Titius – Bode Law

Hi there skeptics,

Today I am going to be blogging about a mathematical formula which has had some interest in astronomy in the past, but has since fallen into the waste-bin of science. It has commonly titled as a law, in almost every reference to it and on the Wikipedia page, however, it is best described as an unproven hypothesis, as it has no evidence to support it. The law attempts to represent the approximate distances of the planets from the sun, using the following formula. a = 4 + n, where n = 0, 3, 6, 12, 24, 48, 96 etc., with each new value for n being double the last value. This gives rise to the numbers 4, 7, 10, 16, 28, 52, 100… divide this by 10, 0.4, 0.7, 1, 1.6, 2.8, 5.2, 10… To the 18th century astronomer, this is an astounding set of numbers.

The law was first formulated in 1766 by Johann Titius, who used this simple formula to get these similar numbers. This looked amazing at first, because these numbers fit almost perfectly with the distances in AU (astronomical units) of all the known planets, Mercury through to Saturn. However, there was one number in the sequence that shouldn’t be there, 2.8, no planet was known 2.8 AU from the sun. But sure enough, almost exactly 2.8 AU from the sun, the dwarf planet Ceres was discovered. This was very exiting for astronomers of the time. Could there be a deep, underlying formula to the planets.

They decided to look further, so they started with the next number in sequence, 19.6, and looked from there, and again, triumph, Uranus was discovered by William Herschel in 1781, and you guessed it, it was 19.2 AU from the sun, a mere 2% off the prediction. At this point, astronomers became drunk with enthusiasm, this number sequence is really working well. They went the next step, 38.8, but no, nothing was found. Neptune eventually became the next planet in order, but at 30.1 AU from the sun, it was 29% off, and the law was waning. Next, Pluto, predicted by Titius – Bode to be 77.2 AU away, alack, incorrect, only 39.5 AU from the sun, a 95% inaccuracy.

By this time, the law had fallen into disrepute. No more Titius – Bode being taken seriously by astronomers. Proponents of the law say that these ratios are being found as correct in other star systems around other stars, but these are stars with 1 or 2 planets, meaning that a ratio can always be found, or fit close, due to the set up of the number system. The idea of there being such a simple number which underlies all of the orbits is not one of favour in the astronomical community.

Who knows, there could be a number formula which describes the orbits of planets around a star. There must be, because they all follow the same laws of gravity. But the idea that there is a simple number sequence, not a large, abstract equation with hundreds of influencing factors, is a fringe opinion. Planets could naturally snap into particular grooves around their sun, but no number sequence has stood up to the challenge yet, so science tells us that it probably won’t exist.

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Another Roy Williams example of idiocy

Hello there, skeptical friends,

Lets all guess what I’m going to be blogging about today? That’s right, I’m sure you all guessed it, I’m going to be continuing my constant crusade against Roy Williams and his idiotic arguments, which seem alright on the surface, but soon seem not so alright when you actually look at them deeply. Today’s post is about an argument which was used by Williams to demonstrate the ‘deep, designed plan’ of the universe. Williams has made the claim that the fact that the moon lines up nicely with the sun, points towards the fact that there is design in the universe.

But unlike ‘the other creationists’, who say that the moon, with its protecting of the earth from asteroids and things, shows that god is looking out for us, Williams makes the claim that the fact that there is a solar eclipse shows proof of a god. This allows for things like the first proof of relativity, (with the measuring of the lensing of the stars) to occur. This is all part of Williams’ “God designed the universe to allow humans to figure out its inner workings.” Idea. I have some rebuttals for this argument.

The first point is that our moon is not that special. The fact that the moon eclipses the sun perfectly once in human history is not a big deal. There are a couple of factors which make this occurrence not all that rare. The distance from the earth to the moon is changing quite a lot, meaning that the size of the moon in the sky changes a lot. This means that sometimes the moon is a bit big for the sun, and sometimes the moon is not big enough to cover the sun completely, this is why you should never look directly at an eclipse. This means that there is a big variance and this leaves a big window.

The other thing that varies a lot in the sun, moon, earth system is the distance from the sun to the earth. This means that the size of the sun in the sky varies a lot. So this opens the window even more. The last thing that would change this is the fact that the moon is getting further and further away from us all the time. This means that at one time in early history, very early history, the moon appeared very large in the sky, and in a few more years, the moon will be very small in the sky, and it will not cover the sun at any time.

The second point against this argument is this. There are a lot of things that could be a certain way, but aren’t, why doesn’t god make them line up nice and pretty?

The last argument I will use is this. The eclipse of 1919 is not the only proof of relativity, there have been thousands of since proofs of relativity, and the only reason why this eclipse is still remembered is because it was the first one.

I will leave you with a humorous quote from Brian Greene, “No matter how hard you try to teach your cat general relativity, you’re going to fail”, If you don’t get it, get of my blog, or read my Quantum Mechanics posts. Brian Greene, A theoretical physicist of some note.

 

An argument from beauty

Today, I had an Ethics and faith lesson with our school father (I go to an Anglican school) and he reminded me of an argument that I have been hearing for a long time. It’s actually three arguments, the first is, “Why is there something rather than nothing?”, the second is “Why do humans and other animals exist?”, and the third is “The earth is so beautiful, it can’t have happened by chance.”His answer to all of these questions is that there must be a supreme being or god who designed it intentionally for us, so it is beautiful and appealing to us. All of these arguments are of the kind ‘post hoc, ergo propter hoc’, and I have covered that in my brief of logical fallacies which can be found on the home page. I will answer these questions in my blog post today.

The first argument, “Why is there something rather than nothing?” This can be explained easily with chance. Simply, there is only one way in which there is nothing, null and void, but there are infinite ways in which something can exist, and seeing that 1/∞ = 0, (1/2 = 0.5… 1/10 = 0.1… 1/100 = 0.01) it just has to happen. No god is needed to explain everything because something must happen. It would be more surprising if there was nothing, and we would need to have a god to explain it, but there would be nobody around to ask the question, and that leads me to the next argument.

“Why do humans and other animals exist?” This is the second question asked by my Ethics and Faith teacher. He says that there must be a god who put life on a planet to explain this. There isn’t a need for this. It has been estimated that there are about 150 billion galaxies in the known universe. There are also anywhere from 10 million to 200 billion stars in a galaxy, I will take an average of 100 billion stars in a galaxy. That comes out at about 15 000 000 000 000 000 000 000 (15 000 billion billion stars.) That means about that many rocky planets, so that means a lot of possibilities for life. The odds are slim for an individual planet, but with that many dice-rolls 10 heads in a row is not un-common.Once there is some sort of self-replicating organism, then evolution takes over and does its thing.

Now, the third argument. “The world is so beautiful, this can’t have happened by chance.” First of all, yes there is beautiful things like rainbows and forests and mountains, but there are equally bad things like some fish species or snakes or spiders and other animals which may kill you, not to mention all of humanities problems. There is as much beautiful stuff as there is not beautiful stuff. This is because the definition of beautiful is ‘the top 50% of things in the world on a scale of beautifulness’. There will always be beautiful things. But just for my teachers sake let’s try and explain why some things are so beautiful. Our subjective grading of what the most beautiful things are is taken from a data set of one.

Say the world was a little less beautiful than what it is, we would still think of the most beautiful things as ‘the most beautiful things’ and the least beautiful things as ‘the least beautiful things.’ If the world was a little more beautiful than what it is, we would still have the same titles for the most beautiful and least beautiful things. We get used to what is beautiful and what is not because we grow up in our world, not another world.

What I’m essentially saying is that things are the way it is because they are the way they are, and we wouldn’t be asking these questions if the world was different. I will leave you with a quote from Richard Dawkins, “The theory of evolution by cumulative natural selection is the only theory we know of that is in principle capable of explaining the existence of organized complexity.” Richard Dawkins, Evolutionary biologist, skeptic, atheist and author of some note.

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