You cannot touch anything. Ever!

Damn Alright then....

nice mirror

 

do people still not get this? its calculus.....

the sum of this infinite series is a FINITE number.....

its like this: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +.... = 1

simple shit

 

woah....this thread kinda reminds me of how no matter how sharp a knife is ....its still a flat surface on the edge...just really really freakin tiny...freaky shit

 

well obviously moving half way isnt all the way. What are you trying to say? If i didnt touch the keyboard, words wouldnt appear on the screen. Are you talking about half lives? chemistry stuff?

 

That really fucked with my head. I spent a long time poking the computer screen after reading all that.

 

dude, wtf are u trying to say. this is common sense! ever heard of high school Calc Class, or did u jsut find this out all on your own? im jsut surprised how amazed you are at something as simple a calc.

 

To let everyone know, everything on this planet that we touch is made entirely of energy. We think we are actually holding it because our brains have been fooled. Also the reason we seem the right way up is yet another mind trick.


So next time you touch a cheese cake or a croque monsieur, remember, it is made entirely of energy. If we were not made of energy, we could not touch the sandwich or if we were aliens from another planet, we could never touch anything unless we used telekenetic powers.

 

i like how you think ... probably because i think the same way. yep.




Grim, go watch What The Bleep Do We Know, right now, if you haven't yet. it talks about what people here are saying... it's very interesting .

 

yes but what is you touching? what about the dead skin cells on your fingertips are they even you? is a detached head without a body bob, or is bob the detached head and the body

 

bob is an illusion so that bob can exist, who knows exactly where he is? bob is boundless but imagine he has boundaries, but he's not very good at specifying where they begin and end...

 

So...all of this new information causes me to wonder one thing.....
*Am I really ever touching myself?*

SERIOUSLY!

 

What The Bleep Do We Know......great movie. Supports the "i think therefore i am" theory, and really dives into to the beginning parts of quantum physics. Watch this movie completely sober and then get very high and think about it. I've even tried the if I believe it then it's real idea when trying to beat traffic or get green lights and it's worked. Also everytime I call my dealer I believe he'll have what I need and he always happens to have just enough. I really believe this movie is the essence of mind fucks.

 

Hey Crummy--wait 'till the wielder of that 2/4 closes the distance by half---whack!Half again--whack!--half again--whack!on and on and on and on--could get tiresome.

 

I thought of this theory when i was a child.

another thought i had when i was a child was -
"if you outrun light, you will beat it to its destination, thus travelling backwards in time."

 

Holy shit I started this thread like 4 years ago and it's still running.

 

What do you think Grim? Still believe its impossible to ever actually touch anything?

I dont buy it myself, I dont have any calculus classes to refer to but when a knife cuts my skin and I feel pain, something has actually touched something else.

 

What we call "touching" is merely the sensation of pressure registered in the nerve cells which is the result of atomic forces interacting. There is never such a thing as CONTACT between the atomic particles involved. It is merely a sensation interpreted by the brain as "touching".

Basically, you cannot, by any human or superhuman effort, "force" two atomic particles to "touch" each other, short of using an "atomic collider", which isn't accessible to the average peeps.

The 2x4 actually causes damage because of the atomic forces, not because they "touched", but because in coming into proximity, they fomented a change in the shape of the molecular structure of your punkin' head.

The reason there is a "bump", swelling into a convex shape rather than a concave, is that the blood is rushing to the area that has been damaged, and is causing a swelling. Here I'm at the end of my extensive store of knowlege, and you must seek help elsewhere. Someone?

Bes' I could do on short notice, boss.

 

^^^^^^
What he said.

 

I'm guessing that the sharpest a knife edge can be is dependent on the size of the atoms or molecules that the metal or ceramic edge is made up of. You can only get an edge as small as a single atom, I would imagine.

Applications where such sharp edges are required are, for instance, in microtomes, which are devices used to cut ultra-thin slices of tissue for microscopic analysis.

The finer the edge, the sooner it will dull.

 

Below, for starters, is a copy-paste from wikipedia link at http://en.wikipedia.org/wiki/Zeno_paradox



In general , as one can observe, a lot of confusion arises from inability to digest seemingly contradicting statements or arguments, thus creating an illusion of paradox which in fact is nothing else but the failure of Mind to comprehend things beyond its' immediate grasp.

I will give you another (not related to Zeno's Paradox) example, that also contributes to much confusion in peoples' minds.

For instance much has been said about a tree falling in the forest and no one being near to hear it. The well known question goes along the lines of asking wether the tree really fell and was there any sound if no one was there to see and hear it?

Complete misunderstanding of what this example and question implies divides most people into two foolish and passionatly arguing with each other groups, whereby some claim that there absolutely IS the "tree and the sound" it makes falling, regardless of anyone being there to see or hear it; with others claiming with equal passion that there IS NOTHING AT ALL, neither the tree, nor the sound , nor any occurence or presence of any physical existence in space-time , nothing whatsoever, as long as there was noone to see and hear it.

Both claims, taken to extreme and near fanatically defended, are equally wrong and the product of shallow minds, of which btw enormous majority of human beings are in possession of.

The truth is simpler and more complex at the same time , thus it successfully evades the senses of those who , for the sake of fun and artistic expression, would best be caricatured as gorillas trying to contemplte the basics of geometry.

And here is what the "falling tree in the forest" implies :

1. It is true that the so called "reality" ,as we know it, is the product of our senses and perception.
So, if you nor anyone else was present at the event then most definitely there was no perception of it.


Even if you were present in there (and for the arguments' sake: with all of your senses), but was the size of the atom within that tree, would you either see or hear anything? It's a rhetorical question, since what you define, perceive and call a "Tree" (as a regular sized human being walking on the surface of the planet Earth) would appear to you (if appeared at all) to be as huge as Milky Way galaxy and the whole picture of a "tree" (to associate it with) would simply be out of your frame of reference. And no need to mention the sound effects in the context.

Thus we arrive to our first observation , which is:
the definition of objects or things, as well as whole of human perception, is purely mental process and nothing but the mental process, with things in themselves lacking both a definition and relation to each other in absence of subjective frame of reference which we call perception.
Much like the chaotic little dots on a piece of paper that turn out to be a photo image of something entirely different, as soon as you remove yourself to a distance where you can see the whole image so you can associate it with already stored in your memory and aquired through experience images, thoughts, concepts and pictures.

However, not the second to mention and equally important to note is the fact that neither the entire space-time nor any elements comprising it disappear and cease their existence simply if there is a lack of perception.
If it were true, then there would be no Universe in existence for billions of years before any conscious creature we know of was there to perceive it (that would preclude the very same conscious beings from coming into existence in the first place).

Things cease to "exist" as perceived in our minds, but who said our minds and perception are the ultimate arbiter and maker of existence per se, in absence of which whole existence would cease to be?



A deeper understanding is miuch like a point in 3D space, sometimes a point that is beyond the reach of your senses.

Think of a point somewhere in the middle of any spherical, hard and impenetrable by light object. All you see ,looking at such object with bare eyes, is the surface of it.
However, given two separate angles/directions from any 2 points on the surface of the object, you can visualize the imaginary point were the two lines would cross.
Kind of hazy and still our of reach for your vision, isn't it?
But that's where the point is, whether you can or can not see it clearly.




________________________________________________________


The arrow paradox
“ If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. ”
—Aristotle, Physics VI:9, 239b5


In the arrow paradox, Zeno states that for motion to be occurring, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher's paradox—a fletcher being a maker of arrows.

Whereas the first two paradoxes presented divide space, this paradox starts by dividing time—and not into segments, but into points.[7]


[edit] Three other paradoxes as given by Aristotle
Paradox of Place:

"… if everything that exists has a place, place too will have a place, and so on ad infinitum."[8]
Paradox of the Grain of Millet:

"… there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially."[9]
The Moving Rows:

"The fourth argument is that concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that between the middle point and the starting-post. This...involves the conclusion that half a given time is equal to double that time."[10]
For an expanded account of Zeno's arguments as presented by Aristotle, see Simplicius' commentary On Aristotle's Physics.


[edit] Proposed solutions
Aristotle remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small.[11] Aristotle solves the paradoxes by distinguishing "things infinite in respect of divisibility" (such as a unit of space that can be mentally divided into ever smaller units while remaining spatially the same) from things (or distances) that are infinite in extension ("with respect to their extremities").[12]

Before 212 BC, Archimedes had developed a method to derive a finite answer for the sum of infinitely many terms that get progressively smaller. (See: Geometric series, 1/4 + 1/16 + 1/64 + 1/256 + · · ·, The Quadrature of the Parabola.) Modern calculus achieves the same result, using more rigorous methods (see convergent series, where the "reciprocals of powers of 2" series, equivalent to the Dichotomy Paradox, is listed as convergent). These methods allow construction of solutions stating that (under suitable conditions), if the distances are decreasing sufficiently rapidly, the travel time is finite (bounded by a fixed upper bound).[13]

Using ordinary mathematics we can calculate both the time and place where Achilles overtakes the tortoise. For example, if Achilles is moving 10 metres/second and the tortoise is moving at 1 metre/second, and if the tortoise has a 100 metre head start, then Achilles will reach the tortoise's starting point in 10 seconds. The tortoise will have moved 10 metres further. Achilles would then run that 10 metres in one second, and the tortoise will have moved one metre further. Zeno argues that every time Achilles reaches the tortoise's last position, the tortoise will have advanced further - but in the next full second Achilles will run another 10 metres, passing the tortoise who will have advanced only one metre. Algebra gives us the distance and time at which Achilles would exactly match the position of the tortoise: 111 1/9 metres after running for 11 1/9 seconds. This is neither an infinite distance, nor an infinite time. While this solves the mathematics of one of the paradoxes, it does not touch the dynamics of any of the three paradoxes - namely, "How is it that motion is possible at all?"

Another proposed solution is to question the assumption inherent in Zeno's paradox, which is that between any two different points in space (or time), there is always another point. If this assumption is challenged, the infinite sequence of events is avoided, and the paradox resolved. Philosophers typically prefer this approach over the mathematics based approaches, since while mathematics can tell us where and when Achilles overtakes the tortoise, it does not explain how these points in space and time can ever be reached. Philosophers claim that the mathematics does not address the central point in Zeno's argument.[14]

Yet another proposed solution, that of Peter Lynds, is to question the assumption that moving objects have exact positions at an instant and that their motion can be meaningfully dissected this way. If this assumption is challenged, motion remains continuous and the paradoxes are avoided.[15] This solution is related to Heisenberg's Uncertainty Principle.

A solution to the arrow paradox is given by Rudy Rucker in Infinity and the Mind: he points out that the motion of the arrow is indeed instantaneously observable due to the small contraction in length the arrow undergoes due to the effects of special relativity.


[edit] Status of the paradoxes today
Mathematicians today[who?] tend to regard the paradoxes as resolved[citation needed], but some philosophers disagree. Bertrand Russell, who was both a mathematician and a philosopher, wrote Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned.[16] The paradoxes certainly pose no practical difficulties.

However, some philosophers insist that the deeper metaphysical questions, as raised by Zeno's paradoxes, are not addressed by the calculus. That is, while calculus tells us where and when Achilles will overtake the Tortoise, philosophers do not see how calculus takes anything away from Zeno's reasoning that there are problems in explaining how motion can happen at all.[17]

Philosophers also point out that Zeno's arguments are often misrepresented in the popular literature. That is, Zeno is often said to have argued that the sum of an infinite number of terms must be infinite itself, which calculus shows to be incorrect. However, Zeno's problem wasn't with any kind of infinite sum, but rather with an infinite process: how can one ever get from A to B, if an infinite number of events can be identified that need to precede the arrival at B? Philosophers claim that calculus does not resolve that question, and hence a solution to Zeno's paradoxes must be found elsewhere.[18]

Physicists point out that in the race, after a few dozen steps, we will have to deal with dimensions where quantum mechanics can’t be disregarded. According to the uncertainty principle those distances are so small that taking a measurement would be pointless, even from a theoretical point of view: uncertainty would be too prominent.[19]

Infinite processes remained theoretically troublesome in mathematics until the early 20th century. L. E. J. Brouwer, a Dutch mathematician and founder of the Intuitionist school, was the most prominent of those who rejected arguments, including proofs, involving infinities.[citation needed] In this he followed Leopold Kronecker, an earlier 19th century mathematician.[citation needed]

However, modern mathematics, with tools such as Kurt Gödel's proof of the logical independence of the axiom of choice and the epsilon-delta version of Weierstrass and Cauchy (or the equivalent and equally rigorous differential/infinitesimal version by Abraham Robinson), argues rigorous formulation of logic and calculus has resolved theoretical problems involving infinite processes, including Zeno's.[20]


[edit] The quantum Zeno effect
In 1977[21], physicists E.C.G. Sudarshan and B. Misra studying quantum mechanics discovered that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. [22] This effect is usually called the quantum Zeno effect as it is strongly reminiscent of (but not fundamentally related to) Zeno's arrow paradox.

This effect was first theorized in 1958.[23]


[edit] Writings about Zeno’s paradoxes
Zeno’s paradoxes have inspired many writers

In the dialogue What the Tortoise Said to Achilles, Lewis Carroll describes what happens at the end of the race. The tortoise discusses with Achilles a simple deductive argument. Achilles fails in demonstrating the argument because the tortoise leads him into an infinite regression.
In Gödel, Escher, Bach by Douglas Hofstadter, the various chapters are separated by dialogues between Achilles and the tortoise, inspired by Lewis Carroll’s works
The Argentinian writer Jorge Luis Borges discusses Zeno’s paradoxes many times in his work, showing their relationship with infinity. Borges also used Zeno’s paradoxes as a metaphor for some situations described by Kafka.
Paul Hornschemeier's most recent graphic novel, The Three Paradoxes, contains a comic version of Zeno presenting his three paradoxes to his fellow philosophers.
Leslie Lamport's Specifiying Systems contains a section (9.4) introducing the character of the Zeno Specifications
Zadie Smith references Zeno's arrow paradox, and, more briefly, Zeno's Achilles and tortoise paradox, at the end of Chapter 17 in her novel White Teeth.
Brian Massumi shoots Zeno's "philosophical arrow" in the opening chapter of Parables for the Virtual: Movement, Affect, Sensation.
Philip K. Dick's short science-fiction story "The Indefatiguable Frog" concerns an experiment to determine whether a frog which continually leaps half the distance to the top of a well will ever be able to get out of the well.

[edit] See also
Zeno machine
Supertask
Thomson's lamp
Balls and vase problem
What the Tortoise Said to Achilles
0.999...
Solvitur ambulando
Incommensurable magnitudes
Quantum Zeno effect



[edit] Footnotes
^ Aristotle's Physics "Physics" by Aristotle translated by R. P. Hardie and R. K. Gaye
^ ([fragment 65], Diogenes Laertius. IX 25ff and VIII 57)
^ Diogenes Laertius, Lives, 9.23 and 9.29.
^ "Math Forum". http://mathforum.org/isaac/problems/zeno1.html.
^ "Zeno's Paradoxes:Archilles and the turtle". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/paradox-zeno/#AchTor.
^ [1]Zeno's Paradoxes Stanford Encyclopedia of Philosophy. Dichotomy
^ [2]Zeno's Paradoxes Stanford Encyclopedia of Philosophy. Arrow
^ Aristotle Physics IV:1, 209a25
^ Aristotle Physics VII:5, 250a20
^ Aristotle Physics VI:9, 239b33
^ Aristotle. Physics 6.9
^ Aristotle. Physics 6.9; 6.2, 233a21-31
^ George B. Thomas, Calculus and Analytic Geometry, Addison Wesley, 1951
^ Kevin Brown, Reflections on Relativity, [3]; Francis Moorcroft, Zeno's Paradox, [4];
^ Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity. Foundations of Physics Letters (Vol. 16, Issue 4, 2003)
^ Bertrand Russell, The Basic Writings of Bertrand Russell, Routledge, 2009, ISBN 9780415472388; p 246.
^ Kevin Brown, Reflections on Relativity, [5]; Francis Moorcroft, Zeno's Paradox, [6]; Alba Papa-Grimaldi, Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition, The Review of Metaphysics, Vol. 50, 1996.
^ Kevin Brown, Reflections on Relativity, [7]; Francis Moorcroft, Zeno's Paradox, [8]; Stanford Encyclopedia of Philosophy, Zeno's Paradox, [9]; Alba Papa-Grimaldi, Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition, The Review of Metaphysics, Vol. 50, 1996.
^ http://www.riflessioni.it/science/achilles-tortoise-paradox.htm
^ Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill Publishing Co.; 3Rev Ed edition (September 1, 1976), ISBN 978-0070856134.
^ Sudarshan, E.C.G.; Misra, B. (1977), "The Zeno’s paradox in quantum theory", Journal of Mathematical Physics 18 (4): 756–763, doi:10.1063/1.523304
^ W.M.Itano; D.J.Heinsen, J.J.Bokkinger, D.J.Wineland (1990). "Quantum Zeno effect". PRA 41: 2295–2300. doi:10.1103/PhysRevA.41.2295. http://www.boulder.nist.gov/timefreq/general/pdf/858.pdf.
^ Khalfin, L.A. (1958), Soviet Phys. JETP 6: 1053

[edit] Further reading
Chan, Wing-Tsit, (1969) A Source Book In Chinese Philosophy. Princeton University Press. ISBN 0691019649
Kirk, G. S., J. E. Raven, M. Schofield (1984) The Presocratic Philosophers: A Critical History with a Selection of Texts, 2nd ed. Cambridge University Press. ISBN 0521274559.
Plato (1926) Plato: Cratylus. Parmenides. Greater Hippias. Lesser Hippias, H. N. Fowler (Translator), Loeb Classical Library. ISBN 0674991850.
Sainsbury, R.M. (2003) Paradoxes, 2nd ed. Cambridge Univ. Press. ISBN 0521483476.

[edit] External links
Wikiquote has a collection of quotations related to: Aristotle
Stanford Encyclopedia of Philosophy: "Zeno's Paradoxes" -- by Nick Huggett.
Brown, Kevin, "Zeno's Paradoxes of Motion," from Reflections on Relativity at MathPages.
Silagadze, Z . K. "Zeno meets modern science,"
BBC article on shortest time measured as of 2004: 10−16 seconds.
Blog "Strange Paths": "Modernity of Zeno's paradoxes."
Platonic Realms: "Zeno's Paradox of the Tortoise and Achilles."
Zeno's Paradox: Achilles and the Tortoise by Jon McLoone, Wolfram Demonstrations Project.
The Dichotomy Paradox a series based solution.
Zeno's paradoxes-wikinfo [10]
Zeno's Paradox from PhilosophyArchive