Board index › Topical Discussion › Computers, Math, Science, and Technology

Why is Math so Powerful?

Page 4 of 8 [ 120 posts ]  Go to page Previous  1, 2, 3, 4, 5, 6, 7, 8  Next

Previous topic | Next topic

ruveyn
Veteran
Veteran

User avatar

Joined: 21 Sep 2008
Age: 88
Gender: Male
Posts: 31,502
Location: New Jersey

23 Oct 2011, 11:26 am

AstroGeek wrote:
1) This brings to mind Carl Sagan's idea that through us the universe has developed a way to understand itself. Quite a beautiful thought...


Pretentious nonsense along with "billyuns and billyuns", "stuhr stuff" and "pale blue dot". Have you ever seen Sagan try to sing like a whale? Look at this:
http://www.youtube.com/watch?v=qKEmj7W_b1c

ruveyn



cw10
Veteran
Veteran

User avatar

Joined: 23 May 2011
Age: 51
Gender: Male
Posts: 973

23 Oct 2011, 3:27 pm

ruveyn wrote:
cw10 wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.


Nature is not sentient. Why should Nature have a language? Most of the Cosmos is devoid of consciousness.

ruveyn


Sentience is based off universal laws and the logic of forces. Forces govern concepts. Concepts are the expression of nature. Language is the expression of concepts. One does not require sentience to form logic. In fact it's quite the opposite.



lau
Veteran
Veteran

User avatar

Joined: 17 Jun 2006
Age: 75
Gender: Male
Posts: 9,795
Location: Somerset UK

23 Oct 2011, 3:32 pm

cw10 wrote:
ruveyn wrote:
cw10 wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.


Nature is not sentient. Why should Nature have a language? Most of the Cosmos is devoid of consciousness.

ruveyn


Sentience is based off universal laws and the logic of forces. Forces govern concepts. Concepts are the expression of nature. Language is the expression of concepts. One does not require sentience to form logic. In fact it's quite the opposite.

I apologise, in advance, but this collection of meaningless sentences made me chortle.


_________________
"Striking up conversations with strangers is an autistic person's version of extreme sports." Kamran Nazeer


cw10
Veteran
Veteran

User avatar

Joined: 23 May 2011
Age: 51
Gender: Male
Posts: 973

23 Oct 2011, 3:35 pm

lau wrote:
cw10 wrote:
ruveyn wrote:
cw10 wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


It's the language of nature.


Nature is not sentient. Why should Nature have a language? Most of the Cosmos is devoid of consciousness.

ruveyn


Sentience is based off universal laws and the logic of forces. Forces govern concepts. Concepts are the expression of nature. Language is the expression of concepts. One does not require sentience to form logic. In fact it's quite the opposite.

I apologise, in advance, but this collection of meaningless sentences made me chortle.


Meaningless only to those who lack the ability to comprehend.



Jono
Veteran
Veteran

User avatar

Joined: 10 Jul 2008
Age: 43
Gender: Male
Posts: 5,651
Location: Johannesburg, South Africa

23 Oct 2011, 4:22 pm

ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


Well mathematics is mostly about patterns, and is developed by starting from a few axioms and then reasoning through deductive. So, if we assume that the universe has order and we know that mathematics is all about orderly patterns, which we develop ourselves through deductive reasoning, then it follows that our mathematics would be sufficient to describe the order in the universe. Even if we find structures in nature that we don't currently have the mathematics for, mathematicians can still develop the mathematics for it, using the same process of starting with axioms and the developing it with deductive reasoning.



Thom_Fuleri
Veteran
Veteran

User avatar

Joined: 7 Mar 2010
Age: 46
Gender: Male
Posts: 849
Location: Leicestershire, UK

23 Oct 2011, 6:04 pm

Either the universe works according to a set of axioms, or it does not.
If it does, mathematics is the study of those axioms, and of course it will make sense.
If it does not, everything is entirely random. A random universe will either make no sense at all, or will occasionally lapse into order. If you keep tossing a coin, it WILL eventually come up heads a hundred times in a row.

So the question is whether this is an ordered universe, or whether it could all fall into chaos at any moment. There's no way to know.



ruveyn
Veteran
Veteran

User avatar

Joined: 21 Sep 2008
Age: 88
Gender: Male
Posts: 31,502
Location: New Jersey

23 Oct 2011, 6:33 pm

Thom_Fuleri wrote:
Either the universe works according to a set of axioms, or it does not.
If it does, mathematics is the study of those axioms, and of course it will make sense.
If it does not, everything is entirely random. A random universe will either make no sense at all, or will occasionally lapse into order. If you keep tossing a coin, it WILL eventually come up heads a hundred times in a row.

So the question is whether this is an ordered universe, or whether it could all fall into chaos at any moment. There's no way to know.


Or the universe makes good sense but the axioms in hand are wrong for the universe. Think of Aristotle's physics of matter and motion. Axiomatic and yet a train wreck.

Later natural philosophers did better than Aristotle.

ruveyn



cw10
Veteran
Veteran

User avatar

Joined: 23 May 2011
Age: 51
Gender: Male
Posts: 973

23 Oct 2011, 6:44 pm

Thom_Fuleri wrote:
Either the universe works according to a set of axioms, or it does not.
If it does, mathematics is the study of those axioms, and of course it will make sense.
If it does not, everything is entirely random. A random universe will either make no sense at all, or will occasionally lapse into order. If you keep tossing a coin, it WILL eventually come up heads a hundred times in a row.

So the question is whether this is an ordered universe, or whether it could all fall into chaos at any moment. There's no way to know.


This is an ordered universe... At the moment. In time it won't be.



shrox
Veteran
Veteran

User avatar

Joined: 11 Aug 2011
Age: 60
Gender: Male
Posts: 3,295
Location: OK let's go.

23 Oct 2011, 6:58 pm

ruveyn wrote:
Don't look a gift horse in the mouth. Just accept the Wonder of it.

ruveyn


Horses can do math...

[youtube]http://www.youtube.com/watch?v=hbgaJvaGUnk&feature=related[/youtube]



HopefulRomantic
Deinonychus
Deinonychus

User avatar

Joined: 11 Aug 2010
Age: 60
Gender: Female
Posts: 399
Location: Atlanta, GA

23 Oct 2011, 7:16 pm

DenvrDave wrote:
Why is math so powerful? Because it is both useful and beautiful at the same time. When used skillfully, mathematics is a universal tool for solving problems. I would posit there is no problem ever solved by a human being or team of human beings that couldn't be described by a mathematical equation. And why is this powerful? Because when faced with a complex or seemingly intractable problem of almost any nature, we can always turn to math to either solve the problem or at least help guide the way. Mathematics can be used to test an almost infinite number of hypotheses. As if that isn't enough, math is a beautiful, logical, and symmetrical language. It has been used to produce musical instruments that create the sweetest sounds, and to produce some of the most stunning works of visual art. Useful and beautiful.



I really enjoyed this post! What can I say - I always loved the arts!



Tadzio
Veteran
Veteran

User avatar

Joined: 2 Sep 2009
Age: 72
Gender: Male
Posts: 877

24 Oct 2011, 12:18 am

shrox wrote:
ruveyn wrote:
Don't look a gift horse in the mouth. Just accept the Wonder of it.

ruveyn


Horses can do math...

[youtube]http://www.youtube.com/watch?v=hbgaJvaGUnk&feature=related[/youtube]


Have you met "Clever Hans"???

Clever Hans was a super smart horse who out-smarted top-notch experts, until they dreamed up abstract excuses to cover their own low brain levels. Google "Clever Hans" for tons of info.

I blamed my super-natural abilities on subliminal communication (like "reading" people's aura).

But back to the "beauty" of Mathematics, mathematics is a tool, not a "Harmony of the Spheres" that might get a person beheaded if they revealed that the square-root of 2 could not be expressed as a ratio of two whole numbers. So sticking with the "beauty" puts the "ad absurdum" in the "reductio".

The purely tool part is very evident with functors, both creative and forgetful ones. They are a TOOL, not a revelatory "fundamental truth of harmony" of quantums or the universes.

Niccolo Tartaglia's "Division of 17 horses" problem, demonstrates the "baseness" of mathematics: A father leaves his 3 sons 17 horses, one son to get one-half the horses, the second son to get a third of the horses, and the third son to get a ninth of the horses. What is the number of horses each son gets???? The answer is not "beautiful", since "division was not done in a proper way", but for practical purposes, why not be "practical"? Hint: add a "dirty" imaginary horse to get 18 horses, then forget the imaginary horse after dividing up the horses.

Tadzio



cw10
Veteran
Veteran

User avatar

Joined: 23 May 2011
Age: 51
Gender: Male
Posts: 973

24 Oct 2011, 12:47 am

Tadzio wrote:

Niccolo Tartaglia's "Division of 17 horses" problem, demonstrates the "baseness" of mathematics: A father leaves his 3 sons 17 horses, one son to get one-half the horses, the second son to get a third of the horses, and the third son to get a ninth of the horses. What is the number of horses each son gets???? The answer is not "beautiful", since "division was not done in a proper way", but for practical purposes, why not be "practical"? Hint: add a "dirty" imaginary horse to get 18 horses, then forget the imaginary horse after dividing up the horses.

Tadzio


Sounds like fractal roughness to me.



Orwell
Veteran
Veteran

User avatar

Joined: 8 Aug 2007
Age: 35
Gender: Male
Posts: 12,518
Location: Room 101

24 Oct 2011, 1:35 am

Tadzio wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


If mathematics is purely deductive, why does all of it depend on induction?
Counting is empirical, and physics was around long before mathematics.

Tadzio

So naive. No, mathematics is purely deductive; all that we say must follow from our axioms. Read a real analysis text sometime and you will see the way mathematicians actually define counting. Nothing empirical enters into it at all.


_________________
WAR IS PEACE
FREEDOM IS SLAVERY
IGNORANCE IS STRENGTH


Tadzio
Veteran
Veteran

User avatar

Joined: 2 Sep 2009
Age: 72
Gender: Male
Posts: 877

24 Oct 2011, 4:09 am

Orwell wrote:
Tadzio wrote:
ruveyn wrote:
Why is mathematics such a powerful tool? It is not empirical. It is purely deductive. But we cannot do physics without it.

ruveyn


If mathematics is purely deductive, why does all of it depend on induction?
Counting is empirical, and physics was around long before mathematics.

Tadzio

So naive. No, mathematics is purely deductive; all that we say must follow from our axioms. Read a real analysis text sometime and you will see the way mathematicians actually define counting. Nothing empirical enters into it at all.


"One, Two, Three: Absolutely Elementary Mathematics [AEM]" by David Berlinski (2011), page 103: "Many of the proofs in AEM proceed by induction. So do many proofs in mathematics generally. The principle is easy to state and difficult to grasp."

I guess I underestimated the "difficult to grasp" part in more ways than one. "The first step: ....inductive base...."

Well, maybe Bertrand Russell, et al., and every math book I ever read was wrong!! ! What's even more strange is that B.F. Skinner held induction somewhat in contempt, and it is most assuredly "WRONG" to agree with Skinner about anything here at WP most always (esp. with all the "Objectivists").

Zero is the only non-negative, non-fractional, sometimes "natural" number that is not empirical. Either that, or you can't count anything in reality land with positive integers as quantity of real things.

Tadzio



Jono
Veteran
Veteran

User avatar

Joined: 10 Jul 2008
Age: 43
Gender: Male
Posts: 5,651
Location: Johannesburg, South Africa

24 Oct 2011, 5:16 am

Tadzio wrote:
"One, Two, Three: Absolutely Elementary Mathematics [AEM]" by David Berlinski (2011), page 103: "Many of the proofs in AEM proceed by induction. So do many proofs in mathematics generally. The principle is easy to state and difficult to grasp."

I guess I underestimated the "difficult to grasp" part in more ways than one. "The first step: ....inductive base...."


That is referring to a method of mathematical proof called mathematical induction. Usually, it is used to prove some statement to be true of all natural numbers. It has absolutely nothing to do with inductive reasoning, rather it a form of rigorous deductive reasoning just like all other methods of mathematical proof:

http://en.wikipedia.org/wiki/Mathematical_induction



Last edited by Jono on 24 Oct 2011, 9:33 am, edited 1 time in total.

Thom_Fuleri
Veteran
Veteran

User avatar

Joined: 7 Mar 2010
Age: 46
Gender: Male
Posts: 849
Location: Leicestershire, UK

24 Oct 2011, 9:22 am

Tadzio wrote:
But back to the "beauty" of Mathematics, mathematics is a tool, not a "Harmony of the Spheres" that might get a person beheaded if they revealed that the square-root of 2 could not be expressed as a ratio of two whole numbers. So sticking with the "beauty" puts the "ad absurdum" in the "reductio".


Beauty is subjective. Tools can be ugly or beautiful, depending on their design - many concepts in mathematics are beautiful because they are elegant and simple (though proving them is often neither!). I have always found fractals to be compelling, and the beauty of these is entirely based upon their mathematics.

Music is mathematical. Harmonies are based on multiples of frequencies. Rhythm is little more than counting in time. Even more, the most beautiful symphony can be encoded onto a CD as nothing more than a sequence of binary digits. Even if you don't find mathematics itself beautiful, it can certainly contain beauty.

Quote:
Niccolo Tartaglia's "Division of 17 horses" problem, demonstrates the "baseness" of mathematics: A father leaves his 3 sons 17 horses, one son to get one-half the horses, the second son to get a third of the horses, and the third son to get a ninth of the horses. What is the number of horses each son gets???? The answer is not "beautiful", since "division was not done in a proper way", but for practical purposes, why not be "practical"? Hint: add a "dirty" imaginary horse to get 18 horses, then forget the imaginary horse after dividing up the horses.


This is nothing to do with mathematics. The very nature of the question is a trick - suppose there were 18 horses to begin with? You're left with an extra horse. The division of the horses is thus not complete, with only 17/18 of them being distributed. The very fact these numbers are used is because this "solution" is manufactured.