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Analog Does Not Exist


artto

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Nope. Actually what I'm saying is that "analog" (literally) does not exist. One is not a subset of the other or vice versa.

What is your definition of analog?

I guess the analog group at work doesn't exist or basically does nothing because we're supposed to be designing analog circuits...[:P]

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t_P = \sqrt{\frac{\hbar G}{c^5}} \approx <br /> 5.39124(27) \times 10^{-44} \mbox{ s}Super Angry

I think this is Max Planck's description of the "resolution" of matter. Which, in short means, that the universe (and it's matter) is not actually continuous. There is literal "no-thing" between things. One common understanding of analog is that between A and B lie infinite points. I believe Planck is saying no to that idea. This is a kind ofpicky argument I would suppose! Geeked

DING!!!

Mark has for the most part answered this correctly. There is also an "extended" idea that goes along with this.

What it boils down to is that (and I'm paraphrasing here ~ I'll have to find and view the old VHS tape ~ LOL) "as scientists began to realize that matter came in bits, and that components of space too came in bits, we wondered if time also came in bits, sort of like the frames in a moving picture. And if it does, how fast are the "pictures" moving and what is the smallest bit of time they can occupy? And the answer to that is determined by the amount of energy it would take to further split the "resolution of matter" as Mark put it. There simply is not enough energy in the universe to reduce a bit of time (or matter) any further. (or something like that ~ remember I'm paraphrasing from 25 years of memory here).

So, there is (according to this theory) no actual continous "flow" of time as we tend to perceive it. [O] It's all digital baby. Yikes. [*-)]

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So, there is (according to this theory) no actual continous "flow" of time as we tend to perceive it.

You conclude that from a little bit of variable crunching and this definition?

In physics, the Planck time, (tP), is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length.[1] The unit is named after Max Planck, who was the first to propose it.

http://en.wikipedia.org/wiki/Planck_time

I certainly don't.

You can use dimensional analysis to come up with all sorts of other numbers using any number of other universal constants.

Btw, if you want to define analog as continuous time, then any discrete time system can completely exist within the analog construct.

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Believe it or not, one time in the '60s, a friend and I argued about a matter like this most of the night -- on the phone, with much pacing around our respective floors.
All this reminds me a little too much of Zeno (aka Xeno).
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The nature of matter, space, and time notwithstanding, when taken to mean "continuously variable", analog definitely does not exist. One always runs up against the resolution problem when measuring or generating an "analog" signal.

An analogy allows us to compare things which have similarities. This does not mean that something that is analogous to another thing is identical to it.

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So, there is (according to this theory) no actual continous "flow" of time as we tend to perceive it.

You conclude that from a little bit of variable crunching and this definition?

In physics, the Planck time, (tP), is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length.[1] The unit is named after Max Planck, who was the first to propose it.

http://en.wikipedia.org/wiki/Planck_time

I certainly don't.

You can use dimensional analysis to come up with all sorts of other numbers using any number of other universal constants.

Btw, if you want to define analog as continuous time, then any discrete time system can completely exist within the analog construct.

Ummm, you're not quite grasping what I (tried) to explain. This has nothing to do with dimensional analysis per se'. And I'm saying that according to this particular (modern relatively recent) theory, that the time contraint has to do not only with the dimensional aspect but also with energy requirements and available energy resources to reduce particle size any futher (or something like that).

I'll have to dig up the video quote my source a little better. I need to transfer it do DVD anyway.

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The quantization levels for any given system are instrinsicly dependant upon the boundaries of that system...which is to say that intermediate energy levels are attainable by changing the boundaries. This fundamental understanding is extremely important to the entire field of semi-conductor physics, where simple devices like diodes or copper cables wouldn't be able to function otherwise.

To put it another way, in order to say that the world cannot be continuous is to say that you can identify an impossible energy state. The problem is, I'd wager that any system can be manipulated in such a way that any energy state is obtainable. Proving or disproving it analytically would require some assumptions about the universe that we're not able to make, but I think it's kind of missing the point altogether anyway.

Just to beat the 100Hz analogy to death...

Let's say you've got a perfect FFT that provides instantaneous information only about 100Hz. If you look at the signal for only 9ms, then you're not going to see anything on the FFT, but that doesn't mean there isn't some kind of continuous signal present. Right at the 10ms mark the 100Hz signal will appear instantaneously and then continue to exist until the signal is stopped. Does it make sense to then claim nothing existed for the first 9ms, and the entire universe must be discontinuous because of this one example? Obviously I'm cheating because the problem starts off stating that there is something for the first 9ms to point out the inability to observe what is actually happening. But the whole point of the analogy is to ask the question...how do you know there isn't something inbetween? If even for an instantaneously short amount of time?

I believe the Heisenberg Uncertainty Principal answers the question, which basically states that you can't precisely know both the position and the momentum at the same time. If you know the position, then how do you know you're not at an intermediate energy state? Just something to think about...

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RockOnKlipsch ~ sort of ~ picked up on the idea. He at least recogonized the equation and probably knows who Max Plack is. But he took the whole idea in the wrong direction by the question he posed, so I had to answer No.

Actually, the toilet paper example sort of hints at the answer (the "idea"). Wink

So you're saying this equation wipes out the $hit we thought was correct?

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