Thread: Interesting, surprising facts

Awesome idea for a thread. I have a bunch of these rattling around in my brain somewhere, though it's hard to dredge them out.

One of my favourite surprising facts is that there are an infinite quantity of whole numbers, and an infinite quantity of decimal numbers, but there are more decimal numbers than whole numbers.

Hmm... oh, when you sneeze because you have some kind of a bug, that's not an adaptation of the human body 'getting rid' of the bug. That's an adaptation of the bug, messing with your nose nerves to spread itself as far and wide as possible.

Originally Posted by Xei

Hmm... oh, when you sneeze because you have some kind of a bug, that's not an adaptation of the human body 'getting rid' of the bug. That's an adaptation of the bug, messing with your nose nerves to spread itself as far and wide as possible.

Hmm, are you sure this is a fact? How well established is it? I did a quick google search, and as far as I could tell it is a hypothesis, but I may have misunderstood.

Can't remember where I got it from.

Of course, animals evolved to sneeze before pathogens took advantage of it. In fact they may have evolved it to get rid of them. But once the mechanism was in place, it was fairly certain that the pathogens would evolve to trigger it.

All the gold ever mined could fit into a 20 metre cube.

My hubby has told me that fact about gold. I still find it incredibly hard to believe

Originally Posted by Xei

Awesome idea for a thread. I have a bunch of these rattling around in my brain somewhere, though it's hard to dredge them out.

One of my favourite surprising facts is that there are an infinite quantity of whole numbers, and an infinite quantity of decimal numbers, but there are more decimal numbers than whole numbers.

Hmm... oh, when you sneeze because you have some kind of a bug, that's not an adaptation of the human body 'getting rid' of the bug. That's an adaptation of the bug, messing with your nose nerves to spread itself as far and wide as possible.

why would this first one be surprising..... look at first five positive whole numbers 1, 2, 3, 4, 5 and look at decimal numbers in that range..... how much decimal number's are there between just 1 and 2 ? lol 1.000001...1.000002.........1.00021545454 lol it's infinite lol I guess....now how much are there between 1 and 5 whole numbers decimal....so for every whole number there is even a million more decimal so I guess that's the reason there are more decimal numbers and idk and if between every whole number was a million of decimals then for 100 whole numbers there would be like 100 million decimals and for 1000 whole nubers there would be 1000 million decimals so I guess it's the reason there are more decimals or at least th

Originally Posted by Zhaylin

My hubby has told me that fact about gold. I still find it incredibly hard to believe

Actually, I usually use a 20 metre cube to envisage the current population of Earth. It's roughly 8,000,000,000, which is 2000*2000*2000. So the number of people on Earth is the same as the number of centimetre cubes in a 20 metre cube (or the same as the number of millimetre cubes in a 2 metre cube).

So if you distributed all the gold ever mined equally to everybody alive on Earth, we'd each get a cubic centimetre.

Originally Posted by Karloky

why would this first one be surprising..... look at first five positive whole numbers 1, 2, 3, 4, 5 and look at decimal numbers in that range..... how much decimal number's are there between just 1 and 2 ? lol 1.000001...1.000002.........1.00021545454 lol it's infinite lol I guess....now how much are there between 1 and 5 whole numbers decimal....so for every whole number there is even a million more decimal so I guess that's the reason there are more decimal numbers and idk and if between every whole number was a million of decimals then for 100 whole numbers there would be like 100 million decimals and for 1000 whole nubers there would be 1000 million decimals so I guess it's the reason there are more decimals or at least th

This same argument would tell you that there are more fractions than whole numbers. But there are actually the same quantity of fractions as whole numbers.

Meaning of life is 42... rotated, "2b."
The meaning of life is "to be."


2b.JPG

The PIE and "to be" tricks for me are the kind of facts that lend credibility to the "life is a dream" hypothesis.

Originally Posted by TiredPhil

Meaning of life is 42... rotated, "2b."

The meaning of life is to be upside down?

Originally Posted by Xei

The meaning of life is to be upside down?

Bats figured this out a long time ago. Humans still have so much to learn.

As for my contribution; there are more stars in the universe than there are grains of sand on all the beaches and deserts of Earth.

18 Microwave Snacks You Can Cook In A Mug

most of this.

Originally Posted by TiredPhil

Meaning of life is 42... rotated, "2b."
The meaning of life is "to be."


2b.JPG

I thought it was where do I belong?

Originally Posted by Zhaylin

My hubby has told me that fact about gold. I still find it incredibly hard to believe

Gold is the only metal that doesn't break down over time.

Originally Posted by Heavy Sleeper

Bats figured this out a long time ago. Humans still have so much to learn.

As for my contribution; there are more stars in the universe than there are grains of sand on all the beaches and deserts of Earth.

For some reason I thought you said stairs at first and tried to imagine how that was possible for a good few seconds. Think I'm losing my mind lately.

Originally Posted by Dianeva

For some reason I thought you said stairs at first and tried to imagine how that was possible for a good few seconds. Think I'm losing my mind lately.

All those stairs and no wheelchair access. This is exactly why we need a space elevator!

Cat spray can smell worse than skunk spray.

And can happon even more often too.

Originally Posted by Karloky

why would this first one be surprising..... look at first five positive whole numbers 1, 2, 3, 4, 5 and look at decimal numbers in that range..... how much decimal number's are there between just 1 and 2 ? lol 1.000001...1.000002.........1.00021545454 lol it's infinite lol I guess....now how much are there between 1 and 5 whole numbers decimal....so for every whole number there is even a million more decimal so I guess that's the reason there are more decimal numbers and idk and if between every whole number was a million of decimals then for 100 whole numbers there would be like 100 million decimals and for 1000 whole nubers there would be 1000 million decimals so I guess it's the reason there are more decimals or at least th

Neither is bigger actually, as they're both infinite. But this is something I have to discuss with my math teacher at university, he's a cool dude and he will like it. I'll report back.

Originally Posted by Athylus

Neither is bigger actually, as they're both infinite. But this is something I have to discuss with my math teacher at university, he's a cool dude and he will like it. I'll report back.

There are different levels of infinity. In this case, you have infinity times infinity decimals.

Originally Posted by Dianeva

Whether something is interesting or not is subjective. But please try to include only facts that will be legitimately surprising and interesting to most people. Not just little-known obscure facts that are neither relevant nor very surprising.

------

This is an amazing coincidence I've just come across. I wouldn't be surprised if a lot of other people have already heard this, but somehow I've never heard it before.

Spoiler for Amazing PIE fact:

It gets better. Did you know that the formula for the approximate volume of a pizza is Pi(Z*Z)A?
Pizza..jpg

Originally Posted by dutchraptor

It gets better. Did you know that the formula for the approximate volume of a pizza is Pi(Z*Z)A?
Pizza..jpg

I dispute that, as those are not the common symbols to use for that. The most common way of writing it would probably be π∙r²∙h

Originally Posted by khh

I dispute that, as those are not the common symbols to use for that. The most common way of writing it would probably be π∙r²∙h

That's ridiculous, you can use whatever the hell you want. Since when must you use the letter h to do represent a variable height.

Originally Posted by Athylus

Neither is bigger actually, as they're both infinite. But this is something I have to discuss with my math teacher at university, he's a cool dude and he will like it. I'll report back.

I actually agree with you, even though I know the reasoning. Your math teacher will no doubt tell you that there are less decimal numbers than whole numbers. And this is true in a way. In most cases, if you can map one set one-to-one with items from another set and use up all the items from the first set, but not even come close to using up all the items from the second set, then there must be more items in the second set than the first set. For example, you could map numbers from positive integers to positive decimals like so:
1 = 1.1
2 = 1.12
3 = 1.123
4 = 1.1234
5 = 1.12345
....
14 = 1.1234567891011121314
15 = 1.123456789101112131415
...

You could go on and on like that until you get:
∞ = 1.1234567891011121314151618.....100101102103...... .

You've then mapped every single positive integer to a unique decimal number, and you still have so many decimal numbers left over (nothing that isn't in the 1.1-1.3 range has been used). There are still an infinite number of decimal numbers left after the mapping.... so there must be infinitely more decimal numbers than positive integers.

That's the reasoning anyway. And in a way this makes sense, perhaps it's useful in some situations. But I think, on a more common-sense level, one infinity can't be greater than another. Infinity is a concept, not an actual number, though it can be treated like a number in some circumstances. And the concept of infinity refers to some abstract quantity which is by definition greater than any amount we can possibly name. To say that ∞1 > ∞2 contradicts the definition of infinity. Because by definition nothing can be greater than ∞2.

Originally Posted by dutchraptor

That's ridiculous, you can use whatever the hell you want. Since when must you use the letter h to do represent a variable height.

Well if you can name them whatever you want then there are a lot more chances for it to spell a name. It doesn't seem like such an amazing coincidence. I mean you could say there's a box with length B, width O and height X..... What's the volume? BOX! !!!!!

The Capgras Delusion is a psychological disorder where you think everybody you know has been replaced with an impostor.

A cool hypothesis to explain this (and one which has some evidence, I think) is that the neural pathways from the part of the brain which recognises people to the part of the brain which causes an emotional response has been in some way severed. So you see your loved ones and yet don't feel any kind of emotions towards them. Your brain rationalises this by insisting that they're somebody different.

The Fregoli delusion is the opposite. You think that different people are in fact one person. It's pretty funny, really.

Originally Posted by Marvo

There are different levels of infinity. In this case, you have infinity times infinity decimals.

Ah well, technically the infinity of the whole numbers (let's call it N0) multiplied by itself should be the number of pairs of whole numbers (in the same way that multiplying 2 by 3 means count how many points there are in a 2 by 3 grid), in other words the number of whole points in the first quadrant of the plane, but this turns out just to be equal to the original infinity; i.e. N0*N0 = N0. That's surprising fact #2 about infinity.

The infinity of decimals, call it N1, turns out that it should equal, if anything, 2 to the power of N0. But this turn out to be impossible to prove from the axioms of number theory or set theory, and in fact you can consistently take it to be either true or false. Extremely surprising fact about infinity #3.

Originally Posted by Dianeva

There are still an infinite number of decimal numbers left after the mapping.... so there must be infinitely more decimal numbers than positive integers.

Technically this reason doesn't work. For example, you could double every whole number. This mapping sends every whole number to every even number inside the whole numbers. There are an infinity quantity of whole numbers still left after the mapping, but you can't then conclude that there are infinitely more whole numbers than whole numbers.

In the same way you could map the infinite quantity of decimal numbers into the space between, say, -1 and 1.

The problem is that you're trying to show that there are some decimals left untouched no matter what mapping you use, not that any specific map fails (it's always possible to come up with maps which fail). In other words, given a map from the whole numbers to the decimals, you need to find a methodical way of producing a decimal which can't be touched anywhere on the list. There's an ingenious way of doing this.

That's the reasoning anyway. And in a way this makes sense, perhaps it's useful in some situations. But I think, on a more common-sense level, one infinity can't be greater than another. Infinity is a concept, not an actual number, though it can be treated like a number in some circumstances. And the concept of infinity refers to some abstract quantity which is by definition greater than any amount we can possibly name. To say that ∞1 > ∞2 contradicts the definition of infinity. Because by definition nothing can be greater than ∞2.

Perhaps I've become numb through overexposure, but I don't feel there's anything wrong with it. The maths of different infinities does behave in a nice consistent way, anyway. I'd turn what you said on its head and interpret it in the opposite way - these results simply tell us that our intuitions about infinity are inconsistent.

After all... the infinity of the decimals is bigger than the infinity of the whole numbers. But surely we don't want to say the infinity of the whole numbers is not infinite? There's always a bigger whole number than any whole number you can think of. They go on forever and ever. We've gotta call them infinite.

Originally Posted by AURON

18 Microwave Snacks You Can Cook In A Mug

most of this.

I just tried the chocolate chip cookie in a cup recipe. It rocks.