Again. The universe is just one vastly large set of mathematically describable interactions. How the subsets of mathematical interactions are are parsed into disciplines doesn't change that.
Abstractions are just a set of artificial assumptions about the actual interactions which may or may not be correct. As long as your assumptions are correct for the scale you are examining, your described outcomes will be correct as well. All physical sciences are engaged in discovering ever more correct abstractions (assumptions). The fact we don't know them all doesn't mean something at a less granular level doesn't actually happen - like objects touching.
Everything else is obfuscating bullshit hiding reality behind a layer of insider lingo. Go ahead an believe otherwise if you want but that won't change the fact that things actually touch.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
Edit: You don't discover assumptions. Science is actually founded on the principle of minimizing the number of assumptions needed to understand a system. In fact, the exact opposite of what you argue...
This is kind of where this is going, but I've always kind of assumed that "objects" don't really "touch" at all, and that to assume that they did was to presume the "thingness" of the object itself.
I should also say that it is a semantic point with regard to objects touching...Is your cut off at the 70% orbital overlap level or the 50%?
Precisely why I brought in the point of not having to go into quarks and string theory and all that, and brought up orbital probabilities*. What is touching? What is empty space?
I say (I assume, define personally) that things touch because there is evidence of electron repulsion. I touch my mouse because I feel a force between the mouse surface and my hand surface brought about by repulsion of the two molecular electrons. I define/ assume touching as the feeling of repulsive forces.
%Of orbital overlap of quantum electron probalities of molecules is beyond our ability to measure at this stage, right?
*I forgot electron orbitals that we know about come about from starting with the Hydrogen atom. At this stage we still can't work out electron probability 3d-space for molecules? Wow... lots of work still to be done.
This is kind of where this is going, but I've always kind of assumed that "objects" don't really "touch" at all, and that to assume that they did was to presume the "thingness" of the object itself.
Currently in our science the "thingness" of the object is assumed/ proven by the process of observation - ie, there is someway to prove that it is actually there. Eg. the pattern observable when atoms are smashed together, you can then "prove" that subatomic particles such as bosons and mesons and those kind of particles exist.
It "started" at a Newtonian level, we know the moon is a "thing" that exists because we can observe it, and also we can observe the effect of forces exterted on/ exerted by the "thing". In this case gravitational forces and light reflection is proof of the "thingness" of the moon.
About objects touching, that goes back to semantics as hardeeharhar says of how you define touching -- electron orbital probabilities, string theory, and again, how to define empty space....
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
This is great that you have mentioned this. Math for Math's sake does exist as a field of study in and of itself.
Using Maths for physics problems is Applied Math, but there is Math just for Math -- something I feel is so abstract, but I suppose I'm glad people do it because eventually with all those theorems and stuff it can be Applied to useful problems in the "real world".
Yes -- a "real mathematician" doing advanced Masters and phDs and post-doctoral work in Maths researches all sorts of stuff, especially the super weird crap of trying prove theorems that have not been proven yet. Theorems and proofs and all that jazz. Mindf*ck stuff if you're not in that field.
Just look at this from our Apple cheerleaders Wolfram Research:
Eg. Fermat's Theorem in this case. On the page there is no application to the "real world" although Applied Mathematicians have probably used it in various areas. There are links to other stuff there that's "pure mathematics"
Let's not make the mistake of implying that the instrumental imprecision of defining the smallest possible unit of space time to be used in defining the boundary between objects has anything to do with transcendental numbers, except insofar transcendental numbers might be used to describe some aspect of such a unit. The infinitude of irrationals and such is of a very different order of epistemology than the "fuzziness" of the world at very small scales, which in fact the point of "paradox" in the original post.
I agree to the extent of what I understand. CosmoNut is trying to ask what he is "missing". He has not defined a "proffessional" Paradox like the kinds the "scientific community" is dealing with.
CosmoNut, IMHO, this is what you are "missing"
1. You propose a situation whereby two objects are moving towards each other, each time moving half the distance between them. Yes, at some point in time, the space between them will become sooooo small that essentially Newtonian physics is no longer relevant, we get into the Quantum physics realm and all the "weirdness" associated with it - which we have tried to describe above. This small distance is not as small as you think, we can think in terms of one Angstrom. Ten billion angstroms equal 1 meter. So AFAIK there is no specific definition where Quantum physics take over but certainly once you hit 1 Angstrom and less Quantum mechanics and the weirdness of atomic- and subatomic-particle interactions start to apply. At this stage the "Newtonian-style view" of an electron orbiting the nucleus like the earth around the sun is total rubbish.
2. You made a huge jump in tying together the maths side of things and the physics side of things. You started with saying, let's assume 0.000000000000....000001 approximates to essentially zero. Then you JUMP to the conclusion of these numbers relating to a scale of space between two objects. Then you jump again to the conclusion that "I approximate 0.0000000.....0000001 to zero therefore the real-world space between two objects at that level must also be zero". So like it has been said before, currently in our understanding there is a Physics "real world" situation and we use Applied Maths to tackle the issue. Going the other way round does not make sense in this case because you are taking an abstracted Mathematical idea and then "dumping" it onto the real world. The title of this thread itself is problematic because the way you defined it -- taking an abstracted mathematical situation and then "duct-taping" it onto a physical situation.
3. "Decimals can't be infinite" ... Who says so? If we just look at the Mathematical implications of that, again this is the third issue of what you are "missing". Why is 1+1 = 2? Only because by convention. Mathematicians do all sorts of weird stuff in the "pure maths" area. For example, depending on what they are trying to do and the conventions of the field they are working with, they can say Decimals are infinite or decimals are not, they can say all sorts of things, depending on the problem they are working on. Just take Pi - we think of it as 22/7 and it just goes on forever. But actually 22/7 is GREATER than Pi.
I would assume then from this that those programs that use computers to derive all the values of pie, do not just take 22 and divide it by 7. They use other formulas to work out the millions of digits or whatever. Stupid irrational numbers, so irrational
Disclaimer: Again, as is my understanding at this point in time and I can't believe my brain is still handling at least 10% of this mindf*ck stuff.
"The dichotomy paradox leads to the following mathematical joke. A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t==10, d/4 at t==20, d/8 at t==30, and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes."
I've taken the engineer-style approach in my statement no.1 above. At the end of the day it comes down to our individual/ fields-of-study approaches, assumptions, perceptions and observations of distance and time.
Extra Credit: Two objects are 1 metre apart. They move towards each other, by one quarter the distance separating them every one second (i.e., if they are distance d apart at time 0, they are d/2 at t==1, d/4 at t==2, d/8 at t==3, and so on.) Given d = 1 metre At what time t will the distance between the two objects be 1 Angstrom (d/10billion)?
Which of you 1337 pe0pl3s can answer this (my head would burn up in an instant the second I tried to solve this). I suspect this is an easy question though for Maths peoples. I also suspect the answer is *not* 10 billion seconds.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
Duh!!!
Will you quit trying to conjure up bogus points to argue against? Then state them as if I am daft because I must believe them? They are completely your own!!!
I say all reality is describable by math, even though we don't know how to do all those descriptions yet. Which has no direct conflict with your Not all math is applicable to "reality.". That's like saying, right after someone points out all squares are rectangles, -- Not all rectangles are squares!!! OMG this is so wrong!!! -- You might as well claim the price of kumquats in Jakarta disproves my point!
I couldn't give a rats ass about pure mathematics for the sake of pure mathematics (or the price of kumquats in Jakarta), this thread happens to be about applied math and a seeming paradox that really isn't a paradox at all.
Quote:
Edit: You don't discover assumptions. Science is actually founded on the principle of minimizing the number of assumptions needed to understand a system. In fact, the exact opposite of what you argue...
Semantics. Assumptions in an equation, known "factors" in an equation, both are exactly the same thing because in physical reality we don't ever actually "KNOW" everything about everything. The terminology all just depends on which technical philosopher you most recently happen to agree with.
The entire scientific method hinges on testing the hypothesis to enough technocrats satisfaction that we then collectively "bless" the latest "discovery" of something that has been there all along. We treat the blessed idea as a "fact" for lack of anything better and employ it as an "assumption" in just about every use except when we describe it directly, then we label it as a "theory" in the finest print possible and get on with making the next "discovery" that we can use as an assumption in the NEXT "discovery"! See that last sentence? Whatever we "discover" today is just one of our assumptions in what we are trying to "discover" tomorrow.
Anyone who argues with that hasn't been reading or publishing enough lately!
Extra Credit: Two objects are 1 metre apart. They move towards each other, by one quarter the distance separating them every one second (i.e., if they are distance d apart at time 0, they are d/2 at t==1, d/4 at t==2, d/8 at t==3, and so on.) Given d = 1 metre At what time t will the distance between the two objects be 1 Angstrom (d/10billion)?
Which of you 1337 pe0pl3s can answer this (my head would burn up in an instant the second I tried to solve this). I suspect this is an easy question though for Maths peoples. I also suspect the answer is *not* 10 billion seconds.
Between the 33rd and 34th seconds the transition will occur. When in between is entirely dependent on the acceleration characteristics applied to the objects between the sample points. Figuring the remaining distances at the whole seconds is just binary vs base 10 math: 2^(-n) <= 10^(-10) solve for n. 10 seconds and a spreadsheet do that quite effectively.
Okay, so what the answer seems to be is that the numerical cannot be tied to the physical in this case. Not only that, but the actual definition of two objects touching is up for debate.
I did learn something new, however: I'd never heard about the 22/7 thing being approximately equal to pi. Interesting.
I should also say that it is a semantic point with regard to objects touching.
Is your cut off at the 70% orbital overlap level or the 50%
My point exactly, put more succinctly.
Quote:
Originally posted by Hiro
I say all reality is describable by math, even though we don't know how to do all those descriptions yet. Which has no direct conflict with your Not all math is applicable to "reality."
This is why I said lots of people have a problem with string theory. The issue is that string theory is primarily a mathematical abstraction and is so complex that just about any observation, whether valid or not, could potentially be explained. (Sort of a deus ex machina, but we're not getting into that here).
Most of the phenomena that string theory propose we're completely unable to measure at this point, which has led many to criticize string theory as untenable. It's mathematical abstraction taken beyond the point of description, into a realm of creation, almost. Every now and then, the mathematical description has to be tempered with reality.
Between the 33rd and 34th seconds the transition will occur. When in between is entirely dependent on the acceleration characteristics applied to the objects between the sample points. Figuring the remaining distances at the whole seconds is just binary vs base 10 math: 2^(-n) <= 10^(-10) solve for n. 10 seconds and a spreadsheet do that quite effectively.
Lets assume acceleration to be constant. Since it is d/2 at 1sec, d/4 at 2sec, d/8 at 3sec, decceleration can be calculated. Extra Credit Part 2: What is the deceleration in metres per second squared?
Cool. Extra credit for Part 1 to you. Yay! But partial extra credit only. Show your working on how you solve for n ..!
I went for a swim earlier and it dawned on me, yeah, just a matter of 2^x = 10billion. Then just incrementally guess x and calculate the result.
Using a spreadsheet and "guessing" x and seeing how close it is to 10billion is kinda cheating though. Did you just do this?
How would you solve for x without using a spreadsheet/ calculator? Show your working on paper (since symbols don't show up properly on these pages), scan it, and post it.
*sigh* after all the sex, drugs and trance music this is the 1% of my brain and knowledge I use to have that is left over to be barely able to process this. Chemistry, electron orbitals, polynomial maths, Newtonian physics, integration and differentiation. I've totally forgotten how to calculate acceleration/deceleration... Phew \
I'm just dumbfounded that a question about Zeno's Paradox went all sub-atomic and shit.
"all sub-atomic and shit" Well, we just came to a pragmatic approach. Two objects start moving at each other, 1/4 of the distance each second. Initial distance between two objects is 1 metre at 0sec. At 1sec, distance 0.5 metres, 2sec, distance is 0.25sec, etc.
Will they ever touch? Well, around 33seconds, the distance between the two objects is about 1 Angstrom, one-ten-billionth of a metre. Quantum mechanics start to come into play then. From 33seconds onwards that's where it gets "all sub-atomic and shit" because the definition of "touching" then comes into play.
Just asking this again because the question was buried in a post above:
Two objects start moving at each other, 1/4 of the distance each second. Initial distance between two objects is 1 metre at 0sec. At 1sec, distance 0.5 metres, 2sec, distance is 0.25sec, etc.
What is the rate of deceleration of each object in metres/(second squared) ?? I Just can't bloody remember how to calculate it.
Comments
Abstractions are just a set of artificial assumptions about the actual interactions which may or may not be correct. As long as your assumptions are correct for the scale you are examining, your described outcomes will be correct as well. All physical sciences are engaged in discovering ever more correct abstractions (assumptions). The fact we don't know them all doesn't mean something at a less granular level doesn't actually happen - like objects touching.
Everything else is obfuscating bullshit hiding reality behind a layer of insider lingo. Go ahead an believe otherwise if you want but that won't change the fact that things actually touch.
Period.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
Edit: You don't discover assumptions. Science is actually founded on the principle of minimizing the number of assumptions needed to understand a system. In fact, the exact opposite of what you argue...
Is your cut off at the 70% orbital overlap level or the 50%?
I should also say that it is a semantic point with regard to objects touching...Is your cut off at the 70% orbital overlap level or the 50%?
Precisely why I brought in the point of not having to go into quarks and string theory and all that, and brought up orbital probabilities*. What is touching? What is empty space?
I say (I assume, define personally) that things touch because there is evidence of electron repulsion. I touch my mouse because I feel a force between the mouse surface and my hand surface brought about by repulsion of the two molecular electrons. I define/ assume touching as the feeling of repulsive forces.
%Of orbital overlap of quantum electron probalities of molecules is beyond our ability to measure at this stage, right?
*I forgot electron orbitals that we know about come about from starting with the Hydrogen atom. At this stage we still can't work out electron probability 3d-space for molecules? Wow... lots of work still to be done.
This is kind of where this is going, but I've always kind of assumed that "objects" don't really "touch" at all, and that to assume that they did was to presume the "thingness" of the object itself.
Currently in our science the "thingness" of the object is assumed/ proven by the process of observation - ie, there is someway to prove that it is actually there. Eg. the pattern observable when atoms are smashed together, you can then "prove" that subatomic particles such as bosons and mesons and those kind of particles exist.
It "started" at a Newtonian level, we know the moon is a "thing" that exists because we can observe it, and also we can observe the effect of forces exterted on/ exerted by the "thing". In this case gravitational forces and light reflection is proof of the "thingness" of the moon.
About objects touching, that goes back to semantics as hardeeharhar says of how you define touching -- electron orbital probabilities, string theory, and again, how to define empty space....
Not all math is applicable to "reality."
Period.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
This is great that you have mentioned this. Math for Math's sake does exist as a field of study in and of itself.
Using Maths for physics problems is Applied Math, but there is Math just for Math -- something I feel is so abstract, but I suppose I'm glad people do it because eventually with all those theorems and stuff it can be Applied to useful problems in the "real world".
Yes -- a "real mathematician" doing advanced Masters and phDs and post-doctoral work in Maths researches all sorts of stuff, especially the super weird crap of trying prove theorems that have not been proven yet. Theorems and proofs and all that jazz. Mindf*ck stuff if you're not in that field.
Just look at this from our Apple cheerleaders Wolfram Research:
http://mathworld.wolfram.com/FermatsLittleTheorem.html
Eg. Fermat's Theorem in this case. On the page there is no application to the "real world" although Applied Mathematicians have probably used it in various areas. There are links to other stuff there that's "pure mathematics"
("SEE ALSO: Binomial Theorem, Carmichael Number, Chinese Hypothesis, Composite Number, Compositeness Test, Euler's Theorem, Fermat's Little Theorem Converse, Fermat Pseudoprime, Modulo Multiplication Group, Pratt Certificate, Primality Test, Prime Number, Pseudoprime, Relatively Prime, Totient Function, Wieferich Prime, Wilson's Theorem, Witness".)
But, they can send a man to the moon and solve hundreds-year-old theorems but why can't they make my feet smell nice
Let's not make the mistake of implying that the instrumental imprecision of defining the smallest possible unit of space time to be used in defining the boundary between objects has anything to do with transcendental numbers, except insofar transcendental numbers might be used to describe some aspect of such a unit. The infinitude of irrationals and such is of a very different order of epistemology than the "fuzziness" of the world at very small scales, which in fact the point of "paradox" in the original post.
I agree to the extent of what I understand. CosmoNut is trying to ask what he is "missing". He has not defined a "proffessional" Paradox like the kinds the "scientific community" is dealing with.
CosmoNut, IMHO, this is what you are "missing"
1. You propose a situation whereby two objects are moving towards each other, each time moving half the distance between them. Yes, at some point in time, the space between them will become sooooo small that essentially Newtonian physics is no longer relevant, we get into the Quantum physics realm and all the "weirdness" associated with it - which we have tried to describe above. This small distance is not as small as you think, we can think in terms of one Angstrom. Ten billion angstroms equal 1 meter. So AFAIK there is no specific definition where Quantum physics take over but certainly once you hit 1 Angstrom and less Quantum mechanics and the weirdness of atomic- and subatomic-particle interactions start to apply. At this stage the "Newtonian-style view" of an electron orbiting the nucleus like the earth around the sun is total rubbish.
2. You made a huge jump in tying together the maths side of things and the physics side of things. You started with saying, let's assume 0.000000000000....000001 approximates to essentially zero. Then you JUMP to the conclusion of these numbers relating to a scale of space between two objects. Then you jump again to the conclusion that "I approximate 0.0000000.....0000001 to zero therefore the real-world space between two objects at that level must also be zero". So like it has been said before, currently in our understanding there is a Physics "real world" situation and we use Applied Maths to tackle the issue. Going the other way round does not make sense in this case because you are taking an abstracted Mathematical idea and then "dumping" it onto the real world. The title of this thread itself is problematic because the way you defined it -- taking an abstracted mathematical situation and then "duct-taping" it onto a physical situation.
3. "Decimals can't be infinite" ... Who says so? If we just look at the Mathematical implications of that, again this is the third issue of what you are "missing". Why is 1+1 = 2? Only because by convention. Mathematicians do all sorts of weird stuff in the "pure maths" area. For example, depending on what they are trying to do and the conventions of the field they are working with, they can say Decimals are infinite or decimals are not, they can say all sorts of things, depending on the problem they are working on. Just take Pi - we think of it as 22/7 and it just goes on forever. But actually 22/7 is GREATER than Pi.
http://en.wikipedia.org/wiki/A_simpl...2/7_exceeds_pi
I would assume then from this that those programs that use computers to derive all the values of pie, do not just take 22 and divide it by 7. They use other formulas to work out the millions of digits or whatever. Stupid irrational numbers, so irrational
Disclaimer: Again, as is my understanding at this point in time and I can't believe my brain is still handling at least 10% of this mindf*ck stuff.
"The dichotomy paradox leads to the following mathematical joke. A mathematician, a physicist and an engineer were asked to answer the following question. A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are then instructed to advance toward each other by one quarter the distance separating them every ten seconds (i.e., if they are distance d apart at time 0, they are d/2 at t==10, d/4 at t==20, d/8 at t==30, and so on.) When do they meet at the center of the dance hall? The mathematician said they would never actually meet because the series is infinite. The physicist said they would meet when time equals infinity. The engineer said that within one minute they would be close enough for all practical purposes."
I've taken the engineer-style approach in my statement no.1 above. At the end of the day it comes down to our individual/ fields-of-study approaches, assumptions, perceptions and observations of distance and time.
Which of you 1337 pe0pl3s can answer this
Originally posted by hardeeharhar
Not all math is applicable to "reality."
Period.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality.
Math doesn't depend upon confirmation in the real world, and that is a testament to its history and proofs.
Continuing to deny this prevents you from understanding the depth of math.
Duh!!!
Will you quit trying to conjure up bogus points to argue against? Then state them as if I am daft because I must believe them? They are completely your own!!!
I say all reality is describable by math, even though we don't know how to do all those descriptions yet. Which has no direct conflict with your Not all math is applicable to "reality.". That's like saying, right after someone points out all squares are rectangles, -- Not all rectangles are squares!!! OMG this is so wrong!!! -- You might as well claim the price of kumquats in Jakarta disproves my point!
I couldn't give a rats ass about pure mathematics for the sake of pure mathematics (or the price of kumquats in Jakarta), this thread happens to be about applied math and a seeming paradox that really isn't a paradox at all.
Edit: You don't discover assumptions. Science is actually founded on the principle of minimizing the number of assumptions needed to understand a system. In fact, the exact opposite of what you argue...
Semantics. Assumptions in an equation, known "factors" in an equation, both are exactly the same thing because in physical reality we don't ever actually "KNOW" everything about everything. The terminology all just depends on which technical philosopher you most recently happen to agree with.
The entire scientific method hinges on testing the hypothesis to enough technocrats satisfaction that we then collectively "bless" the latest "discovery" of something that has been there all along. We treat the blessed idea as a "fact" for lack of anything better and employ it as an "assumption" in just about every use except when we describe it directly, then we label it as a "theory" in the finest print possible and get on with making the next "discovery" that we can use as an assumption in the NEXT "discovery"! See that last sentence? Whatever we "discover" today is just one of our assumptions in what we are trying to "discover" tomorrow.
Anyone who argues with that hasn't been reading or publishing enough lately!
Originally posted by sunilraman
Extra Credit: Two objects are 1 metre apart. They move towards each other, by one quarter the distance separating them every one second (i.e., if they are distance d apart at time 0, they are d/2 at t==1, d/4 at t==2, d/8 at t==3, and so on.) Given d = 1 metre At what time t will the distance between the two objects be 1 Angstrom (d/10billion)?
Which of you 1337 pe0pl3s can answer this
Between the 33rd and 34th seconds the transition will occur. When in between is entirely dependent on the acceleration characteristics applied to the objects between the sample points. Figuring the remaining distances at the whole seconds is just binary vs base 10 math: 2^(-n) <= 10^(-10) solve for n. 10 seconds and a spreadsheet do that quite effectively.
I did learn something new, however: I'd never heard about the 22/7 thing being approximately equal to pi. Interesting.
Originally posted by hardeharhar
I should also say that it is a semantic point with regard to objects touching.
Is your cut off at the 70% orbital overlap level or the 50%
My point exactly, put more succinctly.
Originally posted by Hiro
I say all reality is describable by math, even though we don't know how to do all those descriptions yet. Which has no direct conflict with your Not all math is applicable to "reality."
This is why I said lots of people have a problem with string theory. The issue is that string theory is primarily a mathematical abstraction and is so complex that just about any observation, whether valid or not, could potentially be explained. (Sort of a deus ex machina, but we're not getting into that here).
Most of the phenomena that string theory propose we're completely unable to measure at this point, which has led many to criticize string theory as untenable. It's mathematical abstraction taken beyond the point of description, into a realm of creation, almost. Every now and then, the mathematical description has to be tempered with reality.
Slashdot had an article on this some time ago.
Between the 33rd and 34th seconds the transition will occur. When in between is entirely dependent on the acceleration characteristics applied to the objects between the sample points. Figuring the remaining distances at the whole seconds is just binary vs base 10 math: 2^(-n) <= 10^(-10) solve for n. 10 seconds and a spreadsheet do that quite effectively.
Lets assume acceleration to be constant. Since it is d/2 at 1sec, d/4 at 2sec, d/8 at 3sec, decceleration can be calculated. Extra Credit Part 2: What is the deceleration in metres per second squared?
Cool. Extra credit for Part 1 to you. Yay! But partial extra credit only. Show your working on how you solve for n ..!
I went for a swim earlier and it dawned on me, yeah, just a matter of 2^x = 10billion. Then just incrementally guess x and calculate the result.
Using a spreadsheet and "guessing" x and seeing how close it is to 10billion is kinda cheating though. Did you just do this?
How would you solve for x without using a spreadsheet/ calculator?
NERDS!!!
*sigh* after all the sex, drugs and trance music this is the 1% of my brain and knowledge I use to have that is left over to be barely able to process this. Chemistry, electron orbitals, polynomial maths, Newtonian physics, integration and differentiation. I've totally forgotten how to calculate acceleration/deceleration... Phew
I'm just dumbfounded that a question about Zeno's Paradox went all sub-atomic and shit.
"all sub-atomic and shit"
Will they ever touch? Well, around 33seconds, the distance between the two objects is about 1 Angstrom, one-ten-billionth of a metre. Quantum mechanics start to come into play then. From 33seconds onwards that's where it gets "all sub-atomic and shit" because the definition of "touching" then comes into play.
Two objects start moving at each other, 1/4 of the distance each second. Initial distance between two objects is 1 metre at 0sec. At 1sec, distance 0.5 metres, 2sec, distance is 0.25sec, etc.
What is the rate of deceleration of each object in metres/(second squared) ?? I Just can't bloody remember how to calculate it.