Modes of thinking

 I’ve written a few posts on creative thinking as well as analytical and critical thinking. But, not that long ago, I read a not-so-recently published book (2015) by 2 psychologists (John Kounios and Mark Beeman) titled, The Eureka Factor; Creative Insights and the Brain. To quote from the back fly-leaf:
 
Dr John Kounios is Professor of Psychology at Drexel University and has published cognitive neuroscience research on insight, creativity, problem solving, memory, knowledge representation and Alzheimer’s disease.
 
Dr Mark Beeman is Professor of Psychology and Neuroscience at Northwestern University, and researches creative problem solving and creative cognition, language comprehension and how the right and left hemispheres process information.
 
They divide people into 2 broad groups: ‘Insightfuls’ and ‘analytical thinkers’. Personally, I think the coined term, ‘insightfuls’ is misleading or too narrow in its definition, and I prefer the term ‘creatives’. More on that below.
 
As the authors say, themselves, ‘People often use the terms “insight” and “creativity” interchangeably.’ So that’s obviously what they mean by the term. However, the dictionary definition of ‘insight’ is ‘an accurate and deep understanding’, which I’d argue can also be obtained by analytical thinking. Later in the book, they describe insights obtained by analytical thinking as ‘pseudo-insights’, and the difference can be ‘seen’ with neuro-imaging techniques.
 
All that aside, they do provide compelling arguments that there are 2 distinct modes of thinking that most of us experience. Very early in the book (in the preface, actually), they describe the ‘ah-ha’ experience that we’ve all had at some point, where we’re trying to solve a puzzle and then it comes to us unexpectedly, like a light-bulb going off in our head. They then relate something that I didn’t know, which is that neurological studies show that when we have this ‘insight’ there’s a spike in our brain waves and it comes from a location in the right hemisphere of the brain.
 
Many years ago (decades) I read a book called Drawing on the Right Side of the Brain by Betty Edwards. I thought neuroscientists would disparage this as pop-science, but Kounios and Beeman seem to give it some credence. Later in the book, they describe this in more detail, where there are signs of activity in other parts of the brain, but the ah-ha experience has a unique EEG signature and it’s in the right hemisphere.
 
The authors distinguish this unexpected insightful experience from an insight that is a consequence of expertise. I made this point myself, in another post, where experts make intuitive shortcuts based on experience that the rest of us don’t have in our mental toolkits.
 
They also spend an entire chapter on examples involving a special type of insight, where someone spends a lot of time thinking about a problem or an issue, and then the solution comes to them unexpected. A lot of scientific breakthroughs follow this pattern, and the point is that the insight wouldn’t happen at all without all the rumination taking place beforehand, often over a period of weeks or months, sometimes years. I’ve experienced this myself, when writing a story, and I’ll return to that experience later.
 
A lot of what we’ve learned about the brain’s functions has come from studying people with damage to specific areas of the brain. You may have heard of a condition called ‘aphasia’, which is when someone develops a serious disability in language processing following damage to the left hemisphere (possibly from a stroke). What you probably don’t know (I didn’t) is that damage to the right hemisphere, while not directly affecting one’s ability with language can interfere with its more nuanced interpretations, like sarcasm or even getting a joke. I’ve long believed that when I’m writing fiction, I’m using the right hemisphere as much as the left, but it never occurred to me that readers (or viewers) need the right hemisphere in order to follow a story.
 
According to the authors, the difference between the left and right neo-cortex is one of connections. The left hemisphere has ‘local’ connections, whereas the right hemisphere has more widely spread connections. This seems to correspond to an ‘analytic’ ability in the left hemisphere, and a more ‘creative’ ability in the right hemisphere, where we make conceptual connections that are more wideranging. I’ve probably oversimplified that, but it was the gist I got from their exposition.
 
Like most books and videos on ‘creative thinking’ or ‘insights’ (as the authors prefer), they spend a lot of time giving hints and advice on how to improve your own creativity. It’s not until one is more than halfway through the book, in a chapter titled, The Insightful and the Analyst, that they get to the crux of the issue, and describe how there are effectively 2 different types who think differently, even in a ‘resting state’, and how there is a strong genetic component.
 
I’m not surprised by this, as I saw it in my own family, where the difference is very distinct. In another chapter, they describe the relationship between creativity and mental illness, but they don’t discuss how artists are often moody and neurotic, which is a personality trait. Openness is another personality trait associated with creative people. I would add another point, based on my own experience, if someone is creative and they are not creating, they can suffer depression. This is not discussed by the authors either.
 
Regarding the 2 types they refer to, they acknowledge there is a spectrum, and I can’t help but wonder where I sit on it. I spent a working lifetime in engineering, which is full of analytic types, though I didn’t work in a technical capacity. Instead, I worked with a lot of technical people of all disciplines: from software engineers to civil and structural engineers to architects, not to mention lawyers and accountants, because I worked on disputes as well.
 
The curious thing is that I was aware of 2 modes of thinking, where I was either looking at the ‘big-picture’ or looking at the detail. I worked as a planner, and one of my ‘tricks’ was the ability to distil a large and complex project into a one-page ‘Gantt’ chart (bar chart). For the individual disciplines, I’d provide a multipage detailed ‘program’ just for them.
 
Of course, I also write stories, where the 2 components are plot and character. Creating characters is purely a non-analytic process, which requires a lot of extemporising. I try my best not to interfere, and I do this by treating them as if they are real people, independent of me. Plotting, on the other hand, requires a big-picture approach, but I almost never know the ending until I get there. In the last story I wrote, I was in COVID lockdown when I knew the ending was close, so I wrote some ‘notes’ in an attempt to work out what happens. Then, sometime later (like a month), I had one sleepless night when it all came to me. Afterwards, I went back and looked at my notes, and they were all questions – I didn’t have a clue.

A philosophical school of thought with a 2500 year legacy

I’ve written about this before, but revisited it with a recent post I published on Quora in response to a question, where I didn’t provide the answer expected, but ended up giving a very brief history of philosophy as seen through the lens of science.
 
I’ve long contended that philosophy and science are joined at the hip, and one might extend the metaphor by saying the metaphysical bond is mathematics.
 
When I say a very brief history, what I mean is that I have selected a few specific figures, albeit historically prominent, who provide links in a 2500 year chain, while leaving out countless others. I explain how I see this as a ‘school of thought’, analogous to how some people might see a religion that also goes back centuries. The point is that we in the West have inherited this, and it’s determined the technological world that we currently live in, which would have been unimaginable even as recently as the renaissance or the industrial revolution, let alone in ancient Greece or Alexandria.
 
Which philosopher can you best relate yourself to?
 
It would take a certain hubris to claim that I relate to any philosopher whom I admire, but there are some whom I feel, not so much a kinship with, but an agreement in spirit and principle. Philosophers, like scientists and mathematicians, stand on the shoulders of those who went before.
 
I go back to Socrates because I think he was ahead of his time, and he effectively brought argument into philosophy, which is what separates it from dogma.
 
Plato was so influenced by Socrates that he gave us the ‘Socratic dialogue’ method of analysing an issue, whereby fictional characters (albeit with historical names) discuss hypotheticals in the form of arguments.
 
But Plato was also heavily influenced by Pythagorean philosophy, and even adopted its quadrivium of arithmetic, geometry, astronomy and music for his famous Academy. This tradition was carried over to the famous school or Library of Alexandria, from which sprang such luminaries as Euclid, Eratosthenes, who famously ‘measured’ the circumference of the Earth (around 230BC) and Hypatia, the female mathematician, mentor to a Bishop and a Roman Prefect, as well as speaker in the Senate, who was killed for her sins by a Christian mob in 414AD.
 
Plato is most famously known for his cave allegory, whereby we observe shadows on a wall, without knowing that there is another reality beyond our kin, consequently called the Platonic realm. In later years, this was associated with the Christian ideal of ‘heaven’, but was otherwise considered an outdated notion.
 
Then, jumping forward a couple of centuries from Plato, we come to Kant, who inadvertently resurrected the idea with his concept of ‘transcendental idealism’. Kant famously postulated that there is a difference between what we observe and the ‘thing-in-itself’, which we may never know. I find this reminiscent of Plato’s cave analogy.
 
Even before Kant there was a scientific revolution led by Galileo, Kepler and Newton, who took Pythagorean ideals to a new level when they used geometry and a new mathematical method called calculus to describe the motions of the planets that had otherwise escaped a proper and consistent exposition.
 
Then came the golden age of physics that not only built on Newton, but also Faraday and Maxwell, whereby newly discovered mathematical tools like complex algebra and non-Euclidean geometry opened up a Pandora’s box called quantum mechanics and relativity theory, which have led the way for over a hundred years in our understanding of the infinitesimally small and the cosmologically large, respectively.
 
But here’s the thing: since the start of the last century, all our foundational theories have been led by mathematics rather than experimentation, though the latter is required to validate the former.
 
To quote Richard Feynman from a chapter in his book, The Character of Physical Law, titled, The Relation of Mathematics to Physics:


Physicists cannot make a conversation in any other language. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form.
 
And this leads me to conclude that Kant's ‘transcendental idealism’ is mathematics*, which has its roots going back to Plato and possibly Pythagoras before him.
 
In answer to the question, I don’t think there is any specific philosopher that I ‘best relate to’, but there is a school of thought going back 2500 years that I have an affinity for.
 
 
*Note: Kant didn’t know that most of mathematics is uncomputable and unknown.
 

Can relativity theory be reconciled with common sense?

 You might think I write enough posts on Einstein’s theories of relativity, including the last one, but this one is less esoteric. It arose from a question I answered on Quora. Like a lot of questions on Quora, it’s provocative and you wonder whether the questioner is serious or not.
 
Before I came up with the title, I rejected 2 others: Relativity theory for dummies (which seemed patronising) and Relativity explained without equations or twins (which is better). But I settled on the one above, because it contains a thought experiment, which does exactly that. It’s a thought experiment I’ve considered numerous times in the past, but never expressed in writing.
 
I feel that the post also deals with some misconceptions: that SR arose from the failure of the Michelson-Morley experiments to measure the aether, and that GR has no relationship to Newton’s theory of gravity.
 
If the theories of relativity are so "revolutionary," why are they so incompatible with the 'real' world? In others(sic), why are the theories based on multiple assumptions in mathematics rather than the physical world?
 
You got one thing right, which is ‘theories’ plural – there is the special theory (SR) and the general theory (GR). As for ‘multiple assumptions in mathematics’, there was really only one fundamental assumption and that determined the mathematical formulation of both theories, but SR in particular (GR followed 10 years later).
 
The fundamental assumption was that the speed of light, c, is the same for all observers irrespective of their frame of reference, so not dependent on how fast they’re travelling relative to someone else, or, more importantly, the source of the light. This is completely counter-intuitive but is true based on all observations, including from the far reaches of the Universe. Imagine if, as per our common sense view of the world, that light travelled slower from a source receding from us and faster from a source approaching us.
 
That means that observing a galaxy far far away, the spiral arm travelling away from us would become increasingly out-of-sync with the arm travelling towards us. It’s hard to come up with a more graphic illustration that SR is true. The alternative is that the galaxy arms are travelling through an aether that permeates all of space. This was the accepted view before Einstein’s ‘revolutionary’ idea.
 
True: Einstein’s idea was premised on mathematics (not observation), but the mathematics of Maxwell’s equations, which ‘predicts’ the constant speed of light and provides a value for it. As someone said (Heinrich Hertz): “we get more out of [these equations] than was originally put into them.”
 
But SR didn’t take into account gravity, which unlike the fictitious aether, does permeate the whole universe, so Einstein developed GR. This was a mathematical theory, so not based on empirical observations, but it had to satisfy 3 criteria, established by Einstein at the outset.
 
1)    It had to satisfy the conservation laws of energy, momentum and angular momentum
2)    It had to allow for the equivalence of gravitational and inertial mass.
3)    It had to reduce mathematically to Newton’s formula when relativistic effects were negligible.
 
Many people overlook the last one, when they claim that Einstein’s theory made Newton’s theory obsolete, when in fact, it extended it into realms it couldn’t compute. Likewise, Einstein’s theory also has limitations, yet to be resolved. Observations that confirmed the theory followed its mathematical formulation, which was probably a first in physics.

Note that the curvature of spacetime is a consequence of Einstein’s theory and not a presupposition, and was one of the earliest observational confirmations of said theory.
 
 
Source: The Road to Relativity; The History and Meaning of Einstein’s “The Foundation of General Relativity” (the original title of his paper) by Hanoch Gutfreund and Jurgen Renn.
 

Addendum: I elaborate on the relationship between Newton's and Einstein's theories on another post, in the context of How does science work?

The fabric of the Universe

Brian Greene wrote an excellent book with a similar title (The Fabric of the Cosmos) which I briefly touched on here. Basically, it’s space and time, and the discipline of physics can’t avoid it. In fact, if you add mass and charge, you’ve got the whole gamut that we’re aware of. I know there’s the standard model along with dark energy and dark matter, but as someone said, if you throw everything into a black hole, the only thing you know about it is its mass, charge and angular momentum. Which is why they say, ‘a black hole has no hair.’ That was before Stephen Hawking applied the laws of thermodynamics and quantum mechanics and came up with Hawking radiation, but I’ve gone off-track, so I’ll come back to the topic-at-hand.
 
I like to tell people that I read a lot of books by people a lot smarter than me, and one of those books that I keep returning to is The Constants of Nature by John D Barrow. He makes a very compelling case that the only Universe that could be both stable and predictable enough to support complex life would be one with 3 dimensions of space and 1 of time. A 2-dimensional universe means that any animal with a digestive tract (from mouth to anus) would fall apart. Only a 3-dimensional universe allows planets to maintain orbits for millions of years. As Barrow points out in his aforementioned tome, Einstein’s friend, Paul Ehrenfest (1890-1933) was able to demonstrate this mathematically. It’s the inverse square law of gravity that keeps planets in orbit and that’s a direct consequence of everything happening in 3 dimensions. Interestingly, Kant thought it was the other way around – that 3 dimensions were a consequence of Newton’s universal law of gravity being an inverse square law. Mind you, Kant thought that both space and time were a priori concepts that only exist in the mind:
 
But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.
 
And this gets to the nub of the topic alluded to in the title of this post: are space and time ‘things’ that are fundamental to everything else we observe?
 
I’ll start with space, because, believe it or not, there is an argument among physicists that space is not an entity per se, but just dimensions between bodies that we measure. I’m going to leave aside, for the time being, that said ‘measurements’ can vary from observer to observer, as per Einstein’s special theory of relativity (SR).
 
This argument arises because we know that the Universe is expanding (by measuring the Doppler-shift of stars); but does space itself expand or is it just objects moving apart? In another post, I referenced a paper by Tamara M. Davis and Charles H. Lineweaver from UNSW (Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe), which I think puts an end to this argument, when they explain the difference between an SR and GR Doppler shift interpretation of an expanding universe.
 
The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula. (My emphasis)
 
I’m now going to use a sleight-of-hand and attempt a description of GR (general theory of relativity) without gravity, based on my conclusion from their exposition.
 
The Universe has a horizon that’s directly analogous to the horizon one observes at sea, because it ‘moves’ as the observer moves. In other words, other hypothetical ‘observers’ in other parts of the Universe would observe a different horizon to us, including hypothetical observers who are ‘over-the-horizon’ relative to us.
 
But the horizon of the Universe is a direct consequence of bodies (or space) moving faster-than-light (FTL) over the horizon, as expounded upon in detail in Davis’s and Lineweaver’s paper. But here’s the thing: if you were an observer on one of these bodies moving FTL relative to Earth, the speed of light would still be c. How is that possible? My answer is that the light travels at c relative to the ‘space’* (in which it’s observed), but the space itself can travel faster than light.
 
There are, of course, other horizons in the Universe, which are event horizons of black holes. Now, you have the same dilemma at these horizons as you do at the Universe’s horizon. According to an external observer, time appears to ‘stop’ at the event horizon, because the light emitted by an object can’t reach us. However, for an observer at the event horizon, the speed of light is still c, and if the black hole is big enough, it’s believed (obviously no one can know) that someone could cross the event horizon without knowing they had. But what if it’s spacetime that crosses the event horizon? Then both the external observer’s perception and the comoving observer’s perception would be no different if the latter was at the horizon of the entire universe.
 
But what happens to time? Well, if you measure time by the frequency of light being emitted from an object at any of these horizons, it gets Doppler-shifted to zero, so time ‘stops’ for the ‘local’ observer (on Earth) but not for the observer at the horizon.
 
So far, I’ve avoided talking about quantum mechanics (QM), but something curious happens when you apply QM to cosmology: time disappears. According to Paul Davies in The Goldilocks Enigma: ‘…vanishing of time for the entire universe becomes very explicit in quantum cosmology, where the time variable simply drops out of the quantum description.’ This is consistent with Freeman Dyson’s argument that QM can only describe the future. Thus, if you apply a description of the future to the entire cosmos, there would be no time.
 
 
* Note: you can still apply SR within that ‘space’.

 

Addendum: I've since learned that in 1958, David Finkelstein (a postdoc with the Stevens Institute of Technology in Hoboken, New Jersey) wrote an article in Physical Review that gave the same explanation for how time appears different to different observers of a black hole, as I do above. It immediately grabbed the attention (and approval) of Oppenheimer, Wheeler and Penrose (among others), who had struggled to resolve this paradox. (Ref. Black Holes And Time Warps; Einstein's Outrageous Legacy, Kip S. Thorne, 1994)