Today I’m going to talk about an idea I’ve had for a few years. Before Einstein discovered his theory of general relativity the math behind it, about curved space was already discovered for a while, the same is true with the slow discovery of Quantum mechanics, before that started a lot of the math used to describe it was already discovered. In a universe where the math or the idea is always discovered before it is linked to physical properties one could imagine that the idea itself is the cause of the physical properties. So if you would discover something totally new something noone has ever thought of before that idea would create new laws for our universe to follow. At first thought you would think this doesn’t make any sense aren’t the laws of physics eternal governing over both todays world as that of the past. But once you realise that essential things such as nuclear physics can be explained by simple addition, subtraction, multiplication and division it seems a little more plausible, but then you realise Mathematicians have made a lot more math than is used in physics or other sciences this must certainly be a problem? Well it doesn’t have to be, if you imagine that nature slowly tries to implant every idea into itself but tries to do it in a way that is still consistent with its previous state you would get something that slowly becomes more detailed and detailed, something that also happens to our understanding of the universe. In the end it is impossible to prove or disprove this idea at least it is for me, you could probably go a lot further in trying to if you had access to a lot of data and knew exactly when things where first thought of. Also to see that abstract math like the phibonacci series does find its way into nature check out Spirals Phibonacci and being a plant
If you watch the big bang theory (which you totally should) chances are you vaguely remember Sheldon Cooper talking about something called Flatland. Flatland is an satirical novel about Victorian culture with some nice mathematical concepts thrown in which are very well explained, it was written in 1884 by Edwin Abbott Abbott. In my post about Tachyons I talked a lot about string theory, 0 and 1 dimensional objects and more than 3 dimensions, this idea about different dimensional objects is one of the mathematical concepts that is very well explained in Flatland, but If you don’t want to read the novel I will explain it here. If the dot I just used to end the last sentence would have been infinitely small (truly in only one point) it would have been an 0 dimensional object also if _ the line I just used would have totally no width it would have been an 1 dimensional object, if you have a square that has totally no height it would be a 2 dimensional object, if the aforementioned square did have some height it would be a three dimensional object, at this point one would normally stop but mathematically there is no reason to stop at three dimensional objects, there could hypothetically be 4, 5 , 6 , etc dimensional objects sure it’s hard if not impossible for us to really understand what a higher dimensional object would look like, but mathematically we can calculate properties of such higher dimensional objects for example a line has an length L, a square has an Area L2 a cube has an volume L3, if you imagine a 4 dimensional “cube” you could imagine that it would have a property with value L4. If you want to read a little slower more story driven explanation of these concepts read flatland it’s so old that the copyright on it has elapsed but it is still good here are some links
If you want to encrypt an message you need encryption key, a list of numbers that tells you how the normal message is transformed into the encrypted message. Sometimes however it is the case that some part of you encryption key is known by someone you want to hide your message from, in that case there are several ways to still secure your message one of which is using a uneversal hash fuction to transform you encryption key into a shorter but more secure key. A universal hash function has the property that the probability that you get the same key out of two different encryption keys is smaller or equal that 1 over the length of the resulting key. One of the easiest examples of an universal hash function is that of a matrix with at random 1 or 0 in every entry.
A while back I watched some videos from minutephysics about some math and infinity the first one is about a proof that seems to be rather contradictory to other math stuff (and common sense) and the second is both a reaction on the commotion(math jail) over this and some more physics related explanation(go watch the videos their great). The truth about physicist (at least a lot of the ones I know) is that they use a lot of sloppy math which in my opinion is kind of a double edged sword, on the one hand it makes calculations and proofs a lot easier on the other hand in certain (rare) circumstances you can get some things which are completely different from the actual result, but well that’s why we have mathematicians and experiments.
Today I was watching a video from day9 where among other things he told a story about how he asked a girl out by writing an letter in old english and got an java script as answer (if you want to hear the details watch the video) and this reminded me of the time I wanted to sent a girl a valentines day card but wanted to do it anonymus. So what did I do I made a new email adress with my name encrypted in the email adress name, by using an easy encrytion scheme namely taking the first prime number to be “a” the second prime number to be “b” etc (a key like that is called a cryptographic key) and emailed her the drawing I had made and scanned.