2 = 1

So today someone asked me to prove 2 = 1. Here we go.

Take a = 1

12 = a(1)

12 – a2 = a – a2

(1+a)(1-a) = a(1-a)

a + 1 = a

Substituting a = 1,

2 = 1.

As the internet would say, you won’t BELIEVE what we just found out

Hypothesis: Men and women have different attitudes towards safety in public spaces.

Method of analysis: We posted a survey online yesterday (http://bit.ly/1MsrIg6) consisting of ten questions relating mainly to safety practices in public areas. The last question was “What is your gender?” to ensure that responses would not be biased. Respondents were not told that the survey related to gender-specific survey practices.This data was subsequently collated and analysed.

Results: During analysis, although many responses conformed to a few patterns, enabling us to guess the gender of the respondent based on those, as time went on, more and more outliers emerged. You can see the conclusions here:

Survey #2: The future’s closer than you think

And when it gets here, and we’re all living in space settlements (OK, maybe not all), there are factors related to the inhabitants to work out. On a settlement, would you want a chip implanted into your skin? What would you miss about Earth? Do we need democracy? What’s your conception of what your new home would look like? Tell me what you think in this survey: Survey

Thank you for participating!

Survey #1 – Disease Awareness

The Ice Bucket Challenge has been doing the rounds lately, and most people are likely to have heard of it. For those who haven’t, it’s a challenge in which you either drench yourself in ice-cold water from a bucket and donate \$10, or donate \$100 (or an equivalent, whatever’s been decided for your country) to an ALS charity. This is really something Indian people do every day in the summer months (or, more often, something they’d like to do). The whole thing is really a stunt to raise awareness about ALS.

But has it succeeded? To find out, I polled 34 people in my class (all exposed to the Internet) on two questions:

1. Have you heard of the Ice Bucket Challenge?
2. Have you heard of ALS? If so, what is it?

The responses were:

1. Yes and yes – 10. Most people in this category had already taken the challenge, and one even told me how it relates to ALS (which is a disease characterised by partial or complete paralysis, lack of strength in one’s muscles, numbness, and eventually, death.) – apparently, after you douse yourself in cold water, you experience momentary numbness similar to that of an ALS patient.

2. Yes and no – The majority of people were here. 22 out of 34, in fact. Most people knew that it was a disease, but a lot of them didn’t know anything about it – it could very well be the Pneumonia Ice Bucket Challenge, a much more appropriate illness to support by inducing it in oneself. A few people thought it was a heart disease, and a few more a committee or organisation.

3. No and yes – none. Not surprising.

4. No and no – two here, not the sort of people to spend more time on the Internet or with people who are likely to take the challenge than they have to.

So, publicity stunt? Yes. Disease awareness? Not so much.

A parody sonnet

“So is this how all people spoke for years?
In turgid, halting prose that strained their mind?
They must have tired one another’s ears,
But then be forced for to respond in kind.
Just to ensure the rhythm and the rhyme.”
Did Shakespeare think that this’d be a bore,
Or ’twould entertain the people for all time?
Most people would yawn and roll their eyes,
On seeing such a flagrant parody.
But is this not how they’d express their cries,
Those people lasting just in memory?
Though people think that boredom lies within
Shakespeare’s old plays, I know of no such thing.

Sometimes, all the Internet’s resources aren’t enough.

A few days ago, I heard this song at a school event. I didn’t remember the title or any of the lyrics; all I remembered was the tune. I tried asking friends what the song was, downloading apps such as SoundHound; none of those resulted in anything. So, I’m asking the Internet’s residents.

http://picosong.com/5nRs/

Click on the link above to listen to the tune, on my piano (apologies for ambient noise). Please respond!

Question of the Day

I was trying to gauge how useful mathematical education in school really is, or will be in students’ professional lives. So I came up with a survey question:

YES – 13
NO – 20
DON’T KNOW – 10
PARTIALLY* – 2

*These two only saw it as useful for the one tiny fraction on statistics, rather than the trigonometry or calculus that forms the bulk of advanced mathematics in school.

We’ve all seen them. Posts on popular Facebook pages that read something like “if your reading this then your’re parent’s will die within 5 years unless u post this on 20 otehr pictures” (you have no idea how tough that was for me to type). The strange thing is, that might actually be true; but if it is, it’s not because you read a message.

How old is the average Facebook user? Some estimates put it at around 25-30, but I think that chain letters of this type aren’t specific to Facebook, and so, a better estimate might be the median age in general. I’m going to use the US as my basis for doing this, mainly because data’s easier to get.

The US median age is 37 years (data on how this varies across countries/continents/cultures will have to wait for another blog post), and the average new mother in the 1970s (when these people were born) is approximately 25 years. So, five years after the average Facebook user reads a post like this, their mother will be 67 years old, and their father past 70. You’d agree that death at this age wouldn’t be uncommon or unnatural, being just ten years short of the life expectancy (which is measured at birth, so the life expectancy of that generation – the parents of the average Facebook user – would be lower).

The difference between the life expectancy at birth of the generation currently being born (that of the older generation will probably be lower) and the average age of the median person’s mother across various countries is displayed below:

United Kingdom: 12 years

India: 15 years (although health care infrastructure has mostly been established in the past few decades here, so this could be much lower than the rest)

Australia: 14.5 years

Most of the EU: 13 years

So, these chain letters may have a grain of truth to them. However, as responsible users of the Internet and Facebook, don’t take them too seriously. (“Too seriously” could be defined as spending more than about two seconds on them.)

Where Muggle-borns and Squibs Come From

EDIT: I SWEAR I wrote this before seeing a similar, more scientifically rigorous explanation at http://hpmor.com/chapter/23

An integral part of the now-famous Harry Potter series is the purity – or more often, the lack of it – of wizarding blood. Harry is a half-blood, because he’s the child of a pure-blood father and a Muggle-born mother.

There’s no explanation given in the series as to how Squibs (non-magic people of wizarding parentage) or Muggle-borns (self-explanatory term) arise. Here, I present one, based on real-life genetics.

There are two types of gene; dominant and recessive. The dominant one will arise in a child if one copy of it is transmitted, whereas the recessive one needs two copies to be expressed. If we assume that a gene for wizardry can be transmitted just like one for height, or eye colour, everything falls into place.

James Potter came from a line of pure-blood wizards, so it’s safe to say that he had a WW gene configuration (where W is the gene for wizardry, and w is the gene for ‘muggleness’.) Ww is also possible, but not so likely, for reasons I won’t get into here.

Lily Evans, on the other hand, was a Muggle-born witch, which meant that both parents were Muggles, but each with one wizarding gene to pass on. That is, they both had a wW configuration; note that here, w is the dominant gene, and W is recessive. There was a one-in-four chance that Lily would get a W gene from both parents; this applies to any Muggle-born wizard or witch.

Muggle-borns must have two W genes to be a wizard or witch, giving them as much magical ability as any pure-blood (perhaps even more – see Hermione), as it’s possible for a pure-blood to have a Ww configuration.

Squibs are the opposite – they are born to magical parents who both give their recessive w gene, leading to a Muggle born of pure-blood parents. It’s reassuring that, with all its magic, the series still complies with what we know of science.

Tune in next week for my assessment of midi-chlorians!

The Drake equation, here on earth

The Drake equation uses a series of variables to try and estimate the number of possible planets in the galaxy which could send us radio signals:

N = R* * fp * ne * fe * fi * fc * L

Each of these variables is a factor upon which N will depend, like the rate of star formation, and the number of planets that could potentially support life.

Such an approach can be used to estimate a number of quantities. When I became curious about divorce rates and the number of children with divorced parents, I developed one of my own:

CD = CP * MR *(1 – P(D/-C) * (P(D)/P(C)) * FR

I like it both for its mathematical usage and for its collection of random signs and letters that could mean anything until you read the explanation.

CD = Number of children with divorced parents

CP = The population of the country (an obvious starting point)

MR = The marriage rate, generally in the form of marriages per thousand people (e.g. 6.8 per thousand), but here in the form 0.0068

The middle part is based on Bayes’ Theorem, which is a way of working out conditional probabilities, as in, the probability of event A when you know event B happened.

P(D/C) = probability of divorce, given that there is at least one child.

By Bayes’ theorem, P(D/C) = P(C/D)*P(D)/P(C). The only flaw in this is the term P(C/D), which means the probability of a child, given a divorce. However, you can reverse this, so that it’s 1 minus the probability of a divorce, given no children.

P(D) = probability of divorce

P(C) = probability of at least one child (within wedlock).

FR = the fertility rate, the average number of children per family.

Using this equation, the estimated number of children in the US with divorced parents is:

314 million * 0.0068 * (1 – 0.66) * (0.48/0.82) * 1.8 = a little over 750,000 children.

India, with its low divorce rate (the only rates lower than it are in countries where it’s illegal) and high probability of children in a family, has barely 5000 children with divorced parents, in a country with a population four times that of the US. In the UK, there are around 100,000.

However, since this uses the marriage rate, this is divorces per year, meaning that it’s a lot higher. This depends upon the average age of the child(ren) when their parents divorce, which is one statistic I probably won’t find.

Next in the series: how many children have parents who were never married in the first place?