Where do numbers exist?
- Thread starter episodic
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- Feb 7, 2004
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Seriously, maybe why we can't figure out so much in sciences such as physics problems, chemistry problems, etc where the math just does not match the observation, or when huge variables are missing, maybe the reason we can't make these inferences is that we are bound by our mind forcing us to think in a linear fashion. Even when we think spatially, we tend to order our thinking. Maybe we will never be able to understand our world because our mind is a severe limitation - and numbers in the way we percieve them need a major overhaul.
I read in the papers recently that there is a tribe in the Amazon jungle who have no concept of numbers. They cant even be taught to count.
Hayabusa Rider
Admin Emeritus & Elite Member
- Jan 26, 2000
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Hehe,
Math exists because human minds can grasp it. Numbers are artifacts of peoples minds. Merely a useful fiction.
Math exists because human minds can grasp it. Numbers are artifacts of peoples minds. Merely a useful fiction.
Numbers are an abstract concept, just like "happiness" and "sadness" and "stupid".
Understand this, and you will have the world.
Understand this, and you will have the world.
- Feb 7, 2004
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Yea, I propose that numbers are a construct - just as language is - with the same limitations.
For instance - even with translation - you can never truly understand another language unless you are raised in it. Even expert linguists lack some of the intimations of a native speaker.
So how do we know we all percieve numbers the same way? Numbers like 2 and 3 are easy to compare - but in higher math especially abstract algebra and high level calc and discrete mathematics - how are we certain we all percieve this the same way? Is this the reason that a problem will remain unsolved for centuries - despite all mathematicians having access to similar tools to solve it. . . - then one mathematician will look at it and solve it. . . - does this one mathematician know more? Or does his brain just work differently?
For instance - even with translation - you can never truly understand another language unless you are raised in it. Even expert linguists lack some of the intimations of a native speaker.
So how do we know we all percieve numbers the same way? Numbers like 2 and 3 are easy to compare - but in higher math especially abstract algebra and high level calc and discrete mathematics - how are we certain we all percieve this the same way? Is this the reason that a problem will remain unsolved for centuries - despite all mathematicians having access to similar tools to solve it. . . - then one mathematician will look at it and solve it. . . - does this one mathematician know more? Or does his brain just work differently?
Simple answer : Yes
Long answer: It's in the eye of the beholder. I could say the play was brilliant and you could say it was absolute drivel.
you should definitely read this book.
i'm reading it now and it's utterly fascinating.
it addresses the question you're asking in the first 60 pages.
the author says that the abstract concept of actual numbers didn't come to light for a long time.
for example, no one made the connection between two dogs and two days from now for a real long while.
def go check the book out
i'm reading it now and it's utterly fascinating.
it addresses the question you're asking in the first 60 pages.
the author says that the abstract concept of actual numbers didn't come to light for a long time.
for example, no one made the connection between two dogs and two days from now for a real long while.
def go check the book out
There was a show on PBS (possibly Nova) a few years back which explored the concept of counting in animals other than humans. In one experiment, researchers in a protected park (in Madagascar, IIRC) used wild lemurs as their subjects. The researchers were familiar with the local lemurs and were able to individually identify them at a distance so the experiment was not repeatedly conducted using the same lemurs.
The experiments employed techniques similar to those used with human infants; investigating and measuring stimulus, interest and attention span, and habituation and boredom. Basically, the experiment involved a box with differing numbers of apples (or some other fruit lemurs eat). A researcher put an apple in the box (about the size of a cooler on its side) and allowed a wild lemur to see the contents from a distance. Next, the researcher closed the box cover so the lemur could no longer see the apple, and from behind the box and not seen by the lemur, the researcher added (or removed) another apple. The researcher then reopened the front of the box and observed the lemur's reaction.
Measuring the lemur's attention span to varying stimuli - number of apples in this case - allowed the researchers to correlate the lemur's interest with the varying number of apples in the box. When a lemur was shown an apple, the lemur showed interest (food!) If the researchers closed the box, then reopened it with a single apple again, the lemur's interest declined; nothing had changed. On the other hand, if the researcher replaced the single apple with two apples, the lemur showed increased interest; the lemur recognized the number of apples was different. If shown two apples again, the lemur showed less interest; the number of apples had not changed. This process worked up to three (4?) apples - any larger number of apples did not increase the lemur's interest level. The process also worked in reverse; when going from three apples to two, or two apples to one apple, the lemur showed increased interest as measured by increased attention spans. (Eventually, the lemur would get bored and return to the forest.)
By repeating the experiment with numerous lemurs in the park, the researchers determined that lemurs could differentiate between 1, 2, or 3 apples. Basically, lemurs, or at least this species of lemur, could count to 3!
Without getting too verbose, numbers and numerals are symbolic concepts used by humans. For instance, the numeral "4" is just a bunch of lines and has no direct reference to four objects. However, those who use Arabic numerals obviously understand the relationship. Yet the Chinese or Mayan symbols for four objects would be completely unknown symbols to people who use Arabic numerals (excepting those who can read Chinese or Mayan).
On the other hand, counting is a cognitive trait that some animals, (including humans), do possess.
Chimpanzees, with larger brains than lemurs, can also count. Some researchers claim chimps can do some basic arithmetic as well. Try poking around www.pbs.org for some additional info. Here's a Scientific American Frontiers link about chimp counting. You might also poke around Google or pick up an intro Psychology text for more information.
The experiments employed techniques similar to those used with human infants; investigating and measuring stimulus, interest and attention span, and habituation and boredom. Basically, the experiment involved a box with differing numbers of apples (or some other fruit lemurs eat). A researcher put an apple in the box (about the size of a cooler on its side) and allowed a wild lemur to see the contents from a distance. Next, the researcher closed the box cover so the lemur could no longer see the apple, and from behind the box and not seen by the lemur, the researcher added (or removed) another apple. The researcher then reopened the front of the box and observed the lemur's reaction.
Measuring the lemur's attention span to varying stimuli - number of apples in this case - allowed the researchers to correlate the lemur's interest with the varying number of apples in the box. When a lemur was shown an apple, the lemur showed interest (food!) If the researchers closed the box, then reopened it with a single apple again, the lemur's interest declined; nothing had changed. On the other hand, if the researcher replaced the single apple with two apples, the lemur showed increased interest; the lemur recognized the number of apples was different. If shown two apples again, the lemur showed less interest; the number of apples had not changed. This process worked up to three (4?) apples - any larger number of apples did not increase the lemur's interest level. The process also worked in reverse; when going from three apples to two, or two apples to one apple, the lemur showed increased interest as measured by increased attention spans. (Eventually, the lemur would get bored and return to the forest.)
By repeating the experiment with numerous lemurs in the park, the researchers determined that lemurs could differentiate between 1, 2, or 3 apples. Basically, lemurs, or at least this species of lemur, could count to 3!
Without getting too verbose, numbers and numerals are symbolic concepts used by humans. For instance, the numeral "4" is just a bunch of lines and has no direct reference to four objects. However, those who use Arabic numerals obviously understand the relationship. Yet the Chinese or Mayan symbols for four objects would be completely unknown symbols to people who use Arabic numerals (excepting those who can read Chinese or Mayan).
On the other hand, counting is a cognitive trait that some animals, (including humans), do possess.
Chimpanzees, with larger brains than lemurs, can also count. Some researchers claim chimps can do some basic arithmetic as well. Try poking around www.pbs.org for some additional info. Here's a Scientific American Frontiers link about chimp counting. You might also poke around Google or pick up an intro Psychology text for more information.
numbers exsist read this
it gives a bunch of examples. something along the lines of; theres ## number of naturally occuring elements and if you do a bunch of math you get the days of the month/year, minutes of the hour, the time a fetus stays in the womb is the same number as absolute zero, all this other crap that shows you how numbers physically express themselves in nature.
it gives a bunch of examples. something along the lines of; theres ## number of naturally occuring elements and if you do a bunch of math you get the days of the month/year, minutes of the hour, the time a fetus stays in the womb is the same number as absolute zero, all this other crap that shows you how numbers physically express themselves in nature.
Numbers, like all other "concepts" of human thought are abstractions based on observations of physical phenomena. Numbers abstract the visualization of a group of objects. This can be further abstracted to perform "operations" and build more and more concepts upon them.
If two cats are a require a different action than one cat (and we can empirically observe they do) then a dog does recognize numbers though perhaps does not have an advanced realationship with them.
I think what you're really struggling with is language, not numbers per se. There is a certain philosophical difficulty in the realization that our reality is in some at least relational way defined by the words we use to label something.
<---talking out of ass
I think what you're really struggling with is language, not numbers per se. There is a certain philosophical difficulty in the realization that our reality is in some at least relational way defined by the words we use to label something.
<---talking out of ass
XZeroII
Lifer
- Jun 30, 2001
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There is a flaw in the logic for the lemurs. They are assuming that the lemur is getting excited becaue they count more. However, it could be just that there are actually more. If I saw one cake, then two cakes, of course I would be more excited because there are simply more. I can see that more mass exists. They should try one small apple, then replace it with a noticably larger apple and see what the response is. I bet the lemur would get excited simply because there is more mass.
It's a good book, but it doesn't show that numbers exist. It shows that numbers are useful for modelling the physical universe. There are three sentences in this post, but that doesn't mean that the concept three exists in the same way that the configuration of electrons in which this post is stored exists.
You may have a valid point. Before I wrote my original post, I poked around the PBS.org site but was unable to find any online documentation about the show I had seen. The original episode was a number of years ago, and I do not remember all the details of the experiment. (I'm not even positive it was on PBS!). Moreover, it was just a video documentary and not a detailed research paper or thesis that may have been written as well.
Perhaps the researchers used different sized apples or even other objects as control experiments. I really don't know, and such info may not have been included in the video anyway.
With more than 3 apples the lemurs did not show any increased attention span, thus there appears to be a limit on the count ability (or perhaps conservation of mass ability) in lemurs.
A more recent study using lemurs in a lab setting instead of in the wild, seems to contradict your premise that the lemurs would simply be attracted to "more mass".
From a Duke Univ site, using raisins as a stimulus instead of apples, lemurs apparently made no choice based upon mass or count unless forced to do so.
Part of this article also appears on the National Geographic web site.
Your point regarding mass versus count is valid. However, as I did not perform any of the research, I am not qualified or even able to further examine the details and controls of the various experiments. My main point was simply that some animals besides humans appear to have some sense of "counting".
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