Friday, 2 December 2011

The Deterministic Universe

“There is a theory which states that if ever for any reason anyone discovers what exactly the Universe is for and why it is here it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another that states that this has already happened.”
Douglas Adams
The creation of the universe is a mysterious thing (from our viewpoint within its boundaries at least). We can theorize and think ourselves closer and closer to the beginning of time and come up with theories for that beginning that correlate with observations done today. The beginning itself though, and how something could come out of nothing (if it did), could very well be impossible to grasp.

Let us, for discussions sake, create a universe in a state at the start of its time. We will also assume that this state could be exactly described, and that if we knew every underlying parameter we could from it derive the next moment in time. This would mean that the universe was deterministic.

In a deterministic universe we could, assuming that we knew all the input parameters (not worrying about computational limitations) exactly calculate another state that is further along in time. A complication would probably be that if we tried to predict a future state, that state would look different because of us being part of it and thus changing it. Since this is a thought experiment, we will just assume that an observer is able to see the state from the outside without affecting the universe. If this was true then, in a deterministic universe, any passage of time would be a surjective function, where every input state maps to exactly one outcome.

The above version of a universe would not fit very well into the more popular theories of today. In fact everything points to uncertainty being a core principle of the universe. This could very well be true, although it could also be true that the randomness we see is based on some pattern that would only be obvious if we extended our viewpoint to outside the current realm. If there was no way for us to see that pattern, to us the universe would always be uncertain even if the rules controlling it were deterministic.

So let us imagine that the universe has these properties of being entirely predictable from a given initial state. Would that mean that if we started a new universe, the same events would happen and a version of me would end up writing this article again? Well, if we go one step back there is no state before the creation (once again, as far as we know). This could mean that even though the universe would behave the same way from a certain state, it could start from different states (and laws) and such even the deterministic universe is not deterministic if we do not have an initial state.

Time to sum this up. If the universe is deterministic it means that if we have the configuration for a universe at a certain time, all that follows can be inferred from it. If it is not deterministic, then the exact same state could yield something different the second time around. Whichever one it is, from where we stand, it will probably always be unpredictable. Just like the amount of time between these articles some things will always be shrouded in uncertainty.

Sunday, 7 August 2011

Evolutionary Noise

“Most species do their own evolving, making it up as they go along, which is the way Nature intended. And this is all very natural and organic and in tune with mysterious cycles of the cosmos, which believes that there’s nothing like millions of years of really frustrating trial and error to give a species moral fiber and, in some cases, backbone.”
Terry Pratchett
It is time for a thought experiment. Imagine a world where all possible variations of life exist already. In that world we have not yet created any obstacles or limitations. Life just exists and every part of it gets exactly what it needs to survive. This would result in a world where no part of life is more favoured than any other, and all combinations are as likely to survive. We would have what can be compared to a white noise, where every part of the life spectrum exists and is equally strong.

Noise will normally get shaped by different environmental properties. When it bounces somewhere or passes through something, certain frequencies are weakened or die out. The noise is filtered into something. Taking the idea of life as a noise a bit further, we can add filters to our constructed world as well. We can add constraints and obstacles that weaken or kill certain parts of life, thus forming it into a non-uniform shape.

Of course, real-world limitations are not as simple as having one filter shaping all life. For one, the filters will be changing between different geographical locations. There is also the fact that we do not have a static world, so the filters in each location will be changing constantly. An example of a short-term filter transition is the difference between night and day, while a long-term example could be continents drifting apart. Now if, in our sound analogy with an ever-lasting white noise, we would keep changing the filters for the sound, at some point all the frequencies would have been reduced to zero in strength. The same thing would of course happen with life, unless we introduce mutations.

Let us first change our one-dimensional life noise into a two-dimensional landscape, which has hills and valleys corresponding to where life is strong or weak (or even non-existing). There would be areas in this landscape void of life because of environmental filters. If a filter for such a region is lifted, the effect would still be visible afterwards. Now, because of possible mutations in life around the region, life from the outside can sporadically take root in the void area. When we remove a filter, life could slowly grow into that part of the landscape and cover it. There is of course the possibility of a big mutation skipping over a void region. Larger moves have a potential to end up in parts of the landscape where life did not exist yet, but can exist, but if these areas are very small it will be unlikely. This means that we will probably find islands of possible life that never get covered because there is no easy path through the filtered regions.

In the evolutionary approach, we would not have all combinations of life to start with. Instead we would start off with a very narrow peak in the landscape. Because there are already filters in place when life is started, it means that certain parts will be filtered already before anything exists there. Life will only be able to expand using certain open paths (or very unlikely jumps), and those paths can close or open again depending on the changing filters of the world. A region can be open for a while, letting life spread through it to another region, just to close and leave an island of life behind.

One can add more and more dimensions and add interaction between different parts of life (e.g. predator-prey relationships), to make this model more and more complex, but the simple case is enough to give us another viewpoint on evolution. What is the conclusion of all this? Not much. Sometimes looking at things from other angles can give you helpful insights. In other cases it does not, but at least gives you something to occupy your brain with for a while. Just as with life, human thoughts will keep spreading, sometimes mutating into blog posts like this one!

Thursday, 4 November 2010

Influential Information Flow

”He who fights with monsters should be careful lest he thereby become a monster. And if thou gaze long into an abyss, the abyss will also gaze into thee.”
Friedrich Nietzsche
When you want to convey thoughts to someone you translate it into speech or body language. The latter might even happen unconsciously and most of the time you do not have to concentrate on getting a message out unless you are learning a new language. Usually some of these signals and sounds you make will be picked up by another person through his/her different senses. Spoken language will be received by hearing, while body language might be picked up through sight or touch. These signals will be interpreted by the other person and translated into thought again.

Communication is seldom (if ever) perfect, as we can se from all the misunderstandings around us. Languages are too inexact to describe what we mean sometimes. We also make mistakes and try to interpret things from our own view. Another thing that is very important when we convey information is context. The speaker might know something that the listener does not know, which makes the recipient of the message interpret something differently than he was meant to. Speaking different languages is an extreme example of this, where you can only rely on trying to get your message across through body language or some common words.

Another thing that affects communication is when the listener filters the information. An emotion, like anger, could act like a filter and make us less willing to receive whatever is being said. Being tired or not being interested in the topic will also act as filters. Filters might not stop all communication, but a lot more information gets lost on the way or even misinterpreted because of different mental states.

All communication works this way, sending thoughts between people. Sometimes (e.g. when watching television) the thoughts go only in one direction, but most of the time thoughts flow back and forth between people all the time.

Not only communication gets interpreted by the brain. In fact everything that our senses pick up is input. Because everything we feel gets translated into thoughts, our thought patterns get affected by what happens around us. From this we can also draw the conclusion that if there are people around us we will also be affected by them. Because their actions are a result of their thoughts, this would mean that we are influenced by other people's thoughts indirectly. This is not as frightening as it seems most of the time, as you would also influence them back at the same time (except in the case of one-way communication). The filters also come into play—we are more susceptible to influence from people we like for example.

What would happen if these filters were removed? Would thoughts then flow freely between everyone? One could theorize that in that case two different personalities would slowly change towards each-other and converge on a single point. It would be more complex in a huge population and you would get background noise in the form of environmental input, but our filters could actually be what creates our individuality.

Friday, 2 July 2010

Probabilities of Averages

Consider something that has a very low probability of happening, like rolling the sum of 100 when rolling one-hundred six-sided dice. Since there is only one combination with this sum (i.e. all 100 dice show one pip), the probability of it happening is one in 6100. If the sum we are interested in is instead 101, then one die must end up with two pips showing. This could be any of the dice, so even though the probability of this happening is actually still very small, it is still a hundred times greater than rolling the sum of 100.

Now, when rolling only one die the average roll (over an infinite number of rolls) is 3,5. Of course when rolling only one die the probability is also equal for all results. If we increase the number of dice with one, the average sum will be 7 (3,5*2). If we name the dice d1 and d2 we can describe a roll as [d1, d2]. Rolling the sum of 7 can then be achieved by rolling any of the following combinations: [1, 6], [2, 5], [3, 4], [4, 3], [5, 2], [6, 1]. Each combination has the same probability of 1/36, but when only considering the sum of 7 the probability is as much as 1/6. A higher or lower sum than average will decrease the number of available combinations and thus the probability for the sum, though the probability for each combination will still be the same. At the extreme ends are the sums of 2 ([1, 1]) and 12 ([6, 6]), with one combination each.

With one hundred dice the average roll would be 350 (3,5*100), and just as we saw earlier the probabilities are not spread out evenly over the different sums. This means that a sum of 350 has a bigger probability of happening than other sums. If we would use the notation from above we could describe a roll as [d1, d2,..., dn]. We would then see that just as in the case of two dice, the number of combinations for a sum decreases as we stray away from the average sum, so that it is very likely that we end up with a sum in the vicinity of 350.

So what do I want to say with this? Perhaps nothing more than that I like probabilities. This reasoning can also be applied to a lot of things around us though. The average combination of events around us will lead to something that we can usually predict but the result has a probability of being something else. In fact, according to chaos theory the only reason the laws of physics can be reasonably relied on is that they include so many die rolls that it is too likely for them to not follow the average.

I would like to point something out also about everyday coincidences. When something strange with a low probability happens it might not be as strange as we would like to think. In the period when one unlikely event happened, millions of likely events will have happened as well. There is also the fact that it might be likely that something unlikely is to happen even though a particular unlikely event has a very low probability. An example would be to generate a random number between one and a billion, each number has a very small probability but it is very likely that we will get one of those numbers still.

It is getting more and more probable that this article is getting long-winded so it is very likely that I will end it here.

Saturday, 27 March 2010

Online After-Life

During a person's life his or her presence online keeps changing. Blog posts, tweets, status updates, forum discussions, video clip collections, personal web pages and a lot of other services keep reflecting the person until suddenly, when he or she dies, that presence freezes and becomes a historical reference to the person's life. Some parts of the mark will be erased soon. For example if the person who died had a web hotel that kept a site up, the web hotel will be quick to close down that page once the payments stop.

What happens to other things then? A lot of free services exist on servers around the Internet. There your profile will possibly exist for a very long time if the service provider does not have a policy of removing inactive accounts.

As an example, lets say a person who has a Facebook account dies. All activity on his or her profile will stop. The last status update will be saved as a memory of the person (hopefully something good). All connections will be left, as long as people on the other end do not remove them. The profile will be frozen. If Facebook lives on, after a while some of the contacts will die and there will be a frozen subnet containing profiles of dead people. More and more people will die, at some point resulting in profiles that are not connected to anyone living anymore, thus creating islands which are never or rarely visited. All the time more people will sign up to use Facebook, but there can never be more people signing up than dying or leaving. This means at some point the number of dead people represented on Facebook will surpass that of the living people. Facebook will always contain memories of the people that passed away, even though they will be hidden from new users who only connect to living friends.

The same process takes place all around the web, memories of our lives being saved. Just as in life we probably overestimate the impact that online presence has, but at least we will not be around to be disappointed!

Friday, 26 February 2010

The Chicken and the Egg

Which came first, the chicken or the egg? There seem to be and endless supply of people bringing this question up in different contexts, and each time it is expected to be a question without an answer. This could be true, but it might not as you will see. The question does not have a one ultimate answer, as it depends heavily on the viewpoint one takes when answering.

If we look at it from a purely historical point of view, eggs have been around at least since the dinosaurs were around more than 65 million years ago. Back then no chickens existed as far as we know, so from this viewpoint one can easily answer that the egg came way before the chicken.

Another viewpoint would be from a pure linguistical point. Did the word “egg” exist before the word “chicken”, and if it did, did it mean the same thing as today? This is a very hard question to answer since a language evolves, and tracing the history of a word might gradually change it until it is another word. One would then have to define exactly how much a word is allowed to change before we decide that it is a different word. Of course, if the word existed with another meaning before, we could probably find a point where the meaning changed to what it is today. I do not have a good answer from this line of thought, but if anyone has researched the origin of the words “egg” and “chicken” in detail, please share your findings.

Dropping the language details, lets move backwards in time. If we start with a chicken today it will have come from an egg, which will have come from a chicken and so on. We will at some point reach an ancestor which we would not call a chicken, but lets not dwell on that. This chicken ancestor came from an egg as well, which was probably produced by another chicken ancestor. Somewhere along the line we would reach a living organism that created a copy of itself without an egg (very far back), which at some point evolved into creating protection for its offspring during its first phase. This would then mean that that organism predated the egg as such, and thus the question would be that the chicken came before the egg, although it would an extremely different chicken from the one we have today.

Of course the above reasoning relies heavily on evolution in its explanation. If one were to believe in creationism, then according to Pastafarianism either the chicken or the egg was created by the Flying Spaghetti Monster. This view would actually leave the question as cryptical as the question probably was is intended to be.

So what have we learned here? This could be a very simple question or a very hard one. Whatever your answer to the question you will probably be right from your own perspective, and there are probably more views than I have listed here. This is very apparent when it comes to this question, but the same can be said on almost any question. The viewpoint you take when answering the question will affect the way you interpret it and thus the answer to it.

Monday, 18 January 2010

One Small Leap

First, I would like to explain the concept of the leap second. At first the definition of a second was 1/86400 of a solar day. This was not a good enough standard, so the definition was later changed to the somewhat less comprehensible length of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This gave some new problems since the solar day became approximately 1.7ms longer every century, the reason being that the earth's rotation is slowing down. To counter this sometimes an extra second is added June 30 or December 31. This added second is called a leap second. Worth mentioning is that the decreasing rotation varies based on unpredictable factors like the motion of mass in the center of the earth, which means we have no formula to calculate when the next leap second needs to be added. Instead the leap second is added when the difference between solar day time and the measured time gets too large (0.9).

This gives us some strange effects, especially when trying to calculate the difference between two points in time, where one or more leap seconds have been inserted. Imagine that a leap second was added on December 31 at 11.59.60p.m. The last minute of the year is made one second longer. This means that if were to count the seconds between 8 a.m. December 31 and 8 a.m January 1, we would get a count of 86401. If we were to count the hours instead though, the result would be 24 which, if we translate it into seconds, is 86400 and we just lost a second in the process. (This makes for some strange effects when dealing with date differences in computer systems, but that is not the topic here).

How can this be? Well, it all comes down to the difference between elapsed time and our daily measured time. The reason for the added second is to get our clocks synchronized with the solar time. The elapsed time would be 86401s = 1440m1s = 24h0m1s = 1d0h0m1s, and our clocks are calibrated so that we remove one second from the measurement of time. So what we actually do with the leap second is not to add a second, but instead hide it, delaying the coming of the next day.

We sweep one second under the rug, a little ashamed that we cannot cope with it any other way. Life goes on but the seconds we hide away will always be there in the past as a testimony that not everything can be exact.