Posts Tagged ‘numbers’

Axel’s Universe, And Some Thoughts On The Universe, Creation, Apples And Bits Of String

Wednesday, December 29th, 2010

Having re-thought the origin of species, I became ridiculously ambitious and decided to really go for it and started to tackle Life, The Universe and Everything…

I have come back to science after many years of ignoring it.  At the end of university, it just became something I could not wait to leave behind; it had become a rigid discipline that no longer held any joy.  However, I have continued to relish the heart of science – to wonder at the beauty of the wisteria as it flowers every year outside my back door and the snowdrops and daffodils as they poke out there noses from the hard ground in springtime.  These continue to give me a juvenile sense of frivolous delight and I wonder at the world.  Then on clear dark nights, I look into the heavens and see pinpricks of light and think about planets, stars and the universe and whether there is something out there and what am I actually looking at? 

Science is not just about data, calculations and formulae, but a delight in learning, in having those fleeting glimpses of understanding and the continued amazement in things – for example, while I understand the physics behind flight and density, I still shake my head in amazement when I see an aeroplane fly or a metal ship float on the high seas.  For me, science is not about answers, but about questions and more questions, then again about maybe just one more little question.  For me, there can never be an answer to everything nor the perfect universal equation, but only ever more whys, hows; forever to wonder.

So I have to apologise now for my thoughts as they contain no theories, no experiments, no maths, but are simply random musings, thought experiments, or perhaps even the ramblings of a madman.  Per my blog on evolution, I have written it in the personal form to distinguish it from real science, but perhaps some may find a kernel of reality in it.  These thoughts hold none of the discipline of true scientific thought and maybe are pure and simple nonsense that have been synthesised mistakenly in my mind from lingering memories of interesting and unusual pieces of science mixed in with some misread and misunderstood factoids.  Yet I have been puzzled by ideas of cosmology since my school years and have turned these over like precious stones ever since for over 30 years now.  Every so often, I pick up these gemstones delicately as they are important to me, turn them over, look at them again and put them down like curiosities.  They are like museum exhibits that you know are important but cannot fit them into any overall picture.  Well, I still cannot build them into any masterpiece that will explain the universe to me (or anyone else for that matter), but as they remain perplexing to me and seem to answer some niggles, I thought I would share them.

My journey begins with numbers and mathematics.  I have never been especially good at maths, but have always liked playing with numbers.  However, I struggled with higher maths, which has held back a lifelong fascination with physics, especially quantum physics and cosmology, as my mathematical skills never matched my inquisitiveness.

Numbers are symbols, a human artificial construct.  They make life easier.  So for example, we learn from early age what 0, 1, 2, 3 and so on are and perhaps marvel at a series like 1, 2, 4, 8, 16 etc. However, they are not necessarily complete and do not explain the world as it is, but rather serve to simplify the world around us into an easy and recognisable, universal symbolic language full of neat patterns and models.  But what if numbers are just what I have said pure artifice? A model, a methodology, that acts as the powerful lens through which we try and understand the universe, but nevertheless an artificial set of rules that is simple, communicable and versatile, yet still a human built, and a rather too convenient, model.  The teachers’ answer was always numbers are fundamental and pure, so just accept and get on with it.

Let me explain.  Imagine a chopping board.  Now looking at the chopping board, how many apples are there? None.  Now, place an apple on the board; how many apples are there? One.  Next, add another to give two, and another to give three.  Let us then assume that the universal apple has a mass of 100g, but we had here one apple of 95g, another of 110g and the final one at 103g; now how many apples are there on the board – 3 or 3.08 apples?  Next, take away the apples and ask yourself the question again – how many apples are there?  Is the answer now zero, three or infinity (a number equating to all the apples in the universe that we cannot necessarily see but know to exist in the past, present and future).  Well, it depends on how you look at the question, i.e. is it what you can see on the board, or in your mental kitchen, or the universe throughout time?  That is the crux of the scientific method – setting a framework to test a theory and collecting data within that experimental framework, but what if everything that is interesting was just off screen – like dark matter?  Finally, return the apples to the board and chop one in half and another into quarters and leave one alone; are there one, three or infinity apples?  So numbers simplify how we look at the apples, but they do not give us all the answers, and I really do not know the answer to that final question.  And where would we be as humans before we saw the first apples; would any apples have then existed?

Luckily, life is much simpler and we can make assumptions, since we can live very happily with the idea of there being as many apples as we see at any time within our own personal space, and who actually cares anyway whether there are more or less apples in existence.  Finally, those apples tasted really sweet as I picked them from our garden and, in my opinion, are far better than pears unless poached in red wine or saffron.  So we can make assumptions about life and get by really well without needing to know how many apples, pears or oranges there are now, have been or will be.

But perhaps our numbers are not always correct and as natural as we think them, as there are universal constants like π at 3.1416 and e at 2.7183, which would have been much simpler had they been round numbers that were easier to manipulate.  Also, numbers and constants change – feet and inches morph into metres and centimetres, while grams can be ounces or even cups and these change depending on which side of the Atlantic you live.  Even how we do maths changes and it was not until people started using base 10 that numbers became simpler to manipulate, resulting in a blossoming in theoretical maths.  Even without the ideas of relativity, time changes depending on where you live and what watch you are wearing and I, who do not wear a watch, have my own personal timescale which is particularly random and dependent on a car clock that is out of time by 22 minutes and widening!  So what is Axel’s time?

Then there are imaginary numbers that even characters in Alice in Wonderland would wonder at.  Yet √-1, complex numbers and other imaginary numbers are very real as they form the basis of semiconductors, digital communications and fluid dynamics inter alia, yet we cannot comprehend them and just must dream them.  So not all maths is touchable and pure.

So where does that leave us.  It leaves me perplexed and vexed.

Next, you have the theories of physics, the absolutes.  At school, I learnt of Newtonian mechanics and gravity, of apples that fall to the ground.  However, we then moved on to Einstein, only to discover that gravity does not exist, rather that mass distorts space-time and this deformation results in something we perceive as gravity.  However, we continue to talk and think of gravity, as well as to experience it day in-day out with windfall apples still falling to the ground and no visible sign of space-time becoming deformed in my back garden.  Einstein’s concepts of general relativity enable us to predict everything from big bang to black holes, as well as the expansion of the universe.  But Einstein also predicted dark energy that is pushing space apart, something which no-one has found, and nor does general relativity square up with gravity.  Have we, therefore, found the limit of Einstein’s laws of physics in much the same way that Newtonian physics ran out of gas and (going back a few paragraphs) is c really a constant at 299,792,458 m s-1 or can it change and flex in different parts of the universe or at different times in the development of our universe, and would it be the same in another universe or is it unique to where we exist?

For me, physics and my lack of maths throws up even more questions, but perhaps it can also free me up to think outside of a number system and speculate without the shackles of the scientific straightjacket and perhaps, to disagree with Stephen Hawking, philosophy is not quite dead and people outside of the scientific community can still be allowed to think: How did the universe start? Will the universe end? Is there a way to unify all basic theories of physics? Is light a wave or a particle? What is dark matter?

So I wander further in my mindscape and consider whether our numerical system is flawed.  Sometimes I think that perhaps numbers can be stretched and are flexible so perhaps you could have an imaginary thin 1, a fatter 1 and a high pitched or low pitched 1 and the same with 2, 3 and so on.  That would really cause issues for mathematicians and physicists, but would be a dream for accountants and investment bankers who would jump up and down with joy to know that the universal fudge factor was a real mathematical truth.  Perhaps that answers the question with my apples; each apple is a unit of 1 but that unit can be stretched and contracted, so it actually forms a bell curve around a mean and not just from a statistical perspective but in real universal laws?  How much havoc would that cause if numbers were not natural, unbending and stable but stretchy and creative rather than pure, simple and immutable, but imagine the impact that could have on almost all scientific theory, where the idea of standard deviation was not an error factor but simply a measure of stretchiness?  Perhaps, complex numbers hint that the universe is really a much more difficult question than we have the willingness to believe.

More importantly, I also think about nothing and I mean really nothing. We are taught that 0=0, 1=1, 2=2, 3=3, but what if this could be turned on its head?  Let us think about zero or nothing; these were concepts introduced into maths in ancient India and the Mayan kingdom, but are they real or simply an accounting tool and a mathematical convenience?  Let us think further about the two key numbers, zero and one.  Imagine that 0=1 rather than 0=0 and 1=1.  Why are these the two key numbers? Well, zero is where something does not exist and one encompasses all of something, e.g. every apple in the world (or universe), then all maths does is divide up the units between zero and one and call these numbers.

You can visualise this idea in a thought experiment: take a piece of string: at one end is 0 and the other is 1 and all the way between 0 and 1 are varying degrees of probability or improbability or points between 0 and 1 and so your number scale; now take the piece of string and curve it around so that you have a perfect circle with the 0 touching the 1; imagine they reform into a circle so that on one side of the join you have 0+∞ and on the other 1-∞ (where ∞ is an infinitesimally small amount); what is the number at the point where they touch? For me, I cannot get it out of my head that 0 and 1 must meld together, i.e. 0=1.  So there you have it, the start of the universe without complex maths, just a piece of string and some imagination.  Now this seems nonsense, but no more ridiculous than the √-1.

What would be the reality or consequence of this?  For most of us, not much in the same way as in our apple experiment when we have zero apples; we just buy some more or pick some from the tree, or simply do not care.  But for reality and the universe, perhaps it can answer some questions.  And going back to my thought experiment with the chopping board, you did not have no apples, but really just no visible apples within your observation matrix and apples still exist, i.e. it was not a case of zero, nothing, nada, but just not any in that place.  Therefore, zero, i.e. zero apples, is no more than an accounting convention, i.e. not any apples within my kitchen or personal inventory, rather than there being no apples at all. 

Whereas, at the beginning of the universe, there was nothing and I mean absolutely nothing.  As there was really absolutely completely nothing, you would be at that cusp point and immediately numbers would collapse and zero would really equal one, so at that point of absolute nothingness everything is created.  Think of it reverse, hold out your arms and collect all the mass, energy and dark energy and matter in the universe and bring it into the palm of your hand; now roll it into a ball and squeeze it tight to the size of a table tennis ball – it is a tad heavy but you can do it; now squash it even more down to the size of a water molecule, then an atom – it is really heavy now and quite unpredictable but squeeze even harder until you are at 0+∞mm in diameter.  What happens if you squish it down even more until it is nothing?  Where has all that mass and energy gone?  Are you a magician and it has gone forever or as I have predicted at absolute zero or nothingness everything is created, all matter, all energy, absolutely everything and it blossoms out as a big bang.  So there is no need for any external creators, no need for any complex higher physics, just simple number collapse.  I know that for superinflation to occur you might need a big bounce rather than a big bang, but I am talking about the ur-creation, the original start.  So there is no need for external creators, no external god question of who created god, just a simple fact, nothing simply does not exist, so immediately there must be everything.

Another question, then – what happens in the cosmic web in areas of empty space?  Are there parts of this emptiness that are actually voids and areas or pinpricks of absolute nothingness – if so, then whole new universes could bud out in these regions creating multi-verses.  Or perhaps areas of emptiness oscillate between 0 (pure absolute nothingness) and 1 (existence of everything), creating points that perhaps generate fleeting, massive amounts or smaller quantities of energy and matter (new universes ) that can push apart our universe like wedges driven into rock, but perhaps most of these new universes collapse under their own mass right back down to zero giving the appearance of a void again; effectively rocking from 0 to 1 at the number cusp point, yet still seeming to be nothingness from our position as an external viewer, because we can never see a new universe from where we are watching, nor can we see nearly nothing because we are not wired that way.

To find dark energy, therefore, maybe we should look for nothing rather than something?  I do not believe that nothing exists, so when I look up into the night sky I do not perceive empty voids but everything must be there, somewhere out of sight and out of mind.  Be a child again and think about the air – it is empty and clear, then later you learn it is full of invisible gases as well as bacteria and viruses and dust motes, the stuff of life; or remember the classic experiment with smoke to show Brownian motion where you must infer that there are invisible molecules buffeting the smoke around.  There is something in the void space and perhaps we are just trying too hard to fit it into our own paradigm of the universe and should just suspend our beliefs and dream again – perhaps it is other universes budding out of pinpricks of nothingness, which push out other universes in some never ending fractal pattern?

In fact, the empty space in space is not completely empty and stuff does just appear as if from no-where.  These are vacuum fluctuations where particles and fields appear spontaneously to be created out of nothing.  Hence, there really is no nothingness out there, simply spaces where there is not very much, but where energy and matter can spontaneously appear.  Perhaps that is what the cosmological constant really is – a background count of somethingness, a mysterious creative energy, that stops there being nothing, because nothing creates everything and you cannot have that happening too often, can we now; for my piece of string, it is as if the cusp point, the creation point, is constantly switching from 0=0 to 0=1 to 1=1 and back to 0=0, but instead of netting out to an answer of 0, there is always a remnant of energy that cannot be lost leaving the cosmological constant, effectively the background energy of failed creation events.  Now that means that even though everything was created in the single creation event at T=0 more energy is constantly being created than was possible ab initio and is actually increasing the energy within our universe, so forcing distant supernovas to expand at an ever increasing rate.

Perhaps all I am stating is a truism – we exist, we perceive ourselves as real, therefore the universe must have been created.  Truly, there is no nothing, no non-existence.

Interestingly, this idea of nothing as being not possible, Axel’s theory of the impossibility of impossibility, means that life in the universe had, also, to be created spontaneously straight away.  As the idea of creating life is impossible, it would have to occur immediately; however, can life start more than once in the same universe, now that is so very unlikely that it probably will not have occurred twice?  Does that mean that there are no other inhabited planets in this universe? No, it simply means that the spark of life occurred on creation, but how that has been distributed across the universe is a different question; I am merely saying that spark of life can perhaps only be created once per universe.

To sum up, there is no such thing as nothing, therefore at the point of completely and absolutely nothing, number systems collapse, 0=1 and the universe is created.  Thereafter, whenever there is nothing in existence, energy and matter will perhaps spontaneously be created as new universes (whether big or small), which may exist out of sight and out of mind, or might collapse back down to nothingness, but leaving a residue of energy that will increase the amount of energy in the universe.

Next I get lost in trying to unpick the standard model of everything