John Adam, mathematician and reader of Today’s Word, has contributed some interesting and powerful material in the past. Here is his latest. I think you will enjoy John’s insights.
Heavenly Acoustics
The array below represents, in a sense, two dimensions of time. The speaker utters sounds in time moving downwards. The hearer hears the sounds in time moving to the right. In a world with an odd number of spatial dimensions the hearer hears only the bold and underlined diagonal elements. In a world with an even number of dimensions the hearer hears the increasing longer columns of this array as his time moves to the right.
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT…
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH…
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE…
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS…
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO…
UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU…
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN…
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD…
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO…
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF…
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM…
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA…
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN …
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY…
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW…
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA…
TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT …
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE…
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR…
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS…
‘…his voice was like the sound of many waters.’ Rev. 1:15 (NASB)
In the above passage and several others (e.g. Ezekiel 43:2, Revelation 14:2)** reference is made in some translations to a voice or a sound like ‘many waters’, ‘roaring waters’ or ‘rushing waters’. An interpretation found in several commentaries is that ‘many waters’ is a reference to many people, although an individual is identified as speaking inmany translations of the verses above. Perhaps the sound of a soccer stadium filled with people singing is the nearest equivalent to this acoustic reverberation (as in recent World Cup matches!), but perhaps these verses are indicative of something much more intriguing. I will return to this point below.
About thirty years ago I became intrigued by an article entitled ‘A simple proof that the world is three-dimensional’
http://www.jstor.org/stable/2031482. In the first sentence of the introduction the author (Tom Morley) pointed out that the title was a fraud. He proved nothing as general as that. However, what he did prove was that radially symmetric wave propagation is possible only in spaces with one dimension or three (the former can be disregarded; after all, based on our experience of traffic in tunnels, a one-dimensional world would be unbearably noisy). This means that in three spatial dimensions, a sound with a well-defined beginning and ending (such as a hand clap) will travel outwards from the source and will be heard by everyone as a sharp ‘spike’ of sound. This property also holds true in any space with an odd number of dimensions, i.e. 1, 3, 5, 7, etc. (there is, however, no attenuation of sound in one spatial dimension). But in spaces with an even number of spatial dimensions, 2,4,6, 8, etc. this is not the case. There, the initial clap will possess a ‘tail’ of sound – it will have a definite beginning, but no definite ending, though the tail (and hence sound) will gradually decay in time, without ever becoming zero.
The idea of higher dimensions is all very well as a mathematical and/or philosophical concept, and has been put to good use in books and movies too numerous to mention, but is it at all relevant to us? Putting aside the theories of a possible eight ‘compactified’ spatial dimensions in string theory,http://d0server1.fnal.gov/users/gll/public/edpublic.htm let’s look at things from a more geometric perspective. As a student, I was greatly influenced by the novella ‘Flatland: a Romance of Many Dimensions’, written by Edwin A. Abbott in 1884. The book can be read on several levels, one, it is claimed, being a satirical commentary on Victorian social mores, but I want to focus here on the aspect of ‘many dimensions’. A useful summary of the book may be found here
http://en.wikipedia.org/wiki/Flatland and it can be found online in its entirety here
http://www.geom.uiuc.edu/~banchoff/Flatland/ An important inductive inference from this is that we may be‘embedded’ in a higher-dimensional spatial reality, such that ‘beings’ from higher dimensions could interact with us in much the same way as the visiting Sphere does with the chosen inhabitant, A. Square in Flatland. Such beings could see inside us and our enclosures, appear and disappear at will (reminiscent of the resurrection appearances of Yeshua).
How might this relate to the above passages about sounds and voices in the heavenly realms? Allow me some dimensional speculation. The array below [Attached] represents, in a sense, two dimensions of time. The speaker utters sounds in time moving downwards. The ‘auditor’ hears the sounds in time moving to the right. In a world with an odd number of spatial dimensions the hearer hears only the bold and underlined diagonal elements. In a world with an even number of dimensions the hearer perceives the increasingly long columns of this array as his time moves to the right. Perhaps intelligible understanding of conversations in the heavenly realms will not require higher-dimensional Tweet capabilities, only a willingness to listen carefully to what God is saying – just like ‘down here’, right?
** Rev. 14:2 And I heard a sound from heaven like the roar of rushing waters and like a loud peal of thunder. The sound I heard was like that of harpists playing their harps. (NIV)
Ezekiel 43:2 His voice was like the roar of rushing waters (NIV)
Thank you John. Once again you have proved to me, beyond doubt, that I am apparently BOTH deaf and dumb (not a mean feat)! Thankfully there is no physics exam or IQ tests required in order to enter the Kingdom. Gladly He accepts those who attend to His Word- those many who haven’t a clue what you are communicating and those few who Amen your every word. So thank you for sharing – really. If everyone were all like me, the world would not only be deaf and dumb, but dull as well.
Michael – I am happy to report that I was and am still very much a ‘plodder’ in the intellectual realm, but that means that any professional success I might claim to have is all from the Lord! I love the statement about Sam Gamgee in Tolkien’s ‘Fellowship of the Ring’ that (written from memory here, so it’s probably not accurate) Sam was not terribly bright, but given enough time he could see through a wall. 🙂 I like to think I am made like Sam…
This is a fascinating idea, John. I have wondered many times how we will fully use the currently undeveloped senses that the Creator has put in us, when we come into the next realm. Those who have had experiences where their brain activity had ceased, have sometimes reported stories of very enhanced senses on the other side. It greatly added to the beauty they perceived.
Gayle – it has been said that the most exciting place in the universe is the human mind…
And the most dangerous.
This is very intriguing John. I will read the links a bit later. But what I find most interesting is that everything that has been coming at me for the last few days has something to do with the power of sound and our responsibility to somehow direct it properly.
The following is #9 0f 10 meditations for the days of awe that struck a distinct chord in me. 🙂
It’s bit long but so edifying
The Rabbi’s son
One more day. Just one. That is all we have left Dear Friends.
Just a matter of hours, with a few odd bundles of minutes and seconds thrown in. These are all that stands between us and the time appointed for us to walk with our Creator through the Valley of the Shadow of Death.
A measured number of heartbeats. A limited number of opportunities for showing kindness. A closing window of chances to attempt to reconcile shattered relationships. Only the most poignant prayers of t’shuvah remain available to us. And then we will be called forward, one by one, to review the meaning and quality of the life we have lived thus far, to consider the reality of the judgment we deserve, and to marvel again – we earnestly hope and tentatively trust – at the incomparable wonder of Divine mercy.
This ninth day of Awe is dedicated to the reconnection of our Awestruck Hearts to the deeper levels of meaning of the ninth prophetic empowerment of Sinai. The Holy One proclaimed over us, in the Hebrew tongue:
לֹֽא־תַעֲנֶה בְרֵעֲךָ עֵד שָֽׁקֶר
transliteration: Lo-ta’aneh vere’acha ed shaker
approximate translation: You will not declare a deceptive testimony
concerning your neighbor
The phrase ‘Lo ta’aneh vere’acha ed shaker’ is traditionally translated into English as ‘Thou shalt not bear false witness against your neighbor’. This, in turn, is often shortened in people’s minds to ‘Thou shalt not lie’.
Western mindsets thus seek to limit the application and meaning of the stunning lo ta’aneh . . . empowerment to a simple prohibition of intentionally declaring something one knows to be false. But the Hebrew verb anah, which lies at the root of this empowerment, is much broader and inclusive than either ‘bearing false witness’ or ‘lying’ connote.
Anah means to sing – i.e. to tell a story, create a mood, and influence the people around you, with not only carefully selected words but with an accompaniment of inflections of volume, pitch, and tone, as well as a corresponding display of emotions, facial expressions and body language.
Think of a singer performing an epic ballad on a stage. Everything the singer does on the stage – every movement, every gesture, every facial expression, every crescendo, every rest, every tone, every note – all are part of the presentation of the message of the song.
So it is with every human being. However well we carry a tune, or whether or not we enjoy musical accompaniment, we are all singers, and every sphere of influence we have been assigned is for us a stage. Our Wonderful Creator has gifted each of us with the precious gift of intelligent speech. This gift includes far more than just the capacity to formulate and pronounce words.
The gift of intelligent speech is actually a multi-faceted gift package. Along with the gift of intelligent words He has assigned us a wide variety of accessories to use in order to exercise the gift of intelligent speech in extremely powerful ways on behalf of Him and His Kingdom. We have also each been given an amazing story of hope, joy, and redemption to tell, assigned a series of spheres of influence, and empowered with unique ways to vocalize and express the elements of the story as and when and where and how He stirs them in our souls. The combination of the story of redemption, the spheres of influence assigned, and the methodology of expression forms the essence of our song.
The sole reason we have been given these precious gifts at such a time as this is to release that song.
We have not been given the precious gift of speech to declare the opinions formed in our fallen, fruit of the tree of the knowledge of good and evil poisoned minds as to either the motives or the morality of other human beings.
We are not here at such a time as this to complain about the situations, circumstances, or people in our lives.
We are not here at such a time as this to tattle on, or to formulate, repeat, or nod in agreement with accusations against, our human neighbors – be they individual or corporate or governmental.
We are not given the gifts of life and speech to spout ideology, political philosophy, psychological, sociological or scientific theory. We are not here to spread religion, promulgate doctrine, or swear allegiance to creed.
We are here to sing the Creator’s song. We are here to use the gift of speech to tell the story of hope, of joy, and of redemption. We are here to speak of resolutions and restorations.
We are here to sing to the wells of potential in other human beings, not to rail against their mistakes of judgment and misbehaviors of flesh.
And so the most important question before us this day – before we step with our Creator into the Valley of the Shadow of Death – is ‘what have we been doing with the precious gifts of speech and communication?’.
Have we been singing the song of deliverance the Creator placed us here to sing – or have we been singing the Serpent’s song of negativity?
Have we been furthering the Serpent’s deception regarding any other human being?
Have we been speaking about any other human being’s motives or value to the world as if we had a clue what we were talking about?
Have we been giving our neighbor lip-service which our body language, facial expressions, emotions, and actions belie?
Have we been wasting precious time and influence talking about petty things, irritations, and aggravations that distract from and dilute the effectiveness of the grand song of redemption we are supposed to be releasing upon the earth?
Have we been misrepresenting ourselves as righteous?
Have we been criticizing and judging others as if that was our right, our responsibility, or our purpose?
Time is very, very short. The opportunity to sing the Creator’s song is fading quickly. All words and communications at this point are critical. Let us resolve to use the precious gift of speech and communication wisely, and only for the purposes for which it was given.
Thank you Pam! I am going to have to read this several times through to get every morsel out of it – you have given me much food for thought!
John
John, you are the first person I have heard in many years that shares my love of the depths of Abbott’s Flatland. It sits here on my shelf along with my research books, and gets opened periodically to reorient and shake loose my spiritual “tunnel vision” or my forays “into the weeds.” When I was in college, our groups of math majors spent endless hours following the possibilities of Flatland and mathematical theories or representations of dimensions. I still come back to the mental image and simplicity of the sphere’s interaction to describe to others how G-d is in us, is in the heavens, is surrounding us all at the same time. I also think of the image of the woman, a straight line that could be very visibly blocking or conversely just a point, almost invisible, when I read Skip’s description of the ‘ezer in Guardian Angel. But our discussions really took a turn when we were constructing algebras, sometimes using Flatland’s imagery — algebras where 2+2 did NOT equal four necessarily, mainly because of the other dimensions used. I know the main character in Flatland ended up staying in the “funny farm” for refusing to recant his knowledge of, not one, but two additional dimensions — both an odd and an even number. But I still love to consider your proposal and the endless possibilities. Thank you for shaking us “out of the weeds.”
Donna – this is fascinating. Are you still ‘doing mathematics’?
John
No, John. After eleven semesters of calculus, and computer science in grad school, I ended up in Skip’s first Ph.D. class. I spent a lot of time with the Dean of the Math Dept. in those early years, who would wander off in his lectures showing us the profound beauty and spirituality of math. There were about six of us that stayed close to absorb as much as we could, and got into those long discussions in time off. He was the one who sent me for my first copy of Flatland. He had a glint in his eye when he told us we wouldn’t find the allegory in the literature department, but on the math shelves. It was really exciting to read your post, and wake up old feelings.
To Michael, Gayle, Pam and Donna (and anyone else who has looked at this post), first, thank you so much for your comments. Skip just informed me that it was up (for some reason I no longer get them posts daily, and have to log in daily), and that the formatting of the array had been omitted! The problem is that what Skip received was not in the original format – if you would like to see the original array, slanting from top left to bottom right, let me know your email address and I will send it to you!
Blessings,
John
Please mail me the original array
Bill – see Skip’s note – he’s fixed it!
John
The formatting error was my mistake. I just couldn’t get the web site to accept the original format the John provided. So sorry. I apologize, John. But I am glad the content was communicated. And I will look into why you don’t get these as emails.
please send format — the original array.
Deut 32:4 lahcshmdh@gmail.com
Skip has now fixed the problem, thanks for asking.
I have fixed it now. The array is correct.
Thank you – that’s perfect now!
John
Perhaps this is on a different sphere. I was excited reading the topic, and my thoughts went to Uri Harel (blessed be his name) who discovered that if you assign a music note to each Hebrew alephbet/letter, it brings forth heavenly sounds from the Hebrew Texts of the Bible! He is the founder and director of Music from GOD, translating the Bible into musical notes. Amazing.
FUN stuff. If any are interested, Here is a web sight I bumped into that has an interesting perspective to answer some common perplexities like free will and predestination. http://www.returntogod.com , Look under the topic of BEYOND THE CREATED DIMENSIONS. Fun reading for an afternoon in your sukka.
Shalom all