*Me:* I used to think correlation implied causation. *Me:* Then I watched this video. Now I don't. *Friend:* Sounds like the video helped. *Me:* Well, Maybe.
The video explains that it's not because two elements are correlated that one is the cause of the other. One '''can''' be the cause, but it's not logical to imply it just from their correlation. It was not the floor itself that broke the glass even though it is related to the breaking, it was it's impact with the glass, '''caused''' by gravity.
Nicholas Cage movies are correlated by yet another unmentioned variable: summer. Nicholas Cage is an action movie star. Action movies are generally targeted for summer releases. Summer is also hot, which is the cause behind air conditioner sales and swimming, the latter of which is of course the cause of drowning.
That's true, but the data shows a close correlation over multiple years, not just over the seasons of a given year. It just so happens that the summers of years with more Nicholas Cage movies also happen to have more drownings.
Extrapolation is actually necessary in certain circumstances though - for example predicting growth of global human population, economic forecasts, environmental forecasts regarding climate change.... anything that has to do with the future.
A class on non linear relationships would be FANTASTIC :) And more classes in general (e.g., on general versus mixed effects models; GAMs etc...) Thank you for your dynamism!
It doesn't really matter either way. The general consensus is that the last letters from the latin alphabet, i.e. x, y and z are being used as placeholderds for unknown quantities, whereas letters from the beginning (e.g. a, b and c) or middle (e.g. k, l, m and n) are being used as placeholders for known quantities (to be supplied or deduced when doing a specific example). The placeholders for know quantities may be different in different countries for many reasons (ease of pronounciation, legibility, tradition, etc.). Tradition usually also means that often the same equation uses different placeholders in math and physics. Example: in Math class the may use y = ax + b, in Physics class they may use y = mx + c, just because ... (and then of course in the kinetic equations this becomes e.g. v = at + v0 representing physical quantities).
I feel some people go so far in this argument that they seem to argue the correlation disproves causation. Eg. "thats only correlation it doesnt prove causation, obviously you are wrong" Yes correlation doesnt prove causation, but it most definitely does not disprove causation. Further it might suggest causation, or that a 3rd factor is causing both phenomena to occur. Its frustrating to give data in an argument, to have the other side counter with, "thats only correlation, it doesn't prove causation, you are wrong."
Wait... Technically everything is connected. Maybe the relationship between 2 variables are correlated even tho it doesn't make sense that they cause each other, but that happens because these 2 variables are connected to other variables that we didn't observe yet these variables can indirectly influence the relationship between the main 2 variables we are comparing. So I guess that means, one way or another, correlation DOES imply causation. Error 404
So this was great. You are definetly one of my favorite crash course hosts. And I took statistics back in 1994. I have one question that boggles me. When and who is right, who determines the reality or that there is causation? Example .... cigarette smoking and lung health. The negative effects are clearly visible, the correlation is there ... but is it really the cause? When and how do we get to a positive causality? Or is it left to the interpreter? Or is it just all relative? Or by the end of the day it's meaningless and everyone can make the statement "correlation doesn't equal causality" and your data and beautiful charts and correlations just fizzle out?
That's the tricky part! Ultimately they all need to be interpreted. Overall, there is no true "proof", just higher levels of confidence. I am confident that the city of Paris exists, even though I've never been there. The process generally starts by asking "is this even possible?" and "Does this make some sense?" Then you can go back and try to find some other cause of the data you got. Eventually, you have to do experiments carefully. But even well-planned experiments can have hickups and biases (there have been many cases of seemingly high-confidence experiments not being repeatable by other professionals). Often, multiple experimenters need to come up with the same results on their own (and usually with their own equipment) before the scientific community is convinced. Overall, it's a difficult and time consuming process.
In health data like the lung example, there is a set of criteria called the Bradford-Hill criteria. Google it. This is criteria for determining if something can be considered causation. It is not a checklist: you still need to do your own scientific interpretation. But it’s a good way to get an idea of whether the data your looking at implies causation or not. The criteria are: effect size, consistency, specificity, temporality, biological plausibility, dose-response relationship, coherence, analogous results. Interestingly, Bradford Hill who came up with this list, is the same Hill who co-authored the original Doll and Hill paper that established the linked between smoking and lung cancer!
...how do you fit a regression line through a circle (or fat ellipse) on a 2D-scattered, plot... ...how do you define accuracy where there are fewer data points, even though the fitted-curve looks similar, (do you overlay random information certitude measure sigma bars)... *_...(in case you missed the first question: flip the plot axes for a different regression line...)_*
"Post hoc ergo propter hoc" ("after this, therefore because of this") is one of the most ANNOYING fallacies there are! As well as the related "putting the cart before the horse", or whatever it's officially called (women make less on average, therefore it was intentional) PS don't forget about Simpson's paradox!
Squared correlation r^2 Line of regression Can anyone explain a little more in depth standard deviation? Im still not sure what information it tells us in a scatter plot
"mx + c" is also reasonable in the sense that "c" is often used to refer to some "constant". This is also the explanation for e=mc^2. Because the speed of light in a vacuum is a constant.
Correlation does not neccesarily state that causation is found between two variable. However. don't walk away thinking correlation disproves causation. This isn't politics. There are more than two possibilities. (There are in politics too, but ignore that.) Thanks, and have a good day. As a final note: Time taken to get from point a to point b is negatively correlated with speed. There is (by definition no less) causation there.
Sango, that's a good tip. But I fear that addressing people as the "scientifically illiterate" might not be the best way to get your message across. (What I would give for Crash Course: Rhetoric).
It is absolutely true that everyone begins illiterate, and there should be no shame in that. However, referring to people as such can cause them to misinterpret your message as being condescending, even though you had no intention to be that way. Regardless, they are now slighted, and in retaliation, they ignore your advice, no matter how reasonable it was.
This is fake news. Nearly every person who has an automobile accident is wearing socks. Correlation? I don't think so. I stopped wearing socks years ago and haven't been in a car crash since.
I got in a small accident once because I was driving in sandals and the bottom of the sandal wedged against the floor, preventing me from applying the brakes. I hopped a curb and wedged my front bumper into a wooden fence. I think I learned that it's technically illegal to drive in sandals in my state, but I was never warned about it. I just felt like sharing.
I've seen people both conflate correlation with causation in situations that are clearly coincidence and insist that correlation does not equal causation when the pattern of cause and effect are obvious.
*_...there'd be a negative-correlation where reducing air conditioning increases swimming..._* *_...or, an overriding 'cause' leading to watching-speeding or doing-it, another, negrelation..._* *_...so...what's the mathematically-concisely-stated-statistical-rule for causality-guessing..._* *_...(making statistics, like modulo arithmetic: where compounded moduli may get better)..._*
Anecdotally, after playing Simpsons: Hit & Run (a GTA clone), I genuinely drove more recklessly for a little while. Not like I got into an accident, but like I was cutting corners tighter, and being a little heavier on the pedal. I had to work at it to knock it off. Really really good game though.
Man SOME PEOPLE should listen to this video very fucking closely. I'm getting nauseous every time some oaf wants to support their wildest claims by citing some random statistics.
I love this series! However, you made one, small lie: R^2 does not have to be between zero and one, but can in fact be negative. You spoke of the mx + b, but failed to mention what value it has to determine b (and if chose horribly wrong, it can give you negative R-values, due to estimate a model that is worse than random). Keep up the series! :)
When it's hot, people with no A.C. tend to go to the movies. Movie theaters are usually quite air conditioned and you get to enjoy it for a couple of hours.
Every time I see one of these videos I look at the view count and know that there's that many more people out there that are better educated about this topic and that makes me very optimistic for the future keep up the great work guys
I was TRICKED into watching this by the title. How hard would it be to add, "WARNING! THIS IS STATISTICS, DWEEB" to what appears on my temptation screen? It was really good.
I watched this video without having seen the previous ones, and spent a considerable amount of time wondering "what the heck is an 'old faithful eruption' ?"
(For those who have the same problem: "Old Faithful" seems to be the name of a geyser. (I don't know where it is, but when an English RUclips show refers to a location, person, event or sports ritual you have never heared of, you can be pretty sure it's in North America.)
Guess what, one f(x) = mx + b can, of course, only separate variables linearly. But add more and more of f(x) = mx + b to your model then you enter the world of Neural Networks! ;)
You can "learn" more spurious correlations here: www.tylervigen.com/spurious-correlations and even discover new correlations here! tylervigen.com/discover
If A caused B then there is a correlation between A and B. The rising of the Sun caused the eating of an ice cream by John. Therefore, there is a correlation between the rising of the Sun and the eating of an ice cream by John. My question is, how would you quantify those events and plot the correlation between them on a graph? Would I count the number of times these events occurred? What if an event only causes another once? What if John died after the first ice cream? Can we still say that there was a correlation?
Is anyone else surprised about that slope for heights of dads v. heights of sons ? 0.5 ? Isn't that weird ? At what age were the sons measured ? Surely, height of dad v. height of son should look a little like 1:1 -- otherwise would people not be shorter and shorter ?
Its TIME its always time!!! many many many things are correlated over time but have no real relation. Randomly selected health studies are much less likely to be unrelated. Exists a reddit for unrelated correlation.
The example of changing the units on the y-axis is only relevant if you're not doing your dimensional analysis properly. If the slope of the feet-feet plot is 0.5, then the slope of the meter-feet plot is 0.15m/foot=0.5
@crash course team, not all the graphs in the datasaurus dozen shown in the end doesn't seems like having same correlation coefficient. Few look like having r=1, few r=0. Please correct me if I'm wrong
Gain in my knowledge is perfectly correlated with the number of crash course videos I watch and shows the value of absolute +1 as the correlation coefficient #CrashCourse ..... 😁😁😁
This was the funniest Crash Course video I've ever seen. Her comedic timing is excellent. Though I still don't know if that clever mayor was a man or a woman.
Bah. I know my rock keeps away tigers because I have never seen a tiger for as long as I have had it.
SilortheBlade Makes sense to me
Puppy cat! I didn't know that they'd made a stuffed animal of him. This has greatly improved my day.
does the "r²=0.7" mean that we could predict accurately by 70% ?
yes
air con and conairs 😆
This needs to be mandatory viewing for EVERYONE.
I second that!
*Me:* I used to think correlation implied causation.
*Me:* Then I watched this video. Now I don't.
*Friend:* Sounds like the video helped.
*Me:* Well, Maybe.
lol. Well, probably.
The video explains that it's not because two elements are correlated that one is the cause of the other. One '''can''' be the cause, but it's not logical to imply it just from their correlation. It was not the floor itself that broke the glass even though it is related to the breaking, it was it's impact with the glass, '''caused''' by gravity.
XKCD is a pretty good comic :)
Kachimbo somebody missed the joke
Herodotus Von 8428 no, someone got the joke, but felt the need to expand our knowledge.
Nicholas Cage movies are correlated by yet another unmentioned variable: summer. Nicholas Cage is an action movie star. Action movies are generally targeted for summer releases. Summer is also hot, which is the cause behind air conditioner sales and swimming, the latter of which is of course the cause of drowning.
Pfhorrest Or it could be that people who have endured a Nicholas Cage movie are more likely to drown themselves ...
That's true, but the data shows a close correlation over multiple years, not just over the seasons of a given year. It just so happens that the summers of years with more Nicholas Cage movies also happen to have more drownings.
"Correlation does not equal causation" was my old stats teacher's favourite phrase along with "always interpolate, never extrapolate." :)
Extrapolation is actually necessary in certain circumstances though - for example predicting growth of global human population, economic forecasts, environmental forecasts regarding climate change.... anything that has to do with the future.
Post hoc ergo propter hoc!
When she apologises for using imperial units......
I haven't watched Nicholas Cage movies, AND I haven't drowned. Aha!
"..if people blink more when they're lying!"
Our Professor: 😳
Better explanation then my university level stats class. 👍
This has been my favorite CrashCourse season by far. Really enjoying the material and the host!
I wish all my scatterplots ended up making pictures of dinosaurs.
now go teach the media this so they can stop blaming video games for all the worlds problems
who is here for school
Beware ye who enter this comment section...
That's not the graph Jim Carrey and Jenny McCarthy showed me.
A class on non linear relationships would be FANTASTIC :) And more classes in general (e.g., on general versus mixed effects models; GAMs etc...) Thank you for your dynamism!
Watching Stat for fun again.
Comment containing the word EVERYONE in caps lock.
Child Fs but why
Ok, you talked me into it.
containing the word EVERYONE in caps lock
Everyone needs to see this! Just because things seem connected on the surface doesn’t mean they’re related and Visa Versa!
psst. its vice versa, not visa versa
and if they're not connected then they DON'T CORRELATE. this shit's a red herring.
@@improover113 talking specifically about causal relationships, as the phrase states explicitly
y = mx + b , is this some American standard? In Sweden it's y=kx+m
It doesn't really matter either way. The general consensus is that the last letters from the latin alphabet, i.e. x, y and z are being used as placeholderds for unknown quantities, whereas letters from the beginning (e.g. a, b and c) or middle (e.g. k, l, m and n) are being used as placeholders for known quantities (to be supplied or deduced when doing a specific example). The placeholders for know quantities may be different in different countries for many reasons (ease of pronounciation, legibility, tradition, etc.). Tradition usually also means that often the same equation uses different placeholders in math and physics. Example: in Math class the may use y = ax + b, in Physics class they may use y = mx + c, just because ... (and then of course in the kinetic equations this becomes e.g. v = at + v0 representing physical quantities).
I don't know, Nic Cage may be dragging people to the deep after they see his movies. The evidence is there.
“Mr. Fluffy misses you.”
*pouts thinking of the cat I don’t have missing me*
I feel some people go so far in this argument that they seem to argue the correlation disproves causation.
Eg. "thats only correlation it doesnt prove causation, obviously you are wrong"
Yes correlation doesnt prove causation, but it most definitely does not disprove causation. Further it might suggest causation, or that a 3rd factor is causing both phenomena to occur. Its frustrating to give data in an argument, to have the other side counter with, "thats only correlation, it doesn't prove causation, you are wrong."
EasySnake 100% agree
i've seen this too! It irks me to no end.
This is crash course statistics and statistics is all about probability?
Crash Course, thank you so much. This awesome course is definitively above the curve!
Thank u Crash Course
Islam xDDDD
So no one's commenting how she's got a *puppycat plush toy* behind her?
"Air Cons, and Con Airs"
Amazing
Wait... Technically everything is connected. Maybe the relationship between 2 variables are correlated even tho it doesn't make sense that they cause each other, but that happens because these 2 variables are connected to other variables that we didn't observe yet these variables can indirectly influence the relationship between the main 2 variables we are comparing. So I guess that means, one way or another, correlation DOES imply causation. Error 404
So this was great. You are definetly one of my favorite crash course hosts. And I took statistics back in 1994. I have one question that boggles me. When and who is right, who determines the reality or that there is causation?
Example .... cigarette smoking and lung health. The negative effects are clearly visible, the correlation is there ... but is it really the cause? When and how do we get to a positive causality?
Or is it left to the interpreter? Or is it just all relative? Or by the end of the day it's meaningless and everyone can make the statement "correlation doesn't equal causality" and your data and beautiful charts and correlations just fizzle out?
That's the tricky part! Ultimately they all need to be interpreted. Overall, there is no true "proof", just higher levels of confidence. I am confident that the city of Paris exists, even though I've never been there. The process generally starts by asking "is this even possible?" and "Does this make some sense?" Then you can go back and try to find some other cause of the data you got. Eventually, you have to do experiments carefully. But even well-planned experiments can have hickups and biases (there have been many cases of seemingly high-confidence experiments not being repeatable by other professionals). Often, multiple experimenters need to come up with the same results on their own (and usually with their own equipment) before the scientific community is convinced. Overall, it's a difficult and time consuming process.
In health data like the lung example, there is a set of criteria called the Bradford-Hill criteria. Google it. This is criteria for determining if something can be considered causation. It is not a checklist: you still need to do your own scientific interpretation. But it’s a good way to get an idea of whether the data your looking at implies causation or not. The criteria are: effect size, consistency, specificity, temporality, biological plausibility, dose-response relationship, coherence, analogous results. Interestingly, Bradford Hill who came up with this list, is the same Hill who co-authored the original Doll and Hill paper that established the linked between smoking and lung cancer!
...how do you fit a regression line through a circle (or fat ellipse) on a 2D-scattered, plot...
...how do you define accuracy where there are fewer data points, even though the fitted-curve looks similar, (do you overlay random information certitude measure sigma bars)...
*_...(in case you missed the first question: flip the plot axes for a different regression line...)_*
Nicholas Cage causes air conditioners.
"Post hoc ergo propter hoc" ("after this, therefore because of this") is one of the most ANNOYING fallacies there are! As well as the related "putting the cart before the horse", or whatever it's officially called (women make less on average, therefore it was intentional)
PS don't forget about Simpson's paradox!
Watching this video at work, miss my cat. Burst into tears
Squared correlation r^2
Line of regression
Can anyone explain a little more in depth standard deviation? Im still not sure what information it tells us in a scatter plot
I am also looking for that :/
Y = mx + b?i thought it was c
Phony Aardvark i learned it as y= ax+b
Bryan, what does m stand for? The mmmslope? (I actually don't know the answer, now that I think about it)
O_O *head-explosion*
I know it was c (at least in my part of the world)
"mx + c" is also reasonable in the sense that "c" is often used to refer to some "constant". This is also the explanation for e=mc^2. Because the speed of light in a vacuum is a constant.
The Bee and Puppy-cat doll in the back is sooo cute (๑>◡
without you guys i would not pass my exams thank you so much
This needs to be essential viewing for EVERYONE.
At 0:27, it must have taken everything you had to not blink.
Correlation does not neccesarily state that causation is found between two variable.
However. don't walk away thinking correlation disproves causation. This isn't politics. There are more than two possibilities. (There are in politics too, but ignore that.) Thanks, and have a good day.
As a final note: Time taken to get from point a to point b is negatively correlated with speed. There is (by definition no less) causation there.
Sango, that's a good tip. But I fear that addressing people as the "scientifically illiterate" might not be the best way to get your message across. (What I would give for Crash Course: Rhetoric).
Everyone was illiterate (scientific and otherwise) at one point. It is one's duty to make sure they do not continue to be.
There is no causation only chaos.
It is absolutely true that everyone begins illiterate, and there should be no shame in that. However, referring to people as such can cause them to misinterpret your message as being condescending, even though you had no intention to be that way. Regardless, they are now slighted, and in retaliation, they ignore your advice, no matter how reasonable it was.
kaizersabre, there is no Dana, only ZOOL.
This was very interesting...though, I wonder, just how significant it is ? Can you give me a chi squared on that ?
Statistics should be mandatory lol
This is fake news. Nearly every person who has an automobile accident is wearing socks. Correlation? I don't think so. I stopped wearing socks years ago and haven't been in a car crash since.
I got in a small accident once because I was driving in sandals and the bottom of the sandal wedged against the floor, preventing me from applying the brakes. I hopped a curb and wedged my front bumper into a wooden fence. I think I learned that it's technically illegal to drive in sandals in my state, but I was never warned about it.
I just felt like sharing.
2:56 to the height of the Holy Spirit- 😮💨
I've seen people both conflate correlation with causation in situations that are clearly coincidence and insist that correlation does not equal causation when the pattern of cause and effect are obvious.
*_...there'd be a negative-correlation where reducing air conditioning increases swimming..._*
*_...or, an overriding 'cause' leading to watching-speeding or doing-it, another, negrelation..._*
*_...so...what's the mathematically-concisely-stated-statistical-rule for causality-guessing..._*
*_...(making statistics, like modulo arithmetic: where compounded moduli may get better)..._*
Thank you so much for sharing. You're so much better at explaining than my professor.
I thought the DFTBA speech bubble said USA for some reason for 10s
Me: focus, you have a test this week
Also me: OMG PUPPYCAT!!
Anecdotally, after playing Simpsons: Hit & Run (a GTA clone), I genuinely drove more recklessly for a little while. Not like I got into an accident, but like I was cutting corners tighter, and being a little heavier on the pedal. I had to work at it to knock it off. Really really good game though.
I’ll have you know that my cat, Mr. Whiskers, loves me.
Love this upload 😍
This is the main problem with the CDC
Man SOME PEOPLE should listen to this video very fucking closely. I'm getting nauseous every time some oaf wants to support their wildest claims by citing some random statistics.
The time between my eruptions just ain't what it used to be.
I love this series! However, you made one, small lie: R^2 does not have to be between zero and one, but can in fact be negative.
You spoke of the mx + b, but failed to mention what value it has to determine b (and if chose horribly wrong, it can give you negative R-values, due to estimate a model that is worse than random).
Keep up the series! :)
Squares of real numbers are always nonnegative, by definition. They can never be less than zero -- the square of -5 is 25, for example.
wow! Thank you
This is an epitome of an attractive woman.
When r = 0. We have a correlation of no correlation.
Cool-Cage Act; hilarious.
When it's hot, people with no A.C. tend to go to the movies. Movie theaters are usually quite air conditioned and you get to enjoy it for a couple of hours.
While taking my stats course I started sleep talking and explained empirical rule to my mon
Someone please create a Nicolas Cage task force so that he doesn't star in anymore awful movies
Every time I see one of these videos I look at the view count and know that there's that many more people out there that are better educated about this topic and that makes me very optimistic for the future keep up the great work guys
I can't understand statistics. But the jokes on statistics in the comment section is even harder to understand lol.
Excellent video! Thank you!!!
I was JUST reading up on this in class! 😂
i will like to confirm that is the equation of a line equals y=mx +b or y=mx+c
I was TRICKED into watching this by the title. How hard would it be to add, "WARNING! THIS IS STATISTICS, DWEEB" to what appears on my temptation screen?
It was really good.
I watched this video without having seen the previous ones, and spent a considerable amount of time wondering "what the heck is an 'old faithful eruption' ?"
(For those who have the same problem: "Old Faithful" seems to be the name of a geyser. (I don't know where it is, but when an English RUclips show refers to a location, person, event or sports ritual you have never heared of, you can be pretty sure it's in North America.)
The first eruption scatter plot has a typo
Guess what, one f(x) = mx + b can, of course, only separate variables linearly. But add more and more of f(x) = mx + b to your model then you enter the world of Neural Networks! ;)
Just noticed puppycat on her table! 💗
Guys, Nicholas Cage movies and drownings are both correlated with POPULATION.
Just because the UK joined the EU, it doesn't mean the EU was responsible for improving the economy in the UK. Correlation is not causation.
YES! SHE SAID "VICE-VERSA" INSTEAD OF "VISA-VERSA"! Sorry about the caps. That just bugs me.
Rich people have pools and ACs. Nick Cage aren't exactly the sharpest tools in the shed. It makes sense they both usually drown in pools.
That's a strange dig at vegans named Tyler.
Please do more literature!!
You can "learn" more spurious correlations here:
www.tylervigen.com/spurious-correlations
and even discover new correlations here!
tylervigen.com/discover
If A caused B then there is a correlation between A and B.
The rising of the Sun caused the eating of an ice cream by John.
Therefore, there is a correlation between the rising of the Sun and the eating of an ice cream by John.
My question is, how would you quantify those events and plot the correlation between them on a graph? Would I count the number of times these events occurred? What if an event only causes another once? What if John died after the first ice cream? Can we still say that there was a correlation?
We don't predict the temperature in Fahrenheit we calculate it using the formula (c*9/5)+32
Is anyone else surprised about that slope for heights of dads v. heights of sons ? 0.5 ? Isn't that weird ? At what age were the sons measured ? Surely, height of dad v. height of son should look a little like 1:1 -- otherwise would people not be shorter and shorter ?
It’s interesting that this came out before the pandemic. 🤔 they should’ve used this as part of the vax education 😂
Its TIME its always time!!! many many many things are correlated over time but have no real relation. Randomly selected health studies are much less likely to be unrelated. Exists a reddit for unrelated correlation.
The example of changing the units on the y-axis is only relevant if you're not doing your dimensional analysis properly. If the slope of the feet-feet plot is 0.5, then the slope of the meter-feet plot is 0.15m/foot=0.5
@crash course team, not all the graphs in the datasaurus dozen shown in the end doesn't seems like having same correlation coefficient. Few look like having r=1, few r=0. Please correct me if I'm wrong
Gain in my knowledge is perfectly correlated with the number of crash course videos I watch and shows the value of absolute +1 as the correlation coefficient #CrashCourse ..... 😁😁😁
This was the funniest Crash Course video I've ever seen. Her comedic timing is excellent. Though I still don't know if that clever mayor was a man or a woman.
Those movie computer tick noises (when charts are presented) drive me mad, and I don't even have EQ in my setup to damp them down. Good vid though!
Whenever a plot appears it sounds like a Black woodpecker (Dryocopus martius) :D
Humans are blessed, and cursed, with paraidoli. We crave causations.
Love this video and the channel, also - @1:43 You've spelled eruptions wrong...
Cats don't miss people. They just know when their servants get home.
I don't like her. didnt watch
Nicholas cage has been on board for not not staring in movies since national treasure 2 . He's been intentionally terrible ever since .
Good episode, but some things would need exercise and ‘usage’ in order to be memorized well and longer-term, like r and r squared.