# A descent into chaos

In Physics, most processes are time reversible. That might seem like a really strange concept, but it’s fairly easy if you consider the example of dropping a book. You convert gravitational potential energy into kinetic energy which is then dissipated as heat and sound (generally) when the book hits the floor. Whilst this does not actually happen – what if all that dissipated sound and heat energy was focused in reverse (from the original sequence of events), with the same point of action on the book? Well the book would have precisely the right amount of energy to return to the original place it was dropped from, which would be quite wonderful to watch. Surprisingly no physical laws are violated by the process I have just described – you can go back and forwards and the universe does not break. Well almost – there is a big exception when it comes to reversibility (known as time symmetry) which is entropy. Entropy requires the property which is most excellently named, the arrow of time.

Within a closed system entropy can increase but never decrease, according to the second law of thermodynamics (don’t worry about that (yet)).

Entropy is the level of disorder – but that definition can lead to some misleading ideas. Sometimes it is easier to think of it as being the tendency for things to wander over time. I hate to use this phrase, but it is a tendency towards randomness. Anyone who has looked after more than one child will tell you they have a tenancy to disappear in increasingly  random directions – this is kind of the idea!  There are many crude examples that illustrate this point, so I will give another one here but should caveat these examples are not actual entropy changes, rather a metaphor for randomness in the system to help explain the point. Take the pyramids in Egypt – and perform a thought experiment where the pyramids were not attacked by grotty tourists but instead crumble naturally over time. We fast forward to say 2416 and all we have left is a big pile of crumbled pyramid. If I asked you to sit and wait until the process flowed the other way and reassembled into a pyramid how long would you wait? If the answer involves more than a second you are either in the wrong place; or place far too much faith in people on the internet. The disorder of the system goes one way – a tenancy to crumble.

Often when people think about the principle of entropy, and a system becoming increasingly random over time with no reversibility they point to examples where this logic is flawed. The formation of a crystal is the single best example – a lovely ordered crystalline array in which over time the arrangement becomes more and more regular. It really is very special if you ever get the chance to watch a sped up video. The key difference is that this is an open system – there is an environment around the crystal to which it is open (i.e. the system is not self contained in some imaginary sealed box) so the law need not hold as described above. As we stated the law is for closed systems. So whilst yes you are seeing a reduction in the entropy for the crystal, the poor environment takes the hit with entropy increasing. Overall the second law of thermodynamics has been maintained on the macroscopic scale.

Now before someone of knowledge reads this and calls me up on it – let me highlight that this isn’t a law in the most regular of senses. Do another thought experiment where you place two molecules in a box and leave them on the left hand side. Say there were three possible positions for each molecule – left, center and right. You start with LL and expect entropy to increase as they follow the arrow of time and take one of the other 8 arrangements – although there is nothing preventing the original arrangement. There is actually a 1 in 9 chance you would find them back in their original starting place at any one time, so if 9 people did the experiment 1 might conclude the second law of thermodynamics is totally flawed! But relax – the law of large numbers makes this a law, in the systems of interest to us everything will works the way it should. When you talk about systems with say a mole of particles, you are quite safe to state the increase in entropy as a law; you can try and re-perform the thought experiment with a mole of particles, the numbers will get ugly.

So what is the point of all of this post? The most interesting application of this is the fact that the universe itself forms a closed system in which entropy can increase but not decrease. This is the descent into chaos in which we are all trapped. What’s more, as the only physical process with an arrow of time it may well be the very reason that you cannot remember the future. What started as a rather dull look at 19th century thermodynamics has transformed into a beautiful butterfly. Quiz question; entropy in a black hole, high or low? No peeking.

(I watched interstellar last weekend). The answer is high – very very high, which I hope is what you would expect. Don’t worry if not however; intuition and black holes often don’t often go hand in hand. In fact, nearly all of the entropy in the universe is holed up in a singularity. Whilst you can identify micro-systems within the universe which are open and the second law of thermodynamics is invalid, the sum of it all is a big closed system in which the amount of disorder must be increasing with time. This is the reality we have in our universe.

I have stated the above about fact – but it is actually subject to some fairly current debate. In the most recent advances in Physics there are some mutterings that there may be mechanisms by which the arrow is violated – in a very strange way whereby any trace of it would necessarily be erased from human detection. This is of course highly speculative, however it does have the feel of something we are yet to fully understand.  Stephen Hawking does believe that if entropy were to run backwards, as far as we were concerned time would also be running backwards. If we are to take this view point (which is generally accepted) then as the only time asymmetric process we know of should be the very thing that gives time the illusion of flowing in the direction it does (side note: you need to adjust the definition of a flow, because a flow requires time itself to be a flow. Confusing). The core reason that remember the past but not the future may well be the simple fact that entropy was lower in the past but is higher in the future fixed by the arrow of time – rather than this human construction we have invented so it fits inside our brains better. We must fit to nature, nature will never fit to us.

There is an argument that states a thermodynamic arrow of time is essential for life to develop. If you are a supporter of the anthropic basis you might like this as it must be so because if it were not we wouldn’t be here to question it; as discussed in this post. I wouldn’t like to start an argument because I don’t necessarily disagree with the logic I just don’t think that this is the full answer. I do of  course agree we must for put the thermodynamic arrow of time of the list of factors that allows our universe to be in existence. Without its presence you wouldn’t be able to do so many of the things you need to do in order to sustain life as we know it – converting food to energy is a good example. It feels like the arrow of time will be a focus in the coming years, as our understanding of the universe just like entropy increases with time.

## 57 responses to “A descent into chaos”

1. Not being adept at either mathematics nor deep penetration into sophisticated science the uniformity of processes moving from the past into the future makes me wonder if there is some kind of four dimensional force involved. In previous presentations at this site it was encouraged to take a four dimensional perspective on viewing time and the four cimensional aspect of the universe was some kind of solid block of fixed relationships. Time, as we perceive it of assemblages of various forms of matter moving into various relationships guided by elemental forces is thereby considered as an illusion out of our limited perceptions. Is then entropy some kind of time responsive force directing the way matter seems to rearrange itself through time and is it possible to consider that entropic speeds vary over time and specific circumstance?

On Mon, Nov 21, 2016 at 11:30 AM, Rationalising The Universe wrote:

> Joseph posted: “In Physics, most processes are time reversible. That might > seem like a really strange concept, but it’s fairly easy if you consider > the example of dropping a book. You convert gravitational potential energy > into kinetic energy which is then dissipated as ” >

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2. One other linguistic point I find disturbing is the word “chaos” which implies total disorder. Although time and energy moves matter into different types of order, understanding the forces involved permits each stage of that rearrangement to become predictable which is just a different form of order, not total disorder. Or so I suspect.

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• It is an interesting point you raise about dimensions – it is quite possible that vast amounts of what we do not currently understand is a result of not fully understanding other dimensions within the universe. I think the issue with entropy is that there are small amounts of transformation energy that are lost over time (note NOT destroyed of course) but this energy isn’t recoverable by the system – in other words this is the only area where we cannot “reverse” the energy changes forcing us to only go one way in time. After I wrote this I actually read this really good page on reversibility http://www.mathpages.com/home/kmath552/kmath552.htm – I was tempted to redo this post to incorporate some of the ideas but then remembered I am quite busy! I agree with you on chaos; it’s kind of an objective term. Same as random – terms we do struggle with if not properly defined. Thank you for your very interesting points!

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3. how do we know that universe itself forms a closed system?

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• Short answer: We don’t know as an absolute fact – but it is kind of by construction. A closed system can exchange only energy but not matter. The universe, crudely defined as everything cannot exchange matter – since the very matter is within the universe already. You may well be thinking of the multiverse – something we have discussed regularly. If the multiverse does indeed exist we will need to consider if the universes are isolated or if there can be any exchange at all between them. If the mulitverse is proven to exist then it will raise very profound questions about the interaction with other universes. This is not yet developed enough however to work into scientific theory – we have not yet established if they exist, let alone the mechanisms behind them. Thank you for reading and a very interesting question.

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• I have heard discussions wherein the black holes we now acknowledge are merely one end of some sort of transit. The film you mentioned, Interstellar. presumed a black hole might be a connection through a fold in our universe to defeat the speed of light restriction on interstellar travel but I wonder if they also might be connections to other universes in a multi-universal configuration. If the connection is only limited to a bi-universal system that would still be a closed system but if there are other like universal connections it would, to a degree, intimate more of an open system.

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• Yes exactly – I was reading about the possibility of black holes acting as wormholes through quantum entanglement. I don’t think it so much beats the restriction on speed; rather just provides a path that does not require any great speed. If there were two – or even many then it could perhaps be closed – depends on which way things can flow. Makes me think of those hamster cages with the different areas and the tunnels between them. It is of course totally possible however black holes connect two points in the same universe; although the issue with this is that we have not seen any evidence of a white hole. Ever. This is the strongest observational evidence that there may not be another side.

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• Since a black hole sucks in energy and matter Would a white hole not be a source of energy and matter, appearing, perhaps, as a star? I know that stars can be presumed to generate their own energies out of atomic interactions that are understood but are any stars somewhat mysterious about their energy production? From a different viewpoint, could the original big bang be some kind of white hole?

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• I must disclaim at this point in terms of solid scientific “fact” I am out of my depth – this is totally theoretical speculation. But I would think one issue with this theory is that stars generally have a fairly constant luminosity, changes in which fit in models of nuclear fusion. You would have to imagine the output of a white hole would be considerably more random. There are stars which are a little more confusing – but that said I don’t know of any evidence of something totally beyond the realms of fusion. Plus there is the fact that we have the spectral emission patterns which is consistent with the fusion of light elements. In relation to the big bang that idea would violate the current model – but then the observed universe does not fully fit in the current model so who knows! Some wonderful questions today

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• haha thank you! Goodness how embarrassing. I am a very weak speller but normally it’s okay because of autocorrect… it is when it is another real world I am in trouble!

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4. It would appear some of our best brains are employed on figuring out the end of the universe and they currently have come up with six ideas .
The Big Freeze ( favorite runner ) , the Big rip , the Big crunch , the Big bounce , false vacuum , and my favourite , cosmic uncertainty.
In the freeze the stars burn out and we then get a black hole universe which eventually spreads out into a vast frozen desolation hovering around absolute zero. It seems to me that such a final state would not be one of chaos but one of perfect conformity. If one form of energy such as heat can be converted to another why cannot this process continue back and forth forever ? Or would that be perpetual motion which is said to be impossible?

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• You hit the nail on the head with perpetual motion. One thing you should remember about entropy is it likes to spread heat out. The big freeze would just be the heat death of the universe where everything is so spread out that nothing of any interest could ever happen (i.e. everything is in a low energy state). If this process could continue back and forth forever then things would look very different. I must say that whilst we theorise endlessly about the end of the universe – the most pressing concern is the end of mankind. There are so many factors – both within and outside our control that could go desperately wrong it seems like there are other areas that require attention first.

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• It would appear that what we know as heat is really particle motion and when all motion ceases the end has come . I keep hearing about the enormously high temperature at the moment of the Big bang and the rapid explosive expansion as the activity spreads but hence decreases in violence. If we have overcome the disappointment of not being immortal at a personnel level then why should we not set it aside as a race. Biology has shown the gene has a driving force towards immortality which may well affect our thinking , but I think Hamlet had it right when he said ‘ The rest is silence ‘

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5. No doubt the end of mankind has a personal quality somewhat more pointed than something that might occur many billions of years into the future but, aside from the fact that there may be unknown forces undetectable within the negligible times within human existence, wherein tossing animal entrails to form patterns to determine the future was once an accepted manner of discerning the patterns of destiny, our present methods may eventually prove equally as futile. The realities of the life of any species seem to indicate circumstances offer opportunities for change that will inevitably transform species in all sorts of surprising ways. For example, the current fascination of transporting our civilization into space no doubt will accept the challenges of directed mutation into forms well outside of what we assume is human today. All sorts of environmental attacks on current humans entering the cosmic ecologies which are detrimental, not only in space but also on any planet that invites habitation, quite different from that on Earth. We already understand enough about genetic variation to create out of ourselves variations that might do better on Mars or any of the larger satellites of our neighboring planets and I suspect, if humans can resist the seemingly huge temptation, currently, to end our existence out of the obvious idiocies of our cultural leaders, we shall modify ourselves sufficiently to identify current humanity as a rather primitive and somewhat uninteresting variation of our species potential. Deep integration with our technological tools is already in its initial stages and as it advances there is no telling what odd creatures may result.

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6. Great article! On a rather unscientific diversion, could human culture escape the laws of entropy?

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• Thank you very much! I am glad you enjoyed the article. I really do not think so – although quantum mechanics has taught me never to rule anything as impossible. What are your thoughts?

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• I wonder if joint effort with our eyes on the welfare of future generations could create improvements that would halt, or at least delay, the slide into chaos and catastrophe …but then my teachers always did tell me off for day-dreaming!

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• The process of entropy which, insofar as I understand it, involves the even distribution of energy throughout the universe, is far beyond human intervention in its processes. It involves the energy systems of stars, for one thing, and our influence on the process of even the single very minor star in our planetary system is not even contemplated, not to speak of any possible action.

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• I’m sure you’re right. I was perhaps thinking of the tendency for ‘civilisations’ to collapse, not really a scientific concept.

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• Yes I think there is a crossed wire between a system of particles tenancy to chaos and the model of human civilizations – unfortunately the parallels are uncanny!

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• Yes indeed, always tempting to draw parallels though. I know Einstein got fed up with such interpretations of his relativity theory.

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• Haha, THERE’s a goal! Now all we need to do is make sure our energy consumption doesn’t exceed our technological ability …

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7. “If you are a supporter of the anthropic basis you might like this as it must be so…” Was Boltzmann such a supporter? It would seem so based on his 2nd defense of the 2nd law. His defense still leaves the matter of whether The Past Hypothesis is a law of nature that justifies the 2nd law of thermo. Given that it is, uncommonly – perhaps uniquely? – not of universal-conditional form, it’s always bugged me. Should that hypothesis get off the hook without a search for explanation, as gravity once did? Otherwise we’re left with something far too close to metaphysics for my empiricist nature.

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• I too am uncomfortable with anything too close to metaphysics so I can sympathize with you there! My understanding is that Boltzmann was – of sorts! there is a very interesting and short wikipedia page on the Boltzmann brain which can be found here: https://en.wikipedia.org/wiki/Boltzmann_brain. If I understand you correctly you are looking at the direction of the causation – does the second law imply the past hypothesis or does the past hypothesis imply the second law – whichever it is there needs to be deeper understanding of the mechanism. I wish I had a full answer to that question – although unfortunately I do not. There are some interesting ideas being thrown around including this one here: http://phys.org/news/2009-08-physicist-solution-arrow-of-time-paradox.html. Thank you very much for reading!

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• Since it is a universal observation that differences in adjacent energy levels always tend to become equal does pragmatism apply as a counter to metaphysics? Or has there been discovered an instance wherein high energy levels result somewhere spontaneously within a closed system with no external input?

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8. This is a wonderful read! The idea of entropy has always bothered me slightly, since it tends to make it sound like the entire universe is unbridled chaos, which it is obviously not, everything has an order, and it is hard pressed to deviate, even the deviations are predictable, and chaos is by definition, unpredictable. The more subtle definition of the loss of irretrievable energy makes more sense to me.
Thanks for taking the time to write this all out and post it here!!

Meno

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• Thank you very much for reading! Yes I know exactly what you mean… I like to think of gas in a balloon – it is in an order of sorts, since ignoring any leakage I can define an area where the gas exists. Allow the balloon to pop and it goes wandering and it is far harder to pin down those particles…. sort of the same in the universe. I totally get your discomfort with disorder – a feeling we share!

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• The energy is not lost, it becomes distributed evenly. Useful energy occurs when there is a different energy level and work is possible in the equalization of the energy differences. The universe stops functioning when all energy is equally distributed, whatever that level might be. True randomness is something that cannot be calculated. It can be confused with something that has the potential to be calculated but no means for that calculation exist currently.

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• Agreed jiisand – It is just a fact of energy being too spread out to allow anything of interest to happen in any one place.

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• In a rather odd comparison to gravity wherein all prominences of matter such as mountains and lumps on the ground and all things that stick up tend to fall flat to the ground, so the second law of thermodynamics requires that all high concentrations of energies represent a kind of prominence and they tend to even themselves out so that there is a kind of flattening of energies. Einstein worked out that gravity was a kind of warping of space due to a presence of matter so it was resolved as a form of topology. I wonder if the second thermodynamic law has a kind of similar geometric basis so that high energy areas are driven to somehow conform to an energy geometric.

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• I don’t think we will be gifted with such a nice description for the second law of thermodynamics – purely because it is a statistical phenomena relying on the law of large numbers. That said – I could of course be wrong, it just feels like a more encompassing theory, if one exists, would have to take a different direction

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• Perhaps I am going somewhat wild in this direction but entropy is perhaps a function of time itself and time and space out of relativity are different aspects of the same thing. Since time rate changes as the speed of light is approached would that mean that entropy is equally flexible? and also, in an intense gravity field such as on a large planet or, to get extreme, as one approaches a black hole, does the rate of entropy change? Time is rather peculiar to think about and as with quantum effects I am beginning to suspect that time, like space, may have several directions. How this might affect entropy I cannot figure.

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• I think if the arrow of time is fixed, it would just mean the rate of entropy slowed with the arrow but never flowed backwards as with time dilation… I really need a word that isn’t flow it’s the wrong word for time! Again I think with the black hole example yes the rate should slow with time. This sentence is from a wikipedia page I was reading the other day:

“The only way to satisfy the second law of thermodynamics is to admit that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.”

So you end up with a black hole having high entropy which is confusing I know

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• Thanks for following back!
I think current linguistics are sometimes inadequate for really describing certain ideas, and that’s ok, we do the best we can…

Meno<3

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• Although a balloon can isolate a selection of gas molecules to a certain degree, there are at least several factors which can influence those molecules nevertheless such as the variable altitude of the balloon, stray radiation from light and the cosmos, and even an angry hawk which feels its territorial dominance has been violated. Random influences are pervasive.

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9. Great read- it made me think 💭 which is more that I can say for other blog posts! 😊

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• Thank you very much for visiting and your kind comment! I am glad you enjoyed the post, makes it worthwhile writing them!

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10. Very interesting. I have to read some more of your posts, but I enjoy the questioning of physics in general. It’s been on my problems with physicists, that they tend to be very rigid with little discussion into the why’s and more importantly, the what ifs.
I mean the what if certain theories and beliefs are wrong. But they act mostly like religious zealots.
Being a mathematician (or former, or whatever) I think a little differently. But then again, I think differently than other mathematicians. The scale of issues is very relevant, and based on that scale you may end up with different entropy. You may end up in scales where there is no entropy at all, and others where it is infinite.
But back to the world, and the religion of physics, they are not ready to question.

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• Somewhat along that line an item yesterday (https://science.slashdot.org/story/16/11/30/0255251/theory-challenging-einsteins-view-on-speed-of-light-could-soon-be-tested) indicates that there is now a challenge to the standard speed of light to be tested and a statement that at the origin of the universe that light speed was infinite to assure the density of the universe would be uniform. But to accept that light speed could be infinite contradicts the basic concept of speed itself. Any “infinite” velocity means that there is no movement at all since light is present everywhere without movement and therefore no information out of light is possible. It is probably a linguistic confusion but a very odd one.

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• I had thought of the infinite speed of light, and one of the outcomes could be that there is just one photon, present everywhere. It was closer to philosophy than physics but still interesting to think about regardless. The problem with the challengers to Relativity is the approach they have. Most physicists have only the most basic math knowledge. The views I’ve come across are that if a physicist knows some analysis or differential equations he or she is golden. Until a broad unified approach to math is used, then we’re going to have a tough time understanding the way things work.

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• Light is very peculiar indeed. It obviously is a transfer of energy and information but a photon is considered without mass which permits it to travel at light speed but although it has no mass it exerts pressure which violates the basic formula F=MA. Also at light speed there is no time so, in a way it does have infinite speed. These things make no sense to me.
It was Feynman who suggested there is only one electron that bounces back and forth in time becoming a positron when traveling backwards in time.

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• Thank you very much for reading – I am glad you enjoyed the post. I believe that as a Physicist as soon as you loose a questioning mindset you are finished in terms of making progress and confined to becoming an expert on the information that is already known within textbooks. I think there are some physicists who are asking the big questions every day – but I think there are many who are not. Who you end up speaking to can alter perception a lot!

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• It’s why I’m not a physicist lol. I went for math although the same applies there, with the only benefit that you can lock yourself in a room until you get it all on your own, without outside influence. Numbers arent open nor closed minded, they are what they are. But in the end, I don’t think any of us will live through a great scientific breakthrough. The funding, the equipment is locked to those so called researchers, whos sole purpose isnt making breakthroughs but keeping and getting more grant money.

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• The corruption power of money in society seems to burrow into usefulness in a terrible way. Aside from the grant money problem, all sorts of useless and nasty functions of money on Wall Street and in commerce producing useless and harmful social effects which come out of the misuse of money which may destroy the planet for life.

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• I see money as less the issue (coming from somebody disabled and broke that should count, right? lol) but corruption and the zero merit based system we have. Rewards go to the lease deserving, as long as they serve an agenda. Agenda in this case, could mean politics but always corruption, as a goal other than what the primary stated mission. So universities that get grants for protesting students, or diversity versus research that actually pushes the envelope further. Anyone that’s been through gradschool knows, those disertations are a joke, and hardly any of them have any impact. Whatever happened to when a PhD was the expert in a field, not some useless conclusion. It would be harder, but so worth it. Money all of a sudden becomes less of the issue.

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11. Entropy is an interesting topic and occurs more often than we think

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12. Your mind must be a nebula of wonder

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