# 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.

# 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.

# 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!

# A pizza or an ambulance?

Which one gets to your house faster? You’ve all heard it’s the former – but is that really true?

First off, comparing pizza/ambulance arrival times skew the numbers. While ambulances can be called at any time of day (or, indeed, night), pizza delivery is usually around lunch time and dinner time – both of these, particularly the latter, are times in which many more people would be travelling than, say, in the middle of the afternoon. You can’t, after all, predict when you’re going to have emergencies (as a family member once emphatically told a salesperson on the phone), while you can predict when you’re going to be hungry. Pizza is delivered on a motorcycle or scooter, while a typical ambulance is larger than most cars. As such, the ambulance will naturally take longer to arrive if they’re travelling the same distance.

Of course, if I were to do this properly, I’d call, at two different times of day, both a pizza place and an ambulance, and time them both, but nobody will do that, for fear that they’re diverting emergency medical resources from where they’re needed. In the hopefully-unlikely event that anyone in the household requires an ambulance, I certainly wouldn’t be thinking about pizza delivery timings (probably something more like ‘can I drive to the hospital safely?’).

There’s also the factor of accepting deliveries. Papa John’s in India, for instance, states that it only delivers in a range that they can get to within 30 minutes. Ambulances have no such rule, nor can they be allowed to. Of course, ambulance stations/medical centres are supposed to be set up within range of everyone, while pizza places can just set up where there’s a majority of the wealthy population.

But if you just take the facts, then ambulances – at least in the capital – beat pizzas. The response time is (if government statistics can ever be believed) 10 minutes, plus or minus three. The real problem, however, isn’t how fast the ambulances get to your house – it’s whether they’ll come at all. 28% of calls are refused because ambulances aren’t available. But no pizza place will ever refuse your call. If you live in the right range, that is.

# An experiment

AIM: To analyse the win/loss ratio of two friends, A and B, when they toss a coin/play a similar game of equal chance.

THEORY: There are numerous games of chance played when trivial decisions must be made, and while these may be fair, one player will often try to ‘game the game’, by suggesting a ‘best of 3’ or ‘best of 5’ upon losing once or twice.

PROCEDURE:The people were asked to toss a fair coin, after a decision on which player would be heads and which would be tails. A was set to be the winner, and A and B had to play until out of an odd number of tosses, A had won a majority.

OBSERVATIONS:

 Number of trials Frequency 1 16 3 7 5 2 7 3 9 1 21 1 69 1 91 1

The mean of the data above is 8.0625, while the median is 3.

CONCLUSION:

Looking at this logically, if we assume that the first game is lost, at each stage, you must win both games, with probability 0.25. A summation of powers of (0.25) multiplied by the original probability of 0.5 [(0.5) + (0.5)(0.25)1 + (0.5)(0.25)2 + …] results in 0.66….. = 2/3.

[A proof of this can be shown as follows:

x = 1 + 0.25 + 0.0625 + ….

4x = 4 + 1 + 0.25 + 0.0625 + …. = 4 + x

3x = 4

x = 4/3]

Therefore, the data show that if you do not lose all of your games in a best-of-3 (or any successive best-of-2n+1), you will eventually win two-thirds of the time.

# The Coulomb and the Ohm-metre

With apologies to Lewis Carroll. This refers to various SI units.

The ohm was shining on the sea,

Shining with all its might.

He did his very best to make

The circuits smooth and bright.

And this was odd, because it was

The middle of the night.

The hertz was shining sulkily,

Because he thought the ohm

After the circuit broke.

“It’s very rude of him,” she said,

“To make all this a joke!”

The sea was wet as wet could be,

The watts were dry as dry.

You could not see a candela

Not one was in the sky.

There were no joules to fly.

The Coulomb and the Ohm-metre

Were walking at a trot.

They wept like anything to see

Such quantities of watts.

“If this were only cleared away!”

they said, “it is a lot!”

“If seven joules with seven mops

Swept it for half a year,

Do you suppose,” the Coulomb said

“That they could get it clear?”

“I doubt it,” said the Ohm-metre,

And shed a bitter tear.

“O Oersteds, come and walk with us!”

The Coulomb did beseech.

“A pleasant walk, a pleasant talk,

Along the katal beach.

We cannot do with more than four,

To give a mole to each.”

The eldest Oersted looked at him,

But never a word he said.

The eldest Oersted winked at him,

Meaning to say he did not choose

To leave the Oersted-bed.

But four young Oersteds hurried up,

A battery to meet.

Their coats were brushed, their faces washed,

Their shoes were clean and neat.

And this was odd, because, you see,

Four other Oersteds followed them,

And yet another four,

And thick and fast they came at last,

A mole, a mole and more;

All hopping through the frothy waves,

All scrambling to the shore.

The Coulomb and the Ohm-metre

Walked on a mile or so

Although they used kilometres:

“What is a mile?” Who knows?

And all the moles of Oersteds stood

And waited in a row.

“The time has come,” the Coulomb said,

“To talk of many things.

Of Grays – and Volts – and Sieverts,

Of Newtons, and their kings,

And why the Kelvin’s boiling hot,

And whether Moles have wings.”

“But wait a bit,” the Oersteds cried,

“Before we have our chat!

For some of us are out of charge,

And all of us are fat!”

“No hurry!” said the Ohm-metre.

They thanked him much for that.

“It was so kind of you to come!

And you are very nice!”

The Ohm-metre said nothing but

“Cut us another slice:

I wish you were not quite so deaf –

“O Oersteds,” said the Ohm-metre,