The Undemocratic Rebellion

"Mr Stop Brexit" Steve Bray and a Leave campaigner. Credit: Reuters/Toby Melville.

Reading about Brexit recently I encountered one leave supporter describing the current group of remainers and politicians who are campaigning for remain or a blockade for a no deal Brexit as an ‘undemocratic rebellion’. At first, it might seem obvious – the results of the referendum of 2016 have to be honoured: everyone was given an equal chance and right to vote about whether or not we should stay in the EU.

Well, although it is true that based on the vote we should have left the EU, the fact is that I’m not sure that many people – remainers or leavers - knew at that time what leaving the EU was about, or do now in fact! The government had originally called the referendum as an election tactic to try to sway voters leaning towards less mainstream parties, such as UKIP, back to the conservatives. They never believed that it could ever come to anything. The vote was held in the same patronising way that a parent might tell their 10 year old child that they can live on their own.

The problem is, that if that child actually became serious about leaving the house, the parent would then at least try to question the child’s motives and its means of supporting itself once it has left the house: “How are you going to mortgage that flat in Scotland without a job?”.

The government at the time gone went through with its patronising stance, and afforded the voters the same courtesy: a postcard telling them why we’re better off in the EU. They were arrogantly complacent enough to think that a letter through everyone’s door would suffice to quell the discontent that was bubbling across the country at the time.

Unfortunately, we all know the outcome of this complacency, and you might say that the government got what it deserved. But that is not right – why should the majority (the people) be punished for the actions of the minority (the government that failed to run the country sensibly and treated its voters like children). This includes both leave and remain voters, who were given the opportunity to vote without reasons being given for the vote happening in the first place, apart from the conservative government’s need to maintain its vote-grabbing election promises.

Now we are seeing a turn of the tides in the form of anger amongst the remainers who rightly feel cheated by the outcome. They want their say again on whether Britain should remain in the EU.

These people aren’t “salty” or “remoaners”, they are people who, since the referendum, have come to the realisation that we are leaving a community we have been a part of for over 40 years, that forms a major part of the laws and trade of this country and they are rightly worried about the collective future of the people who inhabit it. The leave campaign was run from a similar standpoint in 2015. There were some questionable motivations, but the need to protect democracy and kick out the people running our country for us from the remote distance of Brussels can be understood. Perhaps this is why the repulsion to anything that smells the slightest bit undemocratic is so hated by those who voted leave.

But we cannot simply carry this result through. We need to realise that the entire fiasco that has been the country since article 50 was triggered has been fuelled not by science, but by opinion. Neither side fully understands the implications of Brexit. The leave campaigners are thrilled, but the truth is that the necessary due diligence has not been carried out – the government has not done what should be its primary job, which is to ensure that the country is safely and fairly run. Now that we are on track to leave the EU by default, people are waking up to that fact and trying to have a proper debate. But it has come too late and it is understandably fuelled by panic.

If the country was a university and Brexit was an exam, people would be furious! The government sprang a test on us at the start of term, then started teaching us the syllabus after everyone had had their grade for the year. Upon finding out that the campaign had been fuelled both by illegal funds and by misinformation about the effects of leaving the EU, people rightly feel cheated. If Brexit were an exam, then it should have been run again to give everyone a fair chance. To be democratic about things, we need an informed debate and then a second referendum.

We need to stop Brexit in its tracks: not permanently, but to carefully consider whether or not we actually want to leave based on real evidence and informed debate, rather than passion. The only way that can happen is by having comprehensive discussions on the subject, framed not as an analysis of what is going to inevitably happen (as government-commissioned reports have been up until now), but as an analysis of whether or not we should be in the EU from the standpoint of a choice being had afterwards. The people deserve the right to have time to think and to make an informed choice. That choice has not been given to them yet and we need it to happen. If such a debate were to happen and it turned out that on balance we would be better off out, then so be it. But we need to have that debate, rather than a decision fuelled by mixed and sporadic analysis funnelled through the media, supporting either leave or remain. We need a balanced and sane discussion about the topic and then a second referendum. We need the government to make up for past errors and do its job. We need to finally be treated as adults who are deciding on their futures, rather than children having fantasies about leaving home.

What is opportunity cost? A matter of life and death.

Opportunity cost is simply the cost of producing a good with reference to what you could have instead produced in the meantime.

You can understand it in terms of the number of hours you have in a day (time is incidentally usually a factor which has to be taken into consideration, along with resources when considering opportunity cost). If you have 12 hours in a day that you can do something useful in, you can do different things. Work, eat, socialise etc.The value of each activity to you as a person may be different, it may even change depending on the number of hours of each thing you do.
If you work for 2 hours you might get 30% of the work you need to do done. Working for another 2 hours might only get you up to 40%, so perhaps you might have better spent those hours resting, or doing something else, so that you can increase the value of the hours you use to work later in the day.
This is a crude explanation of why people take breaks in revision, from an economics perspective.

Another interesting thing to link opportunity cost to, is the production possibilities frontier. Its called a frontier, because it literally is a graphical frontier - a line which divides the areas of the graph where a production point can exist from those that cannot. You can think of the production point as a person on a battlefield. They will have different advantages and disadvantages at different points, perhaps the terrain gets rougher as they go further away from their base. Perhaps they can even cross over into no man's land while still being able to handle the increased difficulty in moving and hiding. It is probably advantageous for them to go further and further away from the base since they will be closer to the enemy and better able to target them. However, if the man decides to stand directly in front of the enemy trench or front line then he is very likely to either get shot cleanly in the face, or simply be taken hostage. The idea is that as the man gets further away from his own base, he is able to aim more accurately (produce more damage), up until a point where he is at the verge of being shot or captured.
Say that there are two enemy bases which he can shoot at, if the man were able to get into a position where he could shoot at just one base, it might not be as efficient, since he would only be able to shoot based on the probability of enemies being in vulnerable positions in one base. If he were as close to the other base as well, while he wasn't shooting at the first base, he could be shooting at the second base, and maximising his DPS (damage per second) - again, doing the same amount of damage in less time is of more intrinsic value (or detriment if you are the enemy). This is gradually become a discussion which sounds more like it is describing a video game than an actual battlefield, but never mind.
So, the man has a problem now. The closer he gets to the other side's base, the further he has to move away from the base he was originally shooting at, because his distraction level is increased by shooting at two bases at the same time. We could in fact draw the two bases on a map and show the limits of the man's reach:

So where is the man's optimum position? Clearly it is the place where he is closest to both bases in terms of distance and where he is ideally safe. We note that if the man travels upwards, he gets closer to the first base, but if he travels right he gets closer to the second base, without affecting his distance from the first base (assuming they are both very long). The man is safest (expends the least amount of effort and produces the least amount of damage) behind his trench in the friendly base.
We note that the red line is the limit of the man's reach. He could be anywhere behind that line. We note that the line is not straight, because the danger and struggle the man faces is not simply linear (it does not increase proportional to) the distance from either base. In fact, it is much more like the force experienced by a negative charge as it approaches an electron, or the force you experience when you press down on a spring, or folding a piece of paper into halves again and again and again. At first it is easy, but as you make progress you get diminishing returns for the same amount of effort you put in (in the case of the electron you would get less distance gained, in the case of the spring, the spring would not get much smaller and in the case of the paper, you would eventually be unable to fold it in half again even though you were trying much harder than you were before).

We can see that because of the diminishing returns the man gets when he tries to approach either of the enemy front-lines, he could substitute some of his gains in one direction for larger gains in the other direction - meaning that he could sacrifice some distance to the orange base for perhaps double the distance to the yellow base. Where is the optimum position? It is where the sum total of the distance to each base is lowest.

The optimum point (assuming that the value of the distance to the bases is proportional to the distance - unlike the danger) is simply the point where the sum of the distances to each base is lowest, or equivalently, the sum of the distances from the man's base in the upwards and rightwards directions is greatest.
If you like maths, you may be thinking that you know exactly how to solve this problem. A common mistake people make is to say that the problem can be solved by finding the point which maximises the radius (or absolute distance from the friendly base). This is incorrect and can be explained by reference to the Pythagorean Theorem, where:

$$x^2 + y^2 = r^2$$

Note that here, if we maximise r, then we are maximising $x^2 + y^2$ rather than $x+y$ (assuming x represents the distance in the rightwards direction and y in the upwards.
Rather we can write:
$z=x+y$
And then we could do partial differentiation with respect to two variables and find the maximum that way.

Linking this back to the production possibilities frontier, the frontier, as you may have guessed - is the line in red and we simply think of the left and bottom sides of the battlefield as axes of a graph (think of someone putting a massive ruler next to them) and also consider the friendly base to be the origin (point (0,0)). Now consider the production point to be the man and you now hopefully understand that the man (or production point) should probably be somewhere in the curved part of the graph. Note that if $x+y$ at the production possibilities frontier was constant then the red line would be a straight line (just equate it to a constant $c$, look: $x+y=c$, $y=-x+c$ i.e. a straight line with a negative gradient and y-intercept c$). You can consider the various values of producing different quantities of two different products (getting closer to any one base), taking into consideration the diminishing returns of production to alter the shape from simply being a straight line. The diminishing returns of production in economics are sometimes explained by the idea that resources being allocated to the production of one product would be more efficient if they were producing a different product. For example, if you focused all of a technology company's resources on producing software, the hardware engineers, who are better at producing hardware, would also work on software, but would produce less value to the company for each hour they worked on the software, compared to if they had been spending those hours working on what they were good, or efficient, at doing.

The Disappearing Plank

What I am about to tell you about is magic - REAL magic - that can be performed using mere mathematics. This is not a trick. It is reality. I will tell you how to make an object disappear instantly.

This relies on the principle of a discontinuity. A discontinuity in mathematics is simply a jump in some form from one value to another without any numbers in between. For example, if the temperature were to suddenly become 30 degrees Celsius this would be a discontinuity, whereas if the temperature were to change in reality it would probably be some intermediate value in between.

Imagine this: a black plank so long that it is infinite in length. Let us imagine that you are able to pass through the plank without it interacting with you, but that at the same time you are still able to see it. Let's imagine you are looking at that plank right now and that the plank itself is parallel to your body. You cannot really know how far the plank is away from you because that would require some point of reference which you do not have with an object that is infinite: you cannot find its centre.

Let us just say that the plank can be seen at an infinite distance. Look at the plank now: what do you see? You simply see a large, black, vertical line stretching upwards and downwards in front of your eyes: like a stripe masking a part of your vision. Let us now say that you are somehow able to rotate the plank: you rotate it and there is no change: the plank remains a black, vertical line in your vision. But something interesting is about to happen...

As you start to become closer and closer to being eye level with the plank you continue to see the plank in exactly the same way, but suddenly the black line disappears! Your vision is restored and the plank is gone! What has happened. The world stays like this for a while, as you stop the plank rotating and wonder where it has gone. You move very slightly upwards and the black stripe is back in your vision: you can see the entirety of the plank. There was no middle ground: you either had that black stripe in your vision or you didn't. The plank was either there or it wasn't and there was no evidence of it fading or coming back into existence.

Don't tell me, show me

“Do not simply tell people what happens in a story - show them”. This is a major pseudo-rule in story telling. Its what turns a series of random events into a story with a plot and individual interpretation.

However, a similar pattern comes up in scientific research. We see that when we are simply told a fact, we have learnt that fact. We are able to tell somebody that ‘A Jaffa Cake is actually a cake, not a biscuit’. Great. That’s great. But what is the significance of that statement? That is the important part. The fact is just the result.

It’s like being told that an interviewer has just rejected you for a job and when you ask why, you are told: ‘Because he wrote “Declined” on your application’. You’re not really getting to the root of the problem.

Unfortunately this is what happens a lot in science: people think that they become smarter by simply learning more and more pieces of information. But that’s all they are: pieces. In the Coursera course ‘Learning how to learn’, the tutors stress the importance of placing what you have learnt in some context: linking it to something. Otherwise, it is like having a small station in your brain that can never again be reached by your train of thought because there are no railway lines to it from other stations you have already discovered. You might even begin to forget about its existence given enough time.

Therefore in science, what is really important is the background story - the set of logical deductions that lead from a simple statement (an axiom) to an often seemingly complicated scientific result, such the reason as to why resistances add in series and follow a different formula in parallel.

There is more than one way to reach the solution and having lots of different methods helps you to really internalise what you are learning and make it seem more natural.

Different paradigms through which we can view the world can often fall under discrete categories due to common patterns in each of them. For example, artists might use the visual senses to convey abstract concepts such as emotions, whereas a poet would our capacity to form mental imagery. The ultimate result is that they want to convey a particular feeling: the state of mind they were in when they splashed their thoughts down onto the page. Since not everyone’s brain is the same, we can’t simply clone and transplant relevant neurons from one person to another, since two different people’s brains (mathematicians for example) may appear to work in the same way from the outside, but inside that black box the scenario may be wildly different. Therefore when we paint, draw, write, or use mathematical language among myriad other things, we are translating our thoughts so that others can read the medium and try to recreate a similar form of the idea.

This is why different learning approaches work for different people: we try to find one which clicks with the way our brain is structured, in a similar mode to tuning an analogue radio using a dial, until we find a frequency that resonates. Before that there may be utter confusion, but at the slightest turn of that dial, everything suddenly slides into place and out of that chaos there comes clarity. This is analagous to that moment when things 'suddenly make sense'. Is there a way to consistently recreate understanding therefore? Perhaps, but I suspect not - since understanding is a very individual thing. But we can become better at recongnising the things that help us to understand, and even expand the ways in which we understand in order to learn new things. Many people simply rely on the basing new things they learn on models of subjects they were good at or loved when they were young. As they get older they get more lazy and don't want to find new ways to learn, preferring to stick to the pattern of mental streets they have already carved out for themselves.

In fact I seem to be closer to understanding what I was thinking about when I set up this strange blog. Though I may have not previously been able to put it into words. Much of this blog is about finding the little similarities across wildly different and sometimes very abstract and philosophical subjects which is very characteristic of this universe of patterns in which we live. For example, strange loops have sparked many interesting thoughts in the past especially, and I hope to find many more links between the things we observe in the future.

I hope what I said resonated with you.

Knowledge

When somebody knows everything, they might be right in their own eyes, but certainly not from a less biased perspective. Knowing everything means that there is nothing you do not understand - and when somebody reaches that level of unwillingness to learn then they are infinitely more stupid than someone who is clueless but is open to new ideas.

To truly "see the bigger picture", we must be willing to see beyond the boundaries allegorised in the picture above.

To infinity and its negative - a demonstration of the nature of space in the universe

This graph is analogical to movement in the universe. It is in fact the graph of the reciprocal of the hyperbolic tan function. What I wanted to demonstrate was the seemingly impossible nature of the graph switching from a value of infinity to negative infinity across the line x=0. I think that when we do discover the exact nature of space in the universe it will be dependent on a curved model in so that the three dimensional plane of space will fold back in on itself, metaphorically speaking, like a sphere so that anyone attempting to reach the edge of the universe will find it is in fact impossible.

A Mathematical Anecdote Analogous to Chemical Resonance

What this little conundrum suggests is that in infinitely switching between two states, the final result is halfway in between. This is the reasoning behind the structure of benzene and the ionic carboxylate group.

s = 1 - 1 + 1 - 1 + ...

(-1) * s = (-1) * (1 - 1 + 1 - 1 + ...)   | *-1

1 + (-1) * s = 1 + (-1) * (1 - 1 + 1 - 1 + ...) | +1

1 - s = 1 - 1 + 1 - 1 + ...

1 - s = s

1 = 2 * s

s = 1/2


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