Appendices
271
The upper equation predicts the mass of the Higgs Boson (see Chap. 9)
to fair accuracy 14 years before the particle was discovered . This is quite an
achievement for a cartoon character. The story is told in the link: [3].
The second relationship: 3987 12 + 4365 12 = 4472 12 is, as noted in
the text, difficult to disprove by evaluating the powers explicitly. However,
considering only the last two digits of each number is sufficient for this
purpose, as can be seen from the following:
A number abcdefg, where a, b, c, etc. are the digits forming the number,
can be split into two parts: i.e., abcdefg = abcde00 + fg, where 0 is the digit
zero.
Squaring the number gives: abcde00 2 + 2.abcde00 x fg + fg 2 .
Because of the zeros, the first 2 terms contribute nothing to the last two
digits of the square, and so can be disregarded.
The same is true if we multiply two different numbers together (or add
them): i.e. only the product (or sum) of the last two digits of each contributes
to the last two digits of the product (or sum). Using this principle it is easy to
show that the last two digits of the left hand side of the above relationship are
not equal to the last two digits of the right hand side, and so the relationship
is invalid.
However, if one were to actually evaluate the terms in the relationship fully,
one would discover that 3987 12 + 4365 12 is close to the twelfth power of
4472.0000000070576171875, which a physicist would argue is near enough
to 4472 12.
A.3.4 Principia Mathematica
Principia Mathematica is a very intense book by Alfred North Whitehead and
Bertrand Russell, written in 3 volumes from 1910 – 1913. Their aim was to
provide a formal logical derivation for all arithmetic. The uncompromising
rigour of their approach is illustrated in Fig. A.6. This excerpt shows us that
at this point in their opus (page 362), Whitehead and Russell have almost,
but not quite, managed to prove that 1 + 1 = 2.
Whitehead and Russell’s book is the starting point for the work of Kurt
Gödel, which we discussed in Chap. 4.
271
The upper equation predicts the mass of the Higgs Boson (see Chap. 9)
to fair accuracy 14 years before the particle was discovered . This is quite an
achievement for a cartoon character. The story is told in the link: [3].
The second relationship: 3987 12 + 4365 12 = 4472 12 is, as noted in
the text, difficult to disprove by evaluating the powers explicitly. However,
considering only the last two digits of each number is sufficient for this
purpose, as can be seen from the following:
A number abcdefg, where a, b, c, etc. are the digits forming the number,
can be split into two parts: i.e., abcdefg = abcde00 + fg, where 0 is the digit
zero.
Squaring the number gives: abcde00 2 + 2.abcde00 x fg + fg 2 .
Because of the zeros, the first 2 terms contribute nothing to the last two
digits of the square, and so can be disregarded.
The same is true if we multiply two different numbers together (or add
them): i.e. only the product (or sum) of the last two digits of each contributes
to the last two digits of the product (or sum). Using this principle it is easy to
show that the last two digits of the left hand side of the above relationship are
not equal to the last two digits of the right hand side, and so the relationship
is invalid.
However, if one were to actually evaluate the terms in the relationship fully,
one would discover that 3987 12 + 4365 12 is close to the twelfth power of
4472.0000000070576171875, which a physicist would argue is near enough
to 4472 12.
A.3.4 Principia Mathematica
Principia Mathematica is a very intense book by Alfred North Whitehead and
Bertrand Russell, written in 3 volumes from 1910 – 1913. Their aim was to
provide a formal logical derivation for all arithmetic. The uncompromising
rigour of their approach is illustrated in Fig. A.6. This excerpt shows us that
at this point in their opus (page 362), Whitehead and Russell have almost,
but not quite, managed to prove that 1 + 1 = 2.
Whitehead and Russell’s book is the starting point for the work of Kurt
Gödel, which we discussed in Chap. 4.