Timeline for How to present mathematics to non-mathematicians?
Current License: CC BY-SA 4.0
23 events
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| Sep 1 at 22:35 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
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| May 4 at 23:04 | comment | added | Goldstern | @QiaochuYuan I wonder if smbc-comics.com/comic/2014-02-16 got this idea from here. | |
| Jul 19, 2020 at 22:28 | comment | added | Andrej Bauer | @benrg: I don't see a problem with my approach. | |
| Jul 18, 2020 at 22:06 | comment | added | benrg |
we live in a three-dimensional space because otherwise we could not tie the shoelaces - but tied shoelaces aren't knotted in the mathematical sense. I feel like there's almost no overlap between knot theory and knots in the ordinary sense of the word, and comparing them gives only the illusion of understanding. Is there really no way to hold hypershoes together by the self-friction of a hypershoelace? I don't have enough physical intuition to work that out, but I'm pretty sure knot theory has nothing to say about it one way or the other.
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| Nov 12, 2018 at 17:13 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
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| Nov 12, 2018 at 16:59 | history | edited | Andrej Bauer | CC BY-SA 4.0 |
Link to an actual talk.
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| May 11, 2017 at 21:21 | comment | added | Ingo Blechschmidt | A friend and I turned two of Andrej's great ideas into talks at the Chaos Communication Congress. For anyone interested in our take on these topics, for instance for giving similar talks, recordings are here: Four dimensions, Infinity. It's helpful to imagine the infinitely many persons to be sitting in the "magical bus of Harry Potter" which has finite length from the outside but is infinitely large from the inside. This way $\omega+1$ is easily visualized as a further person waiting behind the bus. | |
| Nov 27, 2016 at 1:48 | comment | added | Dan Grayson | The colors of the rainbow add 1 dimension, so you can't color every point of the knot a different color in a continuous way, and continuity is required. It's important to mention the rainbow, because other color spaces have other dimensions. | |
| Jan 5, 2014 at 2:09 | comment | added | Nikolaj-K | The german tank problem is related. | |
| Apr 6, 2012 at 20:35 | comment | added | Andrej Bauer | @timur: Consider convex open sets with which we want to cover a wall. It is possible to cover the wall so that each point is covered by at most three tiles, hence the dimension of the wall is no more than 2. It is impossible to cover so that each point is covered by at most two tiles, therefore the dimension of the wall is at least 2. The dimension of the wall is 2, and since its co-dimension in space is 1, the dimension of space is 3. Is that what you asked? | |
| Apr 6, 2012 at 12:23 | comment | added | timur | @Andej: About the bathroom tiling, how do we know we are not in 4 dimensions by counting tiles? I mean, in 3 dimension we only have the lower bound of 3 tiles meeting at a point. | |
| Jan 31, 2011 at 21:07 | comment | added | Zsbán Ambrus | To sigfpe: some mathematicians also always like to see examples or the whole subject starts looking pointless. | |
| Jan 8, 2011 at 18:04 | comment | added | Blue | @Andrej: If someone suggests to me that time is the 4th dimension, I ask, "Then what is the 5th (besides a singing group)? the 6th? the millionth?" :) I advocate for replacing "the" with "a(n)": Time isn't so much "the" 4th dimension as much as it is "a" 4th --as in, "an extra"-- dimension. To help make a conceptual transition between a temporal interpretation of dimension and a geometric interpretation, I suggest a flip-book animation. The animation seems to show action over time, but the flipping clearly demonstrates movement through a dimension perpendicular to the animation's "world". | |
| Dec 1, 2010 at 19:28 | comment | added | Dan Piponi | These are great examples but non-mathematicians always like to see examples or the whole subject starts looking pointless. For example, talking about infinite queues of people can sound like angels on pinheads. (Yes, we could be like Hardy and tell people it's meant to be useless, but I find that attitude obnoxious and wrong.) For example, if I ever talk about knots to non-mathematicians I always mention how cells can remove knots in DNA strands and how we couldn't live without this ability. (And in fact, there are now known to be diseases that are essentially topological problems with DNA!) | |
| Nov 25, 2010 at 1:39 | comment | added | Eric Tressler | I gave a short talk about wallpaper groups, with a lot of pictures by Escher, and then talked about the Penrose tiles, concluding that it's not yet known if there's a single aperiodic tile (I don't count arxiv.org/abs/1003.4279). A highlight was that some physicists were in attendance, and I was able to mention that Penrose worked on the problem years before anyone discovered its connection with quasicrystals and physics. Having colorful pictures was also a huge help in keeping people's attention. | |
| Nov 24, 2010 at 20:01 | comment | added | Qiaochu Yuan | Ordinals are a great example, I think. I am sure I'm not the only one who's played the "I dare you times infinity!" "I dare you times infinity plus one!" game as a child, and it might be fun for people to learn that this can be made precise. | |
| Nov 24, 2010 at 16:29 | comment | added | Steven Gubkin | I once made a ceramic model of a Klein Bottle which was colored so that it did not have any self intersections when you considered color as the 4th dimension. | |
| Nov 24, 2010 at 15:40 | comment | added | Todd Trimble | Actually, I thought the idea of using color was very neat; the two points never actually touch if they have different color coordinates. | |
| Nov 24, 2010 at 14:39 | comment | added | Andrej Bauer | It takes a lot of effort but one can usually come up with nifty explanations of fairly complicated things. | |
| Nov 24, 2010 at 14:38 | comment | added | Andrej Bauer | Well, actually, I asked "what is the fourth dimension?" and someone said "time", and then I explained it need not be. I showed pictures of colored knots and I told people to imagine that the color is "another dimension" just like when they look at a geographic maps and color represents altitude above sea, which is another dimension. I think it went over well. | |
| Nov 24, 2010 at 13:45 | comment | added | JBL | +1, but I'm afraid "we can choose color to be the 4th dimension, so if 2 points are different color they can pass through each other" would lose every nonmathematician I know. | |
| Nov 24, 2010 at 11:56 | history | edited | Andrej Bauer | CC BY-SA 2.5 |
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| Nov 24, 2010 at 11:49 | history | answered | Andrej Bauer | CC BY-SA 2.5 |