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God's Secret Formula: The Deciphering of the Riddle of the Universe and the Prime Number Code
Holding doctorates in chemistry, physics and biology, Peter Plichta applies his multifaceted scientific knowledge to the search for a universal building plan and makes a profound discovery. Plichta shows how a mathematical formula based on prime numbers underlies the mystery of the world. By decoding this fundamental numerical code, Plichta answers questions that have baffled mankind for ages and proves that the universe did not arise out of chance.
- GenresScienceNonfiction
218 pages, Paperback
First published May 1, 1997
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December 23, 2018
I found this book a depressing read. It contains some bad maths, some bad science, some bad logic, and an awful lot of what I can only describe as numerological and religious woo-woo.
Plichta’s big idea is that numbers, and in particular prime numbers, are the key to understanding the universe. His argument runs like this:
Premise 1: All physical processes obey laws based on the natural logarithm.
Premise 2: The decrease in frequency of the prime numbers is also linked to the natural logarithm.
Conclusion: Our physical world must be the result of the distribution of prime numbers.
This is an invalid argument. The form of it is as follows:
Premise 1: a is caused by b
Premise 2: c is caused by b
Conclusion: therefore a is caused by c
This is clearly invalid, since the fact that both a and b are caused by c is not grounds for thinking that a is caused by c.
After this inauspicious beginning, things go from bad to worse. Plichta has noticed that a lot of things in the world come in threes. Space, for example, has 3 dimensions. Time consists of past, present and future. The 90th and 92nd elements in the periodic table break up through 3 radioactive decay series into 3 stable isotopes of lead, releasing 3 types of radiation. And so on and on and on. In fact so many things in the world come in threes that Plichta is convinced that this cannot all be coincidental – it must be the result of deliberate design. And it’s not only the number 3 that he sees all over the place, it’s also the number 19. There are 19 left-oriented amino acids, and there are 19 elements with only one isotope, and there are 19 consonants in the German language.
Er, hang on. The German language?
Yes. You see, Plichta thinks this overall design doesn’t just feature in the physical world, it also features in the human world. If we go back to the number 3 for a moment, he says there are 3 branches of the law – civil, criminal and administrative. In prehistory, there were, according to Plichta, 3 main economic activities carried out by humans – hunting, tilling the soil, and animal husbandry. There are 3 main types of human language – isolating, agglutinative and inflected. And humans themselves, he tells us, are divided into 3 main races – Negroid, Mongoloid and Caucasian.
What does all this prove?
Nothing.
Plichta is relying implicitly on another piece of false reasoning, which we might state as follows:
Premise 1: Lots of things in the world are grouped in 3s.
Premise 2: When you find lots of things in the world in groups of the same number, this is evidence that the grouping must be the result of deliberate design.
Conclusion: The world must be the result of deliberate design.
This time the argument is structurally valid (or very nearly), but there is no reason at all to think that the second premise is true. There are a vast number of things in the world, and it would be very surprising if many of them did not fall naturally into groups of three. In any case, some of Plichta’s threes are very forced. Is it really true, for example, that all prehistoric economic activities fall under the headings of hunting, tilling the soil and animal husbandry? What about trade, which we know was carried on from very early times?
What is fundamentally wrong about Plichta's approach is that he gives up looking for the answers to problems, and basically says 'God did this by magic'. Nowhere in this book does he display a proper scientific approach. He rejects the Big Bang theory, but does not offer an alternative theory that could explain the observed red shift in light from other galaxies or the observed background radiation permeating the universe. He rejects Darwinian natural selection, again without giving an alternative explanation for all the evidence in its favour, such as fossils. He gives two reasons for rejecting Darwin. One is his claim that the human female is the only great ape female to have a clitoris (page 86), which would if it were true be far too slight a piece of evidence to amount to significant grounds for rejecting Darwin, but which in any case appears to be false (see https://books.google.co.uk/books?id=J...).
His second reason is that random events could not have produced the human mind, because random events would accumulate over time and prevented its emergence. This is a mistake. What actually happens in Darwinian evolution is that environment selects those random mutations that improve survival value, and only these are passed on to later generations. False developments therefore do not accumulate, they are weeded out by environmental selective pressures. It is disturbing to find that a professional scientist like Plichta does not understand this.
There is quite a lot of maths in this book. Unfortunately Plichta is not much good at maths. He claims to have discovered that every 3D body has a 4D space around it. He defends his idea by saying that a line drawn on paper is a 1D object in a 2D medium and a piece of paper in a room is a 2D object in a 3D medium, therefore every object needs a medium one dimension greater than itself in which to exist. This is confused. For a start, a piece of paper is not a 2D object but a 3D object - it has thickness, albeit a very slight thickness. A pencil line drawn on the paper is also a 3D object - it consists of 3D molecules arranged in a straight line. Plichta either has not noticed that these objects are in fact 3D or has not realised that this matters, and so he has not realised that the dimensions required for these objects are more than would be required for genuine 1D and 2D objects. If we substitute genuine 1D and 2D objects for the pencil line and the piece of paper, then the 'medium' (a better word would be 'space') in which the object is located need contain no more dimensions than the object itself. A 1D line, for instance, can be located in a 1D space with other 1D lines, all of them organised in a row in a single dimension with gaps between them. Similarly, the space in which a 2D object is located can be a 2D space in which a number of 2D objects are located with 2D gaps between them. There is thus no need for an extra dimension to accommodate objects of any dimensionality whatsoever. 3D objects only need a 3D space in which to be located, not the 4D space Plichta supposes them to require.
We are now halfway through the book, and it is time for Plichta to introduce his big 'discovery', which he calls the Prime Number Cross. This is constructed as follows:
- draw a circle with 24 points marked on it, like a 24-hour clock
- around the circle put the numbers -1 to 22, putting -1 in the 23.00 position, 0 in the 00.00 position, 1 in the 01.00 position, and so on round to 22 at the 22.00 position
- move the numbers -1 and 0 out of their places, and put 23 and 24 there instead
- draw another circle outside the first, and put the numbers 25 to 48 around it, with 25 outside 1, 26 outside 2, and so on round to 48 outside 24
- carry on drawing further circles outwards, 49 to 72, 73 to 96, etc. ad infinitum
- lastly draw straight lines through the prime numbers, starting each time at the centre of the circle.
What results from this is a rather pleasing pattern of eight radiating lines which, as Plichta observes, bears a resemblance to the Cross of the Order of St John. This is what Plichta calls the Prime Number Cross, and he regards it as being of great and profound importance. If you are wondering why we started off putting -1 and 0 on the circle and then almost immediately replaced them with 23 and 24, this is to do with Plichta's idea that pairs of prime numbers on the Prime Number Cross are connected with the electron pairs found in each shell of an atom (I shall not explain this further, since I see no reason to suppose that there is any such connection). Plichta points out that all prime numbers satisfy the formula 6n ± 1, and the prime number pairs are therefore the prime numbers on each side of the number represented as 6n. Thus if n is 1, we have prime numbers 5 and 7, if n is 2 we have 11 and 13, and so on. If n is 0, then according to Plichta the relevant pair of prime numbers are -1 and 1. So he starts by putting these on the circle, and then decides that really they belong in an inner circle of their own. The reason why we plotted 24 numbers round the circle to start with is that up to n = 4, the formula 6n ± 1 always generates two prime numbers, one each side of the 6n, whereas from n = 5 onwards, this doesn't always happen. Plichta therefore considers everything up to n = 4 to be one series, and everything from n = 5 upwards to be a distinct new series, which is why he starts a new circle at that point.
What are we to say about all this?
The first thing to note is that there is no deep significance in the fact that prime numbers can all be represented using the formula 6n ± 1. They can also be represented using the formula 4n ± 1, but you don't see Plichta making a song and dance about that. And they can be represented using either 8n ± 1 or 8n ± 3, and by using either 10n ± 1 or 10n ± 3, and by using 12n ± 1 or 12n ± 5, and so on in a similar way up the even numbers to infinity. These formulae are simply the result of taking a sequence of n numbers and knocking out the ones that couldn't possibly be primes. So for instance a sequence of 6 numbers can be written thus:
6n - 3, 6n -2, 6n -1, 6n, 6n +1, 6n +2
Obviously 6n can't be a prime because it divides by 6, so we knock 6n out. Similarly we knock out 6n - 3, because it divides by 3, and both 6n -2 and 6n + 2 because they divide by 2. The only ones left are 6n -1 and 6n +1, so obviously all prime numbers must satisfy one of these formulae or the other. If we follow the same process with a sequence of 8 numbers running from 8n - 4 to 8n +3, we have to knock out 8n, 8n - 4, 8n - 2 and 8n + 2, leaving 8n - 3, 8n -1, 8n + 1 and 8n + 3 as the only formulae that can be satisfied by a prime number. This is just pedestrian arithmetic, with no profound meaning at all.
The second thing to note is that when Plichta says that the series of primes up to 24 is a different series from the series of primes above 24, he is making an arbitrary choice. The definition of the first series would be 'a series where all the numbers satisfying the formula 6n ± 1 are prime', whereas the definition of the second series would be 'a series where only some of the numbers satisfying the formula 6n ± 1 are prime'. It would be equally valid to say instead that all the numbers form a single series under the second of these two definitions, in which case the distinction between numbers up to 24 and numbers above 24 disappears; and if this distinction disappears, then Plichta has no reason to plot his first circle with 24 numbers around it, or indeed to plot any kind of circle at all.
Putting the above two points together, we can see that Plichta's Prime Number Cross is merely an artifact of two things: his arbitrary choice of 6n ± 1 out of the infinite number of similar formulae, and his equally arbitrary decision to regard numbers up to 24 and numbers above 24 as two distinct series. The Prime Number Cross is therefore the result of arbitrary choices made by Plichta himself, in which case it cannot be an indicator of some profound truth about the universe.
Plichta now goes on to talk about the speed of light, which he argues is a natural constant, like e and pi. Natural constants have absolute values and no units of measurement, so this is a large claim, since the speed of anything is normally calculated as distance over time. On pages 126 and 127 he argues that the speed of light is an absolute value of 300,000,000,000, the point being that this shows once again that God used the number 3 in designing the universe. Plichta is not troubled at all by the fact that light speed is usually given as 299,792,458,000 rather than 300,000,000,000, but nor does he explain why there is a discrepancy. Personally I always prefer reality to theory, and so I will take the usual figure as the right one, which means rejecting Plichta's figure - and if we reject Plichta's figure for the speed of light, I think we also have to reject his notion that God built the number 3 into the speed of light. I also don't see why we should accept the claim that the decimal system was built into the structure of the universe by God (which is what Plichta really means when he says it is not a coincidence) when it seems perfectly obvious that it arose because humans have ten fingers.
What is my final impression of Plichta's book? I think it is worthless. Quite apart from the obvious errors in the book, real science - real investigation of how the world is made - is not done like this, by picking out apparent patterns in things and then ascribing them to the intentions of a deity. If a God is ever to be a rational explanation for how the universe is, this will be because empirical research has revealed (a) the existence of such a God, and (b) the method by which he created the universe. That day is not yet, and I do not think there is any reason to suppose that it will ever dawn.
Footnote: This review covers the first 130 pages of Plichta's book, which is 213 pages long. I hope I may be forgiven for not reviewing the last 83 pages. Quite honestly, I could not face wading through any more of Plichta's pea-brained numerological fantasy.
Plichta’s big idea is that numbers, and in particular prime numbers, are the key to understanding the universe. His argument runs like this:
Premise 1: All physical processes obey laws based on the natural logarithm.
Premise 2: The decrease in frequency of the prime numbers is also linked to the natural logarithm.
Conclusion: Our physical world must be the result of the distribution of prime numbers.
This is an invalid argument. The form of it is as follows:
Premise 1: a is caused by b
Premise 2: c is caused by b
Conclusion: therefore a is caused by c
This is clearly invalid, since the fact that both a and b are caused by c is not grounds for thinking that a is caused by c.
After this inauspicious beginning, things go from bad to worse. Plichta has noticed that a lot of things in the world come in threes. Space, for example, has 3 dimensions. Time consists of past, present and future. The 90th and 92nd elements in the periodic table break up through 3 radioactive decay series into 3 stable isotopes of lead, releasing 3 types of radiation. And so on and on and on. In fact so many things in the world come in threes that Plichta is convinced that this cannot all be coincidental – it must be the result of deliberate design. And it’s not only the number 3 that he sees all over the place, it’s also the number 19. There are 19 left-oriented amino acids, and there are 19 elements with only one isotope, and there are 19 consonants in the German language.
Er, hang on. The German language?
Yes. You see, Plichta thinks this overall design doesn’t just feature in the physical world, it also features in the human world. If we go back to the number 3 for a moment, he says there are 3 branches of the law – civil, criminal and administrative. In prehistory, there were, according to Plichta, 3 main economic activities carried out by humans – hunting, tilling the soil, and animal husbandry. There are 3 main types of human language – isolating, agglutinative and inflected. And humans themselves, he tells us, are divided into 3 main races – Negroid, Mongoloid and Caucasian.
What does all this prove?
Nothing.
Plichta is relying implicitly on another piece of false reasoning, which we might state as follows:
Premise 1: Lots of things in the world are grouped in 3s.
Premise 2: When you find lots of things in the world in groups of the same number, this is evidence that the grouping must be the result of deliberate design.
Conclusion: The world must be the result of deliberate design.
This time the argument is structurally valid (or very nearly), but there is no reason at all to think that the second premise is true. There are a vast number of things in the world, and it would be very surprising if many of them did not fall naturally into groups of three. In any case, some of Plichta’s threes are very forced. Is it really true, for example, that all prehistoric economic activities fall under the headings of hunting, tilling the soil and animal husbandry? What about trade, which we know was carried on from very early times?
What is fundamentally wrong about Plichta's approach is that he gives up looking for the answers to problems, and basically says 'God did this by magic'. Nowhere in this book does he display a proper scientific approach. He rejects the Big Bang theory, but does not offer an alternative theory that could explain the observed red shift in light from other galaxies or the observed background radiation permeating the universe. He rejects Darwinian natural selection, again without giving an alternative explanation for all the evidence in its favour, such as fossils. He gives two reasons for rejecting Darwin. One is his claim that the human female is the only great ape female to have a clitoris (page 86), which would if it were true be far too slight a piece of evidence to amount to significant grounds for rejecting Darwin, but which in any case appears to be false (see https://books.google.co.uk/books?id=J...).
His second reason is that random events could not have produced the human mind, because random events would accumulate over time and prevented its emergence. This is a mistake. What actually happens in Darwinian evolution is that environment selects those random mutations that improve survival value, and only these are passed on to later generations. False developments therefore do not accumulate, they are weeded out by environmental selective pressures. It is disturbing to find that a professional scientist like Plichta does not understand this.
There is quite a lot of maths in this book. Unfortunately Plichta is not much good at maths. He claims to have discovered that every 3D body has a 4D space around it. He defends his idea by saying that a line drawn on paper is a 1D object in a 2D medium and a piece of paper in a room is a 2D object in a 3D medium, therefore every object needs a medium one dimension greater than itself in which to exist. This is confused. For a start, a piece of paper is not a 2D object but a 3D object - it has thickness, albeit a very slight thickness. A pencil line drawn on the paper is also a 3D object - it consists of 3D molecules arranged in a straight line. Plichta either has not noticed that these objects are in fact 3D or has not realised that this matters, and so he has not realised that the dimensions required for these objects are more than would be required for genuine 1D and 2D objects. If we substitute genuine 1D and 2D objects for the pencil line and the piece of paper, then the 'medium' (a better word would be 'space') in which the object is located need contain no more dimensions than the object itself. A 1D line, for instance, can be located in a 1D space with other 1D lines, all of them organised in a row in a single dimension with gaps between them. Similarly, the space in which a 2D object is located can be a 2D space in which a number of 2D objects are located with 2D gaps between them. There is thus no need for an extra dimension to accommodate objects of any dimensionality whatsoever. 3D objects only need a 3D space in which to be located, not the 4D space Plichta supposes them to require.
We are now halfway through the book, and it is time for Plichta to introduce his big 'discovery', which he calls the Prime Number Cross. This is constructed as follows:
- draw a circle with 24 points marked on it, like a 24-hour clock
- around the circle put the numbers -1 to 22, putting -1 in the 23.00 position, 0 in the 00.00 position, 1 in the 01.00 position, and so on round to 22 at the 22.00 position
- move the numbers -1 and 0 out of their places, and put 23 and 24 there instead
- draw another circle outside the first, and put the numbers 25 to 48 around it, with 25 outside 1, 26 outside 2, and so on round to 48 outside 24
- carry on drawing further circles outwards, 49 to 72, 73 to 96, etc. ad infinitum
- lastly draw straight lines through the prime numbers, starting each time at the centre of the circle.
What results from this is a rather pleasing pattern of eight radiating lines which, as Plichta observes, bears a resemblance to the Cross of the Order of St John. This is what Plichta calls the Prime Number Cross, and he regards it as being of great and profound importance. If you are wondering why we started off putting -1 and 0 on the circle and then almost immediately replaced them with 23 and 24, this is to do with Plichta's idea that pairs of prime numbers on the Prime Number Cross are connected with the electron pairs found in each shell of an atom (I shall not explain this further, since I see no reason to suppose that there is any such connection). Plichta points out that all prime numbers satisfy the formula 6n ± 1, and the prime number pairs are therefore the prime numbers on each side of the number represented as 6n. Thus if n is 1, we have prime numbers 5 and 7, if n is 2 we have 11 and 13, and so on. If n is 0, then according to Plichta the relevant pair of prime numbers are -1 and 1. So he starts by putting these on the circle, and then decides that really they belong in an inner circle of their own. The reason why we plotted 24 numbers round the circle to start with is that up to n = 4, the formula 6n ± 1 always generates two prime numbers, one each side of the 6n, whereas from n = 5 onwards, this doesn't always happen. Plichta therefore considers everything up to n = 4 to be one series, and everything from n = 5 upwards to be a distinct new series, which is why he starts a new circle at that point.
What are we to say about all this?
The first thing to note is that there is no deep significance in the fact that prime numbers can all be represented using the formula 6n ± 1. They can also be represented using the formula 4n ± 1, but you don't see Plichta making a song and dance about that. And they can be represented using either 8n ± 1 or 8n ± 3, and by using either 10n ± 1 or 10n ± 3, and by using 12n ± 1 or 12n ± 5, and so on in a similar way up the even numbers to infinity. These formulae are simply the result of taking a sequence of n numbers and knocking out the ones that couldn't possibly be primes. So for instance a sequence of 6 numbers can be written thus:
6n - 3, 6n -2, 6n -1, 6n, 6n +1, 6n +2
Obviously 6n can't be a prime because it divides by 6, so we knock 6n out. Similarly we knock out 6n - 3, because it divides by 3, and both 6n -2 and 6n + 2 because they divide by 2. The only ones left are 6n -1 and 6n +1, so obviously all prime numbers must satisfy one of these formulae or the other. If we follow the same process with a sequence of 8 numbers running from 8n - 4 to 8n +3, we have to knock out 8n, 8n - 4, 8n - 2 and 8n + 2, leaving 8n - 3, 8n -1, 8n + 1 and 8n + 3 as the only formulae that can be satisfied by a prime number. This is just pedestrian arithmetic, with no profound meaning at all.
The second thing to note is that when Plichta says that the series of primes up to 24 is a different series from the series of primes above 24, he is making an arbitrary choice. The definition of the first series would be 'a series where all the numbers satisfying the formula 6n ± 1 are prime', whereas the definition of the second series would be 'a series where only some of the numbers satisfying the formula 6n ± 1 are prime'. It would be equally valid to say instead that all the numbers form a single series under the second of these two definitions, in which case the distinction between numbers up to 24 and numbers above 24 disappears; and if this distinction disappears, then Plichta has no reason to plot his first circle with 24 numbers around it, or indeed to plot any kind of circle at all.
Putting the above two points together, we can see that Plichta's Prime Number Cross is merely an artifact of two things: his arbitrary choice of 6n ± 1 out of the infinite number of similar formulae, and his equally arbitrary decision to regard numbers up to 24 and numbers above 24 as two distinct series. The Prime Number Cross is therefore the result of arbitrary choices made by Plichta himself, in which case it cannot be an indicator of some profound truth about the universe.
Plichta now goes on to talk about the speed of light, which he argues is a natural constant, like e and pi. Natural constants have absolute values and no units of measurement, so this is a large claim, since the speed of anything is normally calculated as distance over time. On pages 126 and 127 he argues that the speed of light is an absolute value of 300,000,000,000, the point being that this shows once again that God used the number 3 in designing the universe. Plichta is not troubled at all by the fact that light speed is usually given as 299,792,458,000 rather than 300,000,000,000, but nor does he explain why there is a discrepancy. Personally I always prefer reality to theory, and so I will take the usual figure as the right one, which means rejecting Plichta's figure - and if we reject Plichta's figure for the speed of light, I think we also have to reject his notion that God built the number 3 into the speed of light. I also don't see why we should accept the claim that the decimal system was built into the structure of the universe by God (which is what Plichta really means when he says it is not a coincidence) when it seems perfectly obvious that it arose because humans have ten fingers.
What is my final impression of Plichta's book? I think it is worthless. Quite apart from the obvious errors in the book, real science - real investigation of how the world is made - is not done like this, by picking out apparent patterns in things and then ascribing them to the intentions of a deity. If a God is ever to be a rational explanation for how the universe is, this will be because empirical research has revealed (a) the existence of such a God, and (b) the method by which he created the universe. That day is not yet, and I do not think there is any reason to suppose that it will ever dawn.
Footnote: This review covers the first 130 pages of Plichta's book, which is 213 pages long. I hope I may be forgiven for not reviewing the last 83 pages. Quite honestly, I could not face wading through any more of Plichta's pea-brained numerological fantasy.
September 3, 2013
quasi Crank Physics
August 2, 2021
Delusional, at the very least.
Displaying 1 - 3 of 3 reviews