Will we ever know if Pi is a "normal" or "non-normal" irrational number? Is it within the realm of possibility that we will ever find out? | AskScience Blog

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Monday, August 21, 2017

Will we ever know if Pi is a "normal" or "non-normal" irrational number? Is it within the realm of possibility that we will ever find out?

Will we ever know if Pi is a "normal" or "non-normal" irrational number? Is it within the realm of possibility that we will ever find out?


Will we ever know if Pi is a "normal" or "non-normal" irrational number? Is it within the realm of possibility that we will ever find out?

Posted: 20 Aug 2017 02:02 PM PDT

According to what I've heard, a "normal" irrational number is one whose digits contain every conceivable combination of numbers (including, for example, the social security numbers of everyone who has ever had an SSID in alphabetical order), while a "non-normal" irrational number is one whose digits are infinite but do not contain every possible combination of numbers.

So I guess I have two questions:

1) Will we ever know which of these categories Pi falls under

and

2) How is it possible to have an infinite number of non-repeating numbers without any patterns that doesn't eventually run through every possible numeral combination?

Edit: thank you for all the awesome answers! I now totally understand question #2 and would like to propose another question for anyone who sees this after this edit:

What is an example of a normal irrational number and how can we prove that a number is normal? (Is a normal number defined as any irrational number that contains all the digits of its respective base an infinite number of times...or...?)

submitted by /u/starbounder333
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If Mars at some point had oceans that were filled with life similar to our own, would there still be oil there despite the harsh Marian conditions and what we know about the planet?

Posted: 21 Aug 2017 05:51 AM PDT

The liver breaks down alcohol, but what does it break it down into?

Posted: 20 Aug 2017 04:09 PM PDT

Basically the title

submitted by /u/GeorgieWashington
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Are there any noticeable differences in the behavior of pets raised in different cultures?

Posted: 20 Aug 2017 08:21 PM PDT

Why do most of the tall structures have a needle type thing on top of them?

Posted: 20 Aug 2017 07:15 PM PDT

Like in this picture - https://drive.google.com/file/d/0B5gYDDbu6LmQOXVMZEdDa21LZ0k/view?usp=drivesdk I am new to reddit, I didn't know where to ask, but hope you guys understand me.

submitted by /u/malivp3494
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Why are lightning bolts blue?

Posted: 20 Aug 2017 03:43 PM PDT

Please clear things up for me about the Great Barrier Reef. How much is gone, how much is bleached, can it be saved, what are the long term effects?

Posted: 21 Aug 2017 05:50 AM PDT

Why do eyeglasses "work" even when held at arm's length?

Posted: 20 Aug 2017 04:45 PM PDT

My understanding is that myopia makes images focus in front of the retina. Let's say that in my case it's 1cm. If I pulled my glasses forward 1cm, shouldn't it be the same as having uncorrected vision? Instead, I can see things clearly (even if a little distorted) if I look through eyeglasses even if I hold them a metre away from my eyes. How does that work?

submitted by /u/awh
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If a planet is a gas giant, where does the sky start and the body of the planet begin? Is the entire planet just sky?

Posted: 21 Aug 2017 06:58 AM PDT

Is it possible for meteoroids carrying microorganisms from Earth to travel to another planet, such as Mars, and seed life onto them?

Posted: 21 Aug 2017 12:01 AM PDT

And if possible, how likely is a situation like this to occur successfully?

submitted by /u/Atomo500
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When a meteor impacts the moon, does the Earth feel any consequences?

Posted: 20 Aug 2017 08:24 PM PDT

I understand that very small meteors impact the moon somewhat frequently, but as indicated by the surface of the moon, much larger meteorites have struck it as well.

Assuming a reasonably sized meteor, at what point does a meteor destined to strike the moon pose a risk to Earth? And as a follow up, in what way(s)?

submitted by /u/Scuzzboots
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Are there different "invisible" inks that can only be seen from different UV wavelengths?

Posted: 20 Aug 2017 12:11 PM PDT

For example, could you have one of those hidden message pens sold in stores that couldn't be viewed by another different pen because it uses a different wavelength of light? Or are all the inks visible from any UV light?

And aside from theoretical, is this already a thing?

submitted by /u/Kymysto
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Would a jar that had an absolute vacuum float or sink in water or air?

Posted: 20 Aug 2017 11:23 PM PDT

How to visualise unpolarised light?

Posted: 21 Aug 2017 02:15 AM PDT

I initially thought that unpolarised light was just a single pair of electric and magnetic field waves changing rotations really quickly, giving it the effect of having "random" rotations.

Secondly, I thought of quantum effects being present, where the wave position and rotation would be in superposition until it was observed. But this doesn't make sense, as this would mean you could polarise light just by looking at it. (or the wave function collapses into a point photon, which has no polarisability)

I've read on several websites that unpolarised light is basically both the electric and magnetic fields of light, oscillating in random directions and at different phase differences.

So does it seem that the unpolarised light following the direction of the wave could be visualised as a cylinder? The radius of it being the amplitude of the waves, to be clear. In addition, the "volume" of this cylinder consists of fluctuations in both the electric and magnetic field.

submitted by /u/LECAGO
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Why is the lather of a soap always white, no matter it’s original colour?

Posted: 20 Aug 2017 11:35 AM PDT

Why is Pluto's argument of periapsis 113°?

Posted: 21 Aug 2017 04:52 AM PDT

Looking up the argument, it is quoted as 113.834° (Wikipedia).

This implies that Pluto is closest to the Sun when it is 113° from the first point of Aries, i.e. when it is in roughly the 24th point of Cancer.

However, Pluto was last at perihelion in 1989, when it was in mid-Scorpio. I would have expected its argument of perihelion to be more like 225° based on this knowledge...

Why doesn't the argument of perihelion point to the correct location?

NB: this is not an issue of axial precession and the drift of the constellations with respect to the tropical Zodiac co-ordinate system, that shift is less than 30°, and does not explain this large offset.

submitted by /u/SolFreer
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How are there different forms of ice and how do they work?

Posted: 20 Aug 2017 09:01 PM PDT

I've read that there can be all different types of ice. That don't necessarily have to be cold. Mainly on other planets and stuff, but how is this possible and how does this work? How can it have more than one solid form? Is "hot ice" a thing just held together by pressure and not temperature at all?

submitted by /u/a-blessed-soul
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Do people with artificial hearts burn less energy?

Posted: 20 Aug 2017 01:09 PM PDT

edit: After doing some research it seems artificial heart tech is far less portable than i had thought

submitted by /u/strategosInfinitum
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When did different eye colors emerge in humans, and do we know anything about ancient ancestral eye color?

Posted: 20 Aug 2017 10:49 AM PDT

Why does the USS Indianapolis seem to be in much better condition than the Titanic when it was first found, when the amount of time between the sinking and discovery of each ship was about the same?

Posted: 20 Aug 2017 12:18 PM PDT

The rate of obesity has increased worldwide in recent years. What effect does genetics have on obesity, and are there any specific genes that have a larger impact than others in determining risk of obesity?

Posted: 20 Aug 2017 04:01 PM PDT

If the color white reflects all light and mirrors reflect all light, why don't they look the same?

Posted: 20 Aug 2017 01:37 PM PDT

How are flu vaccines made every year before flu season?

Posted: 20 Aug 2017 06:35 PM PDT

AFAIK, the flu changes and adapts every year requiring us to get the shots every year but how are they made before the new flu strain is even out?

submitted by /u/DangerousViews
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