Modern science often leads towards a very blind pathway. For instance, a few entries back I brought up Occam’s razor, this entry we’re going to explore it further. A simple calculation for Pi is 7/22. Of course it’s wrong, and we know this. Realistically speaking in science we would never, ever require more than the first 11 decimal places of Pi, for just about any computation you can think of (yes building a circle the size of the universe out of hydrogen atoms requires 39 decimal places, but that’s irrelevant as it’s useless hypothetical’s). Computer programmers generally use up to 20 digits.

What if you didn’t need to know 11 decimal places in the first place, what if you only needed to know 8? In that case you could use 355/113, and it would always be accurate. You would be taught this simple pattern: 113355, spit in two 113-355 and put the bigger on top. But we need 11 decimal places, right? So what if Pi = 3.14159265358? That’s a LOT simpler than having a transcendental number. It’s what’s called a Rational Number, whereas Pi is actually an Irrational Number.

What if you didn’t know Pi was transcendental? It is extremely difficult to prove that a number is transcendental, especially if there is no meaning ascribed to an infinite recession of decimal places. That is, what difference does it make if Pi’s decimal places are infinitely long if you can only use the first 11 anyway? They have no purpose, no meaning, no reason for being.

This raises the obvious question – how do we know that Pi has to be irrational? The answer is simple, Pi is computed using the laws of Mathematics, and not the laws of science. Under mathematics it can be proven definitively that the ratio between a circle’s diameter and circumference references an infinite regression of precision. This causes a major problem for science however, because the best we can do is approximate, and often Occam’s unhelpful razor is used to dismiss intelligent theories that are more complex or involve more numbers.

We don’t know who first discovered Pi or when, but it has been used for thousands of years. Around 1900BC the Egyptians were known to have used the approximation of 256/81 – correct to the first decimal place. That makes it about 99.4% accurate to the true value of Pi. Long before this the Egyptians integrated Pi into the construction of at least most of their pyramids in a variety of different ways. Consider the Great Pyramid of Giza. It was built c. 2560BC. It was originally 280 cubits high and each side was built as close as possible to 440 cubits long, making the parameter 1760 cubits long. Pi is found as 22/7 in this ratio: 1760/280 = 2 x 880/280 = 2 x 22/7. 22/7 is actually significantly more accurate than 256/81, 22/7 is 99.96% accurate. This is pretty conclusive evidence that they didn’t use 256/81 when building the great pyramid, or the size of the sides would have been 442 cubits long.

If you could reduce the speed of light to Planck Time, then how would you represent it? If you look in any science book older than about 10 years that cites the value of Planck Time, it will say the value is 6.6262…x10^-34. You look at anything today and the value is 6.626**0**6… x10^-34 (they may even add a few more decimal places).

But we know we sometimes run into trouble if we try to use Pi with less than at least 8 decimal places! Where do these numbers come from? When we look hard enough, nature seems to be able to pull new numbers out. Suddenly there’s another decimal place, or there’s a new constant multiplier that applies between different numbers (just as Pi does). Why does the universe use such a complicated number like Pi – does it compute it, if so how?

One of the things that sets science apart from mathematics is its use of numbers. Experimental values are often way off of theoretical values, but even when they’re close to each other we’re still shown greater precision than theoretical models when we look for those numbers experimentally. In either case, it proves we’re just reading the value we can see; this is like trying to compute Pi by measuring the diameter and the circumference; you will always have an error since you can only compute that as a fraction and Pi cannot be written as a fraction.

But it gets us thinking, in science what numbers are rational and what ones aren’t? We can never know if Planck’s Constant is a rational number, because there is no way to tell the difference unless you can see behind the curtain to how the number was generated in the first place. If we didn’t know how to compute Pi, and we didn’t have mathematics only science then we would think it’s a decimal number with a limited number of decimal places, we wouldn’t know wether it had 8, 11 or 20 decimal places, but we would have no reason to imagine further decimal places, where would they come from?

Occam’s razor is unhelpful to science. You can’t tell the difference between whether a number is simple or complex; Occam’s razor tells you “it’s probably simple”. Mathematics tells you that there are relatively speaking “more” complex numbers than there are simple numbers. If that is true then translated into science it means that there are more complexities at rudimentary levels then there are simplicities.

In the late 80’s cosmologists were absolutely certain that the universe was 20 Billion years old – give or take at most 1 billion years. Today they are absolutely certain that the universe is 13.75 Billion years old – give or take at most 170 million years. Do you see how these numbers have changed? When I attacked cosmologists a couple of entries back, I illustrated the point that they believe so strongly in their unproven science that they invent further unproven objects to handle discrepancies. I stumbled across a page today you might find interesting, from serious cosmologists urging for more thought outside of big bang cosmology to be considered in the serious academic studies of the universe. Click Here!

When everything is always followed to its “logical conclusion” science always spits out what it interprets as certainty. But they may be mistaken. The universe began as a chaotic event, and in these respects this means if you were alive to see it you would be unable to predict the results until you watch what happens. The same thing with Langton’s Ant building highways; Langton had no idea that would happen when he invented the concept, it arises out of “chaos”. It gets “stuck” in a never ending loop of moves, like a game of chess with 2 kings left at the end, it would go on forever if allowed to.

But if all you saw were the two kings moving around the board in a chaotic pattern, would you be able to predict – even if you knew the starting conditions – how they came to their present state? Of course not. It could have literally taken tens of trillions of different paths. I know, I know, I’m too modest. There are 265,252,859,812,191,058,636,308,480,000,000 (265.25 Nonillion) possible combinations of what order the other pieces got taken in alone (that’s exactly equal to 30! if you’re wondering how I came to that number). In the same way, a completed Rubik’s Cube will never ever tell you what the starting condition was, all you can possibly observe is the completed state. There are 43,252,003,274,489,856,000 possible states of a Rubik’s Cube (43.25 Quintillion).

The problem with the theory of the Big Bang is that it sets the starting conditions such that if you were alive to see the starting condition you could have predicted the outcome before you saw it. Doesn’t that violate everything you know about science and chaos or what? It would be the same logic in determining that Langton’s ant started with a highway – which is a mistake, the ant actually starts in chaotic patterns until it eventually gets “stuck” in a loop. The greatest mathematician in the world would be unable to predict it without computing it (in other words, without actually observing it)! Why should the universe behave any differently? The expansion of the universe is a never-ending “cycle”, but just because it has got “stuck” in this cycle does not mean that accurately represents the starting conditions, there could have been some other chaotic event that occurred that gave rise to this “loop” if you will. The only thing that disagrees with this theory is Occam’s razor, but I put it to you that it sounds far more sensible to your average mathematician who loves chaos!

So what we know is we don’t know if the creation of the universe as we observe it was a chaotic event or a uniformly predictable one; both are able (to a degree anyway) to explain how we got into being where we are. I have not read-up on competing theories to the Big Bang, by the way, everything I’m proposing is merely logically formed out of the mathematical point of view, it’s not based on any competing theory or anything I’ve read, just in case you’re wondering. In fact I am aware of the competing theories and none of them prefer to start with a purely chaotic beginning. This is because it’s non-computable, it’s unknowable in a very real sense. It’s like saying we know from the point where the universe began expanding but before that precise moment (that some believe was the Big Bang) we think there was a chaotic event that built this model, and we can’t know what it was because it’s impossible to determine the starting conditions.

Ah, wouldn’t that sit well with the cosmologists of today?