybe, the love attraction is stronger than gravity attraction.
=.