I am not sure what I will be writing before I do, it's a way to bring some well needed chaos to the mix. If there ever were a tool to record thoughts blogging is as close as I've gotten. I believe I have two things occupying my mind a bit more than other things currently so let's make use of that. One of the parts is a talk I had with my wife yesterday about mathematics and paradoxes especially infinity. The other part would be an event that made me think about the availability of knowledge at large, I believe.
So about mathematical paradoxes and infinities I received a book for Christmas on paradoxes. It's a popular science piece which isn't usually something I delve into but it's by all means interesting enough to warrant some interest. My wife on the other hand reads a lot and she doesn't mind the occasional popular scientific piece every now and again. So she picked up the book at once and yesterday she was excited to talk some infinity. I guess my favorite part of the discussion were the example from Hilbert's Hotel which gives some examples of pretty concrete infinity. Basically the idea is that you have a hotel where there is infinitely many rooms and all rooms are booked. Now someone enters and ask to book a room you would answer: "Well, there is an infinity of rooms, so that shouldn't be a problem", right? I mean there is an infinity of rooms there can't be a problem, on the other hand all rooms are booked, which would pose a problem if you had a finite number of rooms. So to solve that initial problem you might for example, ask all your guests to move one room up, so everyone moves from room n to room n+1 that way the first room is free right? So your new guest can move into room 1. I don't mean to go in depth of this problem, but wanted to give an example of the type of problems could evolve and solutions.
So more interestingly, I started to realize that I have made use of infinity in solving problems in game-development. Actually, it is assumed in many cases even if it isn't really true, it becomes a finite infinity in many ways and I found it interesting how I haven't really reflected over it and I guess I realized it's paradoxical infinity that messes with my brain while "normal" infinity is more closely related to abstraction. As an example, perhaps the most obvious I can think of, you have ray-picking, for example when clicking with a mouse cursor "into" a 3D scene. There are some steps involved, but I am specifically thinking about a common step used as a test to see whether a polygon could be in the set of possible hits. Here it is common to make use of the equation of a plane (i.e. an infinite plane) to gain information on the possible collision with the ray (in many regards, infinite ray). I hope that it is simple to see that if the ray and the plane are parallel no hit can ever be found. If, however the ray and plane are not there must be a collision somewhere in infinite space, and here you would select a finite length of the ray for the collision-point. However, before we know that there is a collision to find we can abstract away all limitations on the object and only handle infinite planes and infinite rays (or vectors if that help you to think about it). So what I am getting at is that the vast and scary infinity in many cases actually is an abstraction which makes it easier to visualize and wrap your head around the problem, whereas I have always seen infinity as something scary and pretty much just thought of it as one of those complex, difficult subjects which I don't understand. Much like what Georg Cantor did to the findings about infinity by Galileo Galilei really!
So I guess I got a bit cough up here, very specific subject and perhaps some will find it boring, others might think "didn't you already know all that!?" and so on. And yes, I kind of already knew but I realized only now.
So about that knowledge availability I feel tempted to save it for another day as I wrote a bit more about the paradoxes and infinities than I intended. But I am a follow-through type of person, so let's go.
I bought coffee this morning, it happens that I do and I find it quite convenient. When paying I used my master-card a service my bank offers me for a yearly fee. I am happy to pay for the service and my coffee store in turn has a machine which may be used to do the actual transaction. To provide me that service so that I can actually pay using my card the shop keeper pay the bank. I always wondered why the bank isn't paying shops for offering their solution, for me as a consumer I guess it's positive or else there would probably be one system for every credit card issuer and every bank and it would be different in different countries and it would pretty soon be quite bothersome. (or it is at least one way of seeing it).
However, I meant to touch on the subject of embracing knowledge floating around us at all times, I mean it is reasonable to believe that everyone knows something that I don't, right? If it's difficult to get that idea to stick, look around yourself and ask yourself "what is she thinking?", see everyone has at least some knowledge that you don't have. However, I am going to focus on a bit less abstract type of knowledge, just wanted to make the point.
So, back to the payment, (would be embarrassing if I forgot to pay now!), I wondered how it works, what does it cost the shop-keeper to receive my payment? I mean, obviously there is some money going into buying the coffee, providing a place where I can go to pick up my coffee, mugs so that I can actually receive my coffee and there are costs for staff, so the cup of coffee is already quite expensive as an entity. So I want to know how this equation actually looks, and I mean I will have to read up on it if I want to offer that service in the future (which I might, hinthint), so I asked the shopkeeper, I was the only customer and I mean doesn't everyone like small-talk? (Not the language, even if it is pretty cool as well). So I asked him: "What fee do you pay the bank to provide this service?" He answered (and were excited to do so) that it's a one time fee in order to get the machine and the link to the payment-service, and then there is a fee of about 1.50 Kr per transaction which goes to the bank. I implied that it is a pretty backwards system where he actually is providing a service for the bank and that perhaps they should pay him to do so. He laughed and proclaimed that the banks are powerful and make the rules, he continued to say that it is different in different credit-issuers where AmEX is the "worst" as they take about 5 Kr for a transaction. So in effect on my 20 Kr coffee AmEX would get 20% (!) and that is before salaries, paying the products, locale and so on.
Point-time, from a joyous conversation which I believe that were rewarding for both me and the shop-keeper I received some quite valuable information from someone that, I would argue, really is an expert on the subject. I know after those minutes that there is a one-time fee that you have to consider and that you need to take the cost of transactions into account when doing your margin-calculations. Further, I even got a pretty good hint of how the costs look. So if I were to set up shop with card-payments I know that I need to research what the fee to start out is, I also need some statistics on the most frequently used payment-methods and credit issuers for my business would be to estimate the cost it would have on my transactions. I mean it's a huge difference in margin if everyone use 1.50 Kr services compared to if everyone make use of the 5 Kr service.
That's quite enough for today, don't you think? I will try to keep a bit more to the point next time. Again, to write like this provides some well needed chaos to my brain.
Cheers.
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