Point of view switcheroo

Rolling marbles 

Here's a puzzle: Suppose you have N identical marbles rolling along a one dimensional table-top.  Each marble is randomly rolling to the left or to the right, all with the same speed.  Collisions are elastic, which means the marbles just change direction.  What is the maximum amount of time before all the marbles have rolled off the table?

8 marbles with speed 1 on a table of length 1

Answering this question is really difficult if you simply pick an individual marble and try to work out how long it might stay on the table as it bounces back and forth.  But there's a simpler way to look at it.

Prior to each collision you have one marble rolling to the left and one to the right, and afterwards you still have one rolling to the left and one to the right.  If we swap labels following each collision then the labels never change direction.  Now it's easy to see that the answer is the same whether there are 100 marbles or just one.  And all we did was switch our PoV from the masses to the momenta.

 

Replacing your petrol car with a clean green EV

We can apply a similar point of view switcheroo to other questions too.  For example, should you sell your petrol car and buy an electric one?  The trick here is to switch from thinking about your emissions to that of the car.  There are an approximately constant number of cars in the UK, meaning that when one reaches it's end of life (at perhaps 150,000 miles) it is scrapped and replaced by a new car on the UK's roads.  Viewed this way, the only thing that makes any difference is whether or not the new cars being inserted into the pipeline are electric.  So if you are buying a brand new car you can help by making sure it is electric, but if you normally buy cars second hand there's not much difference you can make without giving up driving altogether.

So, whilst ordinary people can't make much of a difference in this area, the government could easily make a very big difference.  For example, by introducing a rule that all new sales must be electric after a given date, like Boris Johnson's government did.  The worst thing it could do is to set that date back, like Rishi Sunak's government has.  And if they were really serious they could bring the date forward and introduce an early scrappage scheme for polluting cars.  Because even the most environmentally conscious driver is not going to scrap a petrol car they could otherwise sell.

Comments

Post a Comment

Popular posts from this blog

How To Make ASCII Diagrams Beautifuller

Image
I've discovered an excellent tool in asciiflow.com .  The website makes it really easy to create ASCII box diagrams like this They put these things in fruit machines you know! This is ideal for source code banners, which I think should contain helpful documentation - but most programmers think it's a good place for the COPYRIGHT information and nothing else. But wait! we can make it beautifuller... and easier to read... by replacing some of the ASCII characters with ones available in UTF-8: There!  Isn't that better?  (Although some purists may object to non-ASCII characters in your code base.) SOURCE CODE: #!/usr/bin/python2 # coding: utf-8 # + gets converted in different ways depending on it's 4 neighbours # # . N . { nsew(N,S,E,W) has bit 3 set if N in "+|<>" # W + E { nsew(N,S,E,W) has bit 2 set if S in "+|<>" # . S . { nsew(N,S,E,W) has bit 1 set if W in "+-^v" # { nsew(N,S,E,W) has bit 0 set if E in
Read more

Calculation of ECS using simple convection model

Image
Contents Intro Simple stratified model Alternative convection model Tropospheric temperature gradient Approach used in convection model Calculation of Radiative Forcing from CO₂ increase Calculation of Radiative Forcing from H₂O increase Calculation of zero-feedback ECS Effect of including feedbacks Effect of water vapour Effect of cloud cover change Effect of sea ice loss Calculation of ECS including feedbacks Limitations One more thing: Changes to Troposphere depth Intro The goal of this post is to see if we can come up with an estimate of Equilibrium Climate Sensitivity using a simple model in which the atmosphere is treated as well-mixed.  By "simple" I mean that using the model will not require any advanced mathematics or computation, but will still be realistic enough to come up with an estimate within the likely range of 2.5 - 4.0°C predicted by the IPCC Assessment Report 6 .  I will try to take as little on trust as possible and show how the results are arrived at.
Read more

Why growth is falling in all developed countries (as a long term trend)

Image
In this post I argue that economic growth is not the normal state of affairs, it is a blip caused by the discovery of a one-off resource of non-renewable energy.   The logistic equation $$ \frac{dy}{dt} = y(1-y) $$ Here's a simple model.  Humans discover an exploitable but limited resource and start consuming it.  The amount consumed, $y(t)$, is a function of time.  The general form of the equation is $\frac{dy}{dt} = \alpha y (\beta - y)$, but if you choose the right units $\alpha$ and $\beta$ both become $1$. Why should this work, in principle? Early on, the factor $1-y$ is approximately $1$ and can be ignored.  So the model states that annual consumption $dy/dt$ starts off proportional to $y$.  In other words, $y$ grows exponentially at first.  This could happen if exploiting the resource enables further exploitation of the resource.  For example, suppose a few humans are shipwrecked on an island with 1000 trees: they take ages to cut down the first tree as they are using their
Read more