Martin Rees – Astrophysicist, Astronomer, Cosmologist

As part of our effort to discern the Top Numbers of Key Importance within our little universe for The Big Board-little universe Project, we have begun to study the work of Lord Sir Martin Rees of Oxford, particularly his book of the title, Just Six Numbers: The Deep Forces That Shape the Universe, 1999, Weidenfeld & Nicolson, London (173 pages)

His six numbers are:

  1. N, the ratio of the strength of the electrical force to the gravitational force (reviewer, Peter Roberts, Visions.
  2. ε (epsilon)( definition of limits?)
  3. Ω (omega), measures the amount of material in the universe
  4.  λ (lambda) (?)
  5. Q,  the degree of structure in the universe
  6. D, the number of spatial dimensions, 3

Here is what Wikipedia says:

Martin Rees’s Six Numbers:

“Martin Rees, in his book Just Six Numbers, mulls over the following six dimensionless constants, whose values he deems fundamental to present-day physical theory and the known structure of the universe:

“N and ε govern the fundamental interactions of physics. The other constants (D excepted) govern the size, age, and expansion of the universe. These five constants must be estimated empirically. D, on the other hand, is necessarily a nonzero natural number and cannot be measured. Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry.

“Any plausible fundamental physical theory must be consistent with these six constants, and must either derive their values from the mathematics of the theory, or accept their values as empirical.”

“A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.”

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Steve Curtis

Steve Curtis is a mathematics teacher at the Curtis School.  He is also a football coach (defensive backs).

This project officially began on December 19, 2011 in Steve’s classroom with his three geometry classes and two ACT preparation classes.  The class learned about base-2 exponential notation by observing nested geometries using the tetrahedron and octahedron.

The process.  These classes went deeper and deeper inside each object by dividing each edge in half and by connecting the  new vertices to create a smaller set of nesting tetrahedrons and octahedrons.  By about the 45th step within — on paper — the size of the tetrahedron and octahedron was about the size of a fermion.  Within about 67 more steps, that size was approaching the Planck Length.  At that time there were about 112 steps within from the size of our original plastic models.

We then went out into the universe by multiplying each edge by 2. Somewhere between 90 and 98 steps, we were in the area of the Observable Universe.  It wasn’t until we followed Planck Time to the Age of the Universe did we finally settle on just over a total of 202 notations.

This project has been under the watchful eye of Steve Curtis right from its beginning.

About   Home

Pi equals 3.1415926535897932384626433832795028…

Pi-unrolled-720.gif

An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian.

A full circle corresponds to an angle of 2π radians.

3.14159265358979323846264338327950288419716939937510

  1. Pi is a constant.
  2. Pi is an irrational number.
  3. Pi is a transcendental number.
  4. Pi is a non-repeating number – no pattern has been identified using computer analysis within over twelve trillion places.
  5. Pi ( π ) is the exact ratio of the circumference of a circle to its diameter.   It is that simple.

Thank you, Wikipedia, for the graphics (above) that demonstrate this simple definition.  There are over 45 Wikipedia articles about pi.

So, what do you make of it?  What is going on?

Perhaps a few more questions and comments would help.

  1. What is it about a circle and sphere that pi is always-always- always true?
  2. How does a number become a constant, irrational and transcendental all at the same time?
  3. Let us compare pi to other unique numbers that have a special role among all numbers.  These are e, 0, 1, and I. They are all magical, but π stands out. So, let’s ask, “What are the shared qualities of these numbers?” Let’s study them to see if we can find any necessary relations.
  4. We have the ratio between a circle and a line. Perhaps this is the fundamental transformation between the finite and infinite? Are circles and spheres always implicating or imputing the infinite?

That is a big question and enough to ponder for awhile.

Notwithstanding, there are many more questions to ask.

Some speculations: Pi may be the key to unlock the small-scale universe within the big Board-little universe
1.   To get to the application of pi  within the Planck Units, we’ll need to emerge from the singularity of the Planck Units.  Is the radian a key to understanding this process?  First, a radius is extended from the singularity.  A radius extends into the preconditions for space and time, a now emergent small-scale universe. It makes that first arc equal to its own length.  It does it again and again and again and again and again (six radians) and then makes that last leap, 2 pi, to complete the circle. Is this a reasonable scenario? Why? Why not?

2. We need to run through dozens of scenarios, often, and slowly and carefully.  What scenarios are perfect and obvious?

3. We are at the singularity of the Planck Units.  We are establishing the foundations for the physical world.  If all things start simply, this must be the place to start.  It doesn’t get more simple and more mysterious. Nothing is a mistake, everything comes from a perfection to a space-time moment, so what could possibly happen?

What happens within the first six doublings?    (to be continued)

For further discussion:
1.  Is the Small-scale Universe the basis for the homogeneity and isotropy of space and time?
2.  Does everything in the universe share some part of the Small-Scale universe?
3.  How is Planck Temperature calculated?  Does it begin with the other Planck Units and expand from that figure at the first notation?

Note:  All of human history has occurred in the last doubling.  Yet, all doublings remain active and current and dynamic.  Continuity trumps time. Symmetries trump space.

What does sleep have to do with anything?  If all time is current, within the moment, we particularize by the day and uniquely within a given waking day.  Sleep seems to bring us into the infinite.  Dreams seem to be the helter-skelter bridge between the finite and infinite.  It seems that these naïve thoughts are worth exploring further.