Is the concept of negative man-made

[pioneer]

In math, the concept of negative numbers is an important concept. But if you look at natural reality, what is a negative apple? If you look at tree, it may not have any apples and it may have some apples, but you won't find a tree with negative apples.

 

Although we all understand the concept of negative, does this reflect natural or man-made?

[Mr Skeptic]

Maybe. You don't have a positive apple either though. We use numbers to model the universe, sometimes more effectively than others. Negative numbers were very disliked when they were first introduced (first accepted by accountants, I think), due to people feeling they are fake. But just like positive numbers they can model the universe just fine. If I borrow an apple and eat it, I call that negative one apple (I owe an apple to someone). If I grow three oranges I call that positive three oranges. If I eat the largest of my oranges, then I call that only positive two oranges. If I instead eat the smallest of my oranges, I still call that positive two oranges, despite having a different amount of orange in both cases. Positive numbers are man-made, negative numbers are man-made, and imaginary numbers are man-made too -- but all of them can model the real world.

[pioneer]

Although all numbers are manmade, in practical reality only the positive concept implies substance. Negative implies a mirror world where there is a deficient of substance.

 

If I borrow $1000, I now have negative $1000. Yet I can buy positive things with this negative money. I don't have to buy only negative apples from the mirror world. Therefore it is actually, positive money, therefore I don't owe anything. This logic doesn't add up, because we have defined negative to mean this was a loan of a positive thing that we will call negative when we write it on the paper.

 

In nature, behavior is part of the natural balance. Humans will define behavior as positive (good) and negative (evil). A good deed plus a bad deed might cancel. But in nature, the same two deeds can add to create a positive effect on substance. Humans define a convention to get a different result.

 

Did the concept of plus and minus help separate humans from nature? It added a mirror world from which the deficit of substance, could be used to tweak substance to create new types of substance.

 

Deficit spending makes use of the mirror world. Pay as you go stays in positive reality. The mirror world of deficit spending create a void in positive reality which will then suck future taxes out of the pocket into the mirror world. Conceptually it alters time, with the future tax money going back into time, via the mirror world, where it comes out of the mirror world, into today, to create new positive substance for today.

Edited December 14, 2010 by pioneer

[Marat]

The whole history of the ontological implications of numbers is fascinating, since there has always been resistance to the introduction of any innovative quantities required by the internal structure of mathematics on the grounds that they were 'unnatural.' Just look at how clumsy Ancient Egyptian arithmetic was because they disliked having any numerators other than 1 in their fractions since they regarded these as unnatural! The Ancient Greeks were bothered by the irrationality of pi, no one likes the fact that 0.999... can be mathematically demonstrated to be equal to 1.0, and even zero was unavailable to early mathematicians because no one thought of it as being a possible quantity.

 

Negative numbers seem quite natural, however, since if I am wearing skates and standing on ice, and I intend to skate three feet due West, but the wind blows me three feet backwards due East, then I seem to have moved -3 feet toward my goal.

 

Martin Heidegger, the early 20th century German Existentialist philosopher, has an argument in his magnum opus, 'Being and Time,' that the absence of something can produce quite a powerful negative experience of emptiness, so this could be used to support the idea that negative quantities are natural. If you are expecting a letter from your girlfriend on Monday but when you open your mail box there is nothing there, you get a very strong, positive sense of nothingness, rather than just a neutral absence of something.

[Bignose]

There are ions with negative charges and ions with positive charges. Though it is arbitrary which one to denote as "positive" and as "negative", it is not arbitrary that when balanced quantities of positive and negatively charged ions combine, you end up with a substance that has no charge. One way or the other, there is a concept of negative and positive that additively combine to zero in nature.

Edited December 15, 2010 by Bignose

[michel123456]

There are 2 kinds of negatives.

There are the mirrored ones, and there are the continuous ones.

 

The mirrored one go like this

<-------zero------->

 

The continuous one go like this

>-------zero------->

 

If you think about it, you will realize that the mathematical negative is continuous. You can change the place of zero on the line of numbers, and decide arbitrarily of a new beginning, nothing will really change. This negative is about eaten apples, and borrowed money. There is nothing weird here. It is only a matter of convention to where to put the zero.

 

The mirrored negative is the most bizarre. The negative apple becomes an "elppa" with the skin inside and the seeds outside, or something like that.

 

Both negatives are human concepts. There may be even a 3rd kind of negative I can't figure right now.

Edited December 15, 2010 by michel123456

[ajb]

The "trouble" with negative numbers is that sets do not have negative cardinality (in the standard sense, though I believe you can define such a notion). This seems to be the root of most misgivings about negative numbers and is quite evident in the opening post. Negative numbers are not "counting numbers".

Edited December 15, 2010 by ajb

[mississippichem]

Isn't this why we call the numbers 1,2,3,4,5,6,7... the set of natural numbers? They are naturally intuitive by observing things like apples unlike negative numbers.

[ajb]

Isn't this why we call the numbers 1,2,3,4,5,6,7... the set of natural numbers? They are naturally intuitive by observing things like apples unlike negative numbers.

 

Yes, then there is the integers which is made of the natural numbers and then including zero.

[michel123456]

The "trouble" with negative numbers is that sets do not have negative cardinality (in the standard sense, though I believe you can define such a notion). This seems to be the root of most misgivings about negative numbers and is quite evident in the opening post. Negative numbers are not "counting numbers".

 

Sure you can. I guess these are new mathematics.

[ajb]

Sure you can. I guess these are new mathematics.

 

I am also told that a fractional cardanality is also possible.

 

If I feel like it I should have a quick look into this...

[pioneer]

The original question was, is negative a manmade concept? Things like fractional cardinals are an invention with practical use. I nature, we can take a big rock and break it into fractions. Each now becomes a little rock and not a fraction of a big rock, unless humans define it like that.

 

Negative has practical use but it not part of nature. Nature uses positive values. There is no need for the mirror world. However, the mirror world does create many practical applications which allows humans to leave the natural world. Nature can't borrow from the future. It is restrained to positive things in the present. It would be like the rabbit borrowing grass from next summer, via the mirror world, to eat now. Comes next summer, the grass that was borrowed is reflected by the field half chewed, having been vacuumed up by the mirror world last winter altering the life forming capability. That would be unnatural, yet humans do it all the time to build manmade reality.

[Marat]

In a sense all concepts, including natural numbers, are man-made abstractions which isolate just one aspect of the sensory continuum around us, and highlight one particular feature of it for emphasis for our own conceptual purposes. It is an act of high conceptual abstraction to note the similarity among several objects, which are always dissimilar in some respects, and then impose on them a numerical framework so that they can be compared in terms of the number of times these abstracted similars recur. So negative numbers are not significantly different from any other numbers by virtue of being 'abstract' rather than 'natural.'

[lemur]

Deficit spending makes use of the mirror world. Pay as you go stays in positive reality. The mirror world of deficit spending create a void in positive reality which will then suck future taxes out of the pocket into the mirror world. Conceptually it alters time, with the future tax money going back into time, via the mirror world, where it comes out of the mirror world, into today, to create new positive substance for today.

Deficit spending is basically giving a gift that has to be paid back. It's like taking an equity mortgage on a house you own and giving the money to your kids to spend. They get the money and think, "great," and hear later that they don't get to inherit the family house because they already blew the money. In the mean time, they think they're doing well because their parents own a house and they got a good education, etc. Another way of looking at it is that the debt is like a deal with the devil. I.e. you get to live it up in the present but in the future you have to become a slave to evil because you sold your soul in exchange for some short-lived pleasure.

Edited December 19, 2010 by lemur

[Marat]

This raises the interesting question of how people used to deal with negative quantities conceptually and numerically before the invention of negative numbers, when mathematicians would still have regarded them as ìmpossible quantities,`as many of the quantities generated by mathematical operations have been thought to be (e.g., square root of negative one). There were certainly debts before there were negative numbers, so how we the complex accountancy issues surrounding them numerically treated.

[michel123456]

The "trouble" with negative numbers is that sets do not have negative cardinality (in the standard sense, though I believe you can define such a notion). (...)

 

Could you please make a try into this? I figure that would set a new understanding of negative squares and maybe could use as a replacement of what we call imaginary numbers. I have a strong feeling physics could be better explained with mirrored mathematics.

Edited December 21, 2010 by michel123456

[John Cuthber]

Unless there is something to do the conceiving, no concept can exist. As far as I know, mankind is the only thing with a conception of negative numbers.

If that's right then the concept of negative numbers is man-made.

[Marat]

But I would argue that that does nothing to impeach their ontological warrant, since all concepts of numbers, and indeed, all concepts, are just human abstractions imposed on artificially insulated slices of the continuum of sensation and labeled with a name. It is tempting to think that if we see four dead branches on the ground in front of us the 'four' is somehow already implicit in the empirical nature of what we are seeing prior to any interpretive act, but in fact the 'fourness' of that ensemble is something we conceptually impose on it, and so it is also 'man-made.' The 19th century German mathematician Gottlob Frege discussed this notion.

[Athena]

Yesterday, there were 16 apples on my tree, today there are only 14, giving me a negative of 2 apples. I do not create this fact, but can precieve it because I can compare what was so yesterday with what is so today.

 

The means, we do not create the negative, but can precieve it, and give it a word representing the reality, and with the word, we can have abstract thoughts about its meaning. It is questionable if the Neanderthal could do this kind of higher thinking. This mental abilty being what makes us like the gods and separates us for the animal kingdom. However, if we are seniors, maybe it is just a faulty memory of 16 apples. What do you imagine? Hum, how different is memory from imagination? To hold an idea that is not manifested truth at this monent in time. But I am sure yesterday there were 16 apples, so there must be a negative 2 and I know I did not create this.

 

Marat, I love your terminology and I hope someday I can speak your language fluently without giving it a thought. However, because I am not there yet, I must ask, are saying there is no such thing as reality? I am sure someone took two of my apples. Now you make me question my sanity.

Edited January 2, 2011 by Athena

[Moontanman]

Yesterday, there were 16 apples on my tree, today there are only 14, giving me a negative of 2 apples. I do not create this fact, but can precieve it because I can compare what was so yesterday with what is so today.

 

I disagree, your ability to perceive this created the idea of a negative, it didn't exist until you perceived it.

 

The means, we do not create the negative, but can precieve it, and give it a word representing the reality, and with the word, we can have abstract thoughts about its meaning. It is questionable if the Neanderthal could do this kind of higher thinking.

 

 

Actually this is not true, Neanderthals are now thought to have been our equals in most ways and possibly superior in some areas, the idea they were mentally inferior is an out dated concept that come from the idea of human superiority over all other creatures, Neanderthals were human, they did the same things we did, made similar tools and toward the end of their existence they made jewelry and fancy tools just like humans did, no reason to think they couldn't perceive the absence of something.

 

 

This mental abilty being what makes us like the gods and separates us for the animal kingdom. However, if we are seniors, maybe it is just a faulty memory of 16 apples. What do you imagine? Hum, how different is memory from imagination? To hold an idea that is not manifested truth at this monent in time. But I am sure yesterday there were 16 apples, so there must be a negative 2 and I know I did not create this.

 

Again, not true, many animals can count and know the difference between the numbers of objects in their environments.

[Athena]

I disagree, your ability to perceive this created the idea of a negative, it didn't exist until you perceived it.

 

 

 

 

Actually this is not true, Neanderthals are now thought to have been our equals in most ways and possibly superior in some areas, the idea they were mentally inferior is an out dated concept that come from the idea of human superiority over all other creatures, Neanderthals were human, they did the same things we did, made similar tools and toward the end of their existence they made jewelry and fancy tools just like humans did, no reason to think they couldn't perceive the absence of something.

 

 

 

 

Again, not true, many animals can count and know the difference between the numbers of objects in their environments.

 

Moonman, I just googled the differences between the Neandertral brain and our brians a couple of days ago. The different shapes of the brains, suggest different mental abilities as well. But this agrument isn't going to go far without an understanding of concrete thinking verses abstract thinking. Not even by age 12 are humans good at abstract thinking. This area of the brain is not fully developed in humans until about age 25. It is unlikely Neanderthals were abstract thinkers, and for sure a horse is not.

 

I am providing a link for those who are curious about the difference between concrete thinking and abstract thinking. http://medical-dicti...ncrete+thinking

 

A Neanderthal would probably notice the missing apples becuase this is a concrete thinking.. However, the Neanderthal is unlkely to have had a notion of naegatives, which an abstract thought.

Edited January 5, 2011 by Athena