# What is the hardest thing for you to wrap your brain around

Maybe the sheer size of the universe? The speed at which light travels? The size of a quark?

Out of all the things in the universe, what is hardest for you to possibly imagine, as long as it's generally accepted it doesn't have to be proven.

For me it's both the size of the universe and the size of a quark. I mean, sitting here trying to wrap my head around how something can be so unbelievably large, yet also thinking how something can be so unbelievably tiny.

Kind of ironic a little bit, how something like a solar system is similar to an atom even though their sizes vary beyond belief.

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I used to have a problem with infinity. I kept using it like it was a number.
For example, I couldn't understand that the amount of numbers between both 0 and 1 and 0 and 2 were both the same.

My brain.

Pythagorean
Gold Member
I haven't quite wrapped my brain around it yet.

drizzle
Gold Member
The structure of the human eye and how the process of vision functions, and then dreams.

What is the hardest thing for me to wrap my brain around? Has to have to been a tarmac road surface ... well, I suppose wrapping my skull around the road and my brain around the inside of my skull is technically more accurate.

Other than that it is probably why anything exists at all (and, please, do not try and expound some hypothesis involving quantum theory and zero point energy fluctuations ... such hypotheses presuppose the existence of a quantum field and so on)

The Riemann Hypothesis. I don't understand it.

But I'm not even very good at differential equations.

MarneMath
The platypus. Need I say more?

Women...

Diamond.
Why diamonds?

I used to have a problem with infinity. I kept using it like it was a number.
For example, I couldn't understand that the amount of numbers between both 0 and 1 and 0 and 2 were both the same.
Aren't some infinities larger than other infinities?

Aren't some infinities larger than other infinities?
In a way, yes, that's what Cantor demonstrated in the late 1800s.

If you took the number of numbers in between 0-1 and divided it by the number of numbers between 0-2, you should get 1/2.

Let x be the number of numbers between 0-1. There are an equal number of numbers between 0-1 and between 1-2, so the number of numbers between 0-2 is x + x, or 2x. So you have x/2x, and even if x is infinity, they cancel (they're the same infinity).

I'm sure mathematicians will murder me for doing it that way, since I probably did all kinds of things wrong, but I think that's the general idea.

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OmCheeto
Gold Member
Why diamonds?

Why diamonds?
Hard to say.

Why diamonds?
Jimmy Snyder likes to joke a lot. Diamonds are extremely hard. His post above mine is also a pun.

How and if an inverse tangent function "jumps" from positive infinity to negative infinity.

Memory.

How tiny chemical reactions and electrical signals can conjure up such vivid memories from 20+ years ago amazes me. Occasionally I have a dream that has been recurring since I was 7-8 years old (currently 27 years old), and it just fascinates me to think about what all is stored in our brain and how some of it surfaces when you least expect it.

In a way, yes, that's what Cantor demonstrated in the late 1800s.

If you took the number of numbers in between 0-1 and divided it by the number of numbers between 0-2, you should get 1/2.

Let x be the number of numbers between 0-1. There are an equal number of numbers between 0-1 and between 1-2, so the number of numbers between 0-2 is x + x, or 2x. So you have x/2x, and even if x is infinity, they cancel (they're the same infinity).

I'm sure mathematicians will murder me for doing it that way, since I probably did all kinds of things wrong, but I think that's the general idea.
The problem is you're using infinity as if it's a number. You added infinity with infinity. That makes no sense if infinity isn't a number.

The problem is you're using infinity as if it's a number. You added infinity with infinity. That makes no sense if infinity isn't a number.
It makes plenty of sense. For every number in the 0-1 set, there is a corresponding number in the 1-2 set. In my example, x is not necessarily infinity, it's the number of numbers in between 0-1.

The concept of infinities cancelling out, and one infinity being "bigger" than the other, is used ALL THE TIME in calculus when dealing with limits. For example, consider (2^x)/(x!) As x goes to infinity, the top and bottom are both infinity. However, the bottom infinity is "larger" so the limit as it goes to infinity is zero.

The concept of infinities cancelling out, and one infinity being "bigger" than the other, is used ALL THE TIME in calculus when dealing with limits. For example, consider (2^x)/(x!) As x goes to infinity, the top and bottom are both infinity. However, the bottom infinity is "larger" so the limit as it goes to infinity is zero.
For x equal to infinity, both the numerator and denominator are infinitely large, but their ratio is not zero.

For x approaching infinity -- but still finite -- the numerator and denominator also have finite values and their ratio is close to zero, but not zero.

Taking the limits of functions like this is not the same as dividing infinity by infinity.

It makes plenty of sense. For every number in the 0-1 set, there is a corresponding number in the 1-2 set. In my example, x is not necessarily infinity, it's the number of numbers in between 0-1.
It is necessarily infinity.
The concept of infinities cancelling out, and one infinity being "bigger" than the other, is used ALL THE TIME in calculus when dealing with limits.
It is, but adding infinity to infinity is not.

encorp
Entropy.

Why it is what it is, and so on.

WannabeNewton