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  • EADD Moderators: Shambles

Did you know.....?

it's not really a paradox.

consider these two numbers:

7.4444444445
7.4444444446

if you add another (single) decimal place, there are 9 numbers between those numbers, right:

7.44444444451
7.44444444452
7.44444444453
7.44444444454
7.44444444455
7.44444444456
7.44444444457
7.44444444458
7.44444444459

so, there are also 9 numbers between:

4.99999999999999999999999999999999999999999999999999999999999999999999999999999
5.00000000000000000000000000000000000000000000000000000000000000000000000000000

right? they are:

4.999999999999999999999999999999999999999999999999999999999999999999999999999991
4.999999999999999999999999999999999999999999999999999999999999999999999999999992
4.999999999999999999999999999999999999999999999999999999999999999999999999999993
4.999999999999999999999999999999999999999999999999999999999999999999999999999994
4.999999999999999999999999999999999999999999999999999999999999999999999999999995
4.999999999999999999999999999999999999999999999999999999999999999999999999999996
4.999999999999999999999999999999999999999999999999999999999999999999999999999997
4.999999999999999999999999999999999999999999999999999999999999999999999999999998
4.999999999999999999999999999999999999999999999999999999999999999999999999999999

but if the 9 in 4.9 recurs infinitely then you can't go another decimal place to add in those numbers.

4.9r might as well be 5 :)

alasdair
 
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omen_owen mk2 said:
4.9 recurring is the same number as 5

x=4.999999...recurring ergo the numbers go on forever
10x=49.99999.....recurrring ergo the numbers go on forever.

subtracting the first equation from the second...

9x=45.0 (everything after the decimal places cancel as they both go on forever and are therefore by definition the same)

simplify to

x=5

therefore...

4.9999...recurring=5

Q.E.D
Click to expand...

Woah, mind spinner.

It's like when physicists discover parts of the universe that defy all recognised laws. When the impossible occurs.

Reality is caving in on me, man...
 
raas_2012 said:
It's like when physicists discover parts of the universe that defy all recognised laws. When the impossible occurs.
Click to expand...

The impossible cannot occur by definition. Would be interested to hear which parts of the Universe defy all recognised laws too if you happen to know of any.

raas_2012 said:
Reality is caving in on me, man...
Click to expand...

Happens all the time. Somebody needs to invent some kinda hat to keep all those spiky shards of shattered reality out.
 
Shambles said:
The impossible cannot occur by definition. Would be interested to hear which parts of the Universe defy all recognised laws too if you happen to know of any...
Click to expand...

Hi shambles. It's obviously not impossible, but we don't know exactly how dark energy and dark matter or inflation fit into our current 'laws' because noone can explain them yet, only fudge current theories to fit them (though there seem to be some tentative progress with inflation recently). Chances are they fit into laws we've already established in some way (like basic rules of causality, energy conservation etc), but there may be more 'laws' we haven't sussed out yet that totally change the picture. Mechanism of collapse of the quantum probability waveform is also still a mystery (though many worlds answers it most directly (but with too wacky an answer for most).
 
If, with each step you take, you walk half way between your position and your destination, you will never get to your destination.. EVER.

(Can this work when moving in smaller steps than planck length? o_O

Exponential growth:

If you place a single piece of rice on the first square of the chess board, two on the next, four on the next, eight on the next and so on.. The final square would have 9,223,372,036,854,780,000 grains of rice on it. The total amount would be 18,446,744,073,709,551,615.

This would weigh 461,168,602,000 metric tons.. Placed end to end the line of rice would be 60,000,000,000,000 miles long.. How far is that? It could reach Alpha Centauri and back.

If you remove the empty space between the electron and nucleus, the entire human race would fit into a sugar cube.

Sagittarius B, the massive space cloud, is made of alcohol.. a billion billion billion litres of it.
 
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^ They're different, are they not?

If you only ever move half way to a point, how would you ever reach that point?
 
Last edited:
rickolasnice said:
60,000,000,000,000 miles long.. How far is that? It could reach Alpha Centauri and back.
Click to expand...

Did you know that the margin of error for the current estimate of the distance to Alpha Centauri (4.366ly) is ±0.007ly. That doesn't sound like much but that is ±41,149,498,700 miles. In case you are wondering, that is roughly equivalent to 86,000 trips to the moon & back.
 
rickolasnice said:
^ They're different, are they not?

If you only ever move half way to a point, how would you ever reach that point?
Click to expand...

It's the same principle, in aristotle's version Achilles is running after a tortoise and even though it's really slow every time he catches up to where the tortoise is it's moved on if even only by a tiny bit so in theory he can never catch it. Except obviously we know this to be untrue....

Check on Zeno's paradoxes, they both fall under that group of motion paradoxes I think. I can't remember who posed the one you are talking about, although it may well be Aristotle again. They are disproved by the same mathematics, as surely they must be able to because we know both problems posed by the two 'paradoxes' are simply not true from what we observe in daily life. Can't remember who solved them, think Zeno was just responsible for grouping them together but not sure.
 
rickolasnice said:
If you remove the empty space between the electron and nucleus, the entire human race would fit into a sugar cube.
Click to expand...

NSFW:
58caeb1d568c85a35a51e2e17676ee4e.jpg
 
Vurtual said:
Hi shambles. It's obviously not impossible, but we don't know exactly how dark energy and dark matter or inflation fit into our current 'laws' because noone can explain them yet, only fudge current theories to fit them (though there seem to be some tentative progress with inflation recently). Chances are they fit into laws we've already established in some way (like basic rules of causality, energy conservation etc), but there may be more 'laws' we haven't sussed out yet that totally change the picture. Mechanism of collapse of the quantum probability waveform is also still a mystery (though many worlds answers it most directly (but with too wacky an answer for most).
Click to expand...

Am aware of those unsolved mysteries - also black holes and big bangs and many other similarly unsolved mysteries - but, as you also mention, they don't so much 'defy all recognised laws' as simply don't have any that really apply yet cos the evidence is not in in enough quantity and detail to go further than tentative, flawed and almost certainly not correct dabbling around the edges of new (to us) physics. This is not the same as defying laws - just that there are no currently accepted laws to cover those situations.

rickolasnice said:
If, with each step you take, you walk half way between your position and your destination, you will never get to your destination.. EVER.

(Can this work when moving in smaller steps than planck length? o_O
Click to expand...

I think the point of Plank Lengths (and other Plank units) is that they are the smallest possible unit allowable for rather technical reasons that I actually do vaguely know but don't expect any mathematical proofs from me anytime soon. Something smaller than the Plank Length (or any other Plank Unit) really would defy the accepted laws of physics but no evidence that anything does - or even conceivably could.

rickolasnice said:
Sagittarius B, the massive space cloud, is made of alcohol.. a billion billion billion litres of it.
Click to expand...

One of the bits about astrology I do approve of is that as a saggy teary arse me and my ilk are not only vast interstellar clouds of pisswater but also the centre of the galaxy and a supermassive black hole. Russell Grant never mentioned this.

rickolasnice said:
I wasn't wondering but am interested =D Danke.
Click to expand...

Check out the Horizon doc on infinity for loads of stuff about paradoxes (including the one you posted) and related matters of the infinite. Truly fascinating - and utterly headmashing - stuff. Did you know that some infinities are bigger than others? Some are really, really big with others only being infinitely big. The whole topic goes more or less along those lines but really is interesting stuff however boggling it may be. If memory serves, they explain the Achilles & The Tortoise paradox in there somewhere too.
 
rickolasnice said:
If you remove the empty space between the electron and nucleus, the entire human race would fit into a sugar cube.
Click to expand...
nice.

i'm told that "If we could magnify the simplest hydrogen atom to the size of the earth, then the nucleus (a proton) would only be about the size of a basketball. It would be at the very center of the earth and that lonely electron would be found somewhere out in earth's atmosphere."

alasdair
 
i think the point of Plank Lengths (and other Plank units) is that they are the smallest possible unit allowable for rather technical reasons that I actually do vaguely know but don't expect any mathematical proofs from me anytime soon. Something smaller than the Plank Length (or any other Plank Unit) really would defy the accepted laws of physics but no evidence that anything does - or even conceivably could
Click to expand...

I cant remember the details but i remember reading something along the lines of : once you get down to planck level, because of heisenbergs uncertainty principal, a sub atomic particle will be in all possible places within the planck length at the same time.. Or something.

This is a must see if any one hasnt: http://htwins.net/scale2/

The scale of the universe =D
 
Sounds slightly fishy on the basis that the point of Planck Units is that they are the smallest possible division of space, time and so forth so there is only one place and only the very smallest possible thing could fit into it and would fill it - quantum innit: discrete not continuous - and Planck Units kinda define the fundamental size of the quanta. It's entirely possible (or indeed likely) that I'm wrong on that but Plank Units come up all the time in my various readings and viewings of related matters and I have always been under the impression they are a bit like what people once thought about the atom: indivisible by definition. There is only one possible position within a Planck Unit.

Alternatively, wiki surely knows a lot better than I and it's entirely possible you are correct.
 
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