6 ms·
Is math big or small?
- N_Lens 6mo agoGood article. Math is smaller than the smallest and bigger than the biggest.
- lioeters 6mo agoIt's also deep, it goes all the way to the bottom. > The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it. -- Freeman Dyson
- contraposit 6mo agoWeird Things Happen When Math Gets Too Expressive https://www.youtube.com/watch?v=EVwQsvof7Hw https://www.youtube.com/watch?v=EVwQsvof7Hw Peano arithmetic is sufficiently expressive enough to be equivalent to any possible future theory of mathematics.
- lioeters 6mo agoEven before I started the video, I had a feeling it was going to lead to a kind of "introspective" mathematics that can reason about its own reasoning. I was not disappointed, thank you. Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340 https://arxiv.org/abs/0903.0340
- contraposit 6mo ago[dead]
- gottheUIblues 6mo agoErr? Peano Arithmetic is provably consistent in ZFC, but it is not in itself (if PA is consistent). Therefore if PA is consistent it is not equivalent to ZFC (regardless of whether ZFC is consistent or not)
- contraposit 6mo agoI am referring to this slide : https://youtu.be/EVwQsvof7Hw?t=1646 https://youtu.be/EVwQsvof7Hw?t=1646
- mkl 6mo ago> When Illustrating a mathematical idea, the first thing you need to decide is the scale. I have spent much of my life illustrating mathematical ideas, and scale is never the first thing I decide. Most commonly it stays abstract and there is no scale; it's flexible and I can zoom in and out at will. Sometimes I will choose a scale partway through or towards the end of an explanation, if I want to use a specific analogy, but I can comfortably rescale it to something else - the scale is never fixed. Interesting to see such a different view.
- seanhunter 6mo agoTotally agree. I really enjoyed the article, and the illustrations are really cool but scale is just something I don’t even consider. Even the very first question baffled me, when it said “Picture a torus. Is it big or small?” I answered an unambiguous “yes”. Also, we haven’t defined measure yet here have we? What does it even mean for something to have scale without measure?
- mkl 6mo agoRight, I immediately saw a torus - it was light blue (that's trivial to change, but I can't have no colour if it's visual) - but it could have been the size of a bacterium or the size of a galaxy. Without any context or application, the size is undefined.
- red75prime 6mo agoWhen you've mentioned that, I've noticed that by default I imagine just a shape devoid of color and texture. But I can imagine a donut, or a blue torus, but I need to explicitly think the word "blue".
- Pay08 6mo ago> Also, we haven’t defined measure yet here have we? Kilograms, obviously.
- Telemakhos 6mo agoThis is one of those places where Plato really is worth reading. Plato has levels of reality that correspond to numbers. The first level, forms (also called "the monad"), is what the statement "Picture a torus" engages: contemplate an ideal torus. That torus won't have a particular color or texture or any accidental quality, just the essence of a torus, which is its shape (because torus is a shape). Size is one of those accidental qualities, and those live in the second level, which Plato calls "the bigger and smaller"—exactly what the question asks you to imagine—or "the dyad." So, the instructions for Plato boil down to an absurdity: "contemplate the monad; what dyad do you see?" The two sentences should have nothing to do with each other in Platonic terms.
- trendbuilder 6mo ago[flagged]
- volemo 6mo agoYes.
- fuglede_ 6mo agoI've always loved this recording of Thurston talking about branched coverings and knot complements using big knots: https://www.youtube.com/watch?v=IKSrBt2kFD4 https://www.youtube.com/watch?v=IKSrBt2kFD4
- sunny678 6mo ago[dead]
- lefra 6mo agoA first-year physics teacher once told the class something that stuck with me (paraphrasing): "Nothing is big or small by itself. I want you to always follow these words with 'compared to ...'".
- cubefox 6mo agoShe: It's not that big. He: I think we can agree everything below the average between a Planck length and the size of the observable universe is objectively small, and everything above is objectively large. Using the geometric mean, that average is about 0.12 mm. Therefore my penis is actually large. She: I shouldn't have married a physicist.
- leni536 6mo agoAverage? So around half the size of the observable universe?
- quietbritishjim 6mo agoThey specified the geometric mean. The arithmetic mean (what you're thinking of) of 1 and 100 is 50.5. The geometric mean of 1 and 100 is 10. It gives a sense of the average magnitude.
- leni536 6mo agoThey edited the comment, previously it did not mention geometric mean.
- cubefox 6mo agoThe geometric mean seems to be the natural mean for relative comparisons between lengths, because the mean of (Planck length, observable universe) is clearly very different from the mean of (house, observable universe).
- zahlman 6mo ago
- cammasmith 6mo agoIt kinda seems like the point of the article was to talk about different mathematical illustrations, not to determine if math was big or small. Even in the article, the conclusion is that it's both. I suspect the only reason for choosing the title is to grab attention (and it worked on me). Of course, I am extra cynical as a number theorist who can't visualize most of my field. I wrote my doctorate on Siegel modular forms, and I can honestly say I have no way to visualize them any further than numbers on a page.
- krm01 6mo agoDoesn’t math come down to =
- gweinberg 6mo agoObviously a torus is the size of a doughnut.
- abdulhaq 6mo agoIf you run a statistical sample on modern maths books, it becomes clear that maths is usually about 6cm x 5cm.