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lördag 15 september 2007

Relativism

It is of course true that we cannot know anything for certain. For all we know, we may be living in "The Matrix", and everything we see is mere computer simulations. Likewise, we can never know for sure that a theory is true in an objective sense. I consider these two statements as uncontroversial, however, when relativists go one step further and argue that all theories are equivalent since no theory can be proven, that is when I must disagree…


People who use this reasoning have completely forgotten about the concept of evidence and prediction. Though a theory can never be proven in the absolute sense it can be better or worse at describing reality. Just as simple example there are people who claim that the world is spherical (or almost spherical), and there are those who claim that it is flat (based on religious reasoning I might add). What predictions does each of these two theories make? Well, one very simple prediction is that a round earth should cast "round" or banana shaped shadows on the moon when the earth is between the sun and the moon. If the earth was flat on the other hand, the shadow should be flat as well. Everyone who has ever gone out to watch the moon knows that the round earth theory gives the more accurate prediction. We cannot know for certain that the earth is round, but the predictions it makes agree with what we see. When a prediction is correct we can call that evidence. My point is simply that people do not walk around and think that the earth being flat and the earth being round are two equivalent theories just because neither can be proven. Almost everyone believes that the earth is round because there is so much evidence in favor of that theory.


I have previously argued that in fact it does not really matter whether a theory is true in the objective sense. As long as a particular theory is very good at predicting the world as we see it, it is a good theory and we should simply act as if it was true. It is this mentality together with the scientific method, which reduces the risk of seeing evidence where there is none that has brought us to where we are today. Here it is important to remember that if a theory is true in the objective sense, then all predictions derived from that theory would have to be true as well.


Relativists also like to point fingers at the scientific method. One frequent argument that you hear from relativists is that throughout history there has been paradigm shifts in almost all sciences. In astronomy for example we have gone from the Copernican system, to the Newtonian, to Einstein's relativity. Furthermore they claim that these paradigm shifts occur, not because latter theories are more accurate, but due to cultural factors. Relativists who use this argument, first of all, forget that history is also a science. They are using evidence which has been produced using the scientific method – the very same method which they are criticizing. Clearly hypocritical...


Besides, it is clear to me that all shifts in astronomy have been progressive. The details of the various paradigm shifts may have been influenced by sociological factors, however, the main reason for all the shifts have been that they make better predictions. Newton's theory of gravitation gives a better description than Copernicus theory, and Einstein's theory of relativity make better predictions than Newton's theory. Old theories are exchanged with new ones when the new ones are better at describing the world as we perceive it.


This will be all I write about relativism for now, but check back later if you want to read more. For some reason I end up in discussions about relativism very often, and therefore I also have many thoughts on the subject. Many of the arguments that I present here have been influenced by this book (see picture above), which I recommend to everyone.

måndag 11 juni 2007

Pragmatism


If you would press me I would have to admit to being a pragmatic. It is, if you will, my preferred philosophy of science. Pragmatism in a nutshell simply says that if a theory is good at predicting the world as we perceive it and if it is useful in the sense that it allows us to create new technologies, then we will accept that theory and use it as if it was true.

Sometimes pragmatic theories are false even though they are pragmatic. Take Newtonian physics for example. Newton's laws can explain an almost limitless amount of experimental observations. The only problem is that it is false. Experiments which are designed so that one outcome would support Newton's theory and the other outcome Einstein's theory shows clearly that the latter set of laws provide you with the more accurate predictions. Yet, because they are so practical, we still use Newton's much less confusing laws for a lot of approximations. So in this case we say that because Newton's laws works really well for almost any calculations we don't care that they are not really true.

What then are we to make of the completely absurd and mind twisting theories of quantum physics, dark energy and the like? These theories, may I remind you, shape the foundation of most new technologies today, and the accuracy of predictions derived from quantum physics is equivalent to measuring the width of the United States with an error margin of about the width of a human hair!!! However, quantum physics also predicts that if there is a cat in a box (Schrödinger's cat, see above), it can be dead and alive at the same time!? To me this sounds like nonsense. I have certainly never seen a cat that is both dead and alive and if someone would say to me that they had seen such a cat I would feel obliged to call a mental institution. In my opinion, the only sensible conclusion is to say that, yes these are absurd theories, but they are indeed incredibly practical, so lets just use them as if they were true until we find something better (if we ever will that is).

I don't think that I am contradicting myself when I say that I also believe and care about what is true in an objective sense. Being a pragmatist, I think, is a progressive way of thinking. After all, if a theory was true in the objective sense then all predictions derived from that theory would also have to be true. To put it another way, the most practical theory of all would be the one that got it right…

I am personally hoping that some day a theory that I can understand and which does not make my head hurt, will come and replace quantum physics, dark energy and other similar theories. But for now I will accept these theories because of the fact that they are practical.

måndag 18 december 2006

The Birthday paradox/problem


Did you know that if you are at a party with 23 people attending, then the probability that two people will share birthday is more than 50%!

I sometimes use this example as a way to show people that our intuitive reasoning with numbers can be quite wrong, and it really works, people shake their head in disbelief when I tell them this statistic. How can this be? To illustrate imagine that there are two people attending a party. There are 364 ways in which the second person will not have the same birthday as the first person. For the third person there are 363 days which are still not occupied. The formula that we get is that the probability that at least two people share the same birthday when there are three people attending is 1-(365*364*363)/(365*365*365) = about 0.01. If you do the same calculation but with 23 people p will be just above 0.5. The general formula is: 1 - (365)(364)(363)...(365 - N + 1)/(365)^N.

Doing this calculation with 40 persons will give you a probability of around 0.9 (see graph above)! Next time you are attending a party with 40 persons or more, why not make the safest bet ever... For more information on this problem as well as a birthday generator which lets you test these claims empirically, go to "http://www.mste.uiuc.edu/reese/birthday/default.html"