Science & Mathematics Unanswerable questions

[BomberGal]

^ When you touch things, you are feeling forces acting between you. You're not actually touching anything. Of course, sub-sub-atomic physics is voodoo to me (probably to everyone - as they say if you think you understand quantum mechanics, you don't) - but as far as I understand, atoms can't actually get that close. And sub-atomic particles in the nucleus which are held together very closely are held that way by the strong nuclear force - a very powerful force, as demonstrated by the fact that the breaking up of it leads to the energy released in atomic bombs.

Obviously. But then I had to get to the halfway point of the big step, and then to the halfway point of that point and the end of the big step, and on and on and on it goes. In theory it should've taken me until the end of time to get to the second point, because I have to pass through an infinite number of halfway points.

Just one of those weird physics things that doesn't make a whole lot of sense when you think about it.

WTF? Are you thinking correctly?

Your steps don't halve themselves each time. Why would you think that? If you take a step halfway to point B, you take another step the same length and reach point B. And even if they did shorten each time, your steps can be longer than the distance between the two points.

It's not a weird physics thing that doesn't make a whole lot of sense. It's your logic.

 

[BarneyBent]

Obviously. But then I had to get to the halfway point of the big step, and then to the halfway point of that point and the end of the big step, and on and on and on it goes. In theory it should've taken me until the end of time to get to the second point, because I have to pass through an infinite number of halfway points.

Just one of those weird physics things that doesn't make a whole lot of sense when you think about it.

Possibly demonstrates that space and time are discrete.

 

[Pie eyed]

^ When you touch things,

Speaking of touching things.....

"It's nifty to look into the chamber and see a clump of ultracold atoms floating there," Hau says. "In this odd state, light takes on a more human dimension; you can almost touch it."

Lene Hau talking about how light appears when it is stationary in her laboratory at Harvard.

 

[ballanFYNE]

Why are good looking women reffered to as Hot?

 

[richoatthedisco]

Zero divided by zero?

Isn't the answer any number?

a/b = c, then b*c = a

12/4 = 3, 3*4 = 12

0/0 = c, then 0*c = 0

0 lots of anything is 0. So c = any number.

That's how I always thought of it.

I was thinking it could be infinity, 1 or 0.

Divide any number by 0 and the answer is infinity.

Divide any number by itself and the answer is 1.

Divide 0 by any number and the answer is 0.

I have read numerous explanations as to why 0 divided by 0 can be either 0, 1 or x.
None make any sense unless elaborate conditions are applied.

Go and get no apples.
Place them on a table.
Now carelfuly divide the no apples into no pieces.
How many peices of apple do you have on the table?

To take this further, distribute 1/5 of the apple peices on the table to one person and 4/5 of the apples to another.
Which has more apple pieces?

Conceptually you could find a theoretical answer which gives you 1, but practically you cannot. The variation lies in how different fields define and treat zero not in the reality.

You're all treating zero as a number, which it's not - it's the lack of number. It's a meaningless question. You might as well try to divide by purple.

 

[Brad Roo]

How many Becquerels in a CPS?

 

[Brad Roo]

You're all treating zero as a number, which it's not - it's the lack of number. It's a meaningless question. You might as well try to divide by purple.

Incorrect.

Explain 10 to the power of zero?

 

[Armitage2Riewoldt]

Incorrect.

Explain 10 to the power of zero?

Yes, but 10^purple = 1 as well. So his point remains valid.

 

[richoatthedisco]

Incorrect.

Explain 10 to the power of zero?

It's a mathematical abstraction. Reasoning is often given as thus:
10^3 = 1 x 10 x 10 x 10 (= 1000)
10^2 = 1 x 10 x 10 (=100)
10^1 = 1 x 10 (=10)
10^0 = 1

But who put the 1s there? Mathematicians. You could just as easily say:
10^3 means three 10s combine to make a product = 1000
10^2 means two 10s combine to make a product = 100
10^1 means one 10 combines to make a product = 10
10^0 means zero 10s combine to make a product = 0

and you'd be equally right, except it doesn't work with negative powers, eg. 10^-1. So what I would suggest is the 'power' notation denotes how many zeroes follow the 1 to the left of the decimal point. Then 10^0 does = 1, not because 0 is a number but precisely because it isn't.

The zeroth power logic makes mathematical sense but it's merely a form of notation. Zero is not a number. I doubt any mathematician would argue it is.

Pie-eyed was on the right track. The question 'how many nothings in something?' has no answer.

 

[Walesy]

But who put the 1s there? Mathematicians.

Those pesky mathematicians!! Always slipping in 1's and 0's where they don't belong!!

 

[Brad Roo]

Mathematics is just another language.

Zero has a value in that instance so it is definitely not nothing.

 

[richoatthedisco]

Mathematics is just another language.

Zero has a value in that instance so it is definitely not nothing.

Zero is not nothing!? Now I've heard it all! I don't know that it has a value, rather a meaning.

To say "I have zero apples on the table" is misleading because it does imply a value for zero. You merely have a table.

 

[Brad Roo]

Zero is a number (0), it denotes something, it has value.

Nothing is an empty set ().

 

[richoatthedisco]

Zero is a not a number (0), it denotes nothing, it has no value. You don't have 'zero' apples, you have nothing. (Or something else.)

 

[SJ]

Zero is an integer.

 

[Brad Roo]

Zero is a not a number (0), it denotes nothing, it has no value. You don't have 'zero' apples, you have nothing. (Or something else.)

This is obviously a bit beyond your scope champ.

Zero is an integer.

Yes, what number isn't?

 

[richoatthedisco]

This is obviously a bit beyond your scope champ.

Or yours chump. I've been to Katamatite.

 

[SJ]

This is obviously a bit beyond your scope champ.



Yes, what number isn't?

richoatthedisco was suggesting zero wasn't a number.

But in answer to your comment, there are many types of numbers which aren't integers.

 

[richoatthedisco]

I'm right.

Nothing highlights the problems we have created for ourselves with zero more than this simple question "Is Zero A Number?". Why? Because the answer is both Yes and No - the "two faces" of zero. Nature does not treat zero as a number - it treats it as "nothing" or the absence of a number, but human beings have invented "number zero" and introduced it into everyday use.

Our "Rules" For Zero

When mathematicians formalised our conventional view of zero, as commonly used in mathemathics, they chose the wrong one. This can be demonstrated simply, as follows:

• If zero is a number, as in the conventional view, then 1/0 = Infinity.
• If 1/0 = Infinity then we can divide a line into an infinite number of zero-sized points.
• If we can divide a line into an infinite number of points then we should also be able to construct a line from zero-sized points. Starting at 0, simply stack up zero-sized points until you get to 1.

Try building a line using only zero-sized points and you soon realise it cannot be done. No matter how many points you add, even an infinite number, you never move from 0.

http://www.palopt.com.au/shjnp/blog/2009_05_may.htm

I always was more a physicist at heart than a mathematician:

What's Wrong?

The view of zero commonly used in maths and physics is a one-dimensional "real" number, situated between -1 and 1 on the number line. Physics actually uses a 0-dimension version: "nothing" or "null". The mathematics of Physics not only supports this, but demands it. It is the only "flavour" of zero that meets the rules required by the mathematics of physics.
The differences between a 0-dimensional and a 1-dimensional zero are few but subtle. In the case of a 0-dimensional "null" there is no value, so mathematical operations can be "incomplete" - there are no results. This lack of result is itself a null, so the result is zero. This does not change addition, subtraction or multiplication, but the result of division by zero is zero, not infinity or "undefined".

Physics >>>>>> Mathematics. Physics is how nature works. Maths is how man symbolises it.

 

[Walesy]

Try building a line using only zero-sized points and you soon realise it cannot be done. No matter how many points you add, even an infinite number, you never move from 0.

Well, technically- you can *never* reach infinity- so logically, the statement is sound.

 

[SJ]

If zero is a number, as in the conventional view, then 1/0 = Infinity.
If 1/0 = Infinity then we can divide a line into an infinite number of zero-sized points.
If we can divide a line into an infinite number of points then we should also be able to construct a line from zero-sized points. Starting at 0, simply stack up zero-sized points until you get to 1.
Try building a line using only zero-sized points and you soon realise it cannot be done. No matter how many points you add, even an infinite number, you never move from 0.

1/0 does not = infinity though.

1/x tends to infinity as x tends to 0.

 

[Brad Roo]

I always was more a physicist at heart than a mathematician:
Physics >>>>>> Mathematics. Physics is how nature works. Maths is how man symbolises it.

Hilarious.

 

[richoatthedisco]

Hilarious.

Location: Katamatite.

39 posts in six and a half hours (one every 10 minutes).

The world is my canvas

Now that's hilarious.

 

[Brad Roo]

39 posts in six and a half hours (one every 10 minutes).

Yeah, so what?

Zero is still a number no matter how many times I post it in six and a half hours.

Your behavior is starting to get a little weird champ.

Now that's hilarious.

I'm sorry mate. You obviously have some kind of reputation to uphold of which I am completely unaware.

 

[BomberGal]

I always was more a physicist at heart than a mathematician:
Physics >>>>>> Mathematics. Physics is how nature works. Maths is how man symbolises it.

Oh come on. Yeah our descriptions of quantum mechanics are totally accurate and not just an attempt at symbolising something we don't really know. Heck, even gravity.

BTW, even in high school maths they teach you it's not accurate to say 1/0 is infinity. Type it into Excel. It's undefined.

And if you measure a response as zero in a test, for example, it doesn't mean the test or the subject do not exist. Or that the response mechanism doesn't exist. Zero is still there...