Marginal Error

Aside from the fact that the news this country has a new Prime Minister who is a racist liar I was bothered by the phrasing on BBC News last night. I haven’t really watched TV news for a long time, I find it patronising and reliant on the personal story rather than the facts, I don’t enjoy watching it. I viewed a little on catch up last night just to see what they said about the tory party leadership result.

BBC News Maths Problem
Marginal Error

Boris Johnson won by a MARGIN of two to one.

Now, what the actual fuck does that mean? I mean, I’m not happy Johnson won but that’s the shitty system we have. I’m really asking what does the phrase “by a margin of two to one” mean?

Does it mean that Boris got around 66% of the vote and Hunt 33% [or thereabouts]? In which case the margin is 1/3 of the electorate or you could even say the majority was 100% of Hunt’s vote. What you can’t say is the MARGIN was a ratio of 2:1 without DEFINING what the other side of the ratio is. Fucking hell, people need to understand that maths and words have meanings.

My instinct is that these numbers are the relative share of the vote, but the news chap doesn’t say that. He says MARGIN. The margin is the majority? I don’t know. How is margin defined in this case. A quick inspection of Wikipedia has the definition that MARGIN is the percentage of the difference relative to total turnout.

So, I think it would be best for the BBC and other news outlets to have used the phrase:

Mr Johnson won with a margin of around 33% of the turnout.

48 Degrees

My newest favourite number is 48 or more accurately arccos (2/3). Other favourite numbers are 5,17, and 309. Although 48 is ten more that the Revolting Cocks song 38, the reason for 48 degrees is explained (mathematically) below, but essentially 48 degrees is the solution to the problem:

A smooth hemisphere with radius, r, is resting in a fixed position on a horizontal plane with its flat face in contact with the plane. A particle of mass, m, is slightly disturbed from rest at the highest point of the hemisphere. Find the angle to the vertical that the particle leaves the surface of the sphere.

Also  this is independent of radius, particle mass and local gravity! Nice.


How to eat an apple

Apart from using a knife (or not) and cutting up an apple I can think of predominantly two ways of eating an apple. This does matter because one way is correct and the other is not so correct.

Circumferential or the Segment method?

A circumferential eater will take a bite, rotate the sphere using the core as the axis and take another bite. This will result in a curve of apple exposed around the great circle of the apple. Then another line of bite is taken from each end (assuming that the eater has a big enough mouth to bite to the core)
A segmental eater takes bites out of the apple from stalk to opposite pole. This results in a segment being eaten and then the apple being rotated to start the process again.
The problem is exposure of the flesh of the apple to the air to turn brown and this needs to be minimised. In the segment method the area exposed for significant time is constant. For the circumferential method the area exposed increases with time.

Area comparison

Which leads to:

Radius comparison

The analysis shows that if your bite radius is greater than 0.140 of the radius of the apple then you should eat in segments. Apart from small mammals the bite radius is going to be more than 14% of the apple radius, unless there is a huge apple variety waiting to be discovered.

Apple Problem

Apple Problem

This post was necessary because every time I eat an apple my wife tells me I am eating it the wrong way.