Category Archives: Brain Research

Your Brain..On Math!

Credit: SciTechDaily

In my earlier blogs, I talked about Math Anxiety, about how the brain creates a sense of Now, and various other fun issues in brain research too. Branching off of my long, professional interest in math education, I thought I would look into how ‘doing’ math actually changes your brain in many important ways, especially for children and adolescents. Brain research has come a long way in the last 15 years with the advent of fMRI and sensors that can listen-in to individual neutrons [1]. For a detailed glimpse of modern research have a look at my reference list at the end of this blog.

Here is what we know about how math affects brain structure and maturation. My previous blog on Math Anxiety covered this topic but here are some additional points.

The Basic Anatomy of Math

First of all, let’s put to rest a popular misconception. Its a complete fallacy that we only use 10% of our brain. The misconception probably arose because glial cells that support neurons account for 90% of the cellular matter in the brain, so neurons account for 10% [9,11,10]. The truth is, by the end of each day, your brain has used nearly all of its neurons to facilitate movement, sensory processing, advanced planning, and even day-dreaming!

The architecture of our brains is controlled by about 86 million neurons and the trillions of synaptic connections between them. At the lowest level, our brains are composed of numerous modules that are specialized for specific tasks. Each has its own local knowledge system and ‘data cache’ and can act much faster than the whole-brain, which is the way evolution designed this system to help us respond quickly and not get eaten. We benefit from this ancient architecture because craftsmen, musicians and dancers cannot tell you how they perform their tasks because it is largely unconscious and controlled by specific modules. [6:p45, 198].

Before the age of 2, children use a general knowledge ‘program’ that takes up all of their working memory [2:p151] to interact with the environment. Children require more working memory to do math than adults. Number facts and basic opeations are not yet in long-term memory so they use more of their prefronal cortex (PFC) to keep math in working memory so that they can solve problems [2:p155]. But through training they develope a growing multitude of specialized modules and automatic ‘subroutines’ for specific tasks and skills. [6:p56]. Consciousness occurs when these non-communicating modules begin to share their knowledge across many communities of modules spanning the entire cerebral network. Some of these global communication pathways are highlighted by the so-called brain connectome map. This sharing of multiple representations of similar knowledge leads to problem solving and creativity which now draw inspiration from the experiences of many different modules [6:p58] spanning the entire cortex.

The wiring diagram of a human brain revealing connections. Courtesy of the consortium of The Human Connectome Project

Development of the Brain

At birth, the average baby’s brain is about a quarter of the size of the average adult brain. Incredibly, it doubles in size in the first year. It keeps growing to about 80% of adult size by age 3 and 90% – nearly full grown – by age 5 [12]. Over 1 million new neural connections are created every second among the synapses of the growing population of neurons and dendrites [13]. What then ensues is a process of pruning as seldome-used connections wither and dissappear while others are strengthened [20].

The growing brain does not start out as a tabla rasa but through genetics and evolution there are already features in place that anticipate the growth of mathematical knowledge.

Number Line Maps

At the most elementary level, neurons already exist at birth that are active for specific numbers. These ‘number neurons’ have been found in both monkeys and in humans. In humans they are mostly found in the lateral prefrontal cortex (l-PFC) and the intraparietal sulcus (IPS). [2:p129], but also the mediotemporal lobe (MTL) [2:p98]

Our brain’s hippocampous has place and grid cells that form a direct map written on its cortex that represents the location of objects in space [7p219]. The posterior cingulate region has neurons tuned to the location of objects in the outside world, and is connected to the parahippocampal gyrus where “place cells’ are found. These neurons fire whenever an animal occupies a specific location in space like the northwest corner of your room. These place cells are so advanced that readout of individual nerve cell firings can be used to tell a researcher where the object is in the subjects visual field of view. This even works when the subject closes their eyes and imagines an animal located there. [4:p149].

A curious feature of how the young brain processes quantities is that it perceives quantities as being located on a mental number line. Called the SNARC Effect, even three-day-old infants will look-right for large quantities and look-left for smaller quantities.[2:236]. That calculation-related activity is being processed like mental movement on a number line was also tested in older subjects by studying neuron activation in the superior parietal lobule (SPL) where information is being manipulated in working memory. They found that eye motion alone predicted the answers to simple addition and subtraction problems [2:239]. So just as the brain uses an internal map in the hippocampus to locate objects in space, it also uses an internal map to locate numbers in space along a line! The number line however is not uniform.

Kindergarten students with no math knowledge see number intervals as quantities mapped out in logarithmic intervals just as many animals do, so that quantities are perceived almost the same way as light brightness or sound volume [2:87]. Large numbers with smaller intervals are crowded together in the right-hand of the mental number line while smaller numbers are more spread out in the left-side of the line.

Meanwhile, the concepts of addition and subtraction are already known to infants as young as nine months[2:196]. Thinking about quantity as symbolic numerals like 1,2,3 etc instead of dots like [.], [..], […] etc at first occupies children up to age 7 who have to use their working memory to keep track of this, but within a few years the relationship between number symbols and dots becomes automatic and unconscious [2:185]. By the way, although algebra looks like a language, algebra is not processed in the brain’s language centers [2:p222] You can think and reason logically without language. In fact, when professional mathematicians are studied and asked to solve advanced problems, their language centers are not activated. Instead, the bilateral frontal, intraparietal and ventrolateral temporal regions were active, which are connected to the regions associated with processing numbers [2:232].

Math Remodels the Brain.

For mathematicians, an interesting recycling of brain areas occurs in order to accommodate advanced mathematics. Afterall, the brain volume is fixed by the volume of the skull, so the only way that new skills are learned and mastered is by appropriating cerebral real estate from other adjacent functions. The inferior temporal gyrus (ITG) is an area where face recognition occurs. For mathematicians, part of this region is invaded by adjacent regions used in number processing [2:191], in some cases making it harder for mathematicians to recognize faces!

Admittedly, this is an extreme result of brain reorganization, but there are other examples that are more relevant to children and young adults and the answer to the question ‘Why do I need to know math?’

Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in  sharing brain regions for other purposes.

Example 1: In my previous blog on Math Anxiety, I mentioned that the sub-region called the dorsolateral prefrontal cortex helps us keep relevant  problem-solving information ‘fresh’ in our working memory. In math it is activated when the individual is keeping track of more than one concept at a time. As it also turns out, this region is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at  having lost.  It is also important in suppressing selfish behavior, fostering commitment in relationships, and most importantly inferring the intentions of others, which is called a Theory of Mind.

Example 2: The long-term effect of not continuing math education and problem-solving in adolescents has also been documented. A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16.  The neurotransmitter called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later.  What was found among the older adolescents was that GABA showed a marked reduction[14]. This neurotransmitter is also correlated with brain plasticity and its ability to reconfigure itself by growing new synapses as it learns new skills or knowledge having npothing to do with math [16].

Example 3: The mediotemporal lobe (MTL)  includes the hippocampus, amygdala and parahippocampal regions, and is crucial for episodic and spatial memory. The MTL memory function consists of distinct processes such as encoding, consolidation and retrieval, and supports many functions including emotion, affect, motivation and long-term memory. The MTL also has numerous number neurons [2:p98] and is involved in processing mathematical concepts. Activity in this region represents a short-term memory of the arithmetic rule, whereas the hippocampus may ‘do the math’ and process numbers according to the arithmetic rule at hand.”[15].

Example 4: Memory-based math problems stimulate a region of the brain called the dorsolateral prefrontal cortex, which has already been linked to depression and anxiety. Studies have found, for example, that higher activity in this area is associated with fewer symptoms of anxiety and depression. A well-established psychological treatment called cognitive behavioral therapy, which teaches individuals how to re-think negative situations, has also been seen to boost activity in the dorsolateral prefrontal cortex. The ability to do more complex math problems might allow you to more readily learn how to think about complex emotional situations in different ways. Greater activity in the dorsolateral prefrontal cortex was also associated with fewer depression and anxiety symptoms. The difference was especially obvious in people who had been through recent life stressors, such as failing a class. Participants with higher dorsolateral prefrontal activity were also less likely to have a mental illness diagnosis.[17]

The bottom line for much of the research on how the brain functions with and without mathematics stimulation is that low numeracy is a bigger problem for the brain than low literacy [2:p307] It affects your economic opportunities in life, handeling personal finances, operating as a savvy consumer, and it even connects with your ability to logically process complex social situations and predict what your best course of action might be in many different circumstances.

Many of the brain regions needed for math performance are still under development between ages of 16 and 26 including most importantly the frontal cortex essential for judgment and anticipating future consequances of actions.

So when a student asks what is math good for, take a step back and walk them through the Big Picture!

Books that are definitely worth the time to read!

[1] The Tell-Tale Brain, V.S. Ramachandran, 2011, W.W. Norton and Co.

[2] A Brain for Numbers, Andreas Nieder, 2019, MIT Press

[3] The Consciousness Instinct, Michael Gazzangia, 2018, Farrar, Straus and Giroux

[4] Consciousness and the Brain, Stanislaus Dehaene, 2014, Penguin Books.

[5] Being You: A new science of consciousness, Anil Seth, 2021, Dutton Press

[6] The Prehistory of the Mind, Stevem Mithen, 1996, Thames and Hudson Publishers.

[7] The Idea of the Brain, Matthew Cobb, 2020, Basic Books

[8] The River of Consciousness, Oliver Sacks, 2017, Vintage Books

[9] Myth: We only use 10% of our brains. Stephen Chew ,2018,

[10] Neurological glial cells –

[11] Unsung brain cells play key role in neurons’ development, 2009, Bruce Goldman,’%20research%20has%20led,90%20percent%20of%20the%20brain.



[14] and DOI:10.1073/pnas.2013155118

[15] Math Neurons” Fire Differently Depending On Whether You Add Or Subtract, 2022,




Math Anxiety: Origins and Cures

Portrait Of Student With Head Down On Stack Of Books

Someone asks you to perform a simple arithmetic calculation, or perhaps you encounter these while doing your income tax. As a consumer you might want to compare the cost of two products with different sales prices. Or perhaps the tags give  you the same product by two different manufactures who tell you the unit cost, but the products are  in either 12-count or 18-count packages. The odds are very good that along with millions of other adults you will have some trepidation in ‘doing the math’. That’s because math anxiety (MA) is endemic not only among US adults but around the world. It crosses ethnic groups, cultures and continents. According to a recent study of MA[1] 93% of all adults in the US suffer from some level of this condition; internationally and across many cultures, this incidence can be over 40%.  It is reinforced by parents, the news media, and even by teachers using outdated pedagogy– all with devastating consequences, long-term. Like ADHD, you can find yourself somewhere on the Math Anxiety Spectrum. Your location might even change as you advance from childhood to adulthood.

Your Brain on Math

The evolution of our brains over millions of years has prepared it to do many kinds of math but often at an unconscious level. We, along with thousands of other species, have an innate ability to compare quantities and figure which is larger. Some species can even count including chimpanzees, crows, bees and frogs[2]. Our brains come hard-wired at birth to understand addition and subtraction. There are actual brain neurons in the parahippocampal cortex that are only active during addition while others are only active during subtraction[3].They also respond when the instruction is written down symbolically as a word or a symbol (five and three  or 5+3).


The number of brain regions involved in mathematics performance reads like a catalog of nearly half of the cerebral cortex itself. This means that many of these math-activated regions are also used for other purposes in the brain. This is a common feature of brain architecture in that regions are recycled to form other neuronal networks depending on the task at hand.

  • Dorsolateral prefrontal cortex
  • Left inferior parietal lobe
  • Left precentral gyrus
  • Left superior parietal lobe
  • Left supramarginal gyrus
  • Left middle temporal gyrus
  • Insula
  • Middle cingulate cortex
  • Middle frontal gyrus
  • Superior temporal gyrus
  • Inferior frontal gyrus
  • Thalamus
  • Bilateral intraparietal region
  • Dorsal prefrontal region
  • Inferior temporal region

As a brain matures, these regions respond to external experiences but are always influenced by innate survival instincts provided by the limbic system composed of the thalamus and the amygdala. When no previous  negative experiences trigger a limbic response for fight-or-flight, all is well.  Even by the age of 7, children still have an enthusiastic and playful attitude towards math. This attitude unfortunately starts to wane in direct proportion to the number of negative performance tests they experience, which is why MA arises.

A common view shared by many MA students is that, unless I can do math quickly, I must not be very good at it. This is also a pervasive attitude among adults who, despite performing well in grade-school math may still not see themselves ‘good’ at math. Math skills are unlike reading skills because there has evolved over time a massive social permissiveness to being a poor math performer that simply  isn’t found in other academic topics.

Thanks to advances in brain research and mapping, we have a ring-side seat into what brain regions and neuronal circuitries are responsible, not only for handling mathematical problem-solving of increased sophistication, but how this process maps into generating anxiety. There is even a specific brain protein called MAOA that correlates with MA and can be used to spy on your emotional state as you are confronted with different problems.

Math comprehension and execution, like our language centers (Broca and Wernicke Regions) are activated primarily in two main regions: The parietal lobe is involved with calculating and processing numbers; The frontal lobe is involved in recalling numerical knowledge and working memory[3].

The sub-region called the dorsolateral prefrontal cortex is most curious because it is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at  having lost. In math this region seems to be activated when the individual is keeping track of more than one concept at a time[2]. This region, which in math helps us keep relevant  problem-solving information ‘fresh’ in our working memory,  is also shared by circuits that allow us to suppress selfish behavior, foster commitment in relationships, and inferring the intentions of others, which is called a Theory of Mind. Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in  sharing brain regions for other purposes.

The Amygdala Hijack

Brain imaging studies[3] show that individuals with MA, not unexpectedly, activate circuits associated with negative emotional processing (amygdala, prefrontal cortex), the experience of pain (insula), but also areas involved with inhibiting irrelevant information, and conflict processing. The emotional control network is activated even before mathematical performance occurs. MA does its dirty work by literally robbing the individual of resources in its working memory so that they no longer have access to recalling how similar problems were previously solved. In fact, actual physical changes to the brains of MA students were found in the amygdala, the anterior corpus callosum, the right inferior frontal sulcus and the pericallosal sulcus. In particular the right amygdala volume is smaller and more reactive in students with MA[4]. Chronic hyperactivity of the amygdala in response to stress results in cellular atrophy and a decreased ability to regulate negative emotions. This effect continues into adulthood, so repeated negative math experiences in childhood alters the way that adults handle MA in a way that is both cumulative and apparently not easily mitigated in adulthood because it involves physical changes (atrophy) to specific brain regions.

One of the most troubling features of exercising a math skill is that the regions used are also connected via neuronal synapses to  the prefrontal cortex and to the amygdala. The PFC is a vital executive brain region used for synthesizing data symbolically, keeping information present in a ‘working memory’ and forecasting what happens next. This means that getting better at math allows your PFC to be trained to make better decisions about the future. But here is the BIG PROBLEM. The amygdala also watches over this process and stamps it with an emotional context. Under conditions were the stress hormone cortisol is elevated, the amygdala sees your current condition as a fight-or-flight situation and ‘hijacks’ your brain. [5]This immediately shuts down your PFC and flavors your conscious thinking with the survival instinct of wanting to flee the situation. Forget about logic and planning – it’s time to run! Of course this is not possible when working on a difficult math problem, plus the hijack has now robbed you of clear executive thinking, planning and working memory, which only increases the cortisol.

Defeating MA

This cycle of increasing stress can be defeated by first recognizing it is happening   (sweaty palms, rapid heartbeat), using deep slow breathing, and especially clearing your mind of intrusive thoughts. It only takes 90 seconds to defeat this progression. But sometimes, putting yourself in a state where MA cannot get a toe-hold is ‘simply’ a matter of not triggering the Amygdala Hijack in the first place. Here are some recommendations for teachers from researchers who have studied this triggering process.

  • Incorporate math into real-world concepts that students understand.
  • Focus on the fun elements of math like pattern making and a curiosity about numbers, not on rote memorization and theory.
  • Have them see how numbers and data literacy surround them in life from supermarket shopping to predicting future trends.
  • Avoid negative self-talk. Train yourself to have a positive attitude.
  • Consider math as a foreign language that takes practice.
  • Break the vicious downward cycle  of a bad test grade leading to lower self-esteem leading to another bad test grade leading to still-lower self-esteem.
  • Never scold a student for being wrong or having failed to perform a ‘simple’ math task.
  • Never tell your child ‘I was never good at math either’. This tells the child they can succeed in life without knowing math, which is demonstrably false in the 21st century.
  • Find ways to provide alternate student assessments rather than timed tests. This is a major source of stress and a key factor in MA.
  • Investigate ‘mixed-ability’ groupings to avoid placing MA student together, which only reinforces and normalizes  MA through peer-pressure.
  • Make math fun with lots of positive reinforcement. This reduces stress and heart rates and mitigates MA.
  • Have parents read math-related bedtime stories.
  • Encourage understanding not rote memorization. STEM professionals are those who think slowly, creatively and deeply..not necessarily quickly.
  • Display ‘anchor charts’ with examples of work, previous problems or formulas as visual clues to recall previous material.
  • Draw or write down facts or relevant equations before working on a math problem
  • Have students describe the problem to a partner to help articulate their thinking
  • Start the class with a ‘diffuser’ such as sharing a joke, or asking ‘who can tell me something we did in class yesterday?”
  • Focus on how a student got their answer and not on it whether it is right or wrong. If incorrect the student may realize this as they explain the process they used.
  • Allow students to post pictures or written explanations of their methods of solving a problem.
  • Pay attention to the words you use. Instead of ‘this is easy’ say ‘this is like the problem we did yesterday”.
  • Always project a positive, confident attitude to support modeling MA-free behavior and attitudes.

Genetic Predispositions

Here’s some bad news. MA might be genetically inheritable. The epigenetic genome controls how genes are expressed. It represents an additional way that traits and tendencies can be passed on. It is well known that traumas to parents can be passed to children, especially starvation and malnutrition. If the starving mother is pregnant, the epigenome she gives to her fetus can cause childhood difficulties in expressing proteins needed for proper digestion. Epigenetics also seems to explain how stress-related disorders can be inherited. According to a review article by TruDiagnostic published in 2020[6], the amount of cortisol in the brain can be regulated by the inherited epigenetic genome and predispose a child to stress-related behavior. It is not impossible that the same transfer of tendencies might happen that predispose the child to MA.  MA seems to result from an interaction of genetic vulnerability with negative experiences learning math. Only an unkind word from a teacher, parent or social group would be enough to set MA in motion, full-blown.

Researchers have also found that a molecular genetic marker called the monoamine oxidase A gene (MAOA) when not expressed at high enough levels correlates with increased MA especially in girls who are known from other studies to be especially susceptible to MA[7]. However, Zhe Wang at Ohio State finds that genetic factors may only account for about 40% of the individual differences in math performance based on a study of 216 twins “If you have these genetic risk factors for math anxiety and then you have negative experiences in math class, it may make learning that much harder.”[8]

MA causes millions of children, especially girls, to not consider STEM careers. This can relegate them to lower-paying jobs that are less quantitative in skill-set. With manual cash registers, some arithmetic acumen was always required even in low-paying sales jobs. Today, change is made with computerized terminals so low-paying jobs require virtually no math and are free of MA triggers.  However, the consequences of not continuing  math education in adolescence can be potentially disastrous not only reducing their career options but in the actual development of their brains.

A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16.  The chemical called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later.  What was found among the older adolescents was that GABA showed a marked reduction[9]. Because this chemical is also involved in brain plasticity and the ability to learn new skills and thinking, this reduction at this critical stage in brain development can have far-reaching impacts into adulthood.

Don’t worry…Be happy

But the good news is the brain is not a static thing. It is very ‘plastic’ when it comes to learning and dealing with new experiences. With patience and a more-supportive classroom environment, students can be shown how to make other associations between math and emotions, but this time ones that mitigate MA.


[1] Brain areas associated with numbers and math, 2018, 

[2] Mental math and the fine-tuning of emotions. Sandra Ackerman, 2017, Dana Foundation Blog,

[3] Dorsolateral Prefrontal Cortex, 2013, Simmon Moss,  and Wikipedia [ref 8]

[4] Neurostructural correlate of math anxiety in the brains of children. Karin Kucian et al,   Translational Psychiatry, 2018; 8:273. Doi: 10.1038/s41398-018-0320-6. And

[5] The stress-learning connection: Manage an Amygdala Hijack in three steps. The Brain Health Magazine, 2022,

[6] Epigenetics and Anxiety – The relationship between genes and stress-related disorders, 2020,

[7] MAOA-LPR polymorphism and math anxiety: A marker of genetic susceptibility to social influences in girls, 2022, Annals of the New York Academy of Sciences 1516(1), DOI:10.1111/nyas.14814.

[8] Who’s afraid of math? Genetics plays a role but researchers say environment still key, 2014,

[9] and DOI:10.1073/pnas.2013155118

This is Not Your Father’s Universe!

When I was learning astronomy in the 60s and 70s, we were still debating whether Big Bang or Stady State were the most accurate models for our universe. We also wondered about how galaxies like our Milky Way formed, and whether black holes existed. The idea that planets beyond our solar system existed was pure science fiction and no astronomers spent any time trying to predict what they might look like. As someone who has reached the ripe old age of 70, I am amazed how much progress we have made, from the discovery of supermassive black holes and exoplanets, to dark matter and gravitational radiation. The pace of discovery continues to increase, and our theoretical ideas are now getting confirmed or thrown out at record pace. There are still some issues that remain deliciously mysterious. Here are my favorite Seven Mysteries of the Universe!

1-How to Build a Galaxy: In astronomy, we used to think that it would take the universe a long time to build galaxies like our Milky Way, Thanks to the new discoveries by the Webb Space Telescope, we now have a ring-side seat to how this happens, and boy is it a fast process!

The oldest galaxies discovered with the Hubble Space Telescope date back to between 400 and 500 million years after the Big Bang. A few weeks ago, Webb spotted a galaxy that seems to have formed only 300 million years after the Big Bang. Rather than the massive galaxies like the Milky Way, these young galaxies resemble the dwarf galaxies like the Large Magellanic Cloud, perhaps only 1/10 the mass of our galaxy and filled with enormus numbers of massive, luminous stars. The above image from Hubble is a nearby galaxy called M-33 that has a mass of about 50 billion suns. There were lots of these smaller galaxies being formed during the first 300 million years after the Big Bang.

It looks like the universe emerged from the Dark Ages and immediately started building galaxies. In time, these fragments collided and merged to become the more massive galaxies we see around us, so we are only just starting to see how galaxy-building happens. Our Milky Way was formed some 1 billion years after the Big Bang, so the galaxy fragments being spotted by Webb have another 700 million years to go to make bigger things. Back in 2012, Hubble had already discovered the earliest spiral galaxy seen by then; a galaxy called Q2343-BX442, camping out at 3 billion years after the Big Bang. In 2021, an even younger spiral galaxy was spotted, called BRI 1335-0417, seen as it was about 1.4 billon years after the Big Bang.

So we are now watching how galaxies are being formed almost right before our eyes! Previous ideas that I learned about as an undergraduate, in which galaxies are formed ‘top-down’ from large collections of matter that fragment into stars, now seem wrong or incomplete. The better idea is that smaller collections of matter form stars and then merge together to build larger systems – called the ‘bottom-up’ model. This process is very, very fast! Among the smallest of these ‘galaxies’ are things destined to become the globular clusters we see today.

2-Supermassive Black Holes: The most distant and youngest supermassive black hole was discovered in 2021. Called J0313-1806, its light left it to reach us when the universe was only 670 million years old. Its mass, however, is a gargantuan 1.6 BILLION times the mass of our sun. Even if the formation of this black hole started at the end of the Dark Ages ca 100 million years after the Big Bang, it would have to absorb matter at the rate of three suns every year on average. That explains its quasar energy, but still…it is unimaginable how these things can grow so fast! The only working idea is that they started from seed masses about 10,000 the mass of our sun and grew from there. But how were the seed masses formed? This remains a mystery today.

3-The Theory of everything: The next Big Thing that I have been following since the 1960s is the search for what some call the Theory of Everything. Exciting theoretical advancements were made in the 1940s and 1960s to create accurate mathematical models for the three nongravity forces, called the electromagnetic, weak and strong forces. Physicists call this the Standard Model, and every physicist learns its details as students in graduate school. By the early 1980s, string theory was able to add gravity to the mix and go beyond the Standard Model. It appeared that the pursuit of a unified theory had reached its apex. Fifty years later, this expectation has all but collapsed.

Experiments at the Large Hadron Collider continue to show how the universe does not like something called supersymmetry in our low-energy universe. Supersymmetry is a key ingredient to string theory because it lets you change one kind of particle (field) into another, which is a key ingredient to any unified theory. So the simplest versions of string theory rise or fall based on whether supersymmetry exists or not. For over a decade, physicists have tried to find places in the so-called Standard Model where supersymmetry should make its appearance, but it has been a complete no-show. Its not just that this failure is a problem for creating a more elegant theory of how forces works, but it also affects astronomy as well.

Personally, when string theory hit the stage in the 1980’s I, like many other astronomers and physicists, thought that we were on the verge of solving this challenge of unifying gravity with the other forces, but this has not been the reality. Even today, I see no promissing solutions to this vexing problem since apparently the data shows that simple string theory is apparently on a wrong theoretical track.

One cheerful note: For neutrinos, the path from theoretical prediction to experimental observation took 25 years. For the Higgs boson, it took 50 years. And for gravitational waves, it took a full 100 years. We may just have to be patient…for another 100 years!

4-Dark Matter: The biggest missing ingredient to the cosmos today is called dark matter. When astronomers ‘weigh’ the universe, they discover that 4.6% of its gravitating ‘stuff’ is in ordinary matter (atoms,. stars, gas, neutron stars etc), but a whopping 24% is in some other ‘stuff’ that only appears by its gravity. It is otherwise completely invisible. Putting this another way, it’s as though four out of every five stars that make up our Milky Way were completely invisible.

Dark matter in Abell 1679.

Because we deeply believe that dark matter must be tracable to a new kind of particle, and because the Standard Model gives us an accounting of all the kinds of elementary particles from which our universe is built, the dark matter particle has to be a part of the Standard Model…but it isn’t!!!! Only by extending the Standard Model to a bigger theory (like string theory) can we logically and mathematically add new kinds of particles to a New Standard Model- one of which would be the dark matter particle. String theory even gives us a perfect candidate called the neutralino! But the LHC experiments have told us for over a decade that there is nothing wrong with the Standard Model and no missing particles. Astronomers say that dark matter is real, but physicists can’t find it….anywhere. Well…maybe not ALL astronomers think it’s real. So the debate continues.

Personally, I had heard about ‘missing mass’ in the 1960s but we were all convinced we would find it in hot gas, dim red dwarf stars or even black holes. I NEVER thought that it would turn out to be something other than ordinary matter in an unusual form. Dark matter is so deeply confounding to me that I worry we will not discover its nature before I, myself, leave this world! Then again, there isnt a single generation of scientists that has had all its known puzzles neatly solved ‘just in time’. I’m just greedy!!!

5- Matter and Antimatter: During the Big Bang, there were equal amounts of matter and anti matter, but then for some reason all the antimatter dissappeared leaving us with only matter to form atoms, stars and galaxies. We don’t know why this happened, and the Standard Model is completely unhelpful in giving us any clues to explain this. But next to dark matter, this is one of the most outstanding mysteries of modern, 21st century cosmology. We have no clue how to account for this fact within the Standard Model, so again like Dark Matter, we see that at cosmological scales, the Standard Model is incomplete.

6- Origin of Time and Space: Understanding the nature of time and space, and trying to make peace with why they exist at all, is the bane of any physicists existence. I have written many blogs on this subject, and have tried to tackle it from many different angles, but in the end they are like jigsaw puzzels with too many missing pieces. Still, it is very exciting to explore where modern physics has taken us, and the many questions such thinking has opened up in surprising corners. My previous blog about ‘What is ‘Now’ is one such line of thinking. Many of the new ideas were not even imagined as little as 30 years ago, so that is a positive thing. We are still learning more about these two subjects and getting better at asking the right questions!

7-Consciousness: OK…You know I would get to this eventually, and here it is! Neuroscientists know of lots of medical conditions that can rob us of consciousness including medical anesthesia, but why we have this sense about ourselves that we are a ‘person’ and have volition is a massively hard problem. In fact, consciousness is called the ‘Hard Problem’ in neuroscience..heck…in any science!

The ‘Soft Problem’ is how our senses give us a coherant internal model of the world that we can use to navigate the outside world. We know how to solve the Soft Problem, just follow the neurons. We are well on our way to understanding it thanks to high-tech brain imaging scanners and cleverly-designed experiments. The Hard Problem is ‘hard’ because our point-of-view is within the thing we are trying to undertand. Some think that our own ‘wet ware’ is not up to the task of even giving us the intelligence to answer this qustion. It will not be the first time someone has told us about limitations, but usually these are technological ones, and not ones related to limits to what our own brains can provide as a tool.

So there you have it.

My impression is that only Mysteries #1 and #2 will make huge progress. The Theory of Everything is in experimental disarray. For antimatter, there has been no progress, but many ideas. They all involve going outside the Standard Model. Dark matter might be replaced by a modification of gravity at galactic and cosmological scales.

Beyond these ‘superficial’ mysteries, we are left with three deep mysteries. The origin of space, time and consciousness remain our 21st century gift to children of the 22nd century!

Check back here in a few weeks for the next blog!

What is ‘Now’?

What is the duration of the present moment? How is it that this present moment is replaced by ‘the next moment’?

Within every organism, sentient or not, there are thousands of chemical processes that occur with their own characteristic time periods, but these time periods start and stop at different times so that there is no synchronized ‘moment’. Elementary atomic collisions that build up molecules take nanoseconds while cell division takes minutes to hours, and tissue cell lifespans vary from 2 days in the stomach lining to 8 years for fat cells (see Cell Biology). None of these jangled timescales collectively or in isolation create the uniform experience we have of now and its future moments. To find the timescale that corresponds to the Now experience we have to look elsewhere.

It’s all in the mind!

A variety of articles over the  years have identified 2 to 3 seconds as the maximum duration of what most people experience as ‘now’, and what researchers call the ‘specious present’. This is the time required by our brain’s neurological mechanisms to combine the information arriving at our senses with our internal, current model of the ‘outside world’. During this time an enormous amount of neural activity has to happen. Not only does the sensory information have to be integrated together for every object in your visual field and cross connected to the other senses, but dozens of specialized brain regions have to be activated or de-activated to update your world model in a consistent way.

In a previous blog I discussed how important this world model is in creating within you a sense of living in a consistent world with a coherent story. But this process is not fixed in stone. Recent studies by Sebastian Sauer and his colleagues at the Ludwig-Maximilians-Universität in Munich show that mindfulness meditators can significantly increase their sense of ‘now’ so that it is prolonged for up to 20 seconds.

In detail, a neuron discharge lasts about 1 millisecond, but it has to be separated from the next one by about 30 milliseconds before a sequence is perceived, and this seems to be true for all senses. When you see a ‘movie’ it is a succession of still images flashed into your visual cortex at intervals less than 30 milliseconds, giving the illusion of a continuous unbroken scene.  (Dainton: Stanford Encyclopedia of Philosophy, 2017).

The knitting together of these ‘nows’ into a smooth flow-of-time is done by our internal model-building system. It works lightning-fast to connect one static collection of sensory inputs to another set and hold these both in our conscious ‘view’ of the world. This gives us a feeling of the passing of one set of conditions smoothly into another set of conditions that now make up the next ‘Now’. To get from one moment to the next, our brain can play fast-and-loose with the data and interpolate what it needs. For example, it our visual world, the fovea in our retina produces a Blind Spot but you never notice it because there are circuits that interpolate across this spot to fill-in the scenery. The same thing happens in the time dimension with the help of our internal model to make our jagged perceptions in time into a smooth movie experience.

Neurological conditions such as strokes, or psychotropic chemicals can disrupt this process and cause dramatic problems. Many schizophrenic patients stop perceiving time as a flow of  linked events.  These defects in time perception may play a part in the hallucinations and delusions experienced by schizophrenic patients according to some studies. There are other milder aberrations that can affect our sense of the flow-of-time.

Research has also suggested the feeling of awe has the ability to expand one’s perceptions of time availability. Fear also produces time-sense distortion. Time seems to slow down when a person skydives or bungee jumps, or when a person suddenly and unexpectedly senses the presence of a potential predator or mate. Research also indicates that the internal clock, used to time durations in the seconds-to-minutes range, is linked to dopamine function in the basal ganglia. Studies in which children with ADHD are given time estimation tasks shows that time passes very slowly for them.

Because the volume of data is enormous, we cannot hold many of these consecutive Now moments in our consciousness with the same clarity, and so earlier Nows either pass into short-term memory if they have been tagged with some emotional or survival attributes, or fade quickly into complete forgetfulness. You will not remember the complete sensory experience of diving into a swimming pool, but if you were pushed, or were injured, you will remember that specific sequence of moments with remarkable clarity years later!

The model-building aspect of our brain is just another tool it has that is equivalent to its pattern-recognition ability in space. It looks for patterns in time to find correlations which it then uses to build up expectations for ‘what comes next’. Amazingly, when this feature yields more certainty than the evidence of our senses, psychologists like Albert Powers at Yale University say that we experience hallucinations (Fan, 2017). In fact, 5-15% of the population experience auditory hallucinations (songs, voices, sounds) at some time in their lives when the brain literally hears a sound that is not there because it was strongly expected on the basis of other clues. One frequent example is that  people claim to hear the Northern Lights as a crackling fire or a swishing sound, because their visual system creates this expectation and the brain obliges.

This, then, presents us with the neurological experience of Now. It is between 30 milliseconds and several minutes in duration. It includes a recollection of the past which fades away for longer intervals in the past, and includes a sense of the immediate future as our model-making facility extrapolates from our immediate past and fabricates an expectation of what comes next.

Living in a perpetual Now is no fun. The famed psychologist Oliver Sacks describes  a patient, Clive Wearing, with a severe form of amnesia, who was unable to form any new memories that lasted longer than 30 seconds, and became convinced every few minutes that he was fully conscious for the first time. “In some ways, he is not anywhere at all; he has dropped out of space and time altogether. He no longer has any inner narrative; he is not leading a life in the sense that the rest of us do….It is not the remembrance of things past, the “once” that Clive yearns for, or can ever achieve. It is the claiming, the filling, of the present, the now, and this is only possible when he is totally immersed in the successive moments of an act. It is the “now” that bridges the abyss.”

Physical ‘Now’.

This monkeying around with brain states, internal model-making and sensory data creates Now as a phenomenon we experience, but the physical world outside our collective brain population does not operate through its own neural systems to create a Cosmic Now. That would only be the case if, for example, we were literally living inside The Matrix….which I believe we are not. So in terms of physics, the idea of Now does not exist. We even know from relativity that there can be no uniform and simultaneous Now spanning large portions of space or the cosmos. This is a problem that has bedeviled many people across the millennia.

Augustine (in the fourth century) wrote, “What is time? If no one asks me, I know; if I wish to explain, I do not know. … My soul yearns to know this most entangled enigma.” Even Einstein himself noted ‘…that there is something essential about the Now which is just outside the realm of science.’

Both of these statements were made before quantum theory became fully developed. Einstein developed relativity, but this was a theory in which spacetime took the place of space and time individually. If you wanted to define ‘now’ by a set of simultaneous conditions, relativity put the kibosh on that idea because due to the relative motions and accelerations of all Observers, there can be no simultaneous ‘now’ that all Observers can experience. Also, there was no ‘flow of time’ because relativity was a theory of worldlines and complete histories of particles from start to finish (called the boundary conditions of worldlines). Quantum theory, however, showed some new possibilities.

In physics, time is a variable, often represented by the letter t, that is a convenient parameter with which to describe how a system of matter and energy change. The first very puzzling feature of time as a physical variable is that all mathematical representations of physical laws or theories show that time is continuous, smooth and infinitely divisible into smaller intervals. These equations are also ‘timeless’ in that they can be written down on a piece of paper and accurately describe how a system changes from start to finish (based on boundary conditions defined at ‘t=0’) , but the equations show this process as ‘all at once’.

In fact, this perspective is so built into physics that it forms the core of Einstein’s relativity theory in the form of the 4-d spacetime ‘block’. It also appears in quantum mechanics because fundamental equations like Schroedinger’s Equation also offer a timeless view of quantum states.

In all these situations, one endearing feature of our world is actually suppressed and mathematically hidden from view, and that is precisely the feature we call ‘now’.

To describe what things look like Now, you have to dial in to the equations the number t =  t(now). How does nature do that? As discussed by physicist Lee Smolin in his book ‘Time Reborn’, this is the most fundamental experience we have about the physical world as sentient beings, yet it is not represented by any feature in the physical theories we have developed thus far. There is no theory that selects t = t(now) over all the infinite other moments in time.

Perhaps we are looking in the wrong place!

Just as we have seen that what we call ‘space’ is built up like a tapestry from a vast number of quantum events described (we hope!) by quantum gravity, time also seems to be created from a synthesis of elementary events occurring at the quantum scale.   For example, what we call temperature is the result of innumerable collisions among elementary objects such as atoms. Temperature is a measure of the average collision energy of a large collection of particles, but cannot be identified as such at the scale of individual particles. Temperature is a phenomenon that has emerged from the collective properties of thousands or trillions of individual particles.

A system can be described completely by its quantum state – which is a much easier thing to do when you have a dozen atoms than when you have trillions, but the principle is the same. This quantum state describes how the elements of the system are arrayed in 3-d space, but because of Heisenberg’s Uncertainty Principle, the location of a particle at a given speed is spread out rather than localized to a definite position.  But quantum states can also become entangled. For these systems, if you measure one of the particles and detect property P1 then the second particle must have property P2. The crazy thing is that until you measured that property in the first particle, it could have had either property P1 or P2, but after the measurement the distant particle ‘knew’ that it had to have the corresponding property even though this information had to travel faster than light to insure consistency.

An intriguing set of papers by physicist Seth Lloyd at Harvard University in 1984 showed that over time, the quantum states of the member particles become correlated and shared by the larger ensemble. This direction of increasing correlation goes only one way and establishes the ‘Arrow of Time’ on the quantum scale.

One interesting feature of this entanglement idea is that ‘a few minutes ago’, our brain’s quantum state was less correlated with its surroundings and our sensory information than at a later time. This means that the further you go into the past moments, the less correlated they are with the current moment because, for one, the sensory information has to arrive and be processed before it can change our brain’s state. Our sense of Now is the product of how past brain states are correlated with the current state. A big part of this correlating is accomplished, not by sterile quantum entanglement, but by information transmitted through our neural networks and most importantly our internal model of our world – which is a dynamic thing.

If we did not have such an internal model that correlates our sensory information and fabricates an internal story of perception, our sense of Now would be very different because so much of the business of correlating quantum information would not occur very quickly. Instead of a Now measured in seconds, our Now’s would be measured in hours, days or even lifetimes, and be a far more chaotic experience because it would lack a coherent, internal description of our experiences.

This seems to suggest that no two people live in exactly the same Now, but these separate Now experiences can become correlated together as the population of individuals interact with each other and share experiences through the process of correlation. As for the rest of the universe, it exists in an undefined Now state that varies from location to location and is controlled by the speed of light, which is the fastest mode of exchanging information.

Read more:

In my previous blogs, I briefly described how the human brain perceives and models space (Blog 14: Oops one more thing), how Einstein and other physicists dismiss space as an illusion (Blog 10: Relativity and space ), how relativity deals with the concept of space (Blog 12: So what IS space?), what a theory of quantum gravity would have to look like (Blog 13: Quantum Gravity Oh my! ), and along the way why the idea of infinity is not physically real (Blog 11: Is infinity real?) and why space is not nothing (Blog 33: Thinking about Nothing). I even discussed how it is important to ‘think visually’ when trying to model the universe such as the ‘strings’ and ‘loops’ used by physicists as an analog to space ( Blog 34: Thinking Visually)

I also summarized the nature of space in a wrap-up of why something like a quantum theory for gravity is badly needed because the current theories of quantum mechanics and general relativity are incomplete, but also point the way towards a theory that is truly background-independent and relativistic (Blog 36: Quantum Gravity-Again! ). These considerations describe the emergence of the phenomenon we call ‘space’ but also down play its importance because it is an irrelevant and misleading concept.

Thinking Visually

Look at the two images  for a few minutes and let your mind wander.

What impressions do you get from the patterns of light and dark? If I were to tell you that the one at the top is a dark nebula in the constellation Orion, and the one on the bottom is a nebula in the Pleiades star cluster, would that completely define for you what you are experiencing…or is there something more going on?

Chances are that, in the top image you are seeing what looks like the silhouette of the head and shoulders of some human-like figure being lit from behind by a light. You can’t quite put your finger on it, but the image seems vaguely mysterious and perhaps even a bit frightening the more you stare at it.

The image on the bottom evokes something completely different. Perhaps you are connecting the translucence and delicacy with some image of a shroud or silken cloak floating in a breeze. The image seems almost ghost-like in some respects…spiritual

But of course this is rather silly” you might say. “These are interstellar clouds, light-years across and all we are doing is letting our imaginations wander which is not a very scientific thing to do if you want to understand the universe.” This rational response then tempts you to reach for your mouse and click to some other page on the web.

What has happened in that split second is that a battle has been fought between one part of your brain and another. The right side of your brain enjoys looking at things and musing over the patterns that it finds there. Alas, it cannot speak because the language centers of the brain live in the left cerebral hemisphere, and it is here that rules of logic and other ‘scientific’ reasoning tools exist. The left side of your brain is vocal, and talking to you right now. It gets rather upset when it is presented with vague patterns because it can’t understand them and stamp them with a definite emotion the way the right hemisphere can. So it argues you into walking away from this challenge of understanding patterns.

If you can suspend this indignation for a moment or two, you will actually find yourself thinking about space in a way that more nearly resembles how a scientist does, though even some scientists don’t spend much time thinking about space. This indifference has begun to change during the last 20 years, and we are now in the midst of a quiet revolution.

There are three child-like qualities that make for a successful scientist:

Curiosity. This is something that many people seem to outgrow as they get older, or if they maintain it as adults, it is not at the same undiluted strength that it was when they were a child.

Imagination. This is something that also wanes with age but becomes an asset to those that can hang on to even a small vestige of it. It is what ‘Thinking out of the box’ is all about.

Novelty. As a child, everything is new. As an adult we become hopelessly jaded about irrelevant experiences like yet another sunset, yet another meteor shower, yet another eclipse. In some ways we develop an aversion for new experiences preferring the familiarity of the things we have already experienced.

If you wish to understand what space is all about, and explore the patterns hidden in the darker regions of nature, you will have to re-acquaint yourself with that child within you. You will need to pull all the stops out and allow yourself to ‘play’ with nature and the many clues that scientists have uncovered about it. You will need to do more than read books by physicists and astronomers. They speak the language of the left-brain . They can help you to see the logical development of our understanding of space and the Void, but they can not help you internalize this knowledge so that it actually means something to you. For that, you have to engage your right-brain faculties, and this requires that you see the patterns behind the words that physicists and astronomers use. To do that, you will need to think in terms of pictures and other types of images. You will need to bring something to the table to help you make sense of space in a way that you have not been able to before. You will need to expand your internal library of visual imagery to help you find analogues to what physicists and astronomers are trying to describe in words and equations. These visual analogues can be found in many common shapes and patterns, some seen under unusual and evocative circumstances. Here are some evocative images that seem to suggest how space might be put together compliments of  a diatom, the painters Miro and Mondrian, dew on a spider web, and atoms in a tungsten needle tip!

Spider web covered with dew drops

Remember, the right brain uses ALL sensory inputs to search for patterns and to understand them. It even uses imaginary information, dreams, and other free-forms to decode what it is experiencing.  

My book ‘Exploring Quantum Space’ is a guidebook that will give you some of the mental tools you will need to make sense of one of the greatest, and most subtle, discoveries in human history. Space, itself, is far from being ‘nothing’ or merely a container for matter to rattle around within. It is a landscape of hidden patterns and activity that shapes our universe and our destiny. You cannot understand it, or sense the awe and mystery of its existence, by simply reading words and following a logical exposition of ‘ifs and thens’. You also have to experience it through evocative imagery and imagination. Space is such a different medium from anything we have ever had to confront, intellectually, that we need to employ a different strategy if we wish to understand it in a personal way. Once we do this, we will be reconnected with that sense of awe we feel each time we look at the night sky.

My next blog about Nothing introduces some of the other ideas and techniques that scientists use to think about the impossible!


Thinking about Nothing

Looking back at the millennia of model building and deduction that has occurred, not a century has gone by when the prevailing opinion hasn’t been that a perfectly empty vacuum is impossible.

Aristotle’s Aether blends seamlessly into the 19th century Ether. In this century, overlapping quantum waves and virtual particles have finally taken root as the New Ether, though it is now infinitely more ephemeral than anything Aristotle or Maxwell could have imagined. We have also seen how the Atomist School of ancient Greece reached its final vindication in the hands of 19th century scientists such as Boltzman. By the 20th century, the Atomist’s paradigm has even been extended to include not just the graininess of matter, but the possible quantum graininess of the vacuum and space itself. In the virtual particles that animate matter, we finally glimpse the world which Heinrich Hertz warned us about nearly a century ago when he said that we would eventually have to reach some accommodation with “invisible confederates” existing alongside what we can see, to make our whole model of reality more logically self-consistent.

Even by the start of the 21st Century, we have reached this accommodation only by shrugging our shoulders and honestly admitting that there are things going on in the world that seem to defy human intuition. What impresses me most about the evolution of our vision of the vacuum is that the imagery we find so potent today is actually in some sense thousands of years old.

It is difficult to imagine that humans would be drawn to the same understanding of physics and astronomy that we now enjoy if our brains had been wired only slightly differently. Without sight and mobility we could not form the slightest notion of 3-D space and geometry. This is what Kant spoke about, what Henri Poincare described at great length without the benefit of 20th century neuroscience, and what Jacob Bronowski described in his book The Origins of Knowledge and Imagination with the benefit of such knowledge. But the object of science is more than just making sense of our senses. It must also guide us towards a deeper understanding of the physical world. This understanding must be self-consistent, and independent of whether we are sensorially or neurologically handicapped. Mathematics as the premier language of physical model building, seems uniquely suited to providing us with an understanding of the physical world. Mathematics lets us see the world in a way that all of the other human languages do not.

If our mathematical understanding of nature is a product of mental activity, and this activity can be physically affected by the hard-wiring of our brain, how do we arrive at a coherent model of the physical world? Can we see in this process any explanation for why certain ideas in physics appear to be so historically tenacious?

It is commonly believed that in order for mathematics and the underlying logic to exist, at the very least a conscious language must be pre-existent to support it. This is the point of view expressed by Benjamin Whorf. But the thoughtful reflections by individuals such as Einstein, Feynman and Penrose point in a very different direction. Einstein once wrote a note to Jaques Hadamard prompted by Hadamard’s investigation of creative thinking,

“…The words of language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements of thought are certain signs ( symbols ) and more or less clear images which can be voluntarily reproduced and combined…The above mentioned elements are, in my case, of visual and some muscular type…”

Roger Penrose echoes some of this same description in his book, The Emperor’s New Mind,

“…Almost all my mathematical thinking is done visually and in terms of non-verbal concepts, although the thoughts are quite often accompanied by inane and almost useless verbal commentary such as ‘that thing goes with that thing and that thing goes with that thing’..”

Freeman Dyson, one of the architects of modern QED had this to say about how Feynman did his calculations,

“…Dick was using his own private quantum mechanics that nobody else could understand. They were getting the same answers whenever they calculated the same problem…The reason Dick’s physics was so hard for ordinary people to grasp was that he did not use equations…Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the pictures gave him the solutions directly with a minimum of calculation…It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial…”

In many instances, the conversion of abstract thinking into conventional language is seen as a laborious, almost painful process. Often words are inadequate to encompass the subtleties of the non-verbal, abstract ideas and their interrelationships. According to Penrose,

“I had noticed, on occasion, that if I have been concentrating hard for a while on mathematics and someone would engage me suddenly in conversation, then I would find myself almost unable to speak for several seconds”

In fact, abstract thinking is often argued to be a right-hemisphere function. Visual or pattern-related thinking and artistic talents are frequently coupled to this hemisphere, and since the language centers are in the left-hemisphere, with such a disconnect between language and abstract thinking, there is little wonder that theoreticians and artists find themselves tongue-tied in explaining their ideas, or are inclined to report that their work is non-verbal.

So the creation of sophisticated physical theories may involve a primarily non-verbal and visual-symbolic thinking processes, often manipulating patterns and only later, with some effort of will, translating this into spoken language or fleshing out the required mathematical details. Could this be why scientists, and artists for that matter have such difficulty in explaining what they are thinking to the rest of the population? Could this be why ancient philosophers managed to land upon archetypes for their Creation legends that seem familiar to us in the 20th century? The symbols that are used appear disembodied, and no amount of word play can capture all of the nuances and motivations that went into a particular interpretive archetypes, and make them seem compelling to the non-mathematician or non-artist. Feynman once wrote about the frustrating process of explaining to the public what goes on in nature,

“…Different people get different reputations for their skill at explaining to the layman in layman’s language these difficult and abstruse subjects. The layman then searches for book after book in the hope that he will avoid the complexities which ultimately set in, even with the best expositor of this type. He finds as he reads a generally increasing confusion, one complicated statement after another,… all apparently disconnected from one another. It becomes obscure, and he hopes that maybe in some other book there is some explanation…but I do not think it is possible, because mathematics is NOT just another language. Mathematics is a language plus reasoning…if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other…”

If this is the mental frame used by some physicists to comprehend physics, it is little wonder that a great chasm exists between the lay person and the physicist in explaining what is going on. The task that even a physicist such as Freeman Dyson had in translating Feynman’s diagrammatic techniques into mathematical symbology, seems even more challenging knowing that Feynman may have had a whole other perspective on visualization via his apparent color-symbol synthesia. The equations below are the current best mathematical expression for the Standard Model in physics, which describes all known particles and fields excepting gravity.

Another feature of thinking that separates scientists and artists from everyone else seems to be the plasticity of the thinking process itself. Scientists flit from one idea to another until they arrive at a model that best explains the available data, although scientists can also get rooted to particular perspectives that are difficult to forget after decades of inculcation. The general adult population prefers a more stable collection of ideas and ‘laws’ which it can refer to over a lifetime.

Where does this all leave us?

The vacuum has been promoted to perhaps the most important clue to our own existence. The difficulty is that we lack a proper Rosetta Stone to translate the various symbolisms we use to describe it. The clues that we do have are scattered among a variety of enigmatic subjects which strain at our best intellectual resources to understand how they are linked together. Could it be that we are lacking an even more potent symbolic metaphor, and an internal non-verbal language, to give it life? Where would such a thing come from?

Spider web covered with dew drops

If we take our clue from how ideas in physics have emerged in the past, the elements of the new way of thinking may be hidden in some unexpected corner of nature. We may find an analogy or a metaphor in our mundane world which, when mixed with mathematical insight, may take us even closer to understanding gravity, spacetime and vacuum. It is no accident that string theory owes much of its success because it asks us to think about quantum fields as ordinary strings operating in an exotic mathematical setting. It is exciting to think that the essential form of the Theory of Everything could be this close to us, perhaps even lurking in a pattern we see, and overlook, in our everyday lives.

Much of this symbolic process may be performed sub-consciously, and only the form of dreams, insights or hunches seem to bring them into consciousness when the circumstances are appropriate. It is, evidently, the non-verbal and unconscious right hemisphere which experiences these ideas. Is there a limit to this process of symbolic thinking? At least a dozen times this century, physicists have had to throw up their hands over what to make of certain features of the world: the collapse of the wave function; quantum indeterminacy; particle/wave dualism; cosmogenesis. Some of these may eventually find their explanation at the next level of model building. Others such as the meaning of quantum indeterminacy and particle/wave dualism, seem to be here to stay.

In working with these contradictions, the human mind prefers the avenue of denial, you can almost hear your inner voice saying “Aw come on, quantum mechanics just can’t be that weird!” or a state of anxiety as the two hemispheres try to fabricate conflicting world models. Little wonder that we have particle/wave duality, the seeming schism between matter and energy, and a whole host of other ‘polar’ ideas in physics, as two separate minds try to resolve the universe into one model or another with the left one preferring time ordered patterns, and the right one, spatial patterns.

It is hard to believe that our brains can control what we experience of the objective world, but we need only realize that the brain actually blindsides us in a variety of subtle ways, from seeing a wider sensory world. The object of science, however, is to discern the shapes of objective laws in a way that gets to the universal elements of nature that are not coupled to a particular kind of brain circuitry. It doesn’t matter if all scientists have anasognosia and see the world differently in some consistent way, what counts is that they must still live by the laws of motion dictated by gravity and quantum mechanics.

Nils Bohr believed atoms are not real in the same sense as trees. The quantum world really does represent a different kind of reality than our apparently naive understanding of macroscopic reality implies. This being the case, we must first ask to what extent fields and the denizens of the quantum vacuum can be represented by any analogy drawn from the macroworld? We already know that the single most important distinguishing characteristic of atomic particles is their spin; far more so than mass or charge. Yet unlike mass and charge, quantum mechanical spin has ABSOLUTELY no analog in the macroscopic world. Moreover, fundamental particles cannot be thought of as tiny spheres of charged matter located at specific points in space. They have no surface, and participate in an infernal wave-like dance of probability, at least when they are not being observed. Yet despite this warning, we feel comfortable that we understand something about what reality is at this scale, in the face of these irreconcilable differences between one set of mental images and what experiments tell us over and over again. What is the true nature of the vacuum? How did the universe begin? I suspect we will not know the answer to these questions in your lifetime or mine, perhaps for the same reason that it took 3000 years for geometers to ‘discover’ non-Euclidean geometry.

At the present time we are faced with what may amount to only a single proof of the parallel-line postulate, unable to see our way through to another way of looking at the proof. There is also the very real worry that some areas of nature may require modalities of symbolic thinking beyond the archetypes that our brains are capable of providing as a consequence of their neural hard-wiring. Today, we have quantum field theory and its tantalizing paradoxes, much as the ancient geometers had their parallel-line postulate. We, like they, scratch the same figures in the sand over and over again, hoping to see the glimmerings of a new world view appearing in the shifting sands. At a precision of one part in a trillion, our quantum theories work too well, and seem to provide few clues to the new direction we must turn to see beyond them.

The primary arbiters we have at our disposal to decide between various interpretive schemes, experimental data, are not themselves in unending supply as the abrupt cancellation of the U.S. Superconducting Super Collider program in 1989 showed. It was replaced by the CERN Large Hadron Collider shown above, but even the LHC may not be large enough to access the new physics we need to explore to further our theories and understanding.

Whatever answers we need seem to be hidden, not in the low- energy world accessible to our technology, but at vastly higher energies well beyond any technology we are likely to afford in the next few centuries. It is easy to provide a jet plane with an energy of 100 billion billion billion volts — its energy of motion at a speed of a few hundred miles per hour, but it is beyond understanding how to supply a single proton or electron with the same energy. On the other hand, our internal symbolic thinking seems to lead us to similar interpretative schemes, and unconscious dualities which may only be a reflection of our own neural architecture, which we all share, and which has remained essentially unchanged for millennia. We visualize the vacuum in the same way as the Ancients did because we are still starting from the same limited collection of internal imagery. At least for some general problems, we seem to have hit a glass ceiling for which our current style of theory building seems to lead us to a bipolar and contradictory world populated by various dualities: matter/energy, space/time, wave/particle. When we finally do break through to a new kind of reality in our experiments, would we be able to recognize this event? Will our brains filter out this new world and show us only the ghostly shadows of contradictory archetypes cast upon the cave wall?

We have seen that many schemes have been offered for describing the essential difference between matter and empty space; many have failed. Theoreticians since Einstein have speculated about the geometric features of spacetime, and the structure of electrons and matter for decades. The growing opinion now seems to be that, ultimately, only the properties of space such as its geometry or dimensionality can play a fundamental role in defining what matter really is. In a word, matter may be just another form of space. If the essence of matter is to be found in the geometric properties of ’empty’ space, our current understanding of space will not be sufficient to describe all of matter’s possible aspects.

Near Death Experiences

A CBS News Survey in 2014  found that 3 in 4 Americans believe in an afterlife. A similar survey in the UK in 2009 found 1 in 2 believe in life after death and 70% believe in the existence of a human soul.

So pervasive is this belief that, amazingly, more Britons believe in life after death than believe in God! This belief in life-after-death is so fundamental to how humans see the world that a 2013 Pew Poll of Americans  found that 13% of athiests also believed in an afterlife!

Luigi Schiavonetti’s 1808 engraving of a soul leaving a body. (Credit: National Gallery of Victoria, Melbourne)

Of course, many will argue that once you are gone you are gone, but in that twilight moment in the minutes and seconds before death, people have been revived through heroic medical interventions and some but not all declare they have experienced ‘something’ absolutely remarkable.

Called Near Death Experiences, entire shelves of books have been written on this subject over the decades since the ground-breaking work of Ceila Green in 1968 and then popularized in 1975 by psychiatrist Raymond Moody. Extensive eye-witness accounts were recorded, classified and sorted into a small number of apparently archetypical scenarios such as tunnels of pure light; out of body experiences; meeting loved ones; indescribable love. According to a Gallup Poll about 3% of Americans claim to have had them.  There were early attempts by Duncan MacDougall in 1901 at detecting the exit of the soul from the body by carefully weighing the patient, but all failed, and were immediately explained by denying that the soul had any weight at all.

Scientists have largely refused to wade into this area of inquiry because, like many other human beliefs, there is enormous public resistance to scientists meddling in such cherished and highly personal ideas shared by virtually all humans, even some athiests! In a classic case of what psychologists call confirmation bias, there is nothing that science can say about this matter that would be trusted unless it lines up exactly to confirm what we have all made up our minds about, literally for millennia. That said, I myself, must tread very carefully as I write this blog because, frankly, those of you reading it have also made up your mind about the subject and I do not want to slap you in the face by disrespecting your fundamental core beliefs, which will always trump anything a scientist can tell you. Even my simple uttering of this disclaimer will be interpreted as me being a condescending scientist…or worse!

But I cannot help myself! I have been curious about this subject all my life, and any new insights I come across in my readings are like candy to my brain. So here goes!

NDEs are not a feature of any other organ than the brain because they involve visual perceptions, bodily sensations, and the knitting together of a story that is later told by the ‘traveler’. All of these are brain functions, so it is no wonder that those who study the clinical aspects of NDEs begin with what the brain is doing. Amazingly, you do not even have to be clinically ‘near death’ to experience them. All that is required is a deep conviction that you ARE dying to trigger them.

What could be a more compelling and simple idea than putting a dying person in a functional magnetic resonance imager (fMRI) or strapping an EEG net to their heads, and literally watching what the brain is doing during one of these events? Well, it would be a heinous experiment and an unwelcomed intrusion on a patient’s privacy, but nevertheless these things do happen accidentally. Cardiac patients who are more likely to die suddenly and be recovered are often monitored for other reasons prior to their NDE, and there are many other indirect ways to snoop on the brain to see what happens too.

We have already learned from fMRI studies that there is a specific brain region that allows you to have a sense of where your body is located in space. In an earlier blog I discussed how removing the stimulation of this normally very active region causes meditators to have the sensation of being ‘at-one’ with the universe. This state can also be reproduced at will through chemical manipulation. The region, when stimulated with an electrode, or during temporal lobe epilepsy, also produces the aura sensation that your Self is no longer anchored to your body in space during so-called Out-of-Body (OBE) events. So, an essential element of your body sense during an NDE can be traced to one specific brain region and whether it’s activity is stimulated or depressed. This region wins both ways because when its electrical activity is gone, you have one ‘cosmic’ sensation of leaving your body, and when it is over-stimulated you have the OBE sensation. As we know, death is the ultimate event that lowers brain activity, or temporarily elevates it in other places as blood flow catastrophically changes. We all have the same brains, so the real question is, why is it that EVERYONE doesn’t have a NDE?

It all seems to depend on how close you get to the precipice of never returning from the journey, and it is the closeness of your brain to this physiological edge that seems to trigger the events leading to this NDE experience. But we do not know for certain.

A 2011 Scientific American article summarized some of these elements announced by brain researchers Dean Mobbs and Caroline Watt.

OBE experiences can be artificially triggered by stimulating the right temporoparietal junction in the brain. Patients with Cotard or “walking corpse” syndrome believe they are dead. This is a condition caused by trauma to the parietal cortex and the prefrontal cortex. Parkinson’s disease patients have reported visions of ghosts. This condition involves abnormal functioning of dopamine, a neurotransmitter that can sometimes but not all the time evoke hallucinations. The common experience of reliving moments from one’s life can be tied to a neural circuit involving the locus coeruleus, which releases noradrenaline during stress and trauma. The locus coeruleus (shown below) is connected to brain regions that are involved with emotion and memory, such as the amygdala and hypothalamus. Finally, a number of medicinal and recreational drugs can mirror the euphoria often felt during NDEs, such as the anesthetic ketamine, which can trigger out-of-body experiences and hallucinations. These discussions of the neural basis for many of the separate elements to NBEs are now part of the official medical explanation in places such as the one found in Tim Newman’s 2016 article in Medical News Today.

Norepinephrine system (Credit: Patricia Brown, University of Cincinnati)

Beware, however, of other articles like the one in The Atlantic called ‘The Science of Near Death Experiences’. This 2015 popularization, written in the typical breezy style of newspaper reporters, also purported to summarize what we know about this condition. Sadly, the reporter spent most of the article interviewing those who experienced it and hardly any column space on actual scientific research. It was a typical ‘puff piece’ that offered nothing more than speculation and very self-serving and bias-affirming pseudoscience, along-side free plugs for many recent, lurid, books and movies about first-person accounts.

The bottom line is that NDEs are by no means common to people who think they are dying, and their incidence crosses many religious boundaries. They remain enormously powerful events that actually change the lives and even personalities of the survivors, and so they are not merely will-o-the-whisp hallucinations. We do know that their detailed descriptions follow specific cultural expectations for what the afterlife is like: a New Guinee tribesman will not describe the event the same way as a southern Evangelical.

We are only beginning to understand how our brains synthesize what we experience into the on-going story that is our personal reality, but we know from the evidence of numerous brain pathologies that this is a highly plastic process in which imagination and emotion blend with hard facts in a sometimes inseparable tapestry. Our senses are objectively known to be fallible in countless ways if left unattended, and how we interpret what we experiences is as much a logical process as a process of out-right confabulation. Like many other events in our lives, NDEs are seen as one experience that our brains work very hard to incorporate into a plausible story of our world. It is this story that through millions of years of evolution allows us to function as an integrated Self,  avoid being injured or eaten, and  propagate our genes to the next generation.

Isn’t it amazing that, against this backdrop of cognitive dissonance, sensory bias, emotional chaos, and evolutionary hard-wiring  we can create a workable story of who we are in the first place?

Check back here on Monday February 28 for my next blog!

2016: A Year Beyond Reason

Psychologists define Cognitive Dissonance as the anxiety (dissonance) felt when people are confronted with information that is inconsistent with their beliefs. If the dissonance is not reduced by changing one’s belief, the dissonance can result in restoring consonance through misperception, rejection or refutation of the information, seeking support from others who share the beliefs, and attempting to persuade others.

In other words, humans can often carry two completely conflicting ideas in their consciousness at the same time. This is a stressful condition, and to alleviate it, we resort to rejecting contrary information, or try to persuade others of the consistency of our viewpoint.

We saw a lot of this condition in 2016!

This is not some liberal psychological plot to disparage the far-right of our political spectrum, but an objective fact of how our brains work. Researchers using functional Magnetic Resonance Imaging (fMRI) have found that cognitive dissonance activated specific brain regions called the dorsal anterior cingulate cortex and the anterior insular cortex. They also found that the more the anterior cingulate cortex signaled a conflict, the more dissonance a person experiences. During decision-making processes where the participant is trying to reduce dissonance, activity increased in the right-inferior frontal gyrus, medial fronto-parietal region and ventral striatum, while activity decreased in the anterior insula. Researchers concluded that rationalization activity, where you are trying to reduce the stress caused by cognitive dissonance, may take place quickly (within seconds) without conscious deliberation, and that the brain may engage emotional responses in the decision-making process.

The problem is that CD leads to other kinds of things that are sometimes harder to discern objectively. Confirmation bias refers to how people read or access information that affirms their already established opinions, rather than referencing material that contradicts them. This bias is particularly apparent when someone is faced with deeply held beliefs, i.e., when a person has ‘high commitment’ to their attitudes. People display confirmation bias when they gather or remember information selectively, or when they interpret it in a biased way. The effect is stronger for emotionally charged issues and for deeply entrenched beliefs. People also tend to interpret ambiguous evidence as supporting their existing position.

We saw a lot of that, too, in 2016.

An interesting study of biased interpretation occurred during the 2004 U.S. presidential election and involved participants who reported having strong feelings about the candidates. They were shown apparently contradictory pairs of statements, either from George W. Bush, John Kerry or a politically neutral public figure. They were also given further statements that made the apparent contradiction seem reasonable. From these three pieces of information, they had to decide whether or not each individual’s statements were inconsistent. There were strong differences in these evaluations, with participants much more likely to interpret statements from the candidate they opposed as contradictory. The participants made their judgments while in an fMRI scanner that monitored their brain activity. As participants evaluated contradictory statements by their favored candidate, emotional centers of their brains were aroused. This did not happen with the statements by the other figures. The experimenters inferred that the different responses to the statements were not due to passive reasoning errors. Instead, the participants were actively reducing the cognitive dissonance induced by reading about their favored candidate’s irrational or hypocritical behavior.

The bottom line is that, thanks to evolution, we have been blessed with a brain that suffers from many different kinds of reasoning pathologies. These may have had survival value in the remote past for making quick judgments in our social groups, or mistaking a distant shadow for a tiger, but now they are liabilities in our far more rational world of science and technology. Scientists spend a lot of time trying to weed out CD and CB from their analyses, and the result is that for 400 years of observing Nature as dispassionately as we can, we have created a marvelously accurate model of our world.

Sadly, CD and CB have at the same time been used to manipulate voters and consumers, with amazing negative consequences. The dissonance is that we fully realize that we are being manipulated by biased information, yet we seem powerless to resist its sirean call. In the current election, voters supporting Trump steadfastly refused to use his frequent and documented lying as grounds for not trusting him.

Some of the worst cases of CD and CB occurred during the 2016 election, and psychologists will be writing papers about it for decades. It all comes down to how people were convinced not to vote in their own self-interest.

How is it that voters whos only insurance came from the ACA voted for a GOP ticket that promised to repeal it? How is it that so many students voted against the democratic candidate who promised to eliminate tuition? How is it that so many poor people voted for an aledged multi-billionaire whose lavish gold-plated lifestyle was the antithesis of a poor person’s lifestyle?  How is it that Clinton and Trump were placed on the same ‘untrustworthy’ pedestal, when evidence showed that Clinton played by the rules and released her income tax statements, while Trump ran a Trump University con job and withheld his?  How is it that Trump’s steadfast attacks against our own intelligence service to defend Putin and Assange are not met with more rejection and patriotic contempt by his followers?

In the end, Trump voters and Red States will be paying a disproportionate economic penalty for letting CD and CB get the better of their reasoning. But because we are all in this together for the next four years, the rest of us will also feel some of this dissonance as well as collateral damage as voters in the red states ask voters in the blue states to bail them out.

Check back here on Saturday, January 14 for the next installment!

Oops…One more thing!

After writing thirteen essays about space, I completely forgot to wrap up the whole discussion with some thoughts about the Big Picture! If you follow the links in this essay you will come to the essay where I explained the idea in more detail!

Why did I start these essays with so much talk about brain research? Well, it is the brain, after all, that tries to create ideas about what you are seeing based on what the senses are telling it. The crazy thing is that what the brain does with sensory information is pretty bizarre when you follow the stimuli all the way to consciousness. In fact, when you look at all the synaptic connections in the brain, only a small number have anything to do with sensory inputs. It’s as though you could literally pluck the brain out of the body and it would hardly realize it needed sensory information to keep it happy. It spends most of its time ‘taking’ to itself.

The whole idea of space really seems to be a means of representing the world to the brain to help it sort out the rules it needs to survive and reproduce. The most important rule is that of cause-and-effect or ‘If A happens then B will follow’. This also forms the hardcore basis of logic and mathematical reasoning!
But scientifically, we know that space and time are not just some illusion because objectively they seem to be the very hard currency through which the universe represents sensory stimuli to us. How we place ourselves in space and time is an interesting issue in itself. We can use our logic and observations to work out the many rules that the universe runs by that involve the free parameters of time and space. But when we take a deep dive into how our brains work and interfaces with the world outside our synapses, we come across something amazing.

The brain needs to keep track of what is inside the body, called the Self, and what is outside the body. If it can’t do this infallibly, it cannot keep track of what factors are controlling its survival, and what factors are solely related to its internal world of thoughts, feelings, and imaginary scenarios. This cannot be just a feature of human brains, but has to also be something that many other creatures also have at some rudimentary level so that they too can function in the external world with its many hazards. In our case, this brain feature is present as an actual physical area in the cerebral cortex. When it is active and stimulated, we have a clear and distinct perception of our body and its relation to space. We can use this to control our muscles, orient ourselves properly in space, walk and perform many other skills that require a keen perception of this outside world. Amazingly, when you remove the activity in this area through drugs or meditation, you can no longer locate yourself in space and this leads to the feeling that your body is ‘one’ with the world, your Self has vanished, and in other cases you experience the complete dislocation of the Self from the body, which you experience as Out of Body travel.

What does this have to do with space in the real world? Well, over millions of years of evolution, we have made up many rules about space and how to operate within it, but then Einstein gave us relativity, and this showed that space and time are much more plastic than any of the rules we internalized over the millennia. But it is the rules and concepts of relativity that make up our external world, not the approximate ‘common sense’ ideas we all carry around with us. Our internal rules about space and time were never designed to give us an accurate internal portrayal of moving near the speed of light, or functioning in regions of the outside world close to large masses that distort space.

But now that we have a scientific way of coming up with even more rules about space and time, we discover that our own logical reasoning wants to paint an even larger picture of what is going on and is happy to do so without bothering too much with actual (sensory) data. We have developed for other reasons a sense of artistry, beauty and aesthetics that, when applied to mathematics and physics, has taken us into the realm of unifying our rules about the outside world so that there are fewer and fewer of them. This passion for simplification and unification has led to many discoveries about the outside world that, miraculously, can be verified to be actual objective facts of this world.

Along this road to simplifying physics, even the foundations of space and time become players in the scenery rather than aloof partners on a stage. This is what we are struggling with today in physics. If you make space and time players in the play, the stage itself vanishes and has to somehow be re-created through the actions of the actors themselves .THAT is what quantum gravity hopes to do, whether you call the mathematics Loop Quantum Gravity or String Theory. This also leads to one of the most challenging concepts in all of physics…and philosophy.

What are we to make of the ingredients that come together to create our sense of space and time in the first place? Are these ingredients, themselves, beyond space and time, just as the parts of a chain mail vest are vastly different than the vest that they create through their linkages? And what is the arena in which these parts connect together to create space and time?

These questions are the ones I have spent my entire adult life trying to comprehend and share with non-scientists, and they lead straight into the arms of the concept of emergent structures: The idea that elements of nature come together in ways that create new objects that have no resemblance to the ingredients, such as evolution emerging from chemistry, or mind emerging from elementary synaptic discharges. Apparently, time and space may emerge from ingredients still more primitive, that may have nothing to do with either time or space!

You have to admit, these ideas certainly make for interesting stories at the campfire!

Check back here on Monday, December 26 for the start of a new series of blogs on diverse topics!

Is Space Real?

I take a walk to the store and can’t help but feel I am moving through something that is more than the atmosphere that rushes by my face as I go. The air itself is contained within the boundaries of the space through which I pass. If I were an astronaut in the vacuum of outer space, I would still have the sense that my motion was through a pre-existing, empty framework of 3-dimensions. Even if I were blind and confined to a wheelchair, I could still have the impression through muscular exertion that I was moving through space to get from my kitchen to my living room ‘over there’. But what is space as a physical thing? Of all the phenomena, forces and particles we study, each is something concrete though generally invisible: a field; a wave; a particle. But space, itself, seems to be none of these. WTF!

Spider web covered with dew drops

Way back in the early 1700s, Sir Isaac Newton proposed that space was an ineffable, eternal framework through which matter passed. It had an absolute and immutable nature. Its geometry pre-existed the matter that occupied it and was not the least bit affected by matter. A clever set of experiments in the 20th century finally demonstrated rather conclusively that there is no pre-existing Newtonian space or geometry ‘beneath’ our physical world. There is no absolute framework of coordinates within which our world is embedded. What had happened was that Albert Einstein developed a new way of thinking about space that essentially denied its existence!

Albert Einstein’s relativity revolution completely overturned our technical understanding of space and showed that the entire concept of dimensional space was something of a myth. In his famous quote he stressed that We entirely shun the vague word ‘space’ of which we must honestly acknowledge we cannot form the slightest conception. In the relativistic world we live in, space has no independent existence. “…[prior-geometry] is built on the a priori, Euclidean [space], the belief in which amounts to something like a superstition“. So what could possibly be a better way of thinking about space than the enormously compelling idea that each of us carries around in our brains, that space is some kind of stage upon which we move?

To understand what Einstein was getting at, you have to completely do away with the idea that space ‘is there’ and we move upon it or through it. Instead, relativity is all about the geometry created by the histories (worldlines) of particles as they move through time. The only real ‘thing’ is the collection of events along each particle’s history. If enough particles are involved, the histories are so numerous they seem like a continuous space. But it is the properties of the events along each history that determine the over-all geometry of the whole shebang and the property we call ‘dimension’, not the other way around.

This figure is an example where the wires (analogous to worldlines) are defining the shape and contours of a dimensional shape. There is nothing about the background (black) space that determines how they bend and curve. In fact, with a bit of mathematics you could specify everything you need to know about the surface of this shape and from the mathematics tell what the shape is, and how many dimensions are required to specify it!

Princeton University physicist Robert Dicke expressed it this way, “The collision between two particles can be used as a definition of a point in [space]…If particles were present in large numbers…collisions could be so numerous as to define an almost continuous trajectory…The empty background of space, of which ones knowledge is only subjective, imposes no dynamical conditions on matter.”

What this means is that so long as a point in space is not occupied by some physical event such as the interaction point of a photon and an electron, it has no effect on a physical process ( a worldline) and is not even observable. It is a mathematical ‘ghost’ that has no effect on matter at all. The interstitial space between the events is simply not there so far as the physical world based upon worldlines is concerned. It is not detectable even by the most sophisticated technology, or any inventions to come. It does not even supply something as basic as the ‘dimension’ for the physical world!

We should also be mindful of another comment by Einstein that “…time and space are modes by which we think and not conditions in which we live“. They are free creations of the human mind, to use one of Einstein’s own expressions. By the way, the 18th century philosopher Immanuel Kant also called the idea of ‘space’ an example of a priori knowledge that we are born with to sort out the world, but it is not necessarily a real aspect of the world outside our senses.

Like a spider web, individual and numerous events along a worldline define the worldline’s shape, yet like the spider web, this web can be thought of as embedded in a larger domain of mathematically-possible events that could represent physical events…but don’t. The distinction between these two kinds of points is what Einstein’s revolutionary idea of relativity provided physicists, and is the mainstay of all successful physical theories since the 1920s. Without it, your GPS-enabled cell phones would not work!

So what are these events? Simply put, according to Physicist Lee Smolin, they are exchanges of information, which are also the interaction points between one particle’s worldline and another particle’s world line. If you think at the atomic level, each time a particle of light interacts with (collides or is emitted by) an electron it generates an event. These events are so numerous the electron’s worldline looks like a continuous line with no gaps between the events. So the shape of one worldline, what we call its history, is a product of innumerable interactions over time with the worldlines of all other objects (photons etc) to which it can be in cause-and-effect contact.

Even though this new idea of space being a myth has gained enormous validity among physicists over the last century, and I can easily speak the language of relativity to describe it, personally, my mind has a hard time really understanding it all. I also use the mathematical theory of quantum mechanics to make phenomenally accurate predictions, but no Physicist really understands why it works, or what it really means.

Next time I want to examine how the history of a particle is more important than the concept of space in Einstein’s relativity, and how this explains the seeming rigidity of the world you perceive and operate within.

Check back here on Thursday, December 15 for the next installment!