There is a famous paradox originating from ancient Greece known as Zeno's Dichotomy Paradox after the Greek Philospher Zeno of Elea. Essentially the argument is as follows. In order to travel any distant (say 1 metre) once must first travel 1/2 metre, however, before travelling 1/2 metre one must travel 1/4 of a metre and so on. The argument concludes that this represents an infinite number of tasks and so cannot be completed in a finite amount of time.
Now, clearly this argument is wrong as we can move and so we must ask what exactly is wrong with the argument? The paradox is most often approached in terms of the convergence of infinite sums. This approach has its merits but in some respects dodges the question asked so instead I will approach it differently.
I contend that one of the initial assumptions is wrong. I say that distance cannot be infinitely subdivided into smaller and smaller pieces. This contention is, however, at odds with the real number system we use for measuring things such as distance. I approach this question using the notion of the Planck length. The Planck length (or distance) is a term stemming from Quantum mechanics (see the wiki page). I don't pretend that the argument I present is in any way tight in terms of formal logic or physics but I propose a solution based on the idea that the Planck length is a possible basic unit of distance meaning that any length (such as a metre) is a multiple of a large but ultimately finite number of Planck lengths. This would mean that the number of tasks is not infinite and so motion is not an impossibility. I leave the argument as it stands -just the bare bones- and leave it to any readers to flesh it out.
Monday 13 June 2011
A Beautiful Video
A beautiful video from youtube user UppruniTegundanna that I stumbled across today:
I particularly love the hands at 1:07 (although according to wiki the hands are actually younger than 9,300 years old and date from around 550 BC and 180 BC). It is videos like this that make me wonder about our own future. Will our graffiti delight distant generations of paleontologists? Will they reflect on our short 80 year lifespans? The power of science is amazing. It also makes me wonder, if a nuclear war breaks out and humanity is brought to its knees what books will constitute the new bible? Will these scattered peoples find tracts of the ancient book 'Harry Potter' dating from before the 'Fall'? Will they interpret religious meanings to the scientific texts of those days? One can only wonder and hope such a situation never occurs/
I particularly love the hands at 1:07 (although according to wiki the hands are actually younger than 9,300 years old and date from around 550 BC and 180 BC). It is videos like this that make me wonder about our own future. Will our graffiti delight distant generations of paleontologists? Will they reflect on our short 80 year lifespans? The power of science is amazing. It also makes me wonder, if a nuclear war breaks out and humanity is brought to its knees what books will constitute the new bible? Will these scattered peoples find tracts of the ancient book 'Harry Potter' dating from before the 'Fall'? Will they interpret religious meanings to the scientific texts of those days? One can only wonder and hope such a situation never occurs/
Jevon's Paradox: Consumption and Resources
In today's society we often hear about climate change and the need to reduce consumption. This post is about an often overlooked element of the debate about energy conservation and the need to control consumption. This post is not about whether or not climate change is happening (I am of the opinion that it most certainly is), instead it is about what we need to do if it is.
It is often said that we need to combat climate change with a dramatic reduction in consumption. This argument is often countered by people concerned about the economic impacts of consumption reduction by the following argument; it is not necassary to reduce consumption as technological advances will increase efficiency dramatically. I will make the argument that this alone is not enough.
When efficiency (say in energy production) is increased it is observed that consumption, likewise, increases. This has been noted since 1865 in 'The Coal Question' a book by William Stanley Jevons and is called 'Jevon's Paradox'. Jevons noted that the increases in the efficiency of the steam engine in his time did not lead to a reduction in coal consumption. Instead due to the decreased cost of running a steam engine the demand for steam engines increased and resulted in demand for coal also increasing.
Now, fast-forward to the modern day and the concerns of climate change and these arguments are being put forward by the likes of Jared Diamond in his book 'Collapse'. It is often touted that the increase in efficieny in the future will lead to a reduction in oil consumption and in pollution due to less oil and other materials being required to maintain current consumption levels. This however assumes that consumption levels will remain the same or are not affected by the increased efficieny. This assumption is, however, wrong. To give an example, if it costs me 50 euro a month less to fill up my car then the odds are that I will spend that extra 50 euro on some other good (or service), a good most likely produced using oil or at the very least transported using oil.
As a result we as humanity cannot rely on increased efficiencies to stave off the very real threat of climate change. What is required is a reduction of consumption or an increase in efficiency coupled with constant consumption levels. A practical example in terms of oil would be a green tax on petrol to ensure that even if oil production becomes more efficient the prices do not fall for the consumer (although such a situation is unlikely to occur). Also, even if we tax pollution and things are produced more cleanly it might not mean a reduction in pollution if more goods are produced following an increase in 'cleanliness'. These are just some issues with regard to consumption and climate change that we face in our modern world.
It is often said that we need to combat climate change with a dramatic reduction in consumption. This argument is often countered by people concerned about the economic impacts of consumption reduction by the following argument; it is not necassary to reduce consumption as technological advances will increase efficiency dramatically. I will make the argument that this alone is not enough.
When efficiency (say in energy production) is increased it is observed that consumption, likewise, increases. This has been noted since 1865 in 'The Coal Question' a book by William Stanley Jevons and is called 'Jevon's Paradox'. Jevons noted that the increases in the efficiency of the steam engine in his time did not lead to a reduction in coal consumption. Instead due to the decreased cost of running a steam engine the demand for steam engines increased and resulted in demand for coal also increasing.
Now, fast-forward to the modern day and the concerns of climate change and these arguments are being put forward by the likes of Jared Diamond in his book 'Collapse'. It is often touted that the increase in efficieny in the future will lead to a reduction in oil consumption and in pollution due to less oil and other materials being required to maintain current consumption levels. This however assumes that consumption levels will remain the same or are not affected by the increased efficieny. This assumption is, however, wrong. To give an example, if it costs me 50 euro a month less to fill up my car then the odds are that I will spend that extra 50 euro on some other good (or service), a good most likely produced using oil or at the very least transported using oil.
As a result we as humanity cannot rely on increased efficiencies to stave off the very real threat of climate change. What is required is a reduction of consumption or an increase in efficiency coupled with constant consumption levels. A practical example in terms of oil would be a green tax on petrol to ensure that even if oil production becomes more efficient the prices do not fall for the consumer (although such a situation is unlikely to occur). Also, even if we tax pollution and things are produced more cleanly it might not mean a reduction in pollution if more goods are produced following an increase in 'cleanliness'. These are just some issues with regard to consumption and climate change that we face in our modern world.
An Evil Deity
I put this question out to the blogosphere about God, Yahweh, Allah [insert deity here] etc. (I will refer to all of the above as 'God'). The question is how do you know God is good? Now to qualify this I'm going to put out a few caveats.
First off, I care little for the semantic "God is defined as good". So, in order to eradicate this pointlessness, I am going to define good in the colloqial sense e.g. not killing is good. In another sense the question could be couched in terms of suffering, how do you know God wants to 'save' us and is not merely revelling in our suffering?
With that out of the way, I will address the next point. Many theists will be reaching for their holy book at this stage and pointing to where it says God is merciful, God is good etc. so I'm going to ask would an evil God not write that he was good? Would an evil God not get his kicks from convincing his hapless creations that he was their route to being 'saved'? Would he not relish in creating a false hope in order to crush it later? Would it not please such a being to see people worship the very cause of their misfortune?
Now, the next objection is generally "why would an evil God even create a universe?". Well, to torture the inhabitants obviously. Indeed, why would any God (whether good or evil) create a universe?
Finally, the theist will say "what about all the good in the world?" Well, as we know, God works in mysterious ways and any seeming kindness is merely part of God's greater (evil) plan.
So, this is the question I put to theists. Many atheists are probably eager to point out the incredible number of atrocities in the Bible (or Qu'ran etc.) but I must ask them to hold. Instead I want to ask the theists how (even if the Bible was squeeky clean) do they know that God is good rather than evil. 'Personal revelation' won't cut it either.
First off, I care little for the semantic "God is defined as good". So, in order to eradicate this pointlessness, I am going to define good in the colloqial sense e.g. not killing is good. In another sense the question could be couched in terms of suffering, how do you know God wants to 'save' us and is not merely revelling in our suffering?
With that out of the way, I will address the next point. Many theists will be reaching for their holy book at this stage and pointing to where it says God is merciful, God is good etc. so I'm going to ask would an evil God not write that he was good? Would an evil God not get his kicks from convincing his hapless creations that he was their route to being 'saved'? Would he not relish in creating a false hope in order to crush it later? Would it not please such a being to see people worship the very cause of their misfortune?
Now, the next objection is generally "why would an evil God even create a universe?". Well, to torture the inhabitants obviously. Indeed, why would any God (whether good or evil) create a universe?
Finally, the theist will say "what about all the good in the world?" Well, as we know, God works in mysterious ways and any seeming kindness is merely part of God's greater (evil) plan.
So, this is the question I put to theists. Many atheists are probably eager to point out the incredible number of atrocities in the Bible (or Qu'ran etc.) but I must ask them to hold. Instead I want to ask the theists how (even if the Bible was squeeky clean) do they know that God is good rather than evil. 'Personal revelation' won't cut it either.
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