Largo
Sport climber
The Big Wide Open Face


May 17, 2013  01:55pm PT

Yes. I see no reason to suppose that mathematics is only an artifact of human consciousness.
Where do numbers exist outside of human consciousness?
It's a trick question, I'll admit, since language and symbols were entirely the fruit of consciousness, meaning without a brain to cook them up, there are no quadratic equations, for example.
There ARE structures in the physical world that correspond to equations or can be numerically described as such, but the descriptions are once again not the real world things. This is underscored by the Second Rule of Mind: The map (here, the math), no matter how accurate, is never the territory itself.
Note that the same mind that wants a God to exist independently of "us," is not fighting to make allmighty numbers the ultimate "standalone" reality.
But we all know that nobody discovered numbers "out there." We opened our eyes and saw things, and assigned numbers as symbolic correlates. Math is just another of our many useful languages. But just as the word "hot" might describe El Cap in August, "hot" is not itself heat.
JL


Malemute
Ice climber
the ghost


May 17, 2013  01:56pm PT

From jogill's link above:
Some men seem to regard life as a talk show on which they are the star guest.
I know a guy like this.
I think of him as 10 pounds of BS in a 5 pound sac.


MH2
climber


May 17, 2013  02:10pm PT

Define "one" incontrovertibly so that I know it when I see it, MH2.
In the history of math no one bothered or needed to define 1 until recently. It was enough to write down rules for operations done with it, such as addition and multiplication. Math is largely about relations among abstract entities. It is sometimes important to set aside any ideas you may have about what a mathematical object is and consider only how it behaves. At other times imagination and personification help. I knew a bright young physics scholar (and climber) at Chicago who could tell you what the various elementary particles sounded like.
However, along with whatever abstract reality the number one may exist in, examples of it can be found in physical reality. Let's imagine that I show you a penny, a sheep, a carrot, and a book. I tell you that although they look different there is one of each. To help the idea I may bring in another penny, sheep, carrot, and book and tell you that there are now two of each. Then I take away a penny and ask you which thing there is now only one of. If you point to the penny, you are getting the idea. Now I bring back the second penny and take away one carrot. Can you still identify which object to use the label one on? The point is that it is possible to separate the concept of number from any particular thing. We give up physical concreteness and gain mathematical insight.
Here is another way show you the number 1, or at least how to construct it.
If L, R are any two sets of numbers, and no member of L is ≥ any member of R, then there is a number {LR}. All numbers are constructed in this way.
Since all numbers come from earlier numbers, how does the system start?
Even before we have any numbers we have the empty set, the set with no members. So the first constructed number is {LR} with L=R=the null set. Call this number 0.
Now we have the null set, { } and the number zero, {  }.
We then get {0 } = 1.
from On Numbers and Games by J.H. Conway
edit for JL
Math is just another of our many useful languages.
If mathematics is just a language how is it that people all over the world for thousands of years have learned same language, often independently of other speakers?


goB
climber
Hebrews 1:3


May 17, 2013  02:11pm PT

Job 38:4 “Where were you when I laid the foundation of the earth?
Tell Me, if you have understanding, 5 Who set its measurements?
...2+2=


MikeL
climber
SANTA CLARA, CA


May 17, 2013  02:58pm PT

MH2:
You proved math with math? Nah, . . . that won't work for me. Petitio Principii.
If there is such a thing as a one, then show it to me. Don't use it as an abstract concept. I mean, it is a concept, isn't it?
The one penny? Where does that one penny start or stop? Do you think that one penny exists indpendently, alone, by itself, without the support of an infinity of other circumstances and conditions? How could that be? Where would it be? When would it be?
Show me a one.
Abstractions, models, frameworks, concepts. All are less than one, to be sure.
Getting dizzy yet? You should be. You're in Jogill's hall of mirrors.
EDIT: Look how you started the proof:
If L, R are any two sets of numbers . . .


jogill
climber
Colorado


May 17, 2013  02:59pm PT

0={ }
1={0}={{ }}
2={0,1}={{ },{{ }}}
etc
This piece of set theoretic formalism is fairly recent.
The father of set theory Georg Cantor suffered for his efforts.
Arguing the realism of mathematics has little merit IMO.
[edit] Jan makes good, informative comments below!


Jan
Mountain climber
Okinawa, Japan


May 17, 2013  03:00pm PT

Is math just another language?
As a student of linguistics, I can say that out of 6,000+ recorded languages, there are only three different ways of ordering grammar. While many of the original discoveries in math were made in either Europe or India by people using an inflective IndoEuropean grammar, math is clearly of a different construction than IE grammar.
Since unrelated peoples with isolative and agglutinative grammars can comprehend math, yet struggle when learning languages with inflective grammar (and vice versa), it seems to me that math is an entirely different system. Chomsky and others search for a universal grammar within languages, but math seems to be a better candidate than any known language.
Ideagrams such as Chinese characters could function as a universal writing system with each pronounced in the native speaker's language. Math and ideagrams being symbols, can we say that the bottom strate of the human mind is symbols and the universe probably as well? God may be a mathemetician but language comes from the mammalian brain.


MikeL
climber
SANTA CLARA, CA


May 17, 2013  03:04pm PT

Jogill, the proof smuggles in numbers and then says, "Viola! A One!"
Please.


Largo
Sport climber
The Big Wide Open Face


May 17, 2013  03:19pm PT

The point is that it is possible to separate the concept of number from any particular thing. We give up physical concreteness and gain mathematical insight.

In exactly the same way that we can separate the concept of a word for color (blue, black, red, green, etc.) from any particular sky, tire, cherry, or meadow. This quite obviously does not magically reify these colors as something beyond symbols for the sky, tires, cherries etc. which gave rise to the symbols in the first instance. The way you have it, the symbols existed before or independent of the things for which they pertain. The fact that we can consider a number as a thing independent of a thing is a function of our discursive minds, which can objectify an idea just as easily as a physical event or thing. But just because our minds work like that doesn't mean the map suddenly becomes the territory. However, a number and any symbol can be considered an article of qualia or the stuff of awareness in every bit as tangible a way as a burning bush or a tomahawk. But note that this process is an internal job, not something that heppens "out there." Trying to deify numbers as having an independent existence from consciousness is just another attempt of us humans to fashion another God, which is always "out there."
edit for JL
Math is just another of our many useful languages.
If mathematics is just a language how is it that people all over the world for thousands of years have learned same language, often independently of other speakers?
Because all math began with people corresponding one sea shell, for example, with one finger, thereby mentally creating a numerical relationship between said finger and said conch. Later we gave a number to this relationship = One. One finger, one conch shell. Once the symbolic numbers exceeded our fingers, numbers took over. Since we all have fingers, we all naturally understand the rudiments of how this all works and got started. But you are wrong in thinking that ALL people all over the world are good with math and can easily understand it. It's like music, or poetry, and so forth. You have to have a certain predisposition to go far with any of these languages, though most can come to appreciate the basics of what is being said.
Hope this helps. The human tendency to reify symbols, things, Gods etc. as having standalone existence is a very strong one not easily seen through.
JL


BASE104
Social climber
An Oil Field


May 17, 2013  03:30pm PT

Math is not a language, but math has developed an exquisite language.
This language is an example of how we have subjective ideas and then make them precisely quantitative and objective. It is probably the best example of this.
I agreed long ago with JL that as humans, we constantly rely on subjective analysis of information that we receive.
Where we part ways is the fact that we can, by using rigorous methods, convey these ideas in a perfectly objective way. I assume that both Mike and JL balance their checkbooks in a similar way, for example, and arrive at a precise balance of their accounts.
This beautiful symbolic language is quite useful in taking an idea, that may be utterly subjective, and checking it to be entirely accurate. I say that this is a method of sharing quantitative information between individuals, even if they speak different languages or have entirely different perceptions. This is one of the great achievements of our species.
There is an ability to follow a method in order to communicate ideas in a way that is immune from bias.
This is a problem in the softer sciences, but as I have been saying, the softer sciences are incredibly relevant and useful. They are just difficult to quantify. There are many things that are difficult to quantify. It doesn't make them imaginary.


WBraun
climber


May 17, 2013  04:01pm PT

Jan  "God may be a mathematician but language comes from the mammalian brain."
No
Language comes from the soul.
Without the soul there is no brain.
The soul controls the brain.
The soul is the seat of consciousness, intelligence and the source of all the material bodies activities.
The brain is just a lump of flesh that the soul works thru to operate the material body ........


MH2
climber


May 17, 2013  04:22pm PT

If there is such a thing as a one, then show it to me. Don't use it as an abstract concept. I mean, it is a concept, isn't it?
Yes. It is a concept. But that is not all it is. If you balk at the concept of 1 penny then I presume you wont agree with other mathrelated statements. If you don't see what Conway is doing, okay, but I say that Conway has the better case. It isn't so much that math is being used to prove a statement about math, but that logic is being used to put foundations under math. Mathematicians did not worry about foundations for millennia, but that has been fixed.
You can claim that there is no such thing as one, but then you have also claimed that logic won't get you anywhere, so you have nothing to make your case with.
edit for JL
But you are wrong in thinking that ALL people all over the world are good with math and can easily understand it.
I did not make that claim. Mayans had a calendar, astronomy, and arithmetic. Other native americans in what is now the U.S. had only counting.
It's like music, or poetry, and so forth.
No. Discoveries in math were made by early Chinese, Hindus, and Greeks. The similarity in the results would be like Beethoven's 9th or Hamlet's soliloquy turning up independently in China, India, and Greece.
Many people think math is just a thing to learn. In fact, the question of what math is and where it comes from is as mysterious as quantum mechanics and other interpretations of the physical world. We are fortunate that math can be developed without worrying about what it IS. The same approach can be taken in physics. Math and physics are accessible to human consciousness but not direct products of it.


Don Paul
Big Wall climber
Colombia, South America


May 17, 2013  04:36pm PT

I can say that out of 6,000+ recorded languages, there are only three different ways of ordering grammar.
This is intriguing and implies that language could be reduced to math formulas. In Spanish you can put the words and phrases in almost any order you want, and I often make weird constructions in English because I'm so used to the freedom of doing that.


Largo
Sport climber
The Big Wide Open Face


May 17, 2013  05:14pm PT

It's like music, or poetry, and so forth.
No. Discoveries in math were made by early Chinese, Hindus, and Greeks. The similarity in the results would be like Beethoven's 9th or Hamlet's soliloquy turning up independently in China, India, and Greece.
No. You lose your way in assuming that each language is bound by the same rules or criteria, when it fact it is not. The criteria for math is that it originally corresponded to things out there in a tangible, one to one relationship. In that sense, the original math, was constrained to work along lines just as proscribed in China as they were in Fort Worth. Plus we humans are predisposed to organize discrete elements in certain ways, just as water runs down hill. What you are ascribing as a fundamental aspect of reality that was discovered whole and en tact by various differing folk across the globe is in fact an example of people learning how their discursive minds work. Because music and literature is not originally constrained by a numerical relationship to things, but rather to the much more amorphous and ever shifting realms of feelings, intuitions, and so forth, we don't see Hamlet appearing in whole cloth in New Guinea as it first appeared in England.
A more interesting question is what BASE contends  that math is not a language, that is, a symbolic system used to talk about "things" and phenomenon. Verily BASE, what is math? And if math is a thing, and all things are by nature physical, where does said math exist independent of things and consciousness?
JL


jogill
climber
Colorado


May 17, 2013  05:30pm PT

Mathematicians did not worry about foundations for millennia, but that has been fixed
Well, more or less. For example, the Axiom of Choice is still somewhat controversial. Odd things happen when one studies the foundation of mathematics  I found it best to leave those dilemmas to set theorists and math logicians.
IMO philosophy of mathematics is a quagmire.
In my own area  classical (complex) analysis  most of the foundation stuff was ironed out well over a hundred years ago. Before then there were questions like "does the sequence <0,1,0,1,0...> 'converge' to some number?"
Verily BASE, what is math? And if math is a thing, and all things are by nature physical, where does said math exist independent of things and consciousness?
Oh my God . . . here we go.
;>(


Marlow
Sport climber
OSLO


May 17, 2013  05:55pm PT

Lost in Language! ;o) MikeL og Largo sager hele tiden av den grenen de sitter på. Anser seg å gjendrive språklig mening ved hjelp av det samme språk. Stunningly stoopeed and repetitively boring.


MikeL
climber
SANTA CLARA, CA


May 17, 2013  07:27pm PT

Mh2:
If you like coincidence then you'll Love Joseph Campbell's recognition that the myth of virgin birth occurred in different times and places across the globe unconnected.
Just like mathematics!


rectorsquid
climber
Lake Tahoe


May 17, 2013  07:33pm PT

Language comes from the soul.
Without the soul there is no brain.
How can that be? I have no soul yet I can write this post with my brain.
Feel free to have as soul but don't force one one me. I'm more than just a toy built by a superior being for amusement and worship.
Dave


WBraun
climber


May 17, 2013  07:49pm PT

^^^^^^^^
I have no soul
Since you have no clue what you are talking about you just made a completely stupid idiotic post.
Most of the time that's what you do here in this thread.



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