Universe mathematically ordered

[viator]

There seem to be a lot of chaotic events in the universe, but in other ways it is well ordered.

One of the problems in the scientific community is having a system of units which are essentially earth-centric. This results in using points of reference that have nothing to do with the rest of the universe. Believe it or not, mathematics allow us to extend our knowledge of the physical world. The article by R. W. HAMMING, "The Unreasonable Effectiveness of Mathematics" explains it better than I can.

http://www.lecb.ncifcrf.gov/~toms/Hammi ... nable.html

Within the article he provides a statement attributed to Pythagoras,

"Pythagoras is the first man to be recorded who clearly stated that "Mathematics is the way to understand the universe." He said it both loudly and clearly, "Number is the measure of all things."

Our understanding of the "physical nature" of the universe would accelerate if we examined it from a natural point of reference.

1420.4057517667 (10^6) a frequency
888.576587631673... (10^6) a frequency

What do those two number have in common? They represent the same spectrum emission but using different units of measure. Many will recognize the first number, it being the frequency of the hyperfine transition emission of neutral hydrogen, it being expressed in SI units. The second number is a mathematically derived value for the same emission but using what I call "Euclidean Electromagnetic Units".

Euclidean Electromagnetic Units are derived using a "natural unit of length", that length being the wavelength of the hyperfine transition emission of neutral hydrogen, and a "natural unit frequency", it being expressed in its radian form. There are two ways to arrive at the 888.57.... number and the following URL presents the simplest process.

http://vip.ocsnet.net/~ancient/Euclidea ... Basics.pdf

I suspect there is a better mathematical process to express the concept shown in the article, but my mathematics are somewhat limited.

[sandy_mcd]

There seem to be a lot of chaotic events in the universe, but in other ways it is well ordered.
The article by R. W. HAMMING, "The Unreasonable Effectiveness of Mathematics" explains it better than I can.
http://www.lecb.ncifcrf.gov/~toms/Hammi ... nable.html

The first article and one referenced in it [The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner http://www.dartmouth.edu/~matc/MathDram ... igner.html] are good reads. I haven't fully comprehended what the authors are saying, but it sounds good to me. The articles are more philosophy than science or math. [Hamming starts off stating this and also refers to "scientists, engineers, and mathematicians" which is a good breakdown in line with my views.] I suspect that whether the universe is exactly in correspondence with simple math may be a subject of contention, but only recall a brief reference by Feynman about it.
The last article about units doesn't seem as insightful to me. I don't see that any advantage would be gained by following the author's recommendation.

[viator]

One of the problems in the scientific community is having a system of units which are essentially earth-centric. This results in using points of reference that have nothing to do with the rest of the universe.

I find most of the people in the scientific community today "doctrinaire" when it comes to the basic units of measure. It is a cultural conditioning that I find disturbing, in that it does not allow one to even consider alternatives.

I was taught what I know about science in the English system of units and have no problems in working with that or the Metric system, or the SI as it is now called. Thus, I am one of the ambivalent ones, it made no difference which one I used, but I also recognized the flaws in both systems. I did not know that a basic system of units could be defined mathematically until I ran across an unusual dimension set .

The methodology shown in the EuclideanUnits-TheBasics.pdf article is simplicity itself, but it does not show the remarkable symmetrical marriage between wavelengths, frequencies and the simplest Euclidean geometric relationships.

My starting point was the dimension set in the last paragraph of the article, 47.713 cm at an angle of 26.25400 degrees, and I did not know its full meaning or where it led. I did know that the linear dimension translated to a frequency of 2Pi (10^8), which to me was a very unique numeric frequency, and I did recognize the significance of the vertical leg dimension.

There are no text books to tell you how to "handle" wavelengths and frequencies when they are made elements of a right triangle. I would like to see the approach someone else would use to analyze the mathematical characteristics of the given dimension and arrive at the same end point for Ce as given in the pdf article. I can provide an article on my approach but I feel this could bias anothers approach. My original approach did highlight the unique geometric symmetry between wavelengths and frequencies when used as elements of a right triangle using the particular triangular relationship shown in Figure 4 of the pdf article.

The current SI system of base units are man defined in a manner that they have no natural relationship to the order of the universe.

[Canuckster1127]

Measurements have little meaning for people unless they are expressed in terms of something common and familiar.

The broader and larger the items measured become the harder it is to place them into a context that is meaningful.

I'm listening to a Book on Tape during my commute right now, Dava Sobel's "The Planets."

I've been something of an amateur astronomer most of my life. Even though I'm familiar with most of the elements of her book in which she systematically and in order works through the planets, it isn't until some things are put into context that some of the marvel I've experienced looking through binoculars or a telescope in the night sky hit again.

Other solar systems are beginning to reveal planets. The manner in which they are identified is usually through some form of gravitational pull or "wobble" that can be measured to yield the existence of a Gas-Giant, similar to our Jupiter.

Jupiter in our Solar system has a greater mass than all other planets combined. That's mind boggling.

And yet, to yield a comparison in these other solar systems, these giant planets are measured by the unit of a "Jupiter." So, there are planets being discovered that are 3, 5 or 12 Jupiters in size revolving around suns that are equally larger in scale than our own.

Measurement used to be a simple matter of fingers, stones in a cup or a cubit (the average length of a male forearm.) As our "universe" has expanded, we've had to develop new units to give it meaning.

There's really, no right or wrong unit in my mind. The question is, does the unit fit the bill to provide for precision, and meaning to the scientific community and then beyond that to the general populace.

I was in Canada when we switched from the Imperial system to the Metric System. I remember being annoyed having to relearn so much. Then I moved to the US and returned to the Imperial. The Metric is actually easier because it is a base 10 system, compared with the Imperial which is base 12 in some cases and all over the map in others. It doesn't really matter to me now. Mathmatics itself doesn't necessarily yield a logical measure in all cases or if there is one, it yields to arbitrary and capricious measures depending upon the whimsey of the early scientists who begin to deal with it and then use what seems best to them at the time.

Mathmatics certainly provides a means to understand the universe physically. It can answer, what, where, how, how many, when, etc. It is patently incapable of answering the question why to a degree or depth that will ever be satisifying to the human soul. The deeper it delves, the more it reveals there is yet to go.

[viator]

Measurements have little meaning for people unless they are expressed in terms of something common and familiar. ...

You being an amateur astronomer already know that astronomers have their own units of measure and they have little meaning for the people at large. Other scientific disciplines have developed their own special units of measure to fit their needs.

I do not understand why people think that a set of "scientific units of measure" has to please everybody outside of the scientific community. There is no reason why there cannot be a set of "units of measure" for commercial and everyday use and another set for scientific use. Separate scientific systems are in de facto use right now but they all try to mesh with the near medieval metric system, which is now called SI.

However, all this rhetoric about making a measurement system something common and familiar is detracting from the original purpose of this post, revealing how relatively "primitive" mathematical and electromagnetic concepts indicate a natural order within what we call the physical universe.

Get down to the basics, is there anything technically wrong in applying numeric values that represent wavelengths and frequencies to the elements of a right triangle?

It takes just a little mathematical and scientific knowledge to realize that the dimension set, 47.713 cm at an angle of 26.25400 degrees, represents a semi-self extracting knowlege set.

I am not a mathematician or a physicist, thus I am limited into how far I can "extend" the knowledge set. The numeric values presented in the EuclideanUnits-TheBasic.pdf article have implications in how certain "units" are defined at the atomic level.

[Canuckster1127]

No. As one set of measurements is pretty much arbitrary compared with another, the value of any given set is its effectiveness in terms of what its purpose is.

Most comparisons end up being in terms of specific ratios that will show regardless of the unit used.

What's the point that you're trying to make? I must be dense, because I'm not seeing it.

[sandy_mcd]

What's the point that you're trying to make? I must be dense, because I'm not seeing it.

Well, I am even denser than Canuckster, because I don't understand the triangle setup.
I see no benefit for much of what is proposed.
If you go up the url, there are more pages. This one http://www.vip.ocsnet.net/~ancient/ScientificUnits.pdf seems to be a bit more basic.
But the first question is: Why?
Why introduce a new system of units? What is the drawback to the system we have now? And why choose this one?
[I can see the argument for getting rid of the English system, as only having one with decimal relationships is easier to deal with, but I can't see any advantage in having a new system.]

... the original purpose of this post, revealing how relatively "primitive" mathematical and electromagnetic concepts indicate a natural order within what we call the physical universe.

Get down to the basics, is there anything technically wrong in applying numeric values that represent wavelengths and frequencies to the elements of a right triangle?

It takes just a little mathematical and scientific knowledge to realize that the dimension set, 47.713 cm at an angle of 26.25400 degrees, represents a semi-self extracting knowlege set.

The only benefits would be for the manufacturers of rulers, clocks, standard references, etc. The economic cost of introducing a new set of scientific units is quite high. Why?
Not only that, the ratio between old and new units is irrational. By multiplying by 2 pi, the author introduces round off errors for conversions.

[viator]

In the first post I presented two frequencies and they represent the same spectrum emission.

1420.4057517667 (10⁶) a frequency
888.576587631673... (10⁶) a frequency

If you noticed, the value for the speed of light in the article
http://vip.ocsnet.net/~ancient/Euclidea ... Basics.pdf
has the same numeric value as the frequency, differing only in unit designators.

The velocity for the speed of light in SI units is exactly the same as that for Ce.

The topic of this post is, "Universe mathematically ordered". The equation group in the article demonstates a natural order, and you can arrive at the same end point from two direction.

[Canuckster1127]

In the first post I presented two frequencies and they represent the same spectrum emission.

1420.4057517667 (10⁶) a frequency
888.576587631673... (10⁶) a frequency

If you noticed, the value for the speed of light in the article
http://vip.ocsnet.net/~ancient/Euclidea ... Basics.pdf
has the same numeric value as the frequency, differing only in unit designators.

The velocity for the speed of light in SI units is exactly the same as that for Ce.

The topic of this post is, "Universe mathematically ordered". The equation group in the article demonstates a natural order, and you can arrive at the same end point from two direction.

Thanks for pointing that out. I believe there is a natural order and relationship within the universe as well. I believe God created it to be that way.

[sandy_mcd]

The topic of this post is, "Universe mathematically ordered". The equation group in the article demonstates a natural order, and you can arrive at the same end point from two direction.

I am not sure what "mathematical order" means. How about a definition and some examples from someone? [Is it just what the first article says - that mathematical formulas can be used to explain many events? If so, this has nothing to do with units, although it can be seen more easily in some coordinate systems, for example, than others.]

[sandy_mcd]

Again, why?
What is the benefit of changing units?
Surely it most be more than that the speed of light and its frequency have the same scalar value.

[viator]

Again, why?
What is the benefit of changing units?
Surely it most be more than that the speed of light and its frequency have the same scalar value. ...

It is why they have the same scalar value. The values are mutually defined mathematically through geometric and electromagnetic relationships, rather than the serial definitions used for SI units. Also, the mathematical process allows the scientific community to have a reference value for the speed of light that can be calculated to millions of significant places, not just the nine significant places using the current measured SI value. Also, it will allow the development of "counters" with precisions that are limited only by our current technology, this because there is a near absolute reference, which everybody will be able to use to whatever precision they desire.

What is more natural than being able to define the speed of light using two constants, and this extracted using well known Euclidean geometry and the many centuries old wavelength frequency relationships formula. The duration of the "unit of time" is a consequence of the relationships, not the starting point as it is with the SI second.

Is it just what the first article says - that mathematical formulas can be used to explain many events? If so, this has nothing to do with units, although it can be seen more easily in some coordinate systems, for example, than others.

Which comes first, the mathematical formula or the event(s) which prompted someone to create an algorithm (formula) to fit the event(s)?

Correct me if I am wrong, but I am unaware of any mathematical formula that was created before some event(s) observation. Event observations include various types of measurements and then someone, using the mathematics of the era, created a formula that would successfully <b>quantify</b> the events characteristics when numeric values were applied to that formula. R.W. Hamming discusses the process in his article.
http://www.lecb.ncifcrf.gov/~toms/Hammi ... nable.html

In many cases, it doesn't make any difference what system of units one uses, Imperial or Metric, and that the speed of light is based upon some earth measurement values. But when you are trying to develop <b>formulas</b> that will explain the very nature of our physical existence it is desirable to use units that are naturally related to each other and the "system".

The natural frequency value of 888.576587631673... (10⁶) has relevance to how energy levels are defined at the atomic level, but I need some assistance from a physicist familiar with how h-bar is defined and used in this process.

[sandy_mcd]

[I've left out some parts of viator's argument which I think are peripheral; I could express my opinion on these if anyone cares.]
[Most information below is from Wikipedia.]

Background
The speed of light (in a vacuum) is constant. The speed is given in units of distance per time. Since the speed of light is a constant, only two of the these three quantities (speed of light, length unit, time unit) can be arbitrarily defined. In the past, the length unit (e.g., meter) and time unit (e.g., second) were defined. Recently (1983) the meter was redefined in terms of the speed of light.
Current definitions are:
Second: the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at rest at a temperature of 0 K. [This value was chosen to correspond as closely as possible to the ephemeris second.]
Speed of Light: In metric units, c is exactly 299,792,458 metres per second.
Meter: (derived from above two definitions) The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

It is important to distinguish between "accuracy" and "precision".

In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeatability, the degree to which further measurements or calculations will show the same or similar results.
The results of calculations or a measurement can be accurate but not precise; precise but not accurate; neither; or both. A result is called valid if it is both accurate and precise.

Comments

Also, the mathematical process allows the scientific community to have a reference value for the speed of light that can be calculated to millions of significant places, not just the nine significant places using the current measured SI value.

There is no point to calculating the speed of light using the proposed definitions to millions of places. Such a number would be precise but not accurate. The millions of digits calculated would be meaningless.

What is more natural than being able to define the speed of light using two constants, ... But when you are trying to develop <b>formulas</b> that will explain the very nature of our physical existence it is desirable to use units that are naturally related to each other and the "system". ... The natural frequency value of 888.576587631673... (10⁶) has relevance to how energy levels are defined at the atomic level, but I need some assistance from a physicist familiar with how h-bar is defined and used in this process.

The "natural frequency" is irrational (using the 2 pi ratio), and provides no benefit. The factor of 10 to the 6th is just randomly thrown in. Energy levels in atoms still need to be measured with respect to some energy scale. Here's the calculation of the H atom hyperfine structure:

If we do neglect the proton spin, then the 1s level is 4-fold degenerate in the state space of two spin 1/2 particles. Can Whf remove this 4 fold degeneracy?
With and and we have

We choose {|n l s j i f mf>} as the eigenbasis of H0. If n=1, l=0, s=j=i=½, f can take on the values 0 and 1. We find that Whf partially removes the degeneracy, splitting the f=0 and f=1 levels. The result is the 21cm line of atomic hydrogen.

It is this ~ 21 cm line which the author propose as a new unit of length. The proposed unit of length does not simplify much as it is a quantity derived from more basic constants. To see what would be more natural, see http://en.wikipedia.org/wiki/Natural_units. In these examples, values of certain basic constants are defined in order to make some equations simpler or more elegant.

My basic question of "Why?" still stands. How does this proposed redefinition using the hyperfine transition wavelength of the H atom and a 2 pi x 10 to the 6th factor help us to "develop <b>formulas</b> that will explain the very nature of our physical existence "? As Hamming and Wigner point out, the adherence to formulas (not a specific set of units) is what demonstrates the mathematical order of the universe.

The origin of this idea can be found at http://www.vip.ocsnet.net/~ancient/Universal.pdf on page 1. The more I read, the odder it sounds. It seems that the author noticed that some trigonometric value for some triangle coincidentally matched the digits for the hyperfine splitting in the H atom and went off from there.

[viator]

[..... Since the speed of light is a constant, only two of the these three quantities (speed of light, length unit, time unit) can be arbitrarily defined. In the past, the length unit (e.g., meter) and time unit (e.g., second) were defined. Recently (1983) the meter was redefined in terms of the speed of light.

I had considered pointing out the technical background on how the "second" and the "meter" were defined, but it seems to bring up emotional responses where there shouldn't be any. I haven't checked the relevant Wikipedia entries recently to see the changes, as the contents are somewhat fluid.

I am glad you used the term "arbitrarily defined" as that puts those two units into their proper perspective. The NIST web site presents the definitions of the base units. The NIST historical content on the second doesn't mention the ephemeris second.

http://physics.nist.gov/cuu/Units/current.html

The documents that describe the selection of the ephemeris second are available at the following URL:

http://www.leapsecond.com/history/1958- ... -Parry.pdf

The purpose of assigning 9,192,631,770 cycle counts of the hyperfine transitions (caesium-133) was to provide scientists with a "stable" reference, since the ephemeris second had variations which were plus or minus 20 counts, this based upon astronomical observations some 53+ years ago.

The Swiss Office of Metrology provides official definitions for the base units but they approach it with a little more honesty.

http://www.metas.ch/en/scales/meter.html

The metre definition assigns a fixed value to the speed of light c. This fundamental constant can therefore no longer be measured; it has been fixed by definition. From this can be concluded that the unit of length is dependent on the unit of time, the second.

Now we are down to one unit that has been arbitrarily defined, the second. The duration of the second is based upon an astronomical observation peculiar to the earth, and I have a hard time considering this the basis for a system of units which is being used to try to understand the "nature of the universe". All the SI "derived units" are defined using the base units.

It is important to distinguish between "accuracy" and precision". ...

In my last post I mentioned "significant figures" in relationship to the speed of light and "precision" in relationship to counters. The speed of light value is calculated using two transcendental numbers thus it can never be absolutely precise, but I wouldn't call 5+ million significant figures inaccurate. Our ability to calculate the number of significant figures is limited only by our computer technology.

The factor of 10 to the 6th is just randomly thrown in.

Not really. When the length 47.713 cm is converted to a frequency it has the value of 628.31 (10⁶). The whole premise of the geometric, wavelength and frequency relationships is based upon electromagnetic values which are typically expressed in megacycles, or megaHz using the Hertz nomenclature.

Energy levels in atoms still need to be measured with respect to some energy scale. ..

I couldn't agree more. The following URL, Node11.html, denotes the energy differences within the various energy splittings of the hydrogen atom. Node9.html is specific to the hyperfine transition.

http://www.pha.jhu.edu/%7Ert19/hydro/node11.html
http://www.pha.jhu.edu/%7Ert19/hydro/node9.html

In equation (86) in the node9 article, the calculation uses variety of symbols representing "units", including c², to determine the energy level in each state (f=0, f=1), and the separation between the two states gives the 5.9 (10^-6) eV value. We know that the numeric value of the speed of light is based upon "arbitrary" units. The eV (electron volt) value is based on the joule, and the joule is based upon the "newton" and the "meter". We know where the meter comes from, and the newton is based upon the SI definition for a kilogram and a time of one "second", and we know where the second comes from. The kilogram is based upon a physical object, and its selection was very arbitrary. Most of the unit definitions are in the dictunit.htm page. The eV definition is in the Wolfram page.

http://www.ex.ac.uk/cimt/dictunit/dictunit.htm
http://scienceworld.wolfram.com/physics ... nVolt.html

If all energy levels are referenced to the frequency of the hydrogen hyperfine transition emission, using the mathematically derived value, you can eliminate all the "arbitrary " units. The "unit of energy" would have a natural relationship to the "unit of time", the "unit of length" and the "speed of light". What would we call the "unit of energy" represented by a frequency of 888.5765876.... (10⁶)? We know imperically that this "unit of energy" will be a very small value, so we might consider randomly throwing in a 10 to the minus 6 scaling factor.

It is this ~ 21 cm line which the author propose as a new unit of length. The proposed unit of length does not simplify much as it is a quantity derived from more basic constants. To see what would be more natural, see http://en.wikipedia.org/wiki/Natural_units. In these examples, values of certain basic constants are defined in order to make some equations simpler or more elegant.

I've been through that wiki article before and it looks like they have added "Stoney Units", which I hadn't heard of before. The "simplified" units do make the equations simpler and seemingly elegant, but when they want to apply "real world" numeric results they still have to convert to SI units, which are burdened with "arbitrary" units. You might want to look at the superstring site for a somewhat simpler description of "Natural Units" used by particle physicists.
http://superstringtheory.com/unitsa.html

We know that scientists that created the various "natural units", where c is equated to "1", did so because the current numeric value is unwieldly and is arbitrary because of the base units. I suspect everyone of those scientists would not hesitate to include the symbols representing the values for the two constants (square root of 2, and 2 pi) in their formulas because they know that many phenomena in the physical world have Pi relationships embedded within them.

One of the committees that provides recommendations to the SI organization has stated this,

- the consensus that now exists on the desirability of finding ways of defining all of the base units of SI in terms of fundamental physical constants so that they are universal, permanent and invariant in time;

http://www.iupap.org/commissions/interu ... 1-2005.pdf

I doubt that they will succeed until they replace the arbitrary value used for the "duration" of the second with a value that is mathematically derived.

The origin of this idea can be found at http://www.vip.ocsnet.net/~ancient/Universal.pdf on page 1. The more I read, the odder it sounds. It seems that the author noticed that some trigonometric value for some triangle coincidentally matched the digits for the hyperfine splitting in the H atom and went off from there.

The Universal.pdf page was one of my first attempts to write down the mathematical characteristics of the geometric electromagnetic relationships. I had not identified the "simple" trigonometric relationships expressed in the EuclideanUnits-TheBasics.pdf page at that time.

Yes, there is an "oddity" in how I found the triangle relationship that used the H atom hyperfine wavelength. I was not looking for it, but it was the eventual result of reading a book that I thought was going to be some casual Winter reading. The book has a strong religious connotation and because of that I do not identify it. If you haven't noticed, the discussion of religion can create strong emotional responses, and I knew this would automatically turn people "off" if I mentioned it such they would never examine the mathematics. The original author of the material included in the book I read did not know what he had, he simply recorded a great many observations, some not originally his. It was not a technical book. I had some familiarity with electromagnetic principles and realized that things stated in the book "did not fit". It took me about a month to gather additional references that covered the same material by different authors and then "fill in" the missing pieces.

As always happens when I become involved in the topic, I again came away with the feeling that "God made the universe out of complex numbers."

I would like to paraphrase Hamming and add, "God made the universe out of transcendental numbers, they go on forever, never ending."

The last paragraph of the Universal.pdf article is a quotation,

The most universal standard of length which we could assume would be the wavelength of a particular kind of light... Such a standard would be independent in any changes in the dimension of the earth, and should be adopted by those who expect their writings to be more permanent than that body. James Clerk Maxwell, 1873

Maxwell made that statement in regards to the controversies at that time related to whether British scientists should accept the meter as an official length.

[sandy_mcd]

The speed of light value is calculated using two transcendental numbers thus it can never be absolutely precise, but I wouldn't call 5+ million significant figures inaccurate. ...

OK, I stand corrected on the accuracy/precision issue on the speed of light. If the speed of light is defined to be the number given, then any number of digits is accurate. But it is even easier in the SI. Since the speed of light is defined to be 299,792,458 meters per second, then even I can add 5 million more significant figures: just append 5 million zeroes. That is much simpler than calculating a product involving pi. So the proposed system is not simpler.

The purpose of assigning 9,192,631,770 cycle counts of the hyperfine transitions (caesium-133) was to provide scientists with a "stable" reference, since the ephemeris second had variations which were plus or minus 20 counts, this based upon astronomical observations some 53+ years ago. ...One of the committees that provides recommendations to the SI organization has stated this,

- the consensus that now exists on the desirability of finding ways of defining all of the base units of SI in terms of fundamental physical constants so that they are universal, permanent and invariant in time;

...

Yes, using some basic stable physical property is better than some unit such as a hand, which varies from person to person, or fraction of a day, which varies over the years. According to the criteria of being "universal, permanent and invariant in time", the SI unit based on a transition frequency of the cesium atom and the proposed system based on the wavelength of the hydrogen atom are both good choices. [Note: not necessarily so on this forum where some may not feel that the speed of light is constant nor that some physical numbers (e.g. radioactive decay rate) are more fundamental than others (e.g. age of the earth).]

Now we are down to one unit that has been arbitrarily defined, the second. The duration of the second is based upon an astronomical observation peculiar to the earth, and I have a hard time considering this the basis for a system of units which is being used to try to understand the "nature of the universe". ... We know that the numeric value of the speed of light is based upon "arbitrary" units. ...If all energy levels are referenced to the frequency of the hydrogen hyperfine transition emission, using the mathematically derived value, you can eliminate all the "arbitrary " units. ...

No, there are still two arbitrary choices. The speed of light is given in units of distance per time. The choice of these units is arbitrary. The SI choices are a constant times a cesium frequency and a given value for the speed of light which fixes the distance unit. The proposed distance unit is the lowest hydrogen hyperfine splitting with a multiple of 2 pi for the other choice. But this is still an arbitrary choice of a universal distance. Why choose a hydrogen hyperfine transition and not some other number, such as the hydrogen Lamb shift (2p(1/2)-->2s(1/2) transition of 28 cm, or some other number? It is still an arbitrary choice of a distance. The 21 cm H distance is not related integrally to other physical distances. Perhaps the Planck wavelength would be a good natural measuring stick.

I suspect everyone of those scientists would not hesitate to include the symbols representing the values for the two constants (square root of 2, and 2 pi) in their formulas because they know that many phenomena in the physical world have Pi relationships embedded within them.

Other numbers such as e, the golden ratio, and the fine structure constant are also embedded in science, but that is no reason to throw them into the definition of a unit either. And we are back to the start:
The proposed system is more complicated.
The proposed system is costly to implement as the units are quite different.
The proposed system does not lead to more readily determining the "formulas that will explain the very nature of our physical existence ". Formulas such as e=mc**2 or F=ma do not depend on the choice of units; units are not specified by the formulas which apply just as well for feet, meters, slugs, dynes, or any other choice of units. And this is back to Hamming's and Wigner's points: it is amazing that so much of nature is invariant to many influences (a ball drops just the same no matter who lets it fall) and formulae are invariant to the choice of units.