The Language of Mathematics

I took a calculus class when I was 18 years old.  It was hard.  I remember studying what I was taught on Monday then being scandalized that something new was being taught on Tuesday before I was really sure I knew how to do Monday’s problems.  I finally figured out how to work Monday’s problems on Friday, but that meant I didn’t catch any of Tuesday – Thursday’s lessons.  Then came the Friday exam.  I got 25% correct.  Monday’s lesson.  This was what the whole semester was like for me.  I had to take Calculus again.

The second time through, I was able to keep up a little better (after all, I knew all the Monday lessons).  But what I remember the most about that course, and what flashes before my eyes every time I hear the word “calculus” after 30 years … is what happened one evening while doing homework in a little cold dorm room at midnight.

The homework that night was one question.  I was already 3 pages into solving that one question.  It had to do with a huge cylinder of water.  Some water was flowing in, but the cylinder had a leak that got bigger as more and more water leaked out of it.  The question was about the volume of water left in the cylinder after a specific period of time.

My pages of work looked something like the illustration above.  At the end was an answer to three decimal places.  Anyone who has done this work knows you are only half done at this point.  I turned back to the beginning and started going over my work to check all the steps and all the math.

As I was doing this, something magical happened.  My brain stopped looking at little numbers and symbols and started to read the math.  The comprehension had nothing to do with the squiggles on the page…and everything to do with it.  My brain was not thinking in words.  It was thinking in numbers and the concepts behind the formulae.  I grokked calculus fully.  *angelic choir sound*

The best analogy will be trying to remember being a child and sounding out each letter of the alphabet in order to read your first word.  Can you remember that transition from a phonetic reading to sight reading?

I was deep deep into that cylinder and that flowing water when my roommate came in and broke the spell.  I was never able to go back there again.  I know that scientists and mathematicians do this every day.  It is not special to them.  It was to me, though.  Very special.  A whole world opened up to me that night.  I got a glimpse of magic that came and went.

I think this happens to artists and musicians as well.  I have found myself lost in that world when painting, when listening to Wagner and Beethoven, and when writing.  There is a creative part of the brain that takes your consciousness and puts it in a timeless place where language only gets in the way of meaning.

Plato called this place the world of forms.  I have been there.

 

Read Full Post »

Jung was an Alchemist

Carl Jung was an important 20th century alchemist, but he did not spend years in a tower with beakers and flasks.  The transformation he searched for was within himself.  Psychology and Alchemy (Princeton University Press 1980) has been widely available, though not so widely accessible,  and  in the 21st century his notebook The Red Book was published (W.W. Norton 2009).

The Red Book is like a journal, but is much more.  He illustrated his dreams and visions.  This drawing of a Mandala reminds me of some of the images in the Voynich Manuscript.  Here is an image from the Red Book and an image from the German alchemy book Die Gab Gottes 1598

Jung said,  “The real mystery does not behave mysteriously or secretively; it speaks a secret language, it adumbrates itself by a variety of images which all indicate its true nature. I am not speaking of a secret personally guarded by someone, with a content known to its possessor, but of a mystery, a matter or circumstance which is “secret,” i.e., known only through vague hints but essentially unknown. The real nature of matter was unknown to the alchemist: he knew it only in hints. In seeking to explore it he projected the unconscious into the darkness of matter in order to illuminate it. In order to explain the mystery of matter he projected yet another mystery – his own psychic background -into what was to be explained.”  —Psychology and Alchemy (Part 3 Chapter 2).

In the Hermetica of Elysium I tried to show both aspects of the medieval alchemists.  I wanted to describe how the people who were focused on earthly treasure and power sought to gain an advantage over their competitors using any means possible…including maintaining a resident alchemist who was supposed to be working on turning base metals to gold, while at the same time he was really working on discoveries of the mind.  This is a fertile field for adventure and excitement…how could a novelist resist?

Jung spent years in research, and his collected works would take years to study.  His ideas about what it means to be a human being have tremendously influenced the field of psychology.  His Synchronicity theories tie in with String Theory and link psychology with theoretical physics in ways that make both psychologists and physicists uncomfortable.

Remember, magic is just science we don’t understand.

 

 

 

 

 

 

Read Full Post »

Newton was an alchemist

Isaac Newton is a man who should need no introduction.  He invented Calculus and discovered the Laws of Motion etc etc.  Kids remember the story of the apple falling from the tree…hopefully kids remember.

Anyway, Newton is the most esteemed scientist, up there in the pantheon with Einstein. (Kids remember him with the crazy white hair)  Does it bother the Materialists that he studied alchemy HARD for many years?  Nope.  They say he was just curious and abandoned the study after he realized it was all BS.  LOL.  I notice the same hard-core scientists say nothing critical about Newton’s fervent religious beliefs.  They can “forgive” him for that, but not for the alchemy.

Let us keep both the baby AND the bathwater.  We may find something valuable there in the muddy midst.

Newton was convinced that as much as he knew about the “nuts and bolts” mechanics of the world, the orchestration of all matter must be presided over by an intelligence.  His alchemy experiments only suggest that he was looking for the link between matter and god.

Modern physicists find themselves in a similar bind.  Most have rejected the idea that there is a god who set the clock ticking in the first place, but the mysteries of subatomic particles continue to plague them.  String Theory is an exciting development over the last 30 years or so that attempts to explain some of the weirdness that goes on at the nano-level of reality.

I read Brian Greene’s “The Elegant Universe” some years back, and delighted in how close physics and “magic” had become, especially if you use the definition that magic is science you don’t understand.  Does your iPhone work like magic?

I watched Greene’s beautiful Nova presentation “Fabric of the Cosmos” recently and waited for someone to say the word, “consciousness”.  Nope.

It is not Newton’s god, but consciousness that is lurking in the bathwater.

The ancient philospohers knew that consciousness plays a part in all manifestations of matter in the universe.  Some physicists did too:  David Bohm , who consulted with Indian guru J. Krishnamurti to see how much physics and mysticism had in common.  Dr. Fred Alan Wolf has quite a few things to say about this as well, and he will make you laugh.

Our new physicists are modern alchemists whether they want to believe it or not.

Read more about how mind and matter connect.

Read Full Post »

Why other people care what you think

This is an example of the fractal Mandelbrot Set.  Giving the image a name isn’t really important, but some folks might see this and think it is an inkblot, similar to what Dr Rorschach flashed at patients to get inside their minds.  It is, and it isn’t.     If you took a magnifying glass and looked at one of the edges you would find a smaller copy of the image.  You could do that forever.

An inkblot test might get 99 people to “see” a butterfly, but the 100th might “see” a pig.  Uhm.  OK.  Is that person wrong?  Crazy?  Who is to say?  Experts?  Psychologists?  Psychiatrists?  a Judge?  In a complex society like ours the answer is ‘yes’.  Someone has to make that judgment.  But let’s step away from the social aspect and look at the blot from an existential aspect.  The pig-seeing person differs from the norm, but that does not make him wrong.

How about the wild rhetoric flying about America today?  You would think there was only one right way to run a country and if you do not agree, you are in league with Satan.  Why do people say, “My way or the Highway” or descend to ad hominem attacks if you do not agree?

So WHY do people get so hot when others disagree with them?  It is because they really really believe that there is only one way or one thought or one true and correct answer.   If you disagree you imply that they are wrong, and that feels like an attack on their fragile egos.

The most vociferous folks will battle to the death to MAKE you see it their way.   But why do they care?

(Read more in a related study here)

The first step in being able to navigate beyond physical reality is to understand how fluid physical reality really is.  Your ego is important.  It is there to focus your consciousness in this particular physical reality.  If you did not have an ego, you would find it difficult to steer.  The ego is like a lens, or the rudder of a ship.  When YOU use it for your own purposes, you have smooth sailing.  When you allow your ego to stomp around reality uncontrolled, you will be in for heavy seas.

You accept that everyone sees the world through the lens of their own egos.  The clearer you grind that lens, the more you will see.  If it is curved or flawed or colored, then everything seen through it will be distorted.  It will seem REAL to you, however.  “What do you MEAN that tree is red?  Of course it is GREEN!”  But if you are looking through a red filter you are just as correct as your friend.  Touch the tree, then.  Does it FEEL red?  You see where I am going with this.  It is foolish to argue with anyone holding on firmly to beliefs they will not release.  You cannot use reason to convince someone something isn’t “true” when they didn’t use reason to place that idea in their minds in the first place.  Just let it go.  It has nothing to do with you.

(an aside:  I am not suggesting that folks should not be activists, merely that shouting at your friend is not the way to share ideas)

When you poke your head through the veil of physical reality, you toss that ego lens back to earth.  Its comforting images will no longer be there to guide you.  The Landmarks will be different.  For example.  You may drift through your living room.  There is your grandfather’s old recliner.  You “blink” and now it looks new, another “blink” and it is not quite the same color.  Now it has an extra cushion.  What is “there” is the idea of your grandfather’s recliner, not the chair you see when you are awake and walking around the physical room.  Plato went into some detail on this idea, so I suppose he traveled the ether himself.  If he participated in the Elysian Mysteries, I am sure he did.

Read Full Post »

Here, There and Everywhere

I hope that anyone who as ever lain on the ground at night and looked at the stars has felt that strange feeling…that wonder, that lifting of one’s mind from the mundane to the profound.  It is hard to really hold on to petty problems when confronted with the greater reality you see before you.  So much of the night sky remains mysterious, even to our modern high priests: the scientists.

The experience of looking at the stars is similar to what happens if you are lucky or skilled enough to find your consciousness outside of your body.  Once you have seen (and felt) the Universe from that perspective, you cannot un-know what you know.

Now what?  It is difficult to rationalize, frustrating to communicate and definitely not parlor conversation.  Even finding others who share a similar experience is NOT what you think.  For example:  You may have had a trip to Paris.  You have photos and memories and a plastic Eiffel Tower.  An acquaintance has also gone to Paris, but 30 years ago…and he stayed in all the most expensive hotels.  Similar, but very different.

Because reality is fluid, and changes with every thought and belief, even two people on the trip at the “same time” will experience a different place.  What may remain the same are certain “feeling tones” that connect the experience.

One of those concepts is the Abyss.  When it is experienced there is a similar feeling (according to the accounts of other people I have read).  What has been accomplished is that folks can get together and agree on a vocabulary!  The Abyss may have been experienced by countless people over the centuries, but each one will come back from their vacation with different photos.  The words they used to describe the experience are similar, yet necessarily different.

One feels acutely every atom, every particle, that makes up what they perceive as their body…then slowly each particle begins to move away from every other.  Sort of like each particle was a positive ion…there is this feeling that each particle MUST repel the others, causing the “body” to dissipate.  This is usually frightening, because we are focused in a physical reality that teaches us we cannot survive without a body.  But of course, the dissipation is not fatal.  Quite the opposite.  But it is a test.  Can you permit the dissolution and yet retain your identity?

I admit I failed this test the first time.  As each particle drifted away I kept saying, “Wait! come back!”.  It is funny in retrospect, but I wish I had been more curious.  Yes.  That is the correct word.  Not “brave” or “daring”, though there is a place for those qualities.  Curious.  The feeling that you want to know more.  And Trust.  I felt I had to hold my “body” together or I would disappear.

The Universe will keep testing you to see if you are ready for the next step on this journey.

Read Full Post »