Don't tell me, show me

“Do not simply tell people what happens in a story - show them”. This is a major pseudo-rule in story telling. Its what turns a series of random events into a story with a plot and individual interpretation.

However, a similar pattern comes up in scientific research. We see that when we are simply told a fact, we have learnt that fact. We are able to tell somebody that ‘A Jaffa Cake is actually a cake, not a biscuit’. Great. That’s great. But what is the significance of that statement? That is the important part. The fact is just the result.

It’s like being told that an interviewer has just rejected you for a job and when you ask why, you are told: ‘Because he wrote “Declined” on your application’. You’re not really getting to the root of the problem.

Unfortunately this is what happens a lot in science: people think that they become smarter by simply learning more and more pieces of information. But that’s all they are: pieces. In the Coursera course ‘Learning how to learn’, the tutors stress the importance of placing what you have learnt in some context: linking it to something. Otherwise, it is like having a small station in your brain that can never again be reached by your train of thought because there are no railway lines to it from other stations you have already discovered. You might even begin to forget about its existence given enough time.

Therefore in science, what is really important is the background story - the set of logical deductions that lead from a simple statement (an axiom) to an often seemingly complicated scientific result, such the reason as to why resistances add in series and follow a different formula in parallel.

There is more than one way to reach the solution and having lots of different methods helps you to really internalise what you are learning and make it seem more natural.

Different paradigms through which we can view the world can often fall under discrete categories due to common patterns in each of them. For example, artists might use the visual senses to convey abstract concepts such as emotions, whereas a poet would our capacity to form mental imagery. The ultimate result is that they want to convey a particular feeling: the state of mind they were in when they splashed their thoughts down onto the page. Since not everyone’s brain is the same, we can’t simply clone and transplant relevant neurons from one person to another, since two different people’s brains (mathematicians for example) may appear to work in the same way from the outside, but inside that black box the scenario may be wildly different. Therefore when we paint, draw, write, or use mathematical language among myriad other things, we are translating our thoughts so that others can read the medium and try to recreate a similar form of the idea.

This is why different learning approaches work for different people: we try to find one which clicks with the way our brain is structured, in a similar mode to tuning an analogue radio using a dial, until we find a frequency that resonates. Before that there may be utter confusion, but at the slightest turn of that dial, everything suddenly slides into place and out of that chaos there comes clarity. This is analagous to that moment when things 'suddenly make sense'. Is there a way to consistently recreate understanding therefore? Perhaps, but I suspect not - since understanding is a very individual thing. But we can become better at recongnising the things that help us to understand, and even expand the ways in which we understand in order to learn new things. Many people simply rely on the basing new things they learn on models of subjects they were good at or loved when they were young. As they get older they get more lazy and don't want to find new ways to learn, preferring to stick to the pattern of mental streets they have already carved out for themselves.

In fact I seem to be closer to understanding what I was thinking about when I set up this strange blog. Though I may have not previously been able to put it into words. Much of this blog is about finding the little similarities across wildly different and sometimes very abstract and philosophical subjects which is very characteristic of this universe of patterns in which we live. For example, strange loops have sparked many interesting thoughts in the past especially, and I hope to find many more links between the things we observe in the future.

I hope what I said resonated with you.

Knowledge

When somebody knows everything, they might be right in their own eyes, but certainly not from a less biased perspective. Knowing everything means that there is nothing you do not understand - and when somebody reaches that level of unwillingness to learn then they are infinitely more stupid than someone who is clueless but is open to new ideas.

To truly "see the bigger picture", we must be willing to see beyond the boundaries allegorised in the picture above.

To infinity and its negative - a demonstration of the nature of space in the universe

This graph is analogical to movement in the universe. It is in fact the graph of the reciprocal of the hyperbolic tan function. What I wanted to demonstrate was the seemingly impossible nature of the graph switching from a value of infinity to negative infinity across the line x=0. I think that when we do discover the exact nature of space in the universe it will be dependent on a curved model in so that the three dimensional plane of space will fold back in on itself, metaphorically speaking, like a sphere so that anyone attempting to reach the edge of the universe will find it is in fact impossible.

A Mathematical Anecdote Analogous to Chemical Resonance

What this little conundrum suggests is that in infinitely switching between two states, the final result is halfway in between. This is the reasoning behind the structure of benzene and the ionic carboxylate group.

s = 1 - 1 + 1 - 1 + ...

(-1) * s = (-1) * (1 - 1 + 1 - 1 + ...)   | *-1

1 + (-1) * s = 1 + (-1) * (1 - 1 + 1 - 1 + ...) | +1

1 - s = 1 - 1 + 1 - 1 + ...

1 - s = s

1 = 2 * s

s = 1/2


Source 

Probability, chaos and the nature of creation

Probability and an elementary, almost axiomatically governing rule of the universe (thoughts given through the analogy of a complex puzzle)

I will attempt in this article to describe my views on how probability plays an intrinsic role in the governing of chaos and the universe as we know it.
Many subscribe to the belief that the universe is fundamentally predictable through mathematics. In fact Einstein once famously said that "God does not play dice with the universe". It turned out, in a sense, that Einstein was wrong. But he was wrong only in the sense that betting companies are wrong to hedge their bets with making money through gambling. The only thing that makes betting companies money is that a probability describing a single event never has a certain outcome, but is in fact a way of describing a myriad of many complex factors which are all mathematical and will hence yield the same result in a great enough sample. Remember that if anything can be conceived to possibly (or impossibly) happen it is possible. It is just that the more likely events occur a higher proportion of the time. Just as we must define limits for integration, without which the sum of any specific value is zero, probability is meaningless when applied to single values. Probabilities are proportions of a sample on a large scale. As the sample size tends to infinity, it is 100% certain that the probabilities will also tend to the actual proportions obtained from the infinite sample.
In fact, the classical mechanics of the universe are simply a large scale description of predictable patterns in probability on a very large scale: the laws which govern these mechanics provide the footholds for mathematics and are maths' only claim to validity. Force is equal to mass multiplied by acceleration because of a repertoire of different subatomic forces, energies, masses - among other things - that all interplay to produce this predictable pattern on the larger scale. At the smallest scale the universe is in fact still affected by what goes on around it. So, in fact one day we might in fact realise - if such a statement is true - that the quantum mechanics are in fact affected by the large scale mechanics of physics and visa versa.
This might be another "strange loop" which could further support Hofstadter's opinion/hypothesis that strange loops are very important. In fact, they might prove to be a stepping stone in understanding how patterns in the universe arise.
On to my main point - an essay to describe evolution in terms of an infinitely complex puzzle and to attempt to shed some of my self-validated insight on intelligence's origins and nature.
Think of an infinitely complex maze, further convoluted by the fact that the maze is affected in strange ways by the way you move through it, so going through the maze to a certain spot - you may only return to your original state through backtracking your steps and actions exactly to your starting point. This can be likened to travelling back in time. You cannot take shortcuts through the maze. Think of intelligence as one possible location in the maze. The achievement of reaching this location (creating intelligence) is only possibly attained through one single route, since there is only one possible route to any single place in the maze. Even if two different routes are exactly the same but for one footstep for example taking a step with the right foot rather than the left foot, this small effect will produce a butterfly effect, meaning that a difference between the two paths will arise which shall become more and more pronounced as you progress further and further away from the location at which you committed this deed.
In fact, the pathways can be thought of as progress through time and the different pathways, in this case, as evolutionary branches on the evolutionary tree of life. In fact, there are many other situations in which this analogy applies anywhere where probability and infinite possibilities play a key role.
Evolution follows the concept of probability. It was infinitely unlikely that "intelligence" as we know it should ever have been developed. In fact, intelligent humans (homo sapiens) have only existed for the equivalent of the blink of an eye in the timeline of the universe, even in the comparatively minute period of existence of life on earth. Had one idiosyncratic genetic mutation not occurred at exactly the right time and place in the past, intelligence might never have existed - or perhaps existed but in an altered form. In fact, we also have to think outside of the internal development of humans. For instance, what could have happened if the individual human or lifeform in which this mutation occurred was killed before it could reproduce. That lifeform would never have passed on the line of material necessary for humans to develop. Therefore the events in the past leading up to this were all important in the timeline in which intelligence was created. In fact, the external effect need not be as extreme as death, but only a small interaction occurring in a different way. Generally - as I alluded to earlier through mentioning the butterfly effect - the further back a change occurs in timelines, the more exponential its effects will become in the future. This is simply due to the nature of chaos.
Chaos is a thing we use to describe infinitely complex physical - or other - processes which we cannot possibly predict - since such an attempt would be paradoxical. This would be because in the act of trying to assess the future of a chaotic system, we ourselves would be changing its course, and would have to include the act of our own prediction in the context: the instrument affects the experiment. It is in fact impossible to ever conduct any "experiment" whether that be a thought experiment or a physical experiment, without in fact affecting the outcome itself. Such an experiment would need to infinitely recurrently apply corrections to the experiment to account for the influence of the experimenting tools themselves. One such thing is the theoretical model of the universe in a computer, which would have to include the computer itself and its effects. This is my view of what we mean by relativity in the universe, and why I believe constancy is the only possible perspective which could help us truly understand how the universe works.
If the impossibility of this supposed trial by error (natural selection in other words) method of obtaining a pathway to intelligence seems too unlikely, then consider this: intelligence did not in fact exist until the moment it was created. We only place such a high value on intelligence because it mystifies us: we do not fully understand the universe or intelligence, because we are using intelligence itself to understand it. In fact, it is questionable whether 'understanding' is something inherent in the universe, or simply another function of intelligence itself - something created from nothing. This also goes for mathematics, science and the content of this article, all of which are functions or consequences of intelligence.
It is almost certain that something infinitely more amazing than intelligence could have been created through natural selection, and that something infinitely more amazing than that could also have been created ad infinitum. There will always be a better possibility for perfection would imply that there are a finite number of outcomes. This can be explained through the nature of creating something from nothing: that something is not defined and so we assume it has "infinite value" - because 'something' is every possibility ever conceived or not conceived. That is the brilliance of creation and possibly why mathematics has evolved as a tool used to describe the universe:
I believe explanation of the power of mathematics can be found through starting with the simple statement 0=0. The rules of algebra dictate that we may apply any transformation to either side as long as we apply it to the other. In the mathematical sense, we might add 2 to either side to give 2=2. But this could also be written 1+1=2. I firmly subscribe to the belief that every action has an equal and opposite reaction is an underlying principle in the creation of the universe. If something is created, its equal and opposite must also be created. Through various transformations things might appear not to sum to 0 in the universe: there are a growing multitude of different physical phenomena that we must look at and consider in describing the universe. Yet, I believe that if all things are reduced to their simplest form - rearranging the equation - this will not result in a solvable equation with universal variables, but a simple statement that can be reduced to 0=0. Of course you would have to "solve simultaneous equations on a grand scale" to achieve this, but in doing so would better understand the patterns of the universe. I think that you must think of forces, energy, fields etc. to all be intrinsically linked and to be of the same sort of substance (i.e. things which exist in this universe the traditional sense) in order for this to be possible, however the universe as we know it is such a complicated soup of all these things that it becomes difficult, almost impossible, to make sense of it in this fashion. I also believe that relativity arises from everything having an equal and opposite as shown by the diagram below, which I shall leave for the reader to consider:

A Blind Man's World

The whispering voices,

The soft-sounding chimes,

The hissing of serpents that slither and slide,

Under and over - around the divide,

Upon which the sighted found all of their pride,

I seem to see darkness and light all the same

And see only that which my mind’s eye portrays.

Great minds often clash yet small minds will not,

For there can be no discourse through blood – only rot,

I feel you, I see you – my eyes I need not,

My sight is the purest – fresh from the cot.