Member 2419
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The great enhancement debate
(M, 31)
Vancouver, US
Immortal since Dec 15, 2009
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    Big numbers and the human mind
    In this day and age, our use of numbers tend to reach certain quantitative values that the human mind can no longer make any sense of. I'd say it's because most of us can't conceive of a model to put exceptionally large numbers into context with. We simply cannot fathom the profound meanings of astronomically large numbers.

    For example, numbers like 1; 2; 14; 20; 50, are all quantities that we encounter quite frequently and therefore we're able to rationalize them with a representative mind model. I've seen 2 dogs side by side, I've seen 20 people in a classroom at once, I've seen 50 jellybeans sitting in a bowl.

    But then we get to numbers like 1,000; 10,000; 20,000. These numbers become increasingly difficult to conceptualize, but we can still grasp the general meaning of such numbers using visual models of large scale things we encounter often in our little realities. I probably couldn't create a clear visual in my head of 10,000 people dispersed across a wide area, some people transcending my subjective field of vision. I can, however, take a well known model, maybe a picture of an aerial view of a sports stadium filled with 10,000 fans, and use that to grasp the meaning of the number 10,000.

    But how about we up the ante a bit. What happens when we try to conceptualize quantities like 1,000,000 or 6,000,000,000? Well, we know that there are 6 billion people on this planet, so you might think that actually, yes, it is possible to conceive of such large numerical values using the human population as your foundational model. But it's not quite that simple. Yes, we have a notion of what 6 billion means based off our knowledge of the human population, but in its true nature the number is so immense that we can't actually grasp the true quantitative significance of that number. Why? Because we haven't a model of 6 billion that's been compressed into something recognizable to the human mind. We can't actually rationalize the immensity of such a number. And that's an immense number indeed!

    Yet, as large as that number seems to be, it's actually relatively small at the cosmic scale. Take for instance the estimation that there are somewhere within the margin of 400 billion stars in our galaxy alone. There are about 100 billion galaxies in the known universe; each comprised of anywhere between hundreds of millions to hundreds of billions of stars. Lastly, take into mind the estimated 70 sextillion stars in the known universe altogether. The human brain is suddenly powerless in generating comprehensible models at such numerical values. While we can hold in our minds the simple notion of 70 sextillion stars, we cannot actually understand what meaning that number holds. Scientific notation also does nothing to broaden this cognitive limit.

    In case you're not familiar with where sextillion lies on the orders of magnitude of numbers, let me show you the suffixes:

    Million: 1,000,000 (10^6)
    Billion: 1,000,000,000 (10^9)
    Trillion: 1,000,000,000,000 (10^12)
    Quadrillion: 1,000,000,000,000,000 (10^15)
    Quintillion: 1.000,000,000,000,000,000 (10^18)
    Sextillion: 1,000,000,000,000,000,000,000 (10^21)

    70 sextillion stars is undoubtedly an incomprehensibly large number.

    Even seeing the raw value of each number set, I still feel a lack of comprehension. Numbers of high orders are literally unfathomable to the human mind until we're able to compress them into something we can visually hold in our minds!

    And this is only the beginning. What about a googolplex? What can we possibly conceive in regards to that? Does this mean that our minds will forever be confined to only understanding numerical values close to our approximate scale of existence within the universe? My own hypothesis concerning this matter suggests the contrary. It's my belief that humans create bigger numbers as a result of our understanding of the state of the universe. Take into consideration the Hunter-Gatherer epoch, where humans only really had to take quantitative note of how many people were in a tribe, or how many animals occupied a hunting area. The scale of numbers needed to survive in an environment was relatively small in those days, compared to today's standards. It seems as though the more secrets humanity unlocks about reality, or the farther we extend our awareness of the universe, the bigger numbers become. I think that the increasing immensity of numbers is reflective of how our brains evolve to comprehend more of the universe. I also think that we have much longer to go in our evolution of intelligence, whether it's via human enhancement or not. Finally, I think that the numbers we perceive as unimaginably large today will be easily conceptualized by future humans who have a deeper understanding of values at astronomical proportions.

    See Large Numbers for further reading.


    Sat, May 29, 2010  Permanent link

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    nagash     Sun, May 30, 2010  Permanent link
    while reading this post, I couldn't keep this quote out of my mind...

    There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.

    Richard Feynman
    US educator & physicist (1918 - 1988)