Human knowledge vs time plot"

Discussion in 'Physics & Math' started by Dinosaur, Jul 3, 2017.

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Your opinion on the above?

Poll closed Aug 2, 2017.
  1. 1

    1 vote(s)
    20.0%
  2. 2

    0 vote(s)
    0.0%
  3. 3

    1 vote(s)
    20.0%
  4. 4

    2 vote(s)
    40.0%
  5. Other

    1 vote(s)
    20.0%
  1. DaveC426913 Valued Senior Member

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    No. I mean your description would not result in the employment of an asymptote in the graph.

    I wasn't describing the line on the graph, I was describing the math used in its creation as per your description.

    What The God said.
     
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  3. QuarkHead Remedial Math Student Valued Senior Member

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    Agreed. To also be pedantic, one would be wise to distinguish between some starting assumptions. I list the 3 that immediately occur to me.....

    1. The natural world (i.e. "Reality") is ultimately comprehensible to the human mind

    2. The natural world is such that the human mind can only hope to ever gain an approximate description of it

    3. There is no way of knowing whether there is such a thing as objective reality - all we can do, as humans, is make measurements and declare that this is the reality as it appears to our limited perceptual abilities.

    Under each assumption, I suspect the answer would be different
     
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  5. Yazata Valued Senior Member

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    There's going to be a problem with identifying distinct items of knowledge so that they can be counted. And different items of knowledge will have different weights. Some items of knowledge are more important than others.

    It's possible to imagine learning trivial things (whether I have any clean socks are in my drawer). And it's possible to imagine biggies like Newton's laws of mechanics. I wouldn't want to weight both of those the same. Newton represented more of an upward spike in the graph.

    Addressing Dinosaur's interesting question, I think that I'd say that a knowledge vs time plot would be a generally upward curve, but on the small scale consisting of a whole succession of abrupt leaps of many different sizes (representing discoveries). There might even be periods where the curve trends downwards, such as dark-ages, where knowledge is lost.

    I don't imagine any asymptotes, since I don't think that knowledge acquisition will ever approach an infinite rate or achieve completion at some distinct point in the future.

    So I'll go with #1 'linear', at least in the sense that it would be linear if you did some curve-smoothing.
     
    Last edited: Jul 10, 2017
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  7. iceaura Valued Senior Member

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    If one can quantify it at all, its growth can be asymptotic
    Well that's the question, isn't it: does the "pace" of knowledge enhancement increase, necessarily, under those terms.

    In other words, is the current state of presumed positive acceleration permanent.

    That is a much different claim than the claim that new knowledge - or even new fields of knowledge - is added every year. It is also more than merely the statement that greater quantities of information are added each year than the year before - both of those are consistent with asymptotic approach.
    I was being even more pedantic and trivial than you assumed - my point merely that an asymptote does not imply an upper bound.
     
  8. Yazata Valued Senior Member

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    We haven't really clarified what is asymptotic to what, but I'm imagining a graph with time as the x axis and amount of knowledge as the y axis.

    So I'm imagining some transcendent future point in time (the Singularity? The Second Coming? The End of Days?) where the graph of the amount of knowledge vs time approaches a vertical line drawn through the x axis at that point in time.

    So the rate at which knowledge is discovered would be approaching infinity and presumably once we pass that point in time, there would be nothing unknown left to know.

    I don't believe it.

    I don't ever anticipate that the rate of discovery will ever approach infinity or that mankind (or our robot offspring) will ever become gods.

    It's more likely in my opinion that we will crash up against some limits to what can be known before everything accelerates madly towards omniscience and divinization. There are obvious problems of space and time, of some places and times always going to be beyond our reach. There may well be limits of human cognition. (Even if future AI might arguably exceed them, they will probably encounter limitations of their own and we humans won't be able to understand their discoveries at any rate.) And there are problems that might just be unanswerable by their very nature - such as 'Why does existence exist in the first place?'

    Once the idea of possible limitations to what can be known by humans is raised, it's possible to imagine a different kind of horizontal asymptote, where knowledge becomes harder and harder to gain, so that increments of learning per unit time grow ever smaller and knowledge asymptotically approaches some maximum amount of knowledge (a horizontal line through the y axis parallel to the x axis. That way the graph would flatten out.

    I don't see that one as very likely either. It might conceivably happen in theoretical physics at some point, when all the fundamental principles are either already known or unknowable by humans, and physics settles into a long senescence clearing up the last few loose ends, trying to imagine applications and making measurements more accurate. Some physicists actually thought that we were there in the late 19th century. (Those last loose-ends undid them.)

    But given the number of stars and planets out there to explore, and the number of questions that potentially can be asked, I don't see a horizontal asymptotic barrier to knowledge ever being a problem for the more exploratory, the more taxonomic, collecting and classifying kinds of science. Exobiology might conceivably become an open-ended treasure chest as might alien history and extraterrestrial psychology. Philosophical problems will always be there and new ones are sure to arise.

    The universe is effectively limitless and the Galactic Survey will always have more work to do. It will likely always be encountering surprising and unexpected things.
     
    Last edited: Jul 10, 2017
  9. DaveC426913 Valued Senior Member

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    Hrm. Then I am confused. Possibly about my aging math skills...

    Oh. Duh. An asymptote means approaching a boundary, but the boundary doesn't have to be horizontal. You could for example, asymptotically approach the line y=x.

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    Duh. Or x=0.
     
  10. DaveC426913 Valued Senior Member

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    True. Although one might not have to account for weight in quantifying it. One might simply count the number of discrete occurrences.
    (The set of pebble-shaped objects on a beach can be tallied without knowing the weight of the boulder-sized ones.)

    But you're still left with what constitutes a discrete unit of knowledge.
     
  11. DaveC426913 Valued Senior Member

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    I think the gist of the OP's question isn't so much the quantifying as the trend.

    My first instinct is to assume some semblance of truth in Lord Kelvin's infamous quote: "There is nothing new to be discovered in physics now, All that remains is more and more precise measurement."

    Once we unify the four forces of nature, we will, essentially, be able to describe the root cause of every action and effect in the universe.

    My second instinct thought, is to not make the same mistake poor Kelvin did.

    Knowledge we don;t know will reveal itself. We will explore strings and branes and stuff we can't even dream of yet.
     
  12. Write4U Valued Senior Member

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    Indeed,
     
  13. John.P Registered Member

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    Knowledge is something that can take several years to discover and learn but it can then be taught in a relative short time compared to the several years of thinking involved by somebody else to create the original notion. People are not really getting smarter over time, it just takes less time to understand the knowledge that is so elegantly explained by the author of the knowledge who has probably spent a near decade understanding the information themselves.
     
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  14. Write4U Valued Senior Member

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    I have very little knowledge or understanding of the the term asymptotic, even after reading the definition, however, since the parabola was used in the equation this may be of interest to more knowledgeable people;

     
  15. DaveC426913 Valued Senior Member

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    Oh my god with the 'Math is the hidden secret' video.

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    I'm going to start insert the word 'math' in random discussions I'm in - maybe starting with the Religion forum - and see if that triggers W4U's "auto-post MitHS video" subroutine.
     
  16. The God Valued Senior Member

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    The OP is talking about a plot between Human Knowledge and time. Let us assume that total known human knowledge is quantifiable, now let us plot the time (year scale) on x-axis and total knowledge on y-axis. The curve will be asymptotic only if growth stops (it will be wild and not the intent of OP to consider asymptote un-parallel to x axis.), so as I said with so much to learn with so many new areas, with improvement in technology, can we foresee a situation in near or far future where the incremental increase in the knowledge becomes zero for a substantial time (for it to make asymptote). No.

    It is quite likely that we may have years of small growth, but growth will never be zero for a long long time to make it look like asymptote.
     
  17. DaveC426913 Valued Senior Member

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    To be clear, it would be asymptotic if growth approaches any steady rate - only one case of which is 0. The graph could asymptotically approach a fixed rate of growth, which would be an asymptote with a positive slope, not horizontal.

    The rightmost diagram is an example of an oblique asymptote:

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    Something such as knowledge could - at least in principle - settle down to a nice, steady growth rate of , say, one published paper per month. (A contrived example, granted. But we should not fix ourselves on a horizontal asymptote without good cause.)
     
    Last edited: Jul 11, 2017
  18. The God Valued Senior Member

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    That's ok, you have defined asymptote which is a simple co-ordinate geometry. I have stated that intent of OP appears to be no growth based asymptote that is parallel to x axis. The biggest problem will be quantifying the knowledge. How many papers are published in one of the Nature journal per year, quantifiable, and more or less constant. This is not asymptotic, this is straight-line. 100 papers a year for number of years become a straight-line, not an asymptote, just being pedao.
     
  19. Write4U Valued Senior Member

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    You would be disappointed, as the concept of religion does not deal with any mathematical function. It is a meta-physical concept and apparently not subject to the mathematical function, such as deterministic causality.

    However, the growth results of religious beliefs can be mathematically quantified.
     
    Last edited: Jul 12, 2017
  20. Write4U Valued Senior Member

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    Well the left most graph (a mathematical representation) would indicate an exponential 0 % growth rate, the center would indicate a exponential 100% growth rate, the right would indicate an exponential growth rate somewhere in between. (see prof. emeritus, Albert Bartlett)

    Perspective!
     
    Last edited: Jul 12, 2017
  21. Counter Registered Senior Member

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    I believe time is a potential. To "have time." I also believe time has not existed forever, but continues to infinity. "For all eternity."
     
  22. river Valued Senior Member

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    Human knowledge has been slowed by the ancient knowledge destroyed .

    By those of before us and those in the 20thcentury and 21first century.
     
  23. Write4U Valued Senior Member

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    What knowledge are you talking about?
     

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