Day four started with The Science of Consciousness. I shall highlight a few of my favourite points and quotes but point you in the direction of Anna’s blog for a more complete account. You could even look up Daniel Bor’s book the Ravenous Mind.
I’m sure few would argue that the meaning of life resides in conscious events, without which life would be a bit dull. There is something unique about the nature of experience, after all we are not all connected as a borg hive mind. Great minds have have pondered what it is to be conscious for centuries, and many will have heard of Cartesian Doubt and Descartes’ “I think, therefor I am” but scientists are now looking at how to measure consciousness in different conscious states, such as those induced by propofol anaesthetic, and conditions such as locked in syndrome. Then are neuropsychological conditions, anosognosia, Capirgras and Cotard delusions, and unilateral spatial neglect, where consciousness is altered and the brain is left trying to work out and make the best sense of the discrepancies it is faced with. But as Nagel said ” without consciousness the mind-body problem would be much less interesting”. It is amazing that the dynamic connection of billions of neurons in our brains, the connectogram, can result in the mind of an individual, and perhaps Huxley is right in saying the most intriguing thing is that we have consciousness at all…
“How is it that anything so remarkable as a state of consciousness comes about as a result of irritating nervous tissue”
Then it was on to The Amazing Brain to find out what the brain is doing when it is using 20% of our energy. Here’s a nice experiment you can do on yourself. If you look around now are you aware of the blood vessels that supply oxygen and nutrients to your eye? No, but in theory we should be able to see these vessels as they lie over the retina blocking parts of our vision. Whilst they are reasonably transparent they would still produce a continuous shadow. Now for the magic bit – our brain manages to fill in the information that is missing by extrapolating the image around the missing bit, we call this adaptation. To be able to see the blood vessel you have to move the shadow the vessels are casting on the retina and do so faster than the brain can adapt. To do this you need a piece of tin foil and something sharp to make a little hole in it. Close one of your eyes and hold the tin foil hole close to the other then shake the foil so the hole is moving and moving the direction light is entering your eye. Look at something plain and fairly bright, like a piece of white paper and you should be able to see some lines across you vision.
Alternatively just watch this video where at the end they show you how to make a small hole with you hand to look through.
Next up Expanding Universes and Minds, which covered Einstein’s general theory of relativity – a partial equation that when solved will have solutions that describe the entire universe. Every solution shows a different picture of the universe in space and time from the birth of the universe all the way to the present day. That’s a lot of solutions! Unfortunately the equation is a little difficult to solve, but the special and simple solutions that have been solved have proven to very accurately describe the universe.
Now for a new piece of gravity that the theory also produced. In addition to Newtons inverse square law of gravity, where if you double the distance between two objects with a specific mass (m) their gravitational attraction with reduce by 1/distance2 (e.g. if you treble the distance attraction will reduce to 1/9), there was an optional extra. Now I am not a mathematician and my A-level math is fading to the back of my mind, accompanying lessons about the slums of Calcutta from geography, and Custer’s Last Stand from history, so when this equation popped up I was a bit flummoxed
Acceleration ∝ -Gm/r2 + Λc2r
The first bit shows that gravity is attractive (as denoted as a negative sign) and I recognise the m/r2, that is just Newton’s inverse square law of gravity again, but what about the rest? Well the second half after the plus sign is Einsteins contribution, the optional extra. “c” is Einsteins “cosmological constant”, because every good equation needs a constant, and the “Λ” is where the magic begins. This capital lambda shows that repulsion between two objects gets bigger as the distance between those two objects gets bigger. So if you have two objects in space that are quite close to each other, say us and our moon, the gravitation attraction is enough gravitational attraction that the objects orbit each other and, as they are close, there is next to no repulsion between the bodies. If we were to move the moon to the other side of the Milky Way (our galaxy that is approximately 100,000 light-years across) the attraction would be next to nothing but the repulsion would have increased substantially.
Now has your nervous tissue been irritated enough or should we move to consider our position in the Universe…
” Far out in the uncharted backwaters of the unfashionable end of the Western Spiral arm of the Galaxy lies a small unregarded yellow sun. Orbiting this at a distance of roughly ninety-eight million miles is an utterly insignificant little blue-green planet whose ape-descended life forms are so amazingly primitive that they still think digital watches are a pretty neat idea…
Douglas Adams, The Hitchhiker’s Guide to the Galaxy
… what difference could a small optional extra gravitational repulsion have for us and our universe? Well firstly if you were to solve the equation with only the lambda term, as in De Sitter’s Accelerating Universe, this would mean the Universe would have no beginning and no end and would increase in size exponentially with time. This would be an open universe but this solution would only happen if there was no matter, nothing to give a mass to the first term in the equation. I would hope you would agree that we exist in our universe (well if you don’t take Cartesian doubt too seriously) so this cannot be the solution for the universe that we are part of.
How about looking to Freidmann for his solutions to the universe? I should probably mention that if you solve an interesting universe it gets named after you, if anyone is up for the challenge. Now Friedmann was an interesting fellow, he set the world ballooning altitude record and by doing so put his sanity into question. He also solved universes with and without the lambda term which were current up to 10 years ago. In his solutions he predicted the universe could either be open – expanding forever, closed – reaching a size at which everything starts getting attracted back together again in a “Big Crush”, or critical – where the mass of the universe is “just right” and it will reach a perfect size and will stop expanding but not start collapsing. The terms of the equation will balance and we will go on forever at a nice manageable size. However Friedman made an assumption, and we all know that if you assume you could make an “ass out of u and me”, he assumed that everything over the whole universe on average is the same.
Next up in this history lesson comes Hubble, a Boxer, lawyer and later an astronomer, who was involved in interpreting the red shift from distant stars that could be used to measure the rate at which the universe was expanding, a light version of the Doppler effect. He showed that the universe is expanding at an increasing rate. It would appear that we won’t be subjected to a big crush in the near future!
So what about the other universes that had been solved from Einstein’s equation? Lemaître solution of the equation actually predicted that the expanding Universe two years before Hubble proved it and gave a suggested estimation of the rate of expansion. Then there is Tolman’s oscillating Universe which predict the existence of multiple births of the universe. The universe is essentially stuck in a loop of expansions and contractions, regenerated each time with a “Big Bang” at the end of each contraction. If the second law of thermodynamics and lambda are included at this point then the oscillations grow and eventually the cyclical “Big Bangs” are escaped and instead of the universe being collapsed and reborn growth will accelerate and an open, ever expanding universe will remain. What if universes are not expanding at the same rate in every direction? On an X,Y,Z plot two directions could be expanding and one imploding, and then there are distorted and even rotating universes. At this point it became all too complicated for me to keep up with special solutions, entropic energy and hot history after an already taxing day. However, I did take away one last point that Gödel’s Rotating Universe is a solution in which time travel could occur. This universe predicts a closed loop in space and time that allows past points to be visited. Unfortunately the solution has such an extra-ordinarily low probability that it is unlikely to occur, but if anyone ever vanishes unexpectedly into thin air Gödel universe will now be my first explanation.
The day ended with a walk though astronomical history with Stuart Clark. Rather than write about all the amazing things Halley, Hooke, Clark and Newton got up to I shall leave you to read about it in The Sensorium of God by Stuart. I will recount a short story of Johannes Kepler to entice you to buy this book. In the 1600s Johannes reasoned that the motion of the planets around the sun was not in fact random but had a mathematical, geometric order. He went to a Duke and proposed the commissioning of a pure silver sculpture to model the planets motion around the sun that people from all over would come to look at. The Duke was not taken by this idea, so instead Kepler said he would make the sculpture out of pipes that would dispense a different liquor characteristic each of the planets. Furthermore, Saturn would dispense a horrible vinegared red for the guest who requested it and everyone would know that person was uneducated and should not be afforded with ones time.
Needless to say that caught the Dukes attention who commissioned the build but on the day all the parts were brought together the sculpture would not fit, after all the planets do not rotate in an aligned, ordered, circular, geometric path. After this humiliation Kepler spent his life researching how the planets do orbit in elliptical paths at a speed dependent on the distance from the sun.