I love this meme. Seems so well argued! Until you realize that the incompressible nature of water means all the energy of impacts and explosions gets transferred extremely rapidly and efficiently into the bodies of the crew.
It’s for this reason that modern cars which crumple up like an empty soda can are much safer than the rigid steel monstrosities of old.
No, in our current best-supported model of the universe (Lambda-CDM) the concept of “before” the Big Bang is meaningless. It is the apex of the spacetime “bell” from which everything emerged.
“Before” the Big Bang is nonsense. It’s equivalent to saying “head north from the North Pole.”
It would only be a temporary fix. Robert Nozick gives the example of the famous basketball player as a critique of John Rawls’ veil of ignorance argument.
Suppose everyone had equal wealth but we remained different individuals with our own personalities, abilities, etc. For simplicity, assume everyone has $100 each and there are a million people in total. Now suppose one person is actually a legendary basketball player (Nozick uses Wilt Chamberlain as an example) and he decides to play basketball in the NBA to entertain everyone else. But he doesn’t do it for free, he charges each person $1 for a ticket to see him play.
If everyone pays to see him play basketball, he becomes a millionaire while everyone else becomes $1 poorer. In effect, the balance of total equality has been broken.
How do you solve this problem? You might say that he’s not allowed to charge $1 for people to see him play basketball but then what you’re really saying is that everyone is not allowed to spend their $1 to see a basketball game. So it’s actually not possible to preserve the state of total equality without taking away people’s economic freedom (that is, the freedom to decide how to spend their $100).
Thus you either gradually revert to inequality or you make all money worthless by taking away people’s choices on what to spend (and so you might as well just have a ration system instead).
There’s a ton of functionality in Photoshop that even pros never use. Every user of Photoshop needs something different from it. Sure, there’s a core of features that everyone uses (and which the Gimp also has) but there’s also countless other niche features that are a crucial part of the workflow for tons of users and they won’t give them up. This is one of the reasons Photoshop is so hard to replace.
It’s also the reason Latex is tough to replace as well. It’s a phenomenon which is not limited to commercial software, that’s for sure.
A bit confusing to read. The points are placed on the y-axis using ordinals rather than cardinals. This means if you were to extend the plotting (say, up to 200) it would cause the existing data points to move around. That’s not usually what we expect when plotting data.
Edit: actually, the problem is more severe than I initially thought. If the y-axis were plotted with cardinals (the way we usually plot data) then the German case would show 10 horizontal lines, immediately revealing a pattern in the data (caused by Germans speaking the ones digit before the tens digit).
There’s a big issue with using weight classes in team sports: player weights vary dramatically. Take the NFL for example. Setting aside the enormous differences in weight between linemen (offensive and defensive) and all other position players, there are also huge weight differences within a given position. For example, quarterback Jared Lorenzen was 6’4” and weighed 275 lbs whereas Russell Wilson is 5’11” and weighs 211 lbs. That’s a huge weight difference!
You can find similar weight differences across players in other leagues (NHL, NBA, and MLB). Weights don’t really correlate with overall skill level though they do somewhat correlate with position and skill set (and height of course).
How would you classify by weight in team sports? You might think to do it by position but none of the leagues require a player to remain at a single position for their career. Players can and do switch positions, and many even do so multiple times during a game. Sports like NBA basketball don’t even have any particular rules about what a player at any given position is allowed/not allowed to do, so the positions on team rosters are more like a suggestion than a requirement.
Billionaires are often workaholics. They work extremely long hours because they’re obsessed with winning, with crushing the competition. I’m sure there are also plenty of billionaires living it up Great Gatsby style but those obviously don’t fit the “hard working billionaire” stereotype.
I’m just imagining a dedicated 2-way cycle path, lined with tall trees the whole way so it’s in the shade most of the day. What a beauty that would be!
I’m already jealous of you Aussies for the affordability of solar and your abundant sunshine making it highly efficient. Up here in Canada where I live solar is mostly a luxury and bike lanes and paths exist but are rather unpleasant to use when they’re covered with snow and ice from December to May.
Is this at a hotel? Just hang a “do not disturb” tag on the pipe to keep the water running!
FOMO.
Or use the dremel to cut a slot in the end of a flat screwdriver.
Yes, and a = v^2/r.
Merry-go-round: small radius, big acceleration!
Earth: big radius, small acceleration.
We have health care in Canada yet still lots of street homeless people. They aren’t getting adequate care at all, yet the cost of caring for them exceeds the average person by many times. Many of them are on a first name basis with all the paramedics and other first responders due to how often they’re taken to the emergency room.
Stats is intuitive but you need a pure math degree to even get started on the foundations (measure theory). Unintuitiveness arises in any subject where they refuse to explain how it works and just give you a bunch of magic formulas to calculate with. Stats just happens to be the most egregious example of this because it requires far more background than most people applying it actually want.
I love this comment!
Your polynomial, f(x) = a + bx +cx^2 + dx^3, is an element of the vector space P3®, the polynomial vector space of degree at most 3 over the reals. This space is isomorphic to R^4 and it has a standard basis: {1, x, x^2, x^3}. Then you can see that any such f(x) may be written as a linear combination of the basis vectors with real valued scalars.
As an exercise, you can check that P3® satisfies some of the properties of vector spaces yourself (existence of zero vector, associativity and commutativity of vector addition, distributivity of scalar multiplication over vector sums).
Continuous functions on [0,1] are vectors. Magnitude and direction are meaningless in that vector space, usually called C[0,1]. Magnitude and direction are not fundamental properties of vectors.
n by m matrices (and the vector spaces to which they belong) are perhaps best thought of similarly to functions and function spaces. Not as geometric objects, but as linear transformations (which they are).
Every vector is a tensor. Matrices are vectors because m by n matrices form vector spaces. Magnitude and direction have nothing to do with the definition of vectors which are just elements of vector spaces.
That’s a philosophical question, not a scientific one, since it’s by definition beyond the ability of science to answer. It suffers from the infinite regress problem which many people invoke God to solve (the uncaused cause) but that’s not very satisfying, is it?