FourDimensional Undecidable “Elementary” Geometry
A few years ago, I realized (with another update here) that the elementary geometry of points, lines, and circles becomes undecidable when it includes screws or spirals. You can think of lines and circles as the onedimensional connected uniform curves in a twodimensional Euclidean space and you can think of spirals, lines, and circles as the onedimensional connected uniform curves in a threedimensional Euclidean space. I'm still not sure of what a complete set of such curves in a fourdimensional space would be like, but it would include some very strange objects.
For example, consider the curve parameterized by \((w,x,y,z)=(\sin t,\cos t,\sin \sqrt{2}t,\cos \sqrt{2}t)\) where \(t\in[\infty,\infty]\). It is easy to see that this is a dense subset of the Clifford torus that's the product of two unit circles centered at the origin (in the \((w,x)\) and \((y,z)\) planes). Unlike the similar curves in two and threedimensional space, this isn't closed.
Question: Would it make more sense to focus on closed, uniform, connected subsets of Euclidean spaces? In two dimensions that would include the empty set, points, lines, circles, and the entire plane. In three dimensions that would include the empty set, points, lines, circles, helices, planes, spheres, cylinders, and the entire space. In four dimensions …
Stupid Petitions Are Not Limited to the Left
According to a recent petition:
We demand that J.K. Rowling grants no less than 18 refugees shelter in her mansions for at least 8 years. She rejects safe immigration, which is why we also demand, that there will be no additional vetting process for these refugees. Her virtuesignaling stems from ignorance, and the 100% effective cure of it will be this drastic change of perspective. To make this group of refugees representative of the situation Europe, we also demand that the group consists of 14 men and 4 women, since over 75% of the millions of refugees are male.
First, if you sound like this, you are doing conservatism wrong:
UPDATE: you can drop off an unwanted baby at a Hobby Lobby and they'll raise it
Second, why are they assuming that letting refugees in means that the State must build homes for them? When someone moves from city X to city Y in the same country, we don't normally assume that the the government of city Y must build the homes.
Third, if the government insists on building homes for newcomers, there might be problems with it irrespective of whether or not there are refugees. Keeping refugees out because the government is spendthrift is like getting a hangover from scotchandsoda and, as a result, swearing off soda.
Finally, if you believe that Americans/British/whoever have the right to rent to refugees, does that imply that you have a moral obligation to do so yourself? If you believe that Americans/British/whoever have the right to smoke dope, does that imply that you have a moral obligation to do so yourself?
Which Trump Did We Elect? An Update
The test case I mentioned here might be happening. I still don't know which Trump we elected, but it's clear that the commenters at Instapundit voted for the bad Trump.
A brief summary of the comments there:
You know everything we said about the RFRA and religious freedom? IT WAS BULSHYTT!
The Reaction to Betsy DeVos Might Explain the Trump Movement
Some of the people reacting to the appointment of Betsy DeVos as Secretary of Education are planning to homeschool their children even despite the fact that she is a proponent of more homeschooling.
Apparently, they have been so brainwashed by standard opinion into believing that conservatives are authoritarian that they plan to get back at antiauthoritarian conservatives by doing something antiauthoritarian.
Question: What happens when someone who insists on being authoritarian believes the same thing? Would that produce someone who defends capitalism by limiting imports and defends American ideals by closing borders?
A Stalin Quote and padic Numbers
According to Joseph Stalin:
A single death is a tragedy; a million deaths is a statistic.
He was, of course, using \(p\)adic numbers. For example: \(\left\vert1\right\vert_2=1>0.015625=\left\vert1000000\right\vert_2\).

