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Well, there's many different kind of numbers, but if we go with natural numbers, they are basically a tool that enables you to count. They have a starting point and are ordered. That enables you to do what we call addition, which is basically the ability to count more than 1 step (as many steps as the number you add). There are two special numbers in that case which have special abilities 1 and 0 (if you want to include 0). 1 is the number that you can "add" to the beginning of the natural numbers to go through all natural numbers without missing one. 0 is the number that you can *add* to a number to get back to itself.
Now, just by thinking about some of the things with natural numbers you can arrive at other numbers. For example by reverse counting (subtracting) we come to a point where you can count below the starting number. So we can extend the Natural Numbers by numbers that go below its initial starting point to get integers.
That won't answer your philosophical question, but I think we can all agree that numbers at least have some relation to the world we perceive. For example grouping disparate things. I may see two cookie, and I see that has a relation to having one cookie, as in that there are more of them. And if I "eat" one of my two cookie I'm getting back to one cookie. As such counting is definitely something that comes pretty natural to us, and describes something we perceive in the universe.
That doesn't answer the question whether numbers are "real", but imo that is ill-defined anyways.
Basically, is math an invention or a discovery? I think, more and more, philosophically we're shifting from the notion of 'invention' (for measuring quantities) to 'discovery' (of the underlying order to the universe).
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That's actually interesting to ponder. But I'm starting to question the objectivity of numbers. I mean, to whom is 1 actually 1. To one person 1 is 1, to another 1 is 4. Numbers have to be defined by us to exist, which is why I think they are more of an invention than a discovery
Lions don't understand the concept of numbers. They also have limited capability for cognitive function.
All a lion would be able to determine is that he has offspring to protect and find food for. Since humans are so intelligent, it's hard for us to imagine the extreme cognitive inferiority of other animals
Broadly speaking: animals seem to understand the concrete world in a concrete way very well, and that would include distinguishing quantities, ie, differentiating among stimuli which differ only in amount. However, there's no symbolic understanding of numbers and number systems, no conceptual context. For animals, a functional understanding of quantity appears based entirely on its relevance to the physical world (essentially, like how humans start off, in learning about numbers).
In interacting with humans, animals can also learn to associate certain "sound labels" (number names) with given sensory impressions of quantity (again, like human babies). But I doubt they see any quantity-impression or sound-label as part of a larger, overriding system of measurement and calculation, a dimension the developing human mind later takes on in its world-view.
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We don't have to physically be out there; we can make accurate measurements with telescopes and other detection devices (eg, recent detection of gravitational waves has further confirmed our mathematical understanding of the inflationary period during the Big Bang). Heck, it's basically how theoretical physicists "envision" the universe: as a set of constants and their dynamic relationships.
It is because numbers are "universal," we've been able to have robot probes fly by multiple planets and moons in our solar system with amazing accuracy. We can predict, years ahead of time, where these celestial bodies will be. And from what we've been able to observe in interstellar or intergalactic space, the properties of super-distant bodies also appear mathematically predictable (eg, I believe it is how the presence of dark matter surrounding our galaxy was discovered, as well as the discoveries of supermassive black holes at the centers of galaxies, and even the discovery that our universe is experiencing accelerated expansion. All done by observation and math).
It is, in fact, the universal applicability of math to virtually everywhere in the observable cosmos that has prompted some scientists to wonder if math is a discovery rather than an invention.
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Last edited by Mindship on Jun 22nd, 2014 at 12:57 PM
Gender: Male Location: 4th Street Underpass, Manhattan
I believe math is an abstract concept which we discovered. The objective existence of numbers is true because practically every observable phenomenon in the universe can be measured quantitatively to a certain degree. The will always be a certain number of protons for each element, a certain amount of atoms in the universe, etc, whether humans were aware of it or not. If theories of the universe being composed of information patterns is true, it would lend credence to mathematics and numbers being an inherent abstract part of our reality.
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Jun 21st, 2014 07:54 AM
How long does that take?
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