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[Ozle]

(I can't explain why pi gets so much more love than e, though. Maybe it's just that geometry is more intuitive than calculus.)

I think part of it is that more people know about pi than e.  Pi is taught in elementary geometry, while e is taught in calculus.

But they work so well together!

[theory]

(I can't explain why pi gets so much more love than e, though. Maybe it's just that geometry is more intuitive than calculus.)

I think part of it is that more people know about pi than e.  Pi is taught in elementary geometry, while e is taught in calculus.

Plus pi is a lot easier to understand.  Anyone can understand why pi is cool: every single circle in the universe obeys the same rule about its size.

Try describing e, on the other hand: e is defined as where e to the power of x is its own derivative.  What's exponentiation?  What's a derivative?  Why is this special?

[SirPeebles]

I like to think of the intuitive connection as follows:

If an object is moving towards you with a speed equal to its distance from you, its motion is described by e.
If an object is accelerating towards you with an acceleration equal to its distance from you, its motion is described by pi.

(Technically I should say proportional, not equal.)

[qmech]

(I can't explain why pi gets so much more love than e, though. Maybe it's just that geometry is more intuitive than calculus.)

I think part of it is that more people know about pi than e.  Pi is taught in elementary geometry, while e is taught in calculus.

Plus pi is a lot easier to understand.  Anyone can understand why pi is cool: every single circle in the universe obeys the same rule about its size.

Try describing e, on the other hand: e is defined as where e to the power of x is its own derivative.  What's exponentiation?  What's a derivative?  Why is this special?

But pi is defined as half the imaginary period of the complex exponential!

[SirPeebles]

The other intuitive way that I wish students were introduced to e is via probability, particularly the following:

You have 1 in X chance of dying each time you perform a certain activity, where X is some large number (e.g. 1 in 1000).  You perform that activity X times.  Then the odds that you survive are about 1 in e.

Giving students a reference point for probability seems more useful in everyday life than a geometric fact about circles.

[blueblimp]

Try describing e, on the other hand: e is defined as where e to the power of x is its own derivative.  What's exponentiation?  What's a derivative?  Why is this special?

Invest $1 at 100% interest compounded daily. After a year, you'll have almost $e.

[florrat]

Also, she says that in calculus you deal with "infinities 2 levels deeper than" countably infinite (around 4:00). I assume that she means with this the cardinality beth-2, which is 2^c (where c is the continuum), but how often do you deal with that when doing calculus? I think never. There are c real numbers, c continuous functions, c differentiable functions, c complex numbers, c open subsets of R^n. What thing has cardinality 2^c when doing calculus?

When typing this up, I was thinking how many topologies there are on an infinite set X. Is it 2^(|X|) or 2^(2^(|X|))?

[SirPeebles]

Also, she says that in calculus you deal with "infinities 2 levels deeper than" countably infinite. I assume that she means with this the cardinality beth-2, which is 2^c (where c is the continuum), but how often do you deal with that when doing calculus? I think never. There are c real numbers, c continuous functions, c differentiable functions, c complex numbers, c open subsets of R^n. What thing has cardinality 2^c when doing calculus?

When typing this up, I was thinking how many topologies there are on an infinite set X. Is it 2^(|X|) or 2^(2^(|X|))?

I remember attending a lecture by a mathematician named Nik Weaver who made this point and explored the study of functional analysis in a restricted axiom system where power sets don't always exist.

One issue is that, while you can talk about whether or not a specific function is continuous, I believe you ran into trouble when you tried to talk about the set of ALL continuous functions.  To specify that set, you begin by considering all functions, then restricting to the subset which satisfy a certain condition (continuity).  So even though the set of all continuous functions has the continuum cardinality, how would you define the set without considering that larger cardinality collection of all functions?

[theory]

You guys are proving my point, in that none of those explanations for why e is special is something sensible to a layman or middle schooler.  Pi is always going to be more special than e, and there shouldn't be anything wrong with that.

[SirPeebles]

You guys are proving my point, in that none of those explanations for why e is special is something sensible to a layman or middle schooler.  Pi is always going to be more special than e, and there shouldn't be anything wrong with that.

When I was in middle school, I played a lot of video games.  One was named Earthbound.  There were a bunch of these really strong items that were rare drops.  You had a 1 in 256 chance of getting one after each encounter with a certain enemy.  I remember thinking at the time that if I battled 256 enemies I'd be guaranteed one.  But no.  After 256 battles, there would be a 1 in e chance of still not getting one.  Man, I wish my math teacher had taught me that.

I don't think I ever made use of circles until physics in high school.  Even in then, just in class.

[Axxle]

I've actually been using phi in the games I'm making more than pi or e, probably since I don't worry about the physics engine too much.  It's great for distribution.

[Jimmmmm]

11664, with a 1024.

[Polk5440]

11,472 on my third try. I figured out an algorithm, got the 1024 block, then messed it up.

I was trying to keep my largest # in a corner (say top right), then next largest blocks around it, etc. Condense towards the top so largest blocks are in top row, increasing left to right. Then in second row focus on getting a big enough number all the way to the left to be able to condense up again.

I had gotten to a point where I was always moving left, right, or up. Then I accidentally hit down .

[Polk5440]

16928... I hit down again.

The self-discipline this takes!

[Jimmmmm]

16852.

[AHoppy]

11,472 on my third try. I figured out an algorithm, got the 1024 block, then messed it up.

I was trying to keep my largest # in a corner (say top right), then next largest blocks around it, etc. Condense towards the top so largest blocks are in top row, increasing left to right. Then in second row focus on getting a big enough number all the way to the left to be able to condense up again.

I had gotten to a point where I was always moving left, right, or up. Then I accidentally hit down .

I've found this works, but you also need to not get in a situation where it forces you to hit down, which I have had a hard time doing...

[eHalcyon]

I showed the game to a friend, who noted that it is very similar to Threes, which is apparently an extremely popular game that launched Feb 10 in the Apple App Store and just recently launched on Android.

[qmech]

When typing this up, I was thinking how many topologies there are on an infinite set X. Is it 2^(|X|) or 2^(2^(|X|))?

I think it's the latter.  There are 2^2^|X| ultrafilters on an infinite set X, and an ultrafilter (together with the empty set) is a very special case of a topology.  (That's right for X = N, but I wouldn't swear to it in general, so don't rely on it for your proof of the Riemann hypothesis.)

[Polk5440]

11,472 on my third try. I figured out an algorithm, got the 1024 block, then messed it up.

I was trying to keep my largest # in a corner (say top right), then next largest blocks around it, etc. Condense towards the top so largest blocks are in top row, increasing left to right. Then in second row focus on getting a big enough number all the way to the left to be able to condense up again.

I had gotten to a point where I was always moving left, right, or up. Then I accidentally hit down .

I've found this works, but you also need to not get in a situation where it forces you to hit down, which I have had a hard time doing...

Oh, right. So what I was doing was if there were two moves to make (without hitting down) play the one that leaves you a move for sure next time, if you are able. Then if you get a bad generation, you still have an option. After playing it a couple more times, I think I got lucky with the generations I had on my 16k run, too. If you have to go down, then the goal is to get those big numbers back to a side as fast as possible and "lock" them again.

I found this "solver" this morning: http://ov3y.github.io/2048-AI/.

[Jimmmmm]

32760, with a 2048 and a 1024.

[Polk5440]

Win!

[Polk5440]

28,108 with one 2048 block. I think I will retire from that game now.

[pingpongsam]

8304 back to something that doesn't make me feel autistic.

[Kirian]

32760, with a 2048 and a 1024.

Oh man, you just needed eight more points...

[eHalcyon]

Finally got it!  Final score 20704.