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Is it just me or does it seem like the more we study the universe the more discrete it becomes? That coupled with weird things like imaginary numbers and magnit
by dcow 8y ago
Is it just me or does it seem like the more we study the universe the more discrete it becomes? That coupled with weird things like imaginary numbers and magnitudes of infinities makes me believe we need a to rewrite most of our math using an axiomatically discrete number system.
- whatshisface 8y agoImaginary numbers and the continuousness of the reals makes physics a lot simpler. In fact any equation written in terms of complex numbers can be written as a system of equations in terms of real numbers, but it is not done because it is easier to just live with complex numbers.
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- rbanffy 8y agoThe discreteness of reality does not affect Math. Real numbers are continuous regardless of their applicability to nature. And there is nothing weird with imaginary numbers. It would be weird if half of the numbers didn't have a square root.
- dcow 8y agoI’m not saying our current system isn’t capable, more that it might not be best suited to describe our physical existence—like how base 16 allows you to visualize the underlying bits better than base 10. Is there any physical law that demands negative numbers? I think not. We just like them.
- nine_k 8y ago> physical law that demands negative numbers Representing velocities relative to a given point? Representing charges?
- dcow 8y agoPositive/negative is really just semantics for something that is the opposite of something else. In both cases you have a quantity of something so you can e.g. take the square root of it perfectly fine. However in a discrete system the square root is only defined for whole number results anyway. For velocities perhaps a polar coordinate system is more “simple”.
- michaelcampbell 8y agoSo taking your last 2 posts... > Is there any physical law that demands [semantics for something that is the opposite of something else]? I think not. Does this sound as absurd to you as it does to me?
- dcow 8y agoMy point is that the mathematic negative/positive duality is often either too specific (doesn’t allow for scenarios where you may have more than two “directions” so we invented dimensions) or too general (allows for negative values where you don’t want them, so we use abs or square things to correct).
- voxl 8y agoIt's not weird at all. Continuity is, in my opinion, less complex than discrete systems. Discrete systems hold much more information and can often be approximated by continuous solutions, but that approximation comes at a loss of information.
- dcow 8y agoI’m arguing for discrete mathematics in physics because it better represents (I think/wonder) the physical universe and doesn’t suffer from loss of fidelity as you point out. Maybe it’s just the vocabulary that’s limiting, but then I’d still argue for a system with appropriately rich vocabulary.
- michaelcampbell 8y agoSo write all of your maths in terms of Planck values.
- trhway 8y ago> does it seem like the more we study the universe the more discrete it becomes the continuity has been a wonderful tool for the last 4 centuries since its development. It is kind of not surprising that such a convenient (and simple in many senses) model starts to show it limitations when stretched to and beyond the edges. It wouldn't the first nor the last time that what we see as edges happens to be horizons of the new deeper levels of science. >using an axiomatically discrete number system we've been there. I think the next step is what is popularly known and manifests itself as fractals - i.e. the p-adic numbers calculus/geometry/etc seems to be an entry point into the post-continuous world where things look continuous at some scales/aspects as well as discrete at another scales/aspects.
- dcow 8y agoWho should I read to learn more about the state of the art in discrete mathematics applied to physics?