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Digitisation interpolation and information

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« Reply #15 on: September 23, 2009, 22:13:19 PM »

That's not what I was aiming at but now that you mention it, I can think of many cases in which this is unquestionably the case... Grin
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« Reply #16 on: September 23, 2009, 22:42:52 PM »

LOL  Grin

But seriously, have I managed to convince you that analogue systems contain far more complexity than any digital system can simulate with complete accuracy?
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« Reply #17 on: September 30, 2009, 21:03:08 PM »

But seriously, have I managed to convince you that analogue systems contain far more complexity than any digital system can simulate with complete accuracy?
Eh? Have you followed what has been said? About the limits of measurement, simulation and digitization? Your question suggests otherwise.
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« Reply #18 on: October 01, 2009, 18:10:50 PM »

I thought I did.  Huh?

Could you perhaps point out the flaw in my reasoning at the link below?

http://forum.skeptic.za.org/science-and-technology/digitisation-interpolation-and-information/msg5795/#msg5795
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« Reply #19 on: October 13, 2009, 08:51:58 AM »

Will get back to this soon. I feel like the March Hare. Wink
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« Reply #20 on: October 13, 2009, 10:20:12 AM »

Please do! Don't worry, I get that a lot.  Grin
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« Reply #21 on: October 14, 2009, 20:31:00 PM »

Apologies for the delayed reply. A busy schedule and this forum being frustratingly unreachable worked in tandem.

Well I suppose you could call it meaning, but not in the usual sense of the word. I'm talking more about the source of the information. Empirical measurement verses theoretical extrapolation.
Mefi's point stands: the "new" info is what you started with plus the applied algorithm. And it's still info no matter how it's represented or how it arose. Given the total info alone how are you going to separate it into subclasses of origin?

Or, perhaps more often, by the original source of the the information?
Info is info no matter where it came from. Sure, we look at the nature of its source to get some idea about its meaning. But meaning isn't info or vice versa.

Agreed, the original information is essentially all we have to work with.
No, you're forgetting the info inherent in the particular algorithm. The algorithm itself is info.

Yes, let's stick with strict interpolation where "the function must go exactly through the data points"
Not a necessary requirement, but okay if you want to take such a limited view of "interpolation".

Analogue [info] is essentially empirical in nature whilst digital is theoretical and predictive.
Where'd you get that!? An electronic analog to e.g. plastic deformation still needs to be measured, scaled and interpreted. Ditto a digital model, and why should analog info not be predictive? Just because digital info is idealized doesn't make it inferior.

Here is an example...
So you think that reaching the limits of the measurable means there must be more info? First, prove it. Second, completely eliminate any possibility that measurement itself is generating the info. Third, whatever the limit of measurement might be, I can add an algorithm that will increase the info content.

Agreed, for storage and transmission of information, digital rules.
Also for quantifying and for extracting new, more useful info and abstract info. There are reasons beyond storage and transmission that digital is king. Processing is one of them. Abstraction is another. Experimental maths wouldn't be possible anywhere near to the degree it is without digital.
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« Reply #22 on: October 14, 2009, 21:30:37 PM »

So you think that reaching the limits of the measurable means there must be more info?

Yes, considering as we take increasingly more accurate measurements we get more information each time, it seems likely that if we could make even more accurate measurements we would get even more information.


First, prove it.


Not sure if this can be done empirically, but the way waves behave suggests the information must be there even if we can't see it. Interpolation is a way of estimating what that info would have been if we could.


 Second, completely eliminate any possibility that measurement itself is generating the info.


That's where QM gets involved again I suppose. I do realise that taking a measurement effects the result, but until you do, the info exists there in it's own system, surely?

This seems remarkably like the old tree falling in the woods and no one hearing it. I think it does still make a sound, and that sound contains information, whether there is anyone there to hear it or not.


Third, whatever the limit of measurement might be, I can add an algorithm that will increase the info content.

I don't doubt it, but all you will get is more points on a graph. It will never result in an uninterrupted probabilistic curve.
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« Reply #23 on: October 31, 2009, 16:47:00 PM »

Yes, considering as we take increasingly more accurate measurements we get more information each time, it seems likely that if we could make even more accurate measurements we would get even more information.
There are limits on the accuracy of measurement. If it can't be measured you can only call it "information" on the understanding that it's actually useless noise. Noise is info too in Shannon's sense.

Not sure if this can be done empirically, but the way waves behave suggests the information must be there even if we can't see it. Interpolation is a way of estimating what that info would have been if we could.
Your view of info is still naive. Once again, interpolation can go far beyond just "guessing" and the "guess" adds info. It looks like you're assuming that spacetime is infinitely divisible and that each subunit can "contain" a non-zero amount of info no matter how finely spacetime is divided. That's not true. Read up on Planck time and Planck distance. It also looks like you're confusing "information" with "accuracy". Greater accuracy or precision need not equal more info. The sentence "This bag contains exactly 24 apples" yields less info than saying "This bag contains between 20 and 30 apples". And even if it were practically possible to measure with 100% accuracy you can still discretize at a finer granularity, adding more info to a digital rendition.

That's where QM gets involved again I suppose. I do realise that taking a measurement effects the result, but until you do, the info exists there in it's own system, surely?
But it doesn't have to be because of QM limits. E.g., the outcome of a temperature measurement of some water will depend in part on details of the technique like the pre-measurement temperature of the thermometer or thermocouple. We can correct for this by a certain calculation but doing that adds info (and accuracy) because knowledge of the physics involved is itself info. We like to think of many things in nature as exactly determined because it makes things fall in line with everyday experience. Science has shattered that way of thinking several times.

This seems remarkably like the old tree falling in the woods and no one hearing it. I think it does still make a sound, and that sound contains information, whether there is anyone there to hear it or not.
How so? The tree still making a sound even if no one ever hears it is an apparently reasonable inference based on the assumption of continuity. However we know matter and energy come in discrete packets. To infer on that basis that there's greater info content in analog systems than in digital representations thereof is hardly defensible.

I don't doubt it, but all you will get is more points on a graph. It will never result in an uninterrupted probabilistic curve.
What is a "probabilistic curve"? I assume you mean "probability density curve" that captures the distribution of "exact" (!) sample values in a digital rendition. Even if what you say was true (which it isn't - it depends on the mathematical treatment used), you don't know that an analog system will do the same. Mathematical models are also idealized and the smooth continuity of real numbers doesn't mean that the world must also be like that. In fact chances are good that it's not.
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