the Desk's Mystery Series gets in deep this time!
©2020 The Media Desk
An online friend of the Desk asked if something their "math teacher" said at the beginning of the semester, and then have repeated every so often, was true.
"Is math the Universal Natural Language she said it was, even including extraterrestrials and ancient civilizations?"
Well. OK... here we go...
As with most things in the Desk's Mystery Series, there is no easy simple direct answer to this one that makes any sense.
No. There's not. And we'll explain that as well.
Meanwhile, we'll take the usual tangents, stop by and see some old friends in the Old World, and make a slight turn to drop into 'warp' and see what's Out There, and how they may add their twos.
And somewhere along the line we'll.....
"Take the last train to ClarksvilleThe fact that this article even exists will surprise some people who know the Desk and how it and Mathematics in general feel about each other. Well, OK. Fair enough. Except this article isn't about DOING the Math. This is about the larger overarching theory of the mathematical representation of the Universe, which isn't math anymore. It's Metaphysics. So we're good. And here it is.
And I'll meet you at the station
You can be there by four-thirty
'Cause I've made your reservation, don't be slow
Oh, no, no, no
Oh, no, no, no
'Cause I'm leaving in the morning
And I must see you again
We'll have one more night together
Till the morning brings my train and I must go..."
-Lyric by Hart and Boyce (full credit and link below)
First a little bit of background.
We'll start with what are called "the counting numbers". You remember them from that row of things above the board, perhaps in the form of a circus train, one elephant riding in a train car, two giraffes in the next car, three lions, four "hey, hey, we're the Monkees!" (more on them later), and so on.
The basic system of counting is the old "tally marks". You see one 'package truck' while on a trip on the highway, one of the kids makes a mark next to the company name on a piece of paper. "There's another one", and another mark. See another one, now there's three marks. A couple more, and they put a diagonal line through them for '5'. When you stop for gas, the kid counts the marks. If you want the fancy name for it it is "unary". As versus what is running your computer which is "binary". With the first, you have one mark, the vertical line for a unit, there is no zero. Some would say the horizontal line for a set of 5 makes it something else, but we're not going down that rabbit hole, it is STILL a single line, all it is doing is indicating a full set of five, or seven or whatever the user wants it to be.
Binary is 0 and 1. Two symbols to do the counting with. So if you see three delivery trucks that would be written as 11, and five would be 101, get it?
One step up from that is the old Roman system, which is actually the Greek system, who lifted a lot of it from the Egyptians, but that's a topic for another time.... where you write your numbers like this: I, VI, XII, LIV (one, six, twelve, fifty-something (for this year's NFL 'big game'). Some claim the Roman system is a "base 10" derivative, but, well, OK, they can say that if they want to. We won't.
The problem with those systems is doing anything above basic addition and subtraction, and even then, anything above the tally of more than a couple of handfuls, literally, becomes cumbersome.
This was somewhat alleviated in the West by the adoption of Arabic numbers (which were 'borrowed' from India) and their system of doing basic arithmetic to keep score of how many of which trucks you see.
Pardon a sudden and dramatic change of direction here, to the East, as it were.
China and other countries in the classical Orient got along quite nicely with their own systems for doing everything from counting sheep to computing their taxes. Of course, they started out with a form of the basic 'tally' system, that evolved into a somewhat more practical form, then they went from there to more functional ways of keeping score.
Oddly enough, the Chinese, and others who based their own systems at least nominally on their basic ideas, had developed both a binary (which we will look at in its modern form and discuss it as used in computers in a moment) and a base 10 system, depending on what they were doing. Apparently, the two symbol system worked better for religious ideas (as in the "Yin / Yang" symbol), while business transactions, up to some algebra and other advances calculations, were done under the other system.
But, again, their complicated number symbols, and the somewhat diverse, and even regional application of them, didn't lend itself to some of the higher functions and the generally accepted meanings and outcomes of the calculations based on them. Everybody pretty much agreed on how to record that there were twelve package trucks in the parking lot, but then coming up with the percentage of the import tax on the various commodities on those trucks was a different story.
And, just for giggles, we're going to go West again, but this time to Central America and the Maya.
Their classic system was something along the lines of a modified Tally Mark system, but they did have a symbol for zero, and knew how to use it as a placeholder of Nul value. But the Maya had something of a similar problem to the Chinese, their system, while as advanced as it could be, had some somewhat arbitrary values depending on who was doing the math, and it didn't really travel well.
Of course, other ancient peoples had their own ways of doing math, and it seems to only be a matter of convenience that the Arabic system of written numbers and their Base Ten came to dominate. It could just as easily been the Babylonian system of Base Sixty that won the day.
Well, in one way, it did win. We still have sixty seconds in a minute and sixty minutes in an hour thanks to them, even though we write them with Arabic numbers instead of their rather complicated marks. We'll hit that while we're waiting on a train later.
Another system that is in common use is seen on Web pages all over the world, and the best example of it is in the Browser Safe Color Pallet, with its Hexadecimal system, which is Base 16.
In "hex" if you've seen fourteen train cars it would be written as E, and the twenty ninth one would be 1D.
There's even a Base 8 "Octal" system, which is 'half' of Hex. In it your 1D train car full of Monkees would be written as 35. And then you can have Base Five, Three, eleven.... base whatever.
Let's move on before we all get a headache.
But is Hex or Binary or any of the others "Natural and Universal"?
The only reason 'base 10', the numbers, zero through nine, then combined to write 14 and 29 and so on, is considered 'natural' is that you can do it on your fingers. And most humans have ten of those, after a fashion.
So, on Earth, it is Natural.
Who's to say that it is Natural elsewhere in the Universe? Yes, we have eight fingers and two thumbs, our friends the 'Squid Guys' don't (a link below explains that one). And there IS at least one other way to count on your fingers and come up with 12, on Each Hand that is. We'll try that later.
But let's look at them from the stance of "nature".
The simplest counting system is Zero, or One. A thing is either there, or it isn't. But then two of them show up. So we have two Ones. Tally marks. But the limitations of that system have been discussed. It's OK for counting sheep, or delivery trucks. But as we saw with those tax guys in China, when you're working on a percentage, things get murky if you don't have concise numbers.
This still doesn't answer the question as to whether Nature Itself prefers to do its own math in Base 10 or any of the other systems we've mentioned. And it most certainly doesn't cover anybody from "Out Yonder" where they aren't able to get First Class Mail.
Let's draw a circle and think about it for a minute.
It really doesn't matter what system of measurement you use to mark out the circumference and then the diameter of the circle. No, it doesn't. You can measure the outside in furlongs, or cubits, or in candy (as we will do in a moment), or anything you want, as long as you use the same consistent system to measure the diameter, the RATIO of the two numbers will work out to something that would be translated into Arabic numbers as 11.00100100001111.
(Oh, sorry, that was Pi in Binary, the code that is essentially what is used in most computers, ones and zeros, Yes or No, endless streams of them rendered into machine language and processed at speeds that we don't have enough room to talk about.)
Pi is usually written as 3.14159265359 in Base 10. The point being that The Ratio itself does not change, only our representation of it does. For instance, in Hex it comes out as 3.243F6A8885A300. And in base 5 you would have: 3.03232214303343, but it is still what you need to multiply or divide by if you have one of the measurements to get the other one. The number of jelly beans needed to go across the middle will be that much fewer than the ones needed to go around the outside of every true circle you can find, every time.
The same is also true for something like the Fibonacci sequence, something the Desk looked at in depth some Fourteen years ago! See link below.
In the old "golden rectangle" sequence, the ratio between the numbers is expressed as "Fn+1 = Fn + Fn-1 (if n is one or greater) ", which works out to 1.618039.... That ratio is going to work out the same, even if it is expressed with different characters, such as in Binary it is: 1.10011110001101111101 .... and our old friend Hex has it as: 1.9E37CDCCA70D1FA33376
But the ratio, because the increase in size from the target object to the next one up would be the same, geometrically speaking, whether you are measuring with a Royal Standard Jellybean Length and writing it in Base 3 script or anything else, would be the same.
OH, and we've GOT to do this, well, no we really don't as everybody is probably confused enough already, but there is a system to represent Whole Numbers, which would be another article, with Fibonacci numbers. There is. And you may go read why anybody would want to at "http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html" (link below). Doing the research for this article the Desk got down to section "3.1 Every number is the sum of some set of Fibonacci Numbers" before its eyes glazed over and it went looking for something stronger than black coffee.
OK, we're done with Systems and all that.
We'll make a quick left turn into another branch of Science and look at something else that MIGHT be a Universal Constant.
One of the diagrams on the Pioneer spacecraft's "greetings from Earth" plaque is the transition of hydrogen.
The designers made the bet that anybody that comes across those pieces of space junk out beyond the Solar System, and look at the advertisement for cheap housing on the third planet SHOULD recognize the two circles and lines as the transition of hydrogen. Or maybe they might think it was some form of "Kilroy was here" and dismiss it as nonsense. Think about it objectively for a moment: just because the human scientists thought that just Everybody would represent the transition of hydrogen with two circles and a couple of short lines and dots, and a line between the circles, and a perpendicular dash below it... really, would THEY?
These same scientists also thought that dash would be universally recognized as a Binary One. Yes, JPL and NASA thought Binary was the best first choice, and then they didn't use it on the planetary map at the bottom of the diagram... go figure.
Even if one is reasonably familiar with atomic structure and the various theories that way, the connected circles with their dots and lines on the plaque could be anything.
And there is no reason to suppose that an alien culture, that may have neutral hydrogen for breakfast, would have a diagram of it as a couple of circles with lines and dots on the can the way we put a cartoon cow on a carton of milk. They may very well have a better way of depicting their breakfast's transition. Which, to us, may look like total nonsense.
Right now, Pioneer 10 is well on its way to Aldebaran, which it will reach in about two million years, give or take a century or two. And 11 is heading in the general direction of Aquila, but that will take even longer. As far as the infamous "heliopause", 11 may already be beyond it and officially in Interstellar Space, 10 is going the other direction, and will take a bit longer given the Sun's general direction of travel and the 'bow shock' of the solar wind against whatever is "out there".
Just for giggles, both are running a bit behind the Voyagers which have officially left our neighborhood.
In short, yes, a depiction of the most common element in the Universe MAY be a good way to let aliens know that you passed your high school chemistry. But, how do you depict it so they recognize it? Maybe with a diagram of it the way atoms are depicted in grade school science books with one being hydrogen and the next being the second most common element, helium?
Or maybe they know about something else that is more common wherever they are from, or they think about them in a totally different way.
Let's try this example.
You ARE back in high school, and, as is the way of things, you overslept, and the bus was running behind, and by the time you got to school, you were so flustered you forgot there was a test today. And you walk into the room and sit down and go through the test, and answer every question.
Except the test was in American Literature. And you wrote all your answers in Conversational French thinking it was a quiz about translating from one to the other and then answering it.
You may have answered the question about Mark Twain correctly, but the teacher will never know. Maybe they'll give you a makeup test, and maybe they won't.
Maybe the aliens will stop by and ask the folks at JPL if their circles were a prescription for Bifocal Glasses or the Transition of Hydrogen. And maybe they won't.
A bit more on the plaque later.
Now, we're going to ask the question the original poster didn't know they were asking, then we'll try to answer it. Yes, we will.
"Does The Creator, GOD, if you will, Count By Base Ten?"
First we'll cite the Creation Myth as depicted in the Bible in Genesis 1, and the Qur'an's Surah 7, it would appear that the Creator used Base 7, six days of work, one day of rest. Other factors of 7, which is a prime number as well, come into play elsewhere in the Scriptures.
Links to both Holy Books below.
There's also references to other numbers, such as 3 which is a prime, 12, which isn't a prime or factor of 7, and then there is 40, and so on.
Does the Almighty favor one set of numbers for doing basic calculations over another? Not by the evidence presented so far.
Let's drop back and punt and see where we land.
Oh, how about that, we landed in India.
Right in the middle of the Upanishads, where we don't see One creation myth like we do in the other traditions. There are several, all apparently taken equally seriously, and none of which talk of a single act of creation with the Creator punching a time clock with a To Do list that says 'day three, create land and plants'.
You can read all of them at the link below to the Sacred-Texts website.
As you do, will will also notice several different ways and styles of numeric reckoning including advanced calculations which are well beyond our work here, such as the square root of two, some of which are laid out on their page at the "storyofmathmatics" website linked below. None of which are a lot of help on our present quest.
There are several websites devoted to the various early civilizations in the Americas, and on them you can find bits about how they did their math. But it comes down to this: They either used a Base 10 system, or they didn't.
Such as the Inca, who were rather late comers to the ball game, but they did show up and made quite the statement when they did. Their 'knotted cord' quipu system was Base 10. It apparently worked well enough to still be in use well into the historic period in parts of South America, long after the Inca had left the scene.
As we've already mentioned the Maya, we'll move on.
We'll look at it like this: The only reason humans as a group of beings that like to count things use some form of Base 10 is because we do. Perhaps because most of us have ten fingers and at least that many toes.
But when you start looking at written expressions of those numbers, especially in languages where the alphabet letters also doubled as written numerals, sometimes well into the twenties before they ran out of letters, things aren't quite so neat and tidy.
Furthermore, there is no reason to suppose that any other group of beings from elsewhere or other when, who perhaps have eight fingers, or maybe twelve, or some other tally of digits, will use our system, expressed in our symbols, and do their math our way.
Of course, until They come Here, or We get Out There and meet Them, we will never know how they do their math.
But the idea that they would recognize Prime Numbers, written in Arabic Base 10 is probably not real credible, and if they used, say, Base 6 math, they might not even recognize our numbers as anything but background noise.
We are well aware that some mathematical types say that any True Independent Prime Number is a prime number no matter what your base system is. Unfortunately, there are also those mathematical types that will say there are different qualities of primes, and coprimes, and so on, and that unless one ends in 1 or 5, or in some cases only three or seven (or was it nine?), that it isn't a true prime, and that it is dependent on the system base. But we're not going to bark at that tree any longer.
The point is that there IS no natural, universal, system of math. What is Natural depends on where you're standing at the time, and Universal may not even be a valid concept for this sort of topic.
And when you're looking at it from out in left field someplace, even the Speed Of Light, that Holy Grail of Earth based Physics isn't as Constant, as we've all been told it is. It is totally dependent on the medium it is passing through, is it a total vacuum or not, the presence of Gravity, and perhaps even the source of the light. Yes, for most purposes, it is as close to a universal constant as just about anything else you can name, but to somebody Out Yonder, is it really. And then you have to figure out how to express that, is it in Furlongs per Second? And, while you're at it, what is the duration of your Second? We'll get to that in a... minute. For today, we'll count our puns in Base Zero.
Even the old master, Albert Einstein realized that the perception, and the measurement, of the speed of light, the "C" in his famous equation, may, in fact, be subjective based on where you are observing the speed of our train from, and the measurement system used.
In his theory, he showed that gravity will interact with light, but he seems to have thought that light would win, maybe, that is, he did until he came up against the conundrum of the Black Hole. But that is way beyond the scope of our current work here.
The point being that if a LOT of gravity will do all sorts of things to light, including throwing it into reverse and preventing it from leaving for Clarksville no matter how long the wavelength of visible light (some radiation CAN escape but that's yet another article) the train is, then maybe even the 'normal' 'background' 'friendly neighborhood' type of gravity can also influence light. To prove this, or disprove it, you'd have to take our train way out beyond Clarksville or any other source of gravity, or to where the influence from this star and that star over there cancel each other out, and then measure the light that's going by. Something that is beyond our capability this week, but just maybe, Those Other Guys have already done it, and that is what they are using for their Universal Constant. Whereas our "speed of light" is measured not only inside Earth's atmosphere, but inside our local gravity well of the Sun, Moon, and everything else around here.
OK, somebody is going to say "but that influence would be negligible given the velocities we're talking about."
Well, maybe. But doesn't that depend on how exacting the value you're using is.
Back to our train. Let's say we're measuring the distance the train covers over a given period of time, there are other possible factors to use, including engine effort, but we'll stick to this one. If you're talking about kilometers per hour, which is a nice way to figure it, you're rounding to the nearest kilometer and the nearest hour. Maybe even rounding up or down by a factor of ten. Try that as the excuse the next time you get a speeding ticket and see how the judge feels about it.
Maybe our 'friends from out of town' don't round their estimates, instead, they take it out to several decimal points to be as very nearly EXACT as it can be.
And now, we're going to talk about minutes and seconds.
Just a few minutes ago we talked about Babylon and their Sumerian Base 60 system, "Sexegesimal" (now that's a word you don't say all the time) for measuring time. And, the number of degrees in that circle we measured earlier, and hours in the day, and so on.
We still use it, some forty five hundred years later.
It is worth noting that their system was based on counting to twelve on one hand, but not on the fingers. Each knuckle on each finger was one, giving a possible three count on each of the four fingers, with the thumb coming in later. So you had a natural twenty four with both hands, then you went on up from there.
Be glad we use the "one thru five" finger system we have when we're doing our taxes.
Which does raise an interesting question. OK, 'a circle' can be sliced into six slices of pizza, all of them '60 degrees' across. Fine. But how did the cook at the Bronze Platter Pizza and Wings shop in Ur know when it was done? What sort of timer did he have to indicate that our order had been in the oven for howevermany minutes it needed to bake on one of the shops namesake Bronze Pans?
We know that somewhere around 2000 to 1500 BC, good water clocks were in use in Egypt, China, and India. ALL of them using the Sumerian 24 hour period for the day. Now, did they manage to calibrate their clocks to One Drip per Second, with some sort of float and pointer, or perhaps a lever on a cup that measured minutes and hours. Just as some old mechanical clocks used to tick every second and a slowly moving minute hand, and even today, you can set some phones to 'keep time' by softly beeping once a second.
It is likely that some sort of similar apparatus was in the cafe in Ur. Although is is also possible they also used candles with regular markings on them that worked at least as well at night as their sundials did during the day.
At any rate... (relax, we're almost out of puns for this one) ...it is enough that they Did mark time as such. Now, to be fair, there is some reasonable speculation that their 'hours' were longer or shorter depending on the sun's position during its seasonal movement in the sky. But, we're OK with one drip from our Pizza Shop Water Clock being One Second.
And how long that Second is depends on how fast our water is dripping. Right?
And how fast our water drips depends on things like... well, the local Gravitational Field for one. As well as everything from the purity of the water to today's air pressure.
OK, so now you see where we were taking the train. If the stationmaster in Clarksville (the Monkees spelled the town without the 'e' with the 's' between Clark and Ville) was using a different 'minute' and 'hour' we might not even recognize the schedule as what it was and think it was the pizza shop menu... well, OK, we're done with that one.
Coming back around the circle.
Now, having said that, we will say this.
There are some things, and we've touched on a couple of them on our way through, one is based on nuclear physics and the other two are based in Geometry. And one of those may be somewhat subjective so we won't dwell on it any more than we have to.
We'll stick to Pi: The ratio between the diameter and the circumference of a circle.
The idea of a circle is something any alien species is going to be familiar with. It is the basic shape of a planet, and a star, and will serve as a fair representation of the former's movement around the latter. Although most orbits are elliptical to a greater or lesser degree, but a circle will do in a pinch. Because they will know it when they see it, and the basic measurements of it will hold true not matter if you are fond of Base 3 math or you do your taxes in base 53 math (one of those primes we mentioned earlier)
But other than drawing a circle on everything we send into space, how do we let Them know that We can do basic arithmetic even if we're currently a bit rusty when it comes to calculations for coaxial warp fields?
Well, we might be better off just drawing circles with a radius on the sides of spacecraft instead of all of the other graffiti that was on the infamous plaque on Pioneer, but that's for others to decide.
And yes, we'll call it graffiti, because, while they did the best they could then (and that's actually rather sad), they got some things wrong on it. It only indicates rings around Saturn when all four Gas Giants have rings, doesn't include the other 'minor planet like objects' since discovered, has the wrong period for a couple of the pulsars, and so on. IF the aliens that come across the thing can't extrapolate its trip back to where it came from, they may never find us. And that might be a good thing.
Time to wrap this one up and catch that train. That's the last pun, we promise.
While, in some respects, Mathematics, or rather Physics, may actually be a Universal language. But the expression of that language, such as what is on the panel on the spacecraft we were talking about, is wholly and completely dependent on who is expressing it, and what foundation they're working from, and how they comprehend things. And then again, it ALSO depends on who is on the other side of that conversation, in this case, this writer, and whether or not that individual, such as in our next example, is totally mad.
This author used to use a simple example to prove that two plus two can equal anything between three and five. There were those who got very angry when it was proven on a chalkboard (yes, we began doing it when you still had a CHALK board) and they sat there and stared at the numbers. Some would object and say that "Two is Two", but then admit that in some cases, 1.7 or 2.3 is also two. Either that or pronounce the Desk dangerously insane, which is also true, and walk away.
If you have a moment, we'll run through it quickly now.
The number two is usually thought of as the whole number expression of values ranging between something over one and a half up to just under two and a half. We'll make those 1.55 and 2.4 for our work here, both of which would equal the whole number "2" in a Government Statistical Office.
If you add 1.55 and 1.55 you get 3.1
Something similar happens when you use the 2.4
And so we come to the end of our essay. If, On Earth, Using Arabic Base Ten Numbers, we have proven that 2 + 2 can equal 5, how can Math be a Universal Language?
it might be better for your final grade if you DON'T run through that with your math teacher until After your diploma is issued!
First, we'll take case of the Monkees "Hey, Hey!"
Last Train to Clarksville, Song by Boyce and Hart, RCA Victor records, single released 1966. https://www.monkees.com/
All the Math: India, Greece, the Maya... all of it: https://www.storyofmathematics.com
A background on Base 8: http://ceadserv1.nku.edu/longa/classes/2008fall/mat115-002/days/bases.html
And while we're at it, Base 5 https://www.basic-mathematics.com/base-five.html
And Base Fibonacci? Yes. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html
Pi in every base system you can name: https://www.virtuescience.com/pi-in-other-bases.html
The Holy Books Mentioned:
Various Hindu books at https://www.sacred-texts.com/
And a different opinion on that plaque we were talking about:
The Pioneer Plaque: Science as a Universal Language
MEDIA DESK articles mentioned and other stuff:
Those "guys" without fingers to count on:
"The Squid Guys are the Good Guys" http://themediadesk.com/newfiles6/squidwar.htm
And a couple of other Science Related Non-Fiction essays:
A great song and some Scientific Hoaxes
The Desk's Non-Fiction and Mystery Series Index http://themediadesk.com/nonfiction.htm
[NOTE: All listed everything and everybody are owned by other entities. No undo disparagement or disrespect is intended. No endorsement of the Desk of them, or by them of the Desk is to be inferred.
The Desk is solely responsible for the analysis and conclusions hereby presented. If the reader has any issues with anything in the article they may contact the Desk through the usual channels.
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