Friday, 10 May 2013

Models and Science

We love to make simplified models. We still use Newtonian models and there is reason. They work most of the time. Even these fall over and we cannot calculate a generalised three body problem of gravitational attraction as put forth by Newton now. If we tried this using Relativistic equations, well we do not have the computational power with all the computer systems on earth and a few lifespans to do that.

Back in 1887, mathematicians Ernst Bruns and Henri Poincaré demonstrated an elegant generalised system that offered proof showing that there is no general analytical solution for the three-body problem when defined using by algebraic expressions and integrals. This does not say that one could not exist, but that it cannot be completed using the mathematics we have at our disposal.

In this, they demonstrated that the motion of three bodies is generally non-repeating, except in special cases. Right now (and as last I know of) we have a total of 16 specific solutions to the three-body problem. The last 13 of these only in the last year (http://arxiv.org/abs/1303.0181).

These are great and have a wonderful purpose, but we need to remember the world is bigger and more complex than we can understand.

Models are just that. When we lose sight of this, we start to lose sight of what we can achieve.

Many models of reality are based on Euclidian space (geometry). The Friedmann–Lemaître–Robertson–Walker metric is an exact solution of Einstein's field equations of general relativity. From it and the general relativistic formula, we find that space is only approximately flat. A good approximation for most purposes, but flat it is not. To really model the world, we have to start with CAT(k) spaces, Hadamard spaces, and constructs such as Hilbert spaces in the Quantum mechanical world.

For the most part, the error rate is small and the calculation cost is such that we use a classical model. This does start to fail in modern applications. For example, the time system on the GPS we need to us a relativistic calculation as the time difference experienced is significantly affected by the differential velocity of the Earth to the satellite. The result would be a large error that continued to grow with the use of a classical model.

Science is all about models. We like to believe we can know it all, but this is most like something that will always lie outside our grasp.

For more on Hilbert Space see:

http://www.math.kun.nl/~landsman/HSQM2006.pdf

http://econ.la.psu.edu/~hbierens/HILBERT.PDF

...

Wednesday, 8 May 2013

Making a pencil

Back in 2007 I talked to Tim Taylor of McAlester. I wrote to him at the time on my plans to make a pencil. At that time I wrote:

I have been told that you have a lecture where you state that there is a high likelihood that there is no person who could make a pencil from scratch.

I would like to put myself forward as the exception for you. I have been called an academic junkie, but I have studied all that is required to do this and also other skills. I learnt how to make charcoal using a medieval clay burner last year. I learnt iron smelting and blacksmithing over a decade ago. Woodwork is a hobby. I have qualifications in Organic Chemistry – so the rubber is easy.

Although I agree that this is not generally useful knowledge, it does help drive home the point of where we are and what society (and yes the economy) really means.

I could have a pencil produced in under 6 months from start to finish if I dedicated my time and was in an iron or bronze rich area. At my current rate it is unlikely that anyone would pay me my current rate, but I do believe that I could manufacture from scratch at least 8000 pencils pa continuously from the point of being setup after 9-12 months – assuming somebody else takes care of food.

I do understand that I will still not make my own pencils however, not only is the quality poor, but the cost is excessive.

I was wrong at that point in thinking I could have completed a pencil and gained the knowledge in something so simple in only six more months (and with my existing knowledge built over a decade). I was not wrong in being able to make a pencil from scratch.

In learning this, I have learnt to smith, to make tools and smelt and many arts that have been neglected by many people.

I have grown my own understanding of many topics and at the root it is other technologies that have allowed me to comprehend a simple item such as a humble pencil.

Tim had stated at the time in an early email:

Thanks for your charming note. The pencil example is from a famous (to teachers of economics) essay written back in 1958. If you want to check it out, it's available on the web at <http://www.econlib.org/LIBRARY/Essays/rdPncl1.html>.

When I'm citing the noone-can-make-a-pencil example in a classroom context, I sometimes(but not always) say: "OK, there's probably someone who can prove me wrong out there -- some professor of metallurgy or chemistry who has an offbeat set of personal hobbies." But in roughly 20 years of using this example, you are the first one to call me on it!  When I next use the example, I'll have to be sure to add that I've heard from one person who can do it. This will lead naturally into the next major subject of the introductory class, which is comparative advantage, and why it wouldn't make economic sense for you to do it. So you see, for a teacher, everything is grist for the mill.

 

At that point I could make a pencil, but not from first principles. This required learning all of the following skills to an adept level:

  • carpentry,
  • forestry
  • geology
  • mining
  • mineral processing
  • black smiting (and I am no artist)
  • Coking
  • Making bricks
  • Steel work
  • and so many things it is not funny. Wait to see the publication.

I ended up doing the standard HB composition.

  • Graphite 68%-wt, Clay 26%-wt, Wax 5%-wt

My beneficiation process is extremely rudimentary but it does work. Making a screen is not a simple process in itself and is one that modern methods can easily improve on the efforts of one person.

I started with  a "Gesner pencil" and slowly gained the level of skill to progress to the Nicholas-Jacques Conte version. In this, the speed of discovery has been amplified and made less expensive through the growth of the Internet. YouTube has a remarkable number of How-Too videos that have accelerated this process and changed the dynamics of the exercise.

I also needed to use other resources. Mixing graphite in a kiln sounds easy, and as my ex-wife had a kiln for pottery, it was. Making a kiln was a separate exercise. Moving from an electric kiln to a Raku pottery kiln I make myself was a large step. Even here I cheated. I made Forty three bricks before I decided to use the other hundred or so from a commercial maker. If I had to make all the bricks I would have needed more time and effort.

Ritter’s paper was essential to this exercise. It started the process of discovery. The part I have not replicated in a natural manner and could not is the sourcing of the knowledge, something like the pencil we take for granted. I have never met Steve Ritter, but owe a debt of gratitude to him and hundreds of people posting on blogs, webpages and lastly via video on YouTube.

Tight now, I am starting to write this on a computer connected to the Internet. The pencil was something I could copy. A piece of 18th century technology. What I could not ever hope to do is to replicate all the knowledge required for a pencil in a single life span without the aid of technology.

So, even now we have something more to add to the process.

I am writing this process up now. I have spent a little over 12 years researching pencils and once I have finished the publication, I shall put them to rest.

Tuesday, 7 May 2013

Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization...

Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization...

Or the author has lost the plot.

I was told to read this book by Philippe van Nedervelde. It would show me the error in my ways in believing in scarcity. The author, K. Eric Drexler has not really come a long way from his 1986 book. He has changed some terms and added the information revolution.

He is right in somethings. The technology he speaks of is around a corner, but not one as close as he proposes. Just as it was not in the book of the 80's where we should all be in abundance. He is again wrong for the same reasons.

One area is an assumption of wants and needs based on today's systems. We know of many materials that will remain expensive. The introduction of the techniques in the book will change society, but they will not remove scarcity.

First, we have to remember that the elements that make many of the items the author talks of will become more and not less scarce. Even common elements such as lithium will become more in demand. Far more than they are now as we move to more advanced materials. This is an increased scarcity, not a removal of economics, a need for more price controls through a market.

Next, we have a remarkable range of new materials. Even assembled on the nano scale, these will not all be manufactured quickly. There will be both time and material limits in the creation of new good.

The author even states how we will progress to control the unknown and unpredictable. He does make a large unscientific flaw here that many now in big data do, he has confused correlation with causation. We remain a long way to understanding the cause of many relationships and the "solutions" are not ones that provide a causal effect.

In adding these technologies, we need to also consider that lower costs in currently difficult to create products will make these mainstream, but at a cost. It will also allow expensive materials. But it will not remove scarcity.

I have more to read, I am just on Chapter 8. But I do not see much better coming from the author.

So far, it is an updated and still wrong version of his work from the 80's. If you take it as a list of great new technology and forget the silly biases and failure to see that new technology brings new challenges, it is ok. But I would not spend money on it (though I did).

Monday, 6 May 2013

On consensus.

I hear a lot about consensus these days.

I am told that “climate science” is “solved” as we have a consensus. I am told that science is about consensus.

Well, consensus has nothing to do with truth. One hundred people who believe a lie do not make the results of a single experiment different. Many people together do not make truth.

For example. Last year I set a question that was particularly difficult. It went to university review. 80% of the students got this question wrong, but they mostly got it wrong in the same way. This is, 70% of the class came up the the same wrong answer. So, the question was reviewed. It was difficult, but the class did choose incorrectly.

That is consensus. The class was in consensus. They saw the question as solved even though the answer was right.

Science is not about consensus. It is about empirical evidence and proof.

To quote:

[The hallmark of empirical progress is not trivial verifications: Popper is right that there are millions of them. It is no success for Newtonian theory that stones, when dropped, fall towards the earth, no matter how often this is repeated. But, ] so-called 'refutations' are not the hallmark of empirical failure, as Popper has preached, since all programmes grow in a permanent ocean of anomalies. What really counts are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes.

Sunday, 5 May 2013

Climate science or climate magic?

In the pseudo-science of climate change theories are fabricated only in order to accommodate known facts.

To be a science, we need to be able to create models that predicted a something new. In climate, this would be to determine the weather, sea temperature and other aspects of climate 10 or even 20 years in advance based on a set of input variables. Right now, we cannot do this and have no clear part to be able to do so.

Climate pseudo-science has in its course of flip flopping models generated many eminently futile prophecies, yet we are still to see a model that makes an accurate prediction. In the 1970’s, it predicted the coming ice age. In the 90’s the global sea level rise of the 2010 era. The pseudo-science camp has been vocal, bold and stunning, but ultimately, they have miscarried any attempt to create a model that has actually worked.

There is one certainty we have with the climate. It changes. We know this as we live in a world where climate has changed from ice ages to heat waves, and all without the help of humanity.

To be a science, climate pseudo-science needs to make a mart in the sand. To make a model and predict, not the past, but the future.

No science…

Some reading a couple people here need... There is a vast distinction between science and the so called mysticism that some people ascribe to the pseudo science that has continued into this modern time.

"so-called 'refutations' are not the hallmark of empirical failure, as Popper has preached, since all programmes grow in a permanent ocean of anomalies. What really counts are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes." [1]

Science predicts and can be tested. To have science, you do not speculate, you set up a path to test a hypothesis and you gather evidence to support or refute it, but it is never proven. All that occurs is that we create better models of the Universe.

Newton was not "wrong". Even now, his theory of gravity is used for many calculations over Relativity even though we know that Relativity is a better and more accurate model.

Why?

The Newtonian calculations are simpler. Even though we can obtain more accurate results when using the Relativistic Newtonian formula, the Newtonian one suffices for many things. We only need to use the more accurate (and more difficult) equations when it is warranted. For instance, in satellite deployment the time drift from the velocity differential is sufficient to make vast errors in the GPS system. These need to be calculated relativistically. That stated, all we use to place a man on the moon is Newtonian calculations.

More, we often choose to use the lower grade older model as it IS better. We know that Newton was approximately correct and that Einstein was closer to the truth, but we cannot always measure the accuracy to a sufficient level to warrant the changes. Sometimes, we cannot calculate all the variables in the model we know to represent the best model of truth as we know it and the only option is to use the older model.

Science is a process of modelling the "truth". This is not who made the Universe. It is not is there something "before" time [2]. It is reality as we perceive it. Kurt Gödel in 1931 with his incompleteness theorems demonstrated mathematically that only the simplest of arithmetic calculations can be complete.

Science is a model of the world. We create better models over time, and we replace some models and keep others with reminders of their inconsistencies even know we know they are not "true". The reason comes when they offer a solution. 

Science is an incomplete model. We do not solve it and we cannot make a hypothesis scientifically about things we cannot test.

What it does offer is a means to see through mysticism and pseudo science.

Formally, Gödel's theorem states, "To every omega-consistent recursive class kappa offormulas, there correspond recursive class-signs r such that neither (v Gen r) nor Neg(v Gen r) belongs to Flg(kappa), where v is the free variable of r" (Gödel 1931).


[1].  http://www2.lse.ac.uk/philosophy/about/lakatos/scienceandpseudosciencetranscript.aspx
[2]. By definition there can be no "before" to the start of the Universe as time is a function of the Universe. It there is a prior to the universe and something that we have "derived" from - it is not a function of time per se.
[3]. http://www.amazon.com/Incompleteness-Proof-Paradox-Godel-Discoveries/dp/0393327604