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InkDark
Carpal Tunnel
Reged: 10/29/07
Posts: 1839
Loc: Montreal, Canada
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The other day I was talking to a college teacher of electrical engineering and he told me that he once asked a math teacher wath were the math teachers studying. The math teacher said "we study the competence of the human brain". I found that answer pretty good.
How would you define math?
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Jimmy
If you could stop time, for how long would you stop it?
"...since that time, I have not complained about the weather one single time. I’m glad there is weather." – Alan Bean, Apollo 12
Edited by InkDark (10/29/09 01:30 PM)
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EdZ
Professor EdZ
Reged: 02/15/02
Posts: 14732
Loc: Cumberland, R I , USA42N71.4W
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Quote:
How would you define math?
A language of numbers rather than letters.
Until you get to higher maths, then it becomes a language of letters all over again!
edz
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Teach a kid something today. The feeling you'll get is one of life's greatest rewards.
member#21
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alanon
Nobody tells me anything
Reged: 06/29/07
Posts: 2642
Loc: Las Vegas
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And then it becomes Greek letters. 
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Alanon the Wizard (a literary character, not the organization)
Dan
12.5" Obsession #1531
WO 98mm FLT (aluminum tube)
WO ZenithStarII 80mm ED
Coronado PST Ha
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Greg K.
Reged: 12/11/03
Posts: 11544
Loc: Clifton Park, NY
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...with really weird punctuation.
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Astro-Tech AT111EDT f/7 - Celestron CGEM
NexStar 11 GPS
Orion SkyView Pro 8EQ (w/ Autostar mod)
15x70 Celestron SkyMasters
Orion 90mm Mak
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Shadowalker
Unpretentious Rocket Scientist
Reged: 11/23/04
Posts: 3560
Loc: Poplarville, MS, USA
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Without consulting Wikipedia I'll take a shot.
Mathematics is a tool, just as language is a tool. It is a tool that can express real world things in unambiguous ways. Our language is useful for expressing certain things, but it's impossible to express how much money is in one's pocket without mathematics. It's impossible to explain Special or General Relativity without mathematics.
Math, in and of itself, is without purpose. It's how we use it that gives it usefulness. To put that another way, there are whole branches of math that explain nothing (at least nothing we know of) but can be logically derived from simple to complex mathematical concepts. Similarly, we can use language to express meaningless thoughts - some of my own posts come to mind - maybe this one.
In a nutshell, and how my engineer's mind understands it: Math is a language tool used to describe unambiguously real world phenomena.
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Tom Nicolaides
http://www.first-light.org
My evil self is at that door, and I have no power to stop it
-- Dr. Edward Morbius
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MMICKELS
Aluminum Knight
Reged: 01/20/04
Posts: 27889
Loc: The Land of Shake and Bake
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Quote:
In a nutshell, and how my engineer's mind understands it
Like this?
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Mark
"Never eat more than you can lift"
Miss Piggy
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mattyfatz
Pooh-Bah
Reged: 12/27/06
Posts: 1297
Loc: Boise Idaho
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Quote:
Quote:
In a nutshell, and how my engineer's mind understands it
Like this?
 
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**Matty**
Stimulating the economy, one piece of equipment at a time.   
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MMICKELS
Aluminum Knight
Reged: 01/20/04
Posts: 27889
Loc: The Land of Shake and Bake
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To me math is a tool not unlike the other tools in my toolbox at work. Math just gets used more than the rest, and never wears out.
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Mark
"Never eat more than you can lift"
Miss Piggy
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Shadowalker
Unpretentious Rocket Scientist
Reged: 11/23/04
Posts: 3560
Loc: Poplarville, MS, USA
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Dilbert. I've been compared to Dilbert.
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Tom Nicolaides
http://www.first-light.org
My evil self is at that door, and I have no power to stop it
-- Dr. Edward Morbius
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star drop
Guilty as Charged
Reged: 02/02/08
Posts: 16404
Loc: Snow Plop, WNY
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You have my deepest sympathies, Tom.
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Ted
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Scott Horstman
Vendor- Backyard Observatories
Reged: 03/11/04
Posts: 8074
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Explanation of math.
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llanitedave
Humble Megalomaniac
Reged: 09/26/05
Posts: 12945
Loc: Amargosa Valley, NV, USA
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Quote:
Dilbert. I've been compared to Dilbert.
At least it wasn't Dogbert.
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"Since the process of science generates more mysteries than it solves, I predict that we'll never learn everything: and we'll continue to generate new ignorance at the speed of knowledge."
"S.O.E." (Sauron's Other Eye), with 16" Royce conical mirror: A permanent work in progress.
10" Homebuilt dob, old Coulter mirror
Under Construction: The "Eye of Sauron" Observatory!
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Erric
member
Reged: 10/26/09
Posts: 35
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Quote:
To me math is a tool not unlike the other tools in my toolbox at work. Math just gets used more than the rest, and never wears out.
So math is an invention, not a discovery?
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llanitedave
Humble Megalomaniac
Reged: 09/26/05
Posts: 12945
Loc: Amargosa Valley, NV, USA
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I'd say it's both. The particular symbolic language that we manipulate is invented, and many of the embellishments that we add to it are invented. But the underlying logic and numeracy, the basic algebraic properties and logical relationships, are discovered.
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"Since the process of science generates more mysteries than it solves, I predict that we'll never learn everything: and we'll continue to generate new ignorance at the speed of knowledge."
"S.O.E." (Sauron's Other Eye), with 16" Royce conical mirror: A permanent work in progress.
10" Homebuilt dob, old Coulter mirror
Under Construction: The "Eye of Sauron" Observatory!
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deSitter
Carpal Tunnel
Reged: 12/09/04
Posts: 2928
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I always liked "the science of drawing necessary conclusions", which distinguishes it from logic, "the science of drawing any conclusions" - C.S. Pierce.
-drl
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Something about the question is disturbing to me.
Math consist of three studies:
Arithmatic - the study of numbers
Geometry - the study of shapes
Analysis - the study of infinity
For many years this has been sufficient for me. I am unable to embrace the question.
Also
A system of language and rules which allow for the modeling of reality in abstraction.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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letimotif
No Complaints
Reged: 05/20/07
Posts: 2019
Loc: Far Flung Isles of Langerhans
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The etymology of mathematics I find instructive. From the Greek word "mathemas" meaning learning, study or science (or, generally speaking, all three).
At its foundation, mathematics permits the study of our Universe.
Although the basics concepts were understood by extremely clever men three hundred years ago, the advent of computer technology gave Dr. Mandelbrot a bully pulpit from which to bring the concepts, and intriguing ramifications, of fractals into the mainstream.
Which begs the question: Arithmetic, Geometry, the Calculus have been around for a while. What have we overlooked? What's next?
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Ah, but a man's reach should exceed his grasp, or what's a Heaven for?
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llanitedave
Humble Megalomaniac
Reged: 09/26/05
Posts: 12945
Loc: Amargosa Valley, NV, USA
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Quote:
A system of language and rules which allow for the modeling of reality in abstraction.
It also allows you to model abstractions in the absence of reality.
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"Since the process of science generates more mysteries than it solves, I predict that we'll never learn everything: and we'll continue to generate new ignorance at the speed of knowledge."
"S.O.E." (Sauron's Other Eye), with 16" Royce conical mirror: A permanent work in progress.
10" Homebuilt dob, old Coulter mirror
Under Construction: The "Eye of Sauron" Observatory!
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matt
Vendor (Scopemania)
Reged: 07/28/03
Posts: 10364
Loc: Chaville, France
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I think the interesting question about math is whether it transcends human thought or not. Is it Something in the Universe which would exist whether Humans exist or not? Is it purely a human construction? Astronomers (and imagers especially) know that the size of image of an object photographed through a telescope is the object's angle (in radians, which is the "natural" measure of arc, not in degrees or grades which are arbitrary units) multiplied by the focal length of the telescope / objective. No adjusting variables. Have you ever been baffled by how extraordinarily simple that is?
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Matt
CI700 mount with various scopes on top.
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Quote:
I think the interesting question about math is whether it transcends human thought or not. Is it Something in the Universe which would exist whether Humans exist or not? Is it purely a human construction?
I assert that the answer is yes. If we find another society of thinking creatures who have the ability to manipulate their environment I am confident that they will have counting numbers and identities that look like 1+1=2 and 1 * 1 = 1. If they are so different from us that they do not find it necessary to do this we may not recognize them as intelligent. It logically follows that they may feel the same way about us.
Quote:
Astronomers (and imagers especially) know that the size of image of an object photographed through a telescope is the object's angle (in radians, which is the "natural" measure of arc, not in degrees or grades which are arbitrary units) multiplied by the focal length of the telescope / objective. No adjusting variables. Have you ever been baffled by how extraordinarily simple that is?
Have you considered that some societies may have adopted the number we call pi as 1. They may then consider the radius of a circle as an irrational number. It is the ratio between the two that I assert that they will know.
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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Scott Horstman
Vendor- Backyard Observatories
Reged: 03/11/04
Posts: 8074
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Quote:
Have you considered that some societies may have adopted the number we call pi as 1.
How could you order 1 Big Mac at the drive through? Wouldn't the kid have to give you 3.14159265 of them? Man to think how bad they screw the orders up NOW!
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matt
Vendor (Scopemania)
Reged: 07/28/03
Posts: 10364
Loc: Chaville, France
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Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
It's certainly convenient, but arbitrary nonetheless, just like the 24 hour day and the 60 minute hour.
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astrotrf
professor emeritus
Reged: 09/30/07
Posts: 709
Loc: Rodeo, NM
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Quote:
Have you considered that some societies may have adopted the number we call pi as 1. They may then consider the radius of a circle as an irrational number. It is the ratio between the two that I assert that they will know.
I don't really see this as being likely. Firstly, a society will invent counting long before they realize that the ratio of the diameter to the circumference of a circle is a constant. Secondly, a diameter, being straight, is an easy thing to measure, and will be determined first before any circumference is measured. Thirdly, adopting pi as one would make counting the number of berries in your hand a quite difficult process. 
It would sure make first-grade arithmetic a trying course! 
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
Well, it *is* an arbitrary choice, but it is NOT a haphazard one.
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Terry (astrotrf)
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Quote:
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
It's certainly convenient, but arbitrary nonetheless, just like the 24 hour day and the 60 minute hour.
My point was to one person a choice is arbitrary and to another it makes since. I thought that the 360 degree choice was silly until I learned of those who made the choice. What I am suggesting is that we are in a poor position to understand the choices of an ET society which we currently can not imagine. The Babylonians liked to be able to divide things without the use of fractions. Who can blame them? Their choice reflected their concerns at that time. They probably thought it was brilliant.
The degree can be divided in to minutia. They choose 60 minutia per degree. They choose to sub divide minutia again forming the second minutia of a degree. Hence, minutes and seconds. These are different from arbitrary choices.
I do not know why there are 24 hours in a day but I am confident that it made since to someone at the time. What I am suggesting is that it may be difficult for us to understand the choices of a society with which we have little in common. This dose not make their choices arbitrary.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Quote:
Quote:
Have you considered that some societies may have adopted the number we call pi as 1. They may then consider the radius of a circle as an irrational number. It is the ratio between the two that I assert that they will know.
I don't really see this as being likely. Firstly, a society will invent counting long before they realize that the ratio of the diameter to the circumference of a circle is a constant. Secondly, a diameter, being straight, is an easy thing to measure, and will be determined first before any circumference is measured. Thirdly, adopting pi as one would make counting the number of berries in your hand a quite difficult process.
It would sure make first-grade arithmetic a trying course!
Not if you were born into a world where the circle is considered more important than a line. Recall that during the development of Astronomy people were obsessed with the perfection of the sphere! So much so that they attempted to force all orbits to be constrained to the surface of spheres. This made since to them and it influenced what they felt was reasonable.
Quote:
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
Well, it *is* an arbitrary choice, but it is NOT a haphazard one.
Perhaps we have different definitions of the word arbitrary.
If n + infinity = infinity then in an example using real numbers the choice of n is arbitrary. Any choice of n is a useful as any other. A choice that is based upon a preference is not arbitrary to me.
In most movie theaters a ticket cost a fixed amount for all choices of seats. To the theater owner your choice is arbitrary. To you it is not. Some people are shorter and choose to sit near an outside aisle so that they can view the screen across the aisle. This would prevent the case where a tall person entering late sits in front of you and blocks your view of the screen. Others hate this choice because people walking in and out will temporarily block their view. Others will want to sit 1/3 of the way between the screen and the projector because this best duplicates the field of view of the photographer. Still others will want to sit in the back because they want the screen to fit into a smaller field of view. To the viewer these choices are not arbitrary even if we do not understand why the choices were made.
For me a choice is not arbitrary if it matters to the person making the choice.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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astrotrf
professor emeritus
Reged: 09/30/07
Posts: 709
Loc: Rodeo, NM
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Quote:
Perhaps we have different definitions of the word arbitrary.
Yes, there are several different connotational meanings of the word. I think, also, that we're looking at the choice from different ends.
I'm looking at it from the a priori end. If someone asked me how to divide a circle, I'd say "Well, the choice is completely arbitrary, in that anything you choose will work. But if you pick 360, it has these nice properties."
I believe you're looking at it from the fait accompli end. You'd say, "360 has these nice properties, so that was deliberately chosen as the way to divide a circle rather than something arbitrary."
To a mathematician, arbitrary means "chosen at random" (and that's the sense in which you are using the word). A more layman-like definition would be "chosen subject only to judgment".
I think we would both agree that the choice of how to divide a circle was unrestricted, and was made based on the desirable arithmetic properties of the number 360.
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Terry (astrotrf)
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matt
Vendor (Scopemania)
Reged: 07/28/03
Posts: 10364
Loc: Chaville, France
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"arbitrary" does not mean "bad", although people often use the word "arbitrary" in the "dictatorial" sense, as in "coach made the arbitrary choice of moving Bubba to tight end". They mean it as in "coach is a clueless dictator". In fact, good or bad, the choice IS arbitrary, since it is a choice. Coach puts Bubba at TE because it fits his schemes and allows Timmy to play fullback. The guy who divided the day into 24 hours and the circle into 360 ° did it because it was convenient for him.
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Matt
CI700 mount with various scopes on top.
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Yes to all. I think we agree.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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