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Something interesting i came across NOT looking for porn just now...



So, in your own words, if you care to, define numbers.

i don't care for a formal definition at 4:30 in the morning, but i'll say this

to understand numbers it helps to understand them with different bases, not just base 10 number system we are used to

base 2
base 6
base 10
base 12
base 16

when you look at them this way it gives you a broader understanding

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.

Thanks, both!

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).

Originally posted by Mindship
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).
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

Originally posted by Firefly218
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

I think a lion knows if it has 2 cubs or 1, whether or not those numbers were ever defined by humans or taught to it in lion school

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

Originally posted by Firefly218
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

I don't think that's true, a lion would definitely (IMO) know how many cubs it has. And can tell the difference between one and two.

It's no lion, but there was a parrot named Alex that could count to 6 among other things.

The youtube video is 7yGOgs_UlEc or just youtube search alex parrot counting
Apparently I still cannot post links How long does that take?

Originally posted by fostersAccount
I don't think that's true, a lion would definitely (IMO) know how many cubs it has. And can tell the difference between one and two.

It's no lion, but there was a parrot named Alex that could count to 6 among other things.

The youtube video is 7yGOgs_UlEc or just youtube search alex parrot counting
Apparently I still cannot post links How long does that take?
Yes the lion would know it has multiple cubs, but it wouldn't be able to identify those cubs by numbers.

Parrots can make the sounds of 1 - 6, but they won't know what they're saying has any meaning.

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.

^

numbers help us on earth... not in the universe.. we haven't been out in the universe to know if our calculations are correct...

So when people say math is the universal language, thats wrong?

Originally posted by Shabazz916
numbers help us on earth... not in the universe.. we haven't been out in the universe to know if our calculations are correct... 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.

Great post.

Originally posted by riv6672
Great post. Thnx. I had a lucid moment.

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.

Originally posted by fostersAccount
i don't care for a formal definition at 4:30 in the morning, but i'll say this

to understand numbers it helps to understand them with different bases, not just base 10 number system we are used to

base 2
base 6
base 10
base 12
base 16

when you look at them this way it gives you a broader understanding
Not really, the base simply decides what symbols (and structure) you use to express a number, but a number is still a number.

11₁₀ = 10₁₁ = 1011₂ are all the same number (subscript denotes base).

Originally posted by Astner
Not really, the base simply decides what symbols (and structure) you use to express a number, but a number is still a number.

11₁₀ = 10₁₁ = 1011₂ are all the same number (subscript denotes base).

That's exactly my point.

Originally posted by fostersAccount
That's exactly my point.
It's just different ways of writing the same number, it doesn't broaden your understanding of them in any sense.

Originally posted by Mindship
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.

they math can't find a plane in the damn water.. so yeah ill believe they can use a microscope to measure darkness

Originally posted by Mindship
'E' always equaled 'mc^2', whether we ever discovered this mathematical relationship or not. We did not invent this relationship, nor others found in nature, only the symbols for expressing them, eg, like the numeral '2'.

Hey, no one's perfect.

thats why it says it only helps us on earth. notice i didnt say in thee sea

Thats a little nitpicky, though..

Originally posted by Astner
We don't know if this expression perfectly describes the phenomena, what we do know is that it describes the phenomena well enough for practical purposes, i.e. atom bombs and nuclear reactors, and that's all we know.A philosophical point, to be sure, and I agree. We don't know if our entire reductive-materialist model is valid, but it is (apparently) quite reliable. And that's good enough to treat what we discover as a "real" deal, a viable as-if, for all current intents and purposes.

Originally posted by Astner
We discovered the phenomena, we invented the expression. My friend, we're basically saying the same thing:Originally posted by Mindship
We did not invent this relationship, nor others found in nature, only the symbols for expressing them.
I think our differences are semantic.

Wars have been fought over semantics.

I think 'numbers' is an invention as it's a lexicon we've imposed on quantitative values which exist independent of our labels, but it's possible that it is also an emergent property of reality (since at a base quantities simply exist, and intelligent life can acknowledge them).

What do they all mean http://3.bp.blogspot.com/_ONRsltnC-wQ/SuykiLd4PDI/AAAAAAAAAFI/k_vdr5gvSWw/s400/20080430201839.jpg

The importance of numbers:

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Any number is merely the measurement of a quantity.

This is the most basic concept.

"The brain does much more than just recollects, it analyzes, synthesizes, it generates abstractions. The simplest thought, like the concept of the number one, is an elaborate logical underpinning."

-Carl Sagan on the human brain.

That quote seems to go back to the lions that were discussed...