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 undergrounder
Registered: 11/10/06
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 Scale and the 5th dimension...
#8353706 - 05/02/08 12:52 PM (6 months, 18 days ago) |
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Scale impacts on the way things work in a massive way. ex:
- Living things that are large have slow matabolisms and live longer, things that are small have very fast matabolisms and live a lot shorter lives.
- Large things essentially experience time slower then small things.
- Tiny things on a Planck scale level work completely differently to things on a subatomic level which in turn are different again to the Newtonian physical laws of big things.
Now if i exist with my centre at point x,y,z and at time t, and i am fairly large like an elephant, then life for me in every way, including the very nature of how my basic physics works, will be completely different to if i exist with my centre at point x,y,z and at time t but i'm only the size of a Planck scale quark.
Doesn't that mean that scale is like a 5th dimension? I understand 'scale' is just a composite of x,y and z, but there are differences there that can't be explained by length, width and breadth alone.
P.S. I'm not a physicist or a mathematician so go easy on me if this sounds like a stupid idea.
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 RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
   
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DieCommie
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8353833 - 05/02/08 01:24 PM (6 months, 18 days ago) |
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I think you are over emphasizing the 'perception' of time as it scales with the size of an organism, to the actual passage of time.
No matter how your brain perceives time, quickly or slowly, basic physics is not completely different.
Quote:
I understand 'scale' is just a composite of x,y and z, but there are differences there that can't be explained by length, width and breadth alone.
I dont get what you mean. How about an example. What is a difference that can't be explained by length, width and breadth alone?
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Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8353931 - 05/02/08 01:59 PM (6 months, 18 days ago) |
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You're incorrect in your statement about equating an organism's size to it's metabolism and it's lifespan.
Box turtles are quite small and can live well over 100 years. Some species of Parrots can live to 80. Koi can live to be nearly 100 and there have even been goldfish surive to 50.
On the other end of the scale you have whales, most of which live to a maximum of 90 (Bowheads being the major exception which may live longer than even the Galapagos turtles) and the longest recorded life of an elephants is around 90 (some debate on it) but closer 70 on average.
I won't even touch on the main argument.
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Katie Couric, while interviewing a Marine sniper, asked :
'What do you feel when you shoot a Terrorist?'
The Marine shrugged and replied,
'A slight recoil
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Seuss
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8354373 - 05/02/08 04:02 PM (6 months, 18 days ago) |
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> Doesn't that mean that scale is like a 5th dimension?
Nope, scale is simply a modifier, or multiplier, or attribute of a shape.
Think of dimensions as shapes, (called rho) and scales as multipliers (attributes) of the shape (called iota). The vector rho defines a shape while the scaler iota defines the size of rho. You are touching on a very complex bit of mathematics.
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Just another spore in the wind.
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DieCommie
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Re: Scale and the 5th dimension... [Re: Seuss]
#8354594 - 05/02/08 05:04 PM (6 months, 18 days ago) |
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What are you talking about man? Topology?
Ive never used an iota in my life. (A good line to remember maybe  )
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Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
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Seuss
Error: divide byzero
Registered: 04/27/01
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8354868 - 05/02/08 06:14 PM (6 months, 18 days ago) |
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> What are you talking about man? Topology?
Very close. Numerical methods for massively parallel computation; basically a formal method to define problems such that they can be mapped, with formal validation, to various computational topologies. My description above isn't super accurate. Iota is actually an operator in the calculus (based on lambda calculus) and behaves much like the APL iota operator.
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 johnm214
Registered: 05/31/07
Posts: 6,924
Loc: Americas
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8354923 - 05/02/08 06:26 PM (6 months, 18 days ago) |
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I get what you're saying I think.
If you look at various equations and mechanisms for the living being, you'll notice that they don't progress linearly as the scale changes.
As an example I used to shoot down the folks claiming that size is illusary and therefore the universe could be a living organism, with solar systems being atoms composing a cell, take a look at the equations for surface area compared to volume of a sphere.
4/3¶r^3= volume of sphere
4pr^2= surface area of sphere
so you'll see the differential of the sphere volume w/ respect to radius is greater than the differential of the surface area w/ respect to the radius, and this means that the volume increases too fast and eventually diffusion will not be an effective means of transport for the cell. This is why fast growing cells are generally small, and larger cells generally grow slower, i.e. plants
You'll find that as the radius increases that the surface area increases slower than the volume, which means less of the cell is available at any given time to the membranes on the cells "wall". This means metabolite export, protein export, and all sorts of other things are dramatically slowed as the cell increases in size, as most rely on simple difusion to transport the stuff from the cell to the membrane "wall" and thus it will take increasingly longer as the cell grows in size.
This is why you cannot have a cell as we know be the size of a person, the surface area would be way too small compared to the contents, and the cell would starve and be utterly useless to the organism. So in this way size IS real. All things are not relative, there is a difference between a bunch of universe sized cells compared to a bunch of small cells.
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undergrounder
Registered: 11/10/06
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Re: Scale and the 5th dimension... [Re: johnm214]
#8356501 - 05/03/08 01:18 AM (6 months, 18 days ago) |
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Quote:
I dont get what you mean. How about an example. What is a difference that can't be explained by length, width and breadth alone?
I don't pretend to know a thing about quantum mechanics, but for instance the physical laws change between the normal world scale, the subatomic scale and the tiny tiny Planck scale, yes?. If you shrunk me down from my current size to that of a quark, then the world around me would be fundamentally different in every way. The very laws of physics have changed yet all that's happened is my length, breadth and width has become smaller.
Quote:
You're incorrect in your statement about equating an organism's size to it's metabolism and it's lifespan.
Box turtles ... whales ... elephants etc.
I know the experience isn't directly corellated, but comparisons within family groups is more appropriate, for instance an elephant lives a lot longer than a human (before humans discovered medicine etc.) which in turn lives longer than a mouse. Similarly, the metabolisms of each are slower to faster according roughly to scale. The same can be seen in birds, a hummingbird flaps its wings faster, its heart beats faster, it lives faster (and its perception of time may well be much slower) than say an eagle, whose wings and heart beats slower and it lives a lot longer. And a dragonfly lives faster again than a hummingbird. A crocodile lives longer, moves slower than a goanna, lives longer/slower than a skink etc. etc.
But what i think i was meaning is better described by what johnm214 explained in reference to cells and how large animals are slower than small animals and therefore WHY matabolism changes more or less with scale.
but you're right i was getting confused over perception vs. time actually changing, i was confused with how gravitational fields change actual time and therefore things that are necessarily big would exist in a different gravitational field. In a similar example, one human twin who lives in the space station will age faster and experience time slower than his twin who lives at sea level for the same amount of time. For him time IS different, if he kept an accurate watch then when the two twins compare the time after X years, the astronaut's watch will be faster and he will be older. But yeah that's unrelated, and that's where i got confused.
And Seuss's explanation makes sense, especially how the three/four normal dimensions exist relative to eachother, but scale is just a multiplier of the previous dimensions, not its own dimension (if i read that right). And come to think about it if a dimension is meant to measure only a single linear change, scale makes changes on more than one front.
Thanks
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
Edited by undergrounder (05/03/08 08:15 AM)
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Stein
Registered: 07/02/03
Posts: 30,754
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8356688 - 05/03/08 03:29 AM (6 months, 18 days ago) |
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Your question sounds pretty complex you should wait for buddhahoodlum to chime in and make sense of it all for everyone to take awe in.
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 16,763
Loc: Caribbean
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8356744 - 05/03/08 04:31 AM (6 months, 18 days ago) |
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> And come to think about it if a dimension is meant to measure only a single linear change, scale makes changes on more than one front.
Yep. In math, we represent scale as a matrix of numbers with each number in the matrix being the scale of a single dimension. To scale a 3D 'thing' a matrix with three numbers would be used (one number would scale x, one would scale y, and one would scale z).
> Your question sounds pretty complex you should wait for buddhahoodlum to chime
Not at all. The OP has legitimate questions and is trying to learn. I don't care what level of education a person has, if they are trying to learn, they have my respect.
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Just another spore in the wind.
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DieCommie
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Re: Scale and the 5th dimension... [Re: Stein]
#8357266 - 05/03/08 11:06 AM (6 months, 17 days ago) |
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Quote:
Stein said:
Your question sounds pretty complex you should wait for buddhahoodlum to chime in and make sense of it all for everyone to take awe in.
Its all clear is you just watch youtube dude!!
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Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
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DieCommie
Ally
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8357409 - 05/03/08 11:45 AM (6 months, 17 days ago) |
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Quote:
I don't pretend to know a thing about quantum mechanics, but for instance the physical laws change between the normal world scale, the subatomic scale and the tiny tiny Planck scale, yes?. If you shrunk me down from my current size to that of a quark, then the world around me would be fundamentally different in every way. The very laws of physics have changed yet all that's happened is my length, breadth and width has become smaller.
Most physicist dont believe the laws of physics change depending on the distance scale you are at. The effects of quantum physics are apparent at human scales, for example blackbody phenomenon. In fact, quantum physics was first invented to explain the blackbody curve!
However, there is the disconnect between quantum and relativity in physics. A disconnect between the very large and the very small. The physical and mathematical models we invent to describe events on these two scales are fundamentally different and dont really mesh. This is where the famous "theory of everything" comes in. Physicists amd mathematicians are working on a theory that will unify these two fields into one theory, because at their heart physicists are reductionists. That is they believe that all physical phenomena can be explained by reducing down to the basic constituents.
Also of interest is emergent properties. Now an emergent property occurs not on a scale from small to big, but on a scale from simple to complex. There are properties that 'emerge' out of complex systems that, at the moment, cannot be explained by the basic constituents. The most glaring example of this is consciousness, which emerges out of an ensemble of many, many particles - yet cannot be explained or predicted using particle physics. To the reductionist this is simply a shortcoming of our ability to apply particle physics to highly complex systems.
In then end, we just dont know if there can be one set of laws that governs the large and the small as well as the simple and the complex. It seems like there should be. It doesnt make logical sense that the rules nature plays by change at different lengths and complexities. But, on the other hand, its foolish to think that nature conforms to our intuition and our logic. Nature has twisted our intuition and logic before (relativity and quantum), it may do so again and we may find that size and complexity determine which rules nature plays by.
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Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
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undergrounder
Registered: 11/10/06
Posts: 1,271
Loc: NSW
Last seen: 4 hours, 17 minutes
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8360347 - 05/04/08 03:45 AM (6 months, 17 days ago) |
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OK so the physics stays the same, but the laws we use to describe it changes, yes? I think i'll leave the QM talk there, don't want to get too deep.
Thanks again
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RIP
Bigger and bolder and rougher and tougher in other words sucka there is no other...
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: undergrounder]
#8364568 - 05/05/08 10:48 AM (6 months, 15 days ago) |
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In a similar example, one human twin who lives in the space station will age faster and experience time slower than his twin who lives at sea level for the same amount of time. For him time IS different, if he kept an accurate watch then when the two twins compare the time after X years, the astronaut's watch will be faster and he will be older. But yeah that's unrelated, and that's where i got confused.
Wouldn't it be the opposite? The astronaut would would age less because of the speed he was traveling at was closer to that of light.
--------------------
Katie Couric, while interviewing a Marine sniper, asked :
'What do you feel when you shoot a Terrorist?'
The Marine shrugged and replied,
'A slight recoil
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deimya
tofu with monocle
Registered: 08/26/04
Posts: 529
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Re: Scale and the 5th dimension... [Re: HagbardCeline]
#8365136 - 05/05/08 01:57 PM (6 months, 15 days ago) |
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To blatantly quote wiki's article on the Twin paradox
Quote:
In physics, the twin paradox is a thought experiment in special relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find he or she has aged less than an identical twin who stayed on Earth. This result appears puzzling, since the situation seems symmetrical, as the latter twin can be considered to have done the travelling with respect to the former. Hence it is called a "paradox". In fact, there is no contradiction and the apparent paradox is explained within the framework of relativity theory, and has been verified experimentally using precise measurements of clocks flown in airplanes.
What lifts the paradox is that the situation is not symmetrical since the space traveling twin is the only one to experience the force needed to make the spaceship do a U-turn back to Earth. Forces implies accelerations and special relativity is not valid when taking accelerated frames of reference into account. General relativity is needed to make sense of this result.
The other funny and unintuitive thing, this time simply in the framework of special relativity, is that before and after making this U-turn, that is when no force are in play but only a relative constant speed between them, both twins see each others' pace as slowed down. Indeed there is no absolute frame of reference so they both are in the same situation relative to the other.
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deimya
tofu with monocle
Registered: 08/26/04
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Re: Scale and the 5th dimension... [Re: deimya]
#8365194 - 05/05/08 02:19 PM (6 months, 15 days ago) |
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Concerning OP's topic, scale is indeed something important with a very real effect when looking at interacting systems. In physics, the importance of scale and the way behaviors change from one to the other is understood in the context of the renormalization group theory, which has also found numerous applications in other fields like sociology, biology, urban development, etc.
The basic intuition of the renormalization group, or simply renormalization for short, is that whenever you are measuring or observing something, you are doing so with a certain "ruler", that is at a certain scale, and thus all effects taking place at much smaller scale might affect the outcome of your measurement without you knowing so. Said otherwise, what you measure at a certain scale gets additional contributions from the average of things going on at a scale you have no access of given the size of your "ruler". In physics, the formalization of this intuition, renormalization, is carried out by integrating (or tracing out, or averaging) over fast acting degrees of freedom, and so degrees of freedom measured at a certain scale get corrected by this averaging.
This process enables one to -partially- understand how the physics at small scale influence, or give rise to the physics at large scale. The interesting thing is that it is possible to show that different small scale physics, different microscopic descriptions can give rise to the very same large scale physics. In the jargon this effect is called universality. That is whether your building blocks for your model are atoms, quantum chocolate fudge, straws or legos, each with their how description and interactions, it is very possible to recover the same macroscopic physics and behaviors between two or all of these models if they fall in the same universality class.
This is still an active area of research in condensed matter physics and high energy physics and the implications and technicalities have not all been worked out yet.
So, yeah, scale has a very real effect.
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maggotz
Registered: 06/24/06
Posts: 5,904
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Re: Scale and the 5th dimension... [Re: deimya]
#8366119 - 05/05/08 07:06 PM (6 months, 15 days ago) |
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Quote:
The other funny and unintuitive thing, this time simply in the framework of special relativity, is that before and after making this U-turn, that is when no force are in play but only a relative constant speed between them, both twins see each others' pace as slowed down. Indeed there is no absolute frame of reference so they both are in the same situation relative to the other.
could you explain this a bit more?
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DieCommie
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Re: Scale and the 5th dimension... [Re: maggotz]
#8366664 - 05/05/08 09:20 PM (6 months, 15 days ago) |
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Its the twin paradox. Each twin is older than the other, which cant happen.
Form the traveling twin's point of view, the earth is moving away at high speeds and the earth's inhabitants are also moving away at high speeds. So, from the astronaut twin's point of view the time on the earth has slowed down. So the astronaut twin calculates that he is older.
From the stay at home twin's point of view, the space ship is moving away at high speeds and the the space ship's inhabitants are also moving away at high speeds. So, from the stay at home twin's point of view the time on the space ship has slowed down. So the stay at home twin calculates that he is older.
They are each older than the other - paradox. The situation is symmetric, each calculates the same thing.
However, the situation is not truly symmetric because in order to accelerate up to high speeds, force is required. So the space ship has to have a force applied to it and the earth does not (or maybe vise versa in some crazy way).
Maybe that clears it up for you a bit. Hopefully he will chime in with a good explanation.
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Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
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deimya
tofu with monocle
Registered: 08/26/04
Posts: 529
Loc: ausländer.ch
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Re: Scale and the 5th dimension... [Re: DieCommie]
#8367802 - 05/06/08 03:31 AM (6 months, 15 days ago) |
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I think your explanation is clearer. But yeah, the symmetry of the situation is broken by four stages of acceleration: initial acceleration from rest to cruise speed, deceleration from cruise speed to a stop, then acceleration back to cruise speed in the opposite direction and final deceleration from cruise speed to rest. The other twin on Earth feels none of these forces, thus the asymmetry of the problem.
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HagbardCeline
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Re: Scale and the 5th dimension... [Re: deimya]
#8367931 - 05/06/08 06:17 AM (6 months, 15 days ago) |
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Just so I'm clear, the astronaut will have aged less though, correct?
--------------------
Katie Couric, while interviewing a Marine sniper, asked :
'What do you feel when you shoot a Terrorist?'
The Marine shrugged and replied,
'A slight recoil
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