Wednesday, 31 January 2007

All at Sea about Pi

The otherwise excellent Penguin Dictionary of Curious and Interesting Numbers states that, “In the Old Testament, 1 Kings 7:23 implies that π is equal to 3”. Since I first read that, I have come across several internet sites that say, either implicitly or explicitly, “The Bible says π = 3, therefore it cannot be trusted.”

1 Kings 7:23-26 describes the Sea in Solomon’s temple that was used by the priests for washing: “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it. … It was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom.”

π is the ratio of the circumference to the diameter of a circle. Here the circumference is given as 30 cubits and the diameter as 10. So the ancient Jews must have thought that π = 30/10 = 3, mustn’t they? Well, no … as I shall try to explain.

First, what is described is a very large, thick basin with a kind of lip to it, “like the rim of a cup, like a lily blossom”. It’s about 4½ metres in diameter, and about 8 centimetres thick. It’s not clear whether the rim-to-rim measurement was internal, or if it included the lip, or somewhere between. Similarly, it’s not stated whether the measurement around it included the lip or not. In fact, the “line … around it” may have been measured round the widest part of the Sea—which may not have been around rim at all: it may have bulged below the rim.

Secondly, the measurements here—and elsewhere in the description of the temple—are approximate. In fact, in the 140 or so verses in the Bible that mention cubits, most only ever refer to whole numbers of them. The remaining dozen or so refer to half-cubit measurements, but that’s the smallest fraction ever used. These are not exact measurements taken from the architect’s drawings.

So even if the measurements are both taken as referring to the same part of the rim, all we can confidently say about π from this passage is that it lies somewhere between about 29½/10½ (≈ 2.81) and 30½/9½ (≈ 3.21).

Friday, 19 January 2007

Justice Down Under

It's not so long ago that an Australian court found Pastor Daniel Scot and a colleague guilty of religious vilification after he criticised Islam in a church seminar - even though his criticisms appear to have been calm, reasonable and based on his considerable knowledge and experience. After two years that case has now been thrown out and a retrial has been ordered: Free speech victory for Australian Pastor.

The experience has been frustrating and exhausting for the pastors involved. As the Herald Sun reports (Pastors' toil and trouble), despite winning their appeal, the pastors must still pay half the costs of their challenge. They have been "harassed, threatened, denounced as bigots and flayed in the papers and on the ABC, and are now deep in debt".

The fallout from that case continues, with John Howard, the Australian prime minster now becoming involved. He has been condemned for sending a taped goodwill message to the group to which the two pastors belong: Group won't reveal PM's message and PM moves to defuse hate row.

The press is now reporting that an Australian Muslim cleric, Sheikh Feiz Mohammed, is distributing DVDs that incite jihad. See, for example, the International Herald Tribune and Herald Sun. Sheikh Mohammed is reported as stating that, "We want to have children and offer them as soldiers defending Islam", and of referring to Jews as "pigs".

It will be interesting to see how the Australian authorities deal with these allegations. On the one hand, I trust that he will be judged fairly. On the other, it must be obvious that these accusations are much more serious than those levelled at Daniel Scot.

Monday, 15 January 2007

Driven Mad

According to UK Government statistics, deaths from road accidents are decreasing. For example, in 2002 there were 3,431 deaths of road users in accidents, compared with an annual average figure of 3,578 in 1994-98, and 5,846 in 1981. The number of pedestrians killed each year has fallen steadily since the mid-1990s, although the number of car users killed was little changed over the same period.

Nevertheless, in my experience, driving standards seem to be slipping. For example, in the relatively short distance I walk during my daily commute, I noticed in just one week the following minor infringements:

  • A driver on the phone, his car swaying around a roundabout.
  • A taxi overtaking a queue of cars (including one police car) on the inside.
  • A car overtaking a bus on the pavement.
  • A motorbike turning left from a right-turn only lane (with no indicators).
  • A car turning left at a crossroads across traffic from a right-turn only lane.
  • A driver in a queue leaning on the horn after a red light just changed.
  • A van driver on the phone.
  • A car stopping well past the line at traffic lights.
  • Four cars turning right from a straight-on-or-left-turn lane.
  • A van going through a red light.
Why is this? Here are some possible reasons:

  • People always seem to be in a hurry to get to work, to get to the shops, to get home again...
  • Perhaps it can be put down to general selfishness; maybe there is less regard for others than there should be.
  • There's a less visible police presence now than I remember in the past.
  • Do the police now turn a blind eye to minor infringements anyway?
  • There seems to be less respect for law in general.
  • Perhaps better car design gives drivers a greater sense of security.
  • With roads generally more crowded than in the past, there's probably a temptation to take extra risks just to make progress.
  • Drivers forget that other vehicles contain real, flesh and blood, people.

It certainly wouldn't hurt drivers to remember the so-called Golden Rule as they get into their cars: So in everything, do to others what you would have them do to you …

Saturday, 6 January 2007

Thermodynamics and Evolution

The ID in the United Kingdom blog has an interesting post that includes Andy Macintosh's comments about the laws of thermodynamics and their relevance to the creation/evolution debate. Some argue that the second law of thermodynamics is irrelevant to the creation/evolution debate because the earth is not a closed system; energy is being continually pumped into it by the sun. However, as Andy points out, energy alone is not sufficient to produce new information. Here's an extract from the quote:

The reason of course why this subject of origins will not go away is that there is a scientific case, whether Dawkins likes it or not, which is a challenge to the neo-Darwinian attempts to explain life in terms of common descent. It is a straightforward case of testable science versus the modern evolutionary ‘just-so’ story telling. Scientists like myself who believe in Creation have no problem with natural selection. It is simply the natural equivalent of artificial selection. But natural selection has no power to create new functional structures. It does not increase information and does not build machines which are not there already (either fully developed or in embryonic form).

The principles of thermodynamics even in open systems do not allow a new function using raised free energy levels to be achieved without new machinery. And new machines are not made by simply adding energy to existing machines. This was the point at issue in the programme of Dec 10th. Intelligence is needed.

And this thesis is falsifiable. If anyone was to take an existing chemical machine and produce a different chemical machine which was not there before (either as a sub part or latently coded for in the DNA template) then this argument would have been falsified. No one has ever achieved this.

Teaser 2

This has been one of my favourites for a while…  If you built a monorail around the equator, 1 mile above the ground, how much longer than the earth's circumference would it be?


2π (that's just over 6¼) miles. (Of course, I've assumed the earth is a perfect sphere.)


At first, it looks as though some crucial information is missing: for example, the radius or diameter of the earth. As it happens, though, the answer is the same however big the planet is.

Suppose the radius of the earth is r miles. Then its circumference is 2πr miles.

The radius of the monorail will be r+1 miles, so its circumference is 2π(r+1) miles. This can be expanded to 2πr + 2π miles.

So, the difference between the two circumferences is 2πr + 2π − 2πr, i.e. , miles.

Tuesday, 2 January 2007

The Essentials?

What are the most basic Christian beliefs? If you were describing the Christian faith to someone, what are the most important truths you would want to explain? A few of us discussed these questions recently. We suggested a list of subjects; then each picked the 4 or 5 that we felt were the most important. Here's the final list. The figures give the number of votes each received. I know it's not perfect, but is not bad for a half an hour or so discussion:

9Adam fell (Genesis 3, Romans 5:12)
8Jesus died (Romans 5:8, The Gospels)
7God made us (Genesis 1:27)
7Sacrifice (1 John 4:10, Isaiah 33:10)
7Everlasting life, heaven (Matthew 25:46)
5We need forgiveness (Romans 3:10-12)
5Repentance (Acts 3:19)
5Jesus paid the price - ransom, redemption, rescue (1 Timothy 2:6)
4We sinned (Romans 3:23)
3Jesus was without sin (Isaiah 53:9)
3Hell (Romans 6:23)
3God is holy (Revelation 4:8, Isaiah 6:3)
3Faith (Hebrews 11:1, Acts 16:31)
2The Bible: authoritative, infallible, inerrant (2 Timothy 3:16, Revelation 22:18)
2Resurrection (Romans 6:5, John 20:8-9)
2Jesus was born (Luke 2:6, Matthew 1:25)
2Trust and obey
1God is ... Spirit, love, just, almighty, omnipresent, omnipotent, omniscient, eternal, three in one, infinite, creator
1Jesus is the messiah
1The kingdom of God
1The church, the body of Christ, universal, catholic, victorious
1Judgment day
1Grace not works