About the Science vs Religion Debate

[DjTj]

Oh Oh I know this one.

10cm*Pi

what he said.

[PokerPacker]

while were on the subject of numbers that don't fall into the domain of rational numbers... how about the number i? pretty fun number isn't it?

[Ancalagon the Black]

Portisizzle, all the questions you're posing about pi were answered hundreds of years ago and fully explored by the time of Cantor. All you have to do is read up on some history of mathematics. Everything & More: A Compact History of Infinity, by David Foster Wallace, is decent (although there are some startling mathematical errors in there...but don't worry, they don't affect his explanations).

[mhd24]

while were on the subject of numbers that don't fall into the domain of rational numbers... how about the number i? pretty fun number isn't it?

i is an imaginary number and part of that domain. It represents the sqrt(-1)

[PokerPacker]

i is an imaginary number and part of that domain. It represents the sqrt(-1)

no, not only is i not rational, its not real. the chart goes as follows:

....Numbers

.._____|_______

..|...................|

Real...........Imaginary

__|__________

|...................|

rational.....irrational

....|

integers

...|

whole

....|

natural

[Ancalagon the Black]

PokerPacker is right. Imaginary numbers cannot be rational numbers, because both irrational and rational numbers are real numbers.

What's even cooler than i is the following equation:

e^(i * pi) + 1 = 0

True and provable.

[PokerPacker]

i don't remember my logarithms anymore, how does that workout?

[Ancalagon the Black]

e^(ix) = cos(x) + i*sin(x) [Euler's formula]

let x=pi

cos(pi) = -1

sin(pi) = 0

so e^(i*pi) = -1 + i*0

so e^(i*pi) + 1 = 0

[PokerPacker]

nevermind, error.

[portisizzle]

Oh Oh I know this one.

10cm*Pi

So the answer is not

10*3.14 = 31.4?

[HOF44]

So the answer is not

10*3.14 = 31.4?

If your trying to be most accurate the answer is 10*Pi. If your doing it for engineering purposes 10*3.14=31.4 might suffice depending on your tolerances.

[Predicto]

My math is REALLY rusty, so bear with me. Isn't pi only complicated because we arbitrarily chose to use a decimal number system (since we have 10 fingers). Wouldn't pi calculate out just fine if we had a mathematic system based on 6 or 12 rather than 10?

I seem to remember something about this from a long time ago, but I may be totally off.

[HOF44]

My math is REALLY rusty, so bear with me. Isn't pi only complicated because we arbitrarily chose to use a decimal number system (since we have 10 fingers). Wouldn't pi calculate out just fine if we had a mathematic system based on 6 or 12 rather than 10?

I seem to remember something about this from a long time ago, but I may be totally off.

That jogs my memory also I think you might be onto something.

[HOF44]

That jogs my memory also I think you might be onto something.

Guess not.

http://users.aol.com/s6sj7gt/picode.htm

Base 26

Base 26 is one of two fairly natural ways of representing numbers

as text using a 26-letter alphabet. The number of interest is

expressed numerically in base 26, and then the 26 different base-26

digits are identified with letters as 0=A, 1=B, 2=C, ... 25=Z.

Here are the first 100 digits of pi expressed in this way:

D.DRSQLOLYRTRODNLHNQTGKUDQGTUIRXNEQBCKBSZIVQQVGDMELM

UEXROIQIYALVUZVEBMIJPQQXLKPLRNCFWJPBYMGGOHJMMQISMS...

Lo! At the 6th digit we find a two-letter word (LO), and only a

few digits later we find the three-letter ROD embedded in the four-letter

TROD. How many other English words can be found if we continue looking?

First, a few pi facts are in order. The digits of pi (in any base)

not only go on forever but behave statistically like a sequence of

uniform random numbers. (Mathematically proving that this is the

case - the "pi is normal conjecture" - is a deep unsolved problem,

but numerical analysis of several billion digits suggests that it is

true.) Consequently, pi in base 26 emulates the mythical army of

typing monkeys spewing out random letters. Among other things, this

implies that any text, no matter how long, should eventually appear

in the base-26 digits of pi!

[Predicto]

Well, scratch that idea.

Good thing I went into Law! :laugh:

[Ancalagon the Black]

Any irrational number (including transcendental numbers like pi) will be unable to be expressed in any base decimal system. Their very name ("irrational") signifies that they cannot be expressed as a ratio of two numbers, which is what decimals are shorthand--or longhand--for.

[Ancalagon the Black]

So the answer is not

10*3.14 = 31.4?

Of course not.

[portisizzle]

Of course not.

So, then tell me....

What is the circumference of a circle with a radius of 5 cm?

[PokerPacker]

So, then tell me....

What is the circumference of a circle with a radius of 5 cm?

10*pi

[dchogs]

So, then tell me....

What is the circumference of a circle with a radius of 5 cm?

isn't that the same question as before?

it has an exact answer 10*pi.

if you need a real number to work with for practical purposes, it depends on how accurate you approximation needs to be. the more accuracy needed, the more accurate your value of pi should be.

[portisizzle]

isn't that the same question as before?

it has an exact answer 10*pi.

if you need a real number to work with for practical purposes, it depends on how accurate you approximation needs to be. the more accuracy needed, the more accurate your value of pi should be.

Then just out of curiosity, are you suggesting that any equation that implements pi would not come to a mathematical answer with a real number?

Take this equation for example....

How do you solve this equation?

[Mooka]

:laugh: This thread is hilarious. Talking about Pi...

Personally, I hate how everyone tries to link the 2. Religion is based on faith. Science is based on observation and experimentation. You can say science is based on faith as well, but thats a pretty loose argument.

If anyone is interested, I do believe we will be able to prove where matter comes from in the near future.(maybe 50-100 yrs) Call me crazy if you want, but we're not as far off as one might think. We're very close to proving new particles exist and proving that dark matter and dark energy exists. If we can prove dark matter does exist, then we can create dark matter particles and experiment with them. This could very well lead to where matter comes from, how the Universe formed, how the Universe is expanding, and can even lead to crazier stuff like theories on different dimensions.

Check out the ATLAS experiment in Geneva if your interested. (A Toroidal LHC ApparatuS) Heres a pic:

The people are the scale, so you see how rediculously big this thing is. Its all underground connected to a half mile tube. Its basically just a very high energy particle detector that will be able to detect single atoms bouncing off eachother, and what type of energy these reactions give off. Believe it or not, this thing is actually very close to being complete. Very interesting stuff, if your an engineer like me anyway.

I don't think its that hard to believe that we could eventually prove the Big Bang thoeory. (or whatever theory comes up next) Capernicus was able to prove the earth was not the center of the Universe by mapping out stars without a telescope. (Galileo was nothing without his data) Erastothanes was able to calculate the circumference of the earth over 2000 years ago.

[portisizzle]

: Call me crazy if you want, but we're not as far off as one might think. We're very close to proving new particles exist and proving that dark matter and dark energy exists. If we can prove dark matter does exist, then we can create dark matter particles and experiment with them. This could very well lead to where matter comes from, how the Universe formed, how the Universe is expanding, and can even lead to crazier stuff like theories on different dimensions.

You're crazy.

So if you (they) are right and there is something called dark matter and dark energy, then what?

Well you would have to ask where did the dark matter or dark energy come from. Wouldn't you have the same problem answering that question as we do now trying to answer where matter comes from?

Still trying to figure out how something came from nothing?

And the reason for the discussion on pi...... well my only point is to say that our math is not perfect. And maybe it is possible that the description of our natural universe will require some different form of math/ science/ philosophy/ theology to come to a proper understanding.

That formula I posted just above? That is Einstein's field equation for general relativity. Pretty important, I would guess. So why is a "number" like pi in this equation? Because it is the best that our math and physics has to offer. And his equation is not as certain as 1+2=3. That is all.

[Prosperity]

Then just out of curiosity, are you suggesting that any equation that implements pi would not come to a mathematical answer with a real number?

Take this equation for example....

How do you solve this equation?

Isn't pi a real number?

[portisizzle]

If your trying to be most accurate the answer is 10*Pi. If your doing it for engineering purposes 10*3.14=31.4 might suffice depending on your tolerances.

How about solving Einstein's Field Equation of general relativity?

is 3.14 sufficient?