At first, I was going to mod your comment down for being hopelessly naive, but then considered that, on the contrary, it might be really deep, so I'm replying instead. You might be looking for something like operator theory, which has been in wide use only for the last century or so. Unfortunately, I can't point you to a good introduction to the topic -- cursory web searches were unhelpful -- but perhaps someone else can.
I watched blind computer scientist T. V. Raman give a lecture in which he played audio Tetris at the end, although he apparently hadn't known to that point that the visual part of audio Tetris (which existed solely for the benefit of the audience) didn't actually work. This appears to be the Emacs code for audio Tetris.
There used to be a common and ridiculous situation where a van full of obvious illegals, no ids, no english, would be stopped and as long as they weren't caught in the act of crossing the border and as long as the driver had a valid license, the cops couldn't do anything.
"Ridiculous"?! I find this to be a common and sensible situation.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
We know from this ten-year-old study that playing bridge boosts your immune system, so clearly some forms of mental exercise have some forms of positive effects. Perhaps a better alternative to Brain Training would be playing bridge on your mobile device.
I, too, struggled with the idea of linking one 3D-torus to another 3D-torus using the fourth dimension. But one visualization made it click for me: do the process in reverse. Start with 3D-torus T1 and 3D-torus T2, linked, in 3D-space S1. Then move T1 into the rest of 4D-space so that it no longer intersects S1; in S1, we are left with T2 linked to nothing. Then move T1 within 4D-space so that it is nowhere near T2. Then move T1 completely back into S1, nowhere near T2. Hey, if you can do that, you can certainly do it in reverse and link T1 to T2.
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At first, I was going to mod your comment down for being hopelessly naive, but then considered that, on the contrary, it might be really deep, so I'm replying instead. You might be looking for something like operator theory, which has been in wide use only for the last century or so. Unfortunately, I can't point you to a good introduction to the topic -- cursory web searches were unhelpful -- but perhaps someone else can.
Your post itself seemed to me to be a bald-faced attempt to make English majors cry.
I watched blind computer scientist T. V. Raman give a lecture in which he played audio Tetris at the end, although he apparently hadn't known to that point that the visual part of audio Tetris (which existed solely for the benefit of the audience) didn't actually work. This appears to be the Emacs code for audio Tetris.
There used to be a common and ridiculous situation where a van full of obvious illegals, no ids, no english, would be stopped and as long as they weren't caught in the act of crossing the border and as long as the driver had a valid license, the cops couldn't do anything.
"Ridiculous"?! I find this to be a common and sensible situation.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
We know from this ten-year-old study that playing bridge boosts your immune system, so clearly some forms of mental exercise have some forms of positive effects. Perhaps a better alternative to Brain Training would be playing bridge on your mobile device.
I, too, struggled with the idea of linking one 3D-torus to another 3D-torus using the fourth dimension. But one visualization made it click for me: do the process in reverse. Start with 3D-torus T1 and 3D-torus T2, linked, in 3D-space S1. Then move T1 into the rest of 4D-space so that it no longer intersects S1; in S1, we are left with T2 linked to nothing. Then move T1 within 4D-space so that it is nowhere near T2. Then move T1 completely back into S1, nowhere near T2. Hey, if you can do that, you can certainly do it in reverse and link T1 to T2.