You know sometimes there is nothing better then getting on your hands and knees on the ground and putting tiles together over thinset placed proper - and so, the edit above today - during the month of gusto on the 11th speaks to that.
You know what the funny thing is - I know I could just do some searching using the current mathematical tools easy and ask the question - what digit is most likely to end a prime number?
Or, better yet, I could take the computers they have nowadays and run the numbers up as high as they could go and then look at the data evident....of course there will be trends there as well....
and then - wa-la -
the code is broken once again but other codes remain and anybody understands a triangle or a 2-dimensional image, must realize there is endless code.....
still, in this season, can't deny - seems time for some code to be broken.
I got ideas on primes and hexagon shapes - I like to share...
I don't have a problem Ken - I just don't have the brain-system to comprehend math beyond grade X! As you say, if/when we can get to meet we can talk it over. Unlike engineering, accountancy & finance is not certain - more an art-form where we 'take a view' and create BS!
I'm pleased to hear "you don't have a problem" cause of course the statement in my comment above was not directed at anybody personally, but rather a statement that I consider my effort to explore these hexagon shape combinations "harmless".....so why could ANYBODY have a problem with that? If they do, as I indicated - tis their "problem" and not mine - my efforts are harmless in regard to this hexagon shape exploration endeavor.
As I got into this effort, I made a commitment to be definitive with respect to six shape possibilities - and that is what I'm doing - keeping my commitment.
Well, here is the proof why any whole number ending in digit #9 is less likely to be prime versus whole numbers ending in digit #3 or digit #7 in base10. Assuming you have read the article, R U Ready?
1. 3*7=7*3=21. 3*9=9*3=27. 7*9=9*7=63. So, giving these each a “count of 1” versus counting them both ways, gives one ending in #1, one ending in #7, and one ending in #3, respectively.
2. The other possibilities are 3 * 3 = 9, 7*7 = 49, and 9*9=81. This gives 2 ending in #9 and one ending in #1.
3. Therefore, per the approach of not “double-counting” forwards and backwards, the totals are two ending in #1 and two ending in #9 versus just one ending in #7 and #3, respectively.
4. Therefore, whole numbers ending in #9 are less likely to be prime versus those ending in either #7 or #3, respectively.
~~
BK
* If somebody wants to prove that incorrect, please do.
Ha Ha - excellent work Ken you are well ahead of me - my math is somewhat basic.. But when I was training as a company secretary in the 1960s we didn't have calculators and had to do all the math in our heads. When trying to balance our ledgers and finding a differnce my mentor said: "if the difference is divisible by 9 you will have a transpositon event."
You realize - all my suppositions above could be made without computers much less calculators. So, there is something to that kind of proof resolute and "analog" in a way versus easy digital proofs vulnerable to error. I mean I could do a search on likelihood of prime numbers per last digit ---- I could do it digitally, but ain't it better to prove it beforehand!
It's always better to deduce the proof Ken. I am a slow learner and therefore have difficulty in remembering formulae so I always go back to first principles
Well, begs the question - what are your first principles?
I mean, I'm not trying to be facetious, cause I think I have a sense of them and that is why I enjoy our discourse, but being you mentioned it, why not elaborate please.
Well anything divisible by 9 is divisible by 3 two times - and any digits that added up are divisible by 3 give a number divisible by 3 itself no matter how many digits - ergo - 1/3 of all numbers are not prime by definition and then when you add a 2 divisor as well as a 5 one, then the number of primes diminishes as numbers get bigger - and that is part of what I'm getting at and maybe it has something to do with transposition and maybe it don't, but let me go check first...oh goodness, transpose means so many things - can you please narrow it down P&S - https://www.merriam-webster.com/dictionary/transposing
OK, if the "difference" is divisible by 9, it depends on the origin of the "difference", but assuming in simple "long math" if I remember my terms, you try to divide one number by another and you have a "remainder" - I'm not sure this difference really matters - it sort of is random, but maybe not?
My guess is a "transposing event" is one where things may not be as they seem.
(plus, if you add the digits up in any whole number and they are divisible by 9, then so is the number - prove that! I mean it is true, so the proof is already in the pudding and I'm sure somebody has demonstrated why it is a truism)
When I began doing manual accounts in early 1960s as an apprentice Company Secretary (purchase ledger in my case), I would post individual Journal entries to the customer's ledger (1,000s). Then - the acid test - I had to total all the new ledger balances (red underline) and using the control account, the total of the journal invoices minus the payments received (per the bank account) must balance.
When it didn't balance and the difference was divisible by 9 then I would look for a transposition error which narrows down the search. NB We didn't actually total all these numbers ourselves but sent them down to the 'Comp-room' where highly trained girls would use their Sumlock Comptometers to add thousands of numbers - (£s, shillings and pence! - L,S,D - Latin) we were never allowed to question their results as they were ALWAYS right! https://americanhistory.si.edu/collections/nmah_690486
That is awesome P&S - that is good stuff......in a way one learns so much when most of the effort is done in the brain......
You know - as a chemical engineer, I remember some of the tests we had and one thing learned over time, was how to avoid making errors in computation....I have many techniques for doing this - sometimes there is a balance twixt expediency and accuracy, but usually accuracy matters more!
I got lots of bean counters in my family - My Grand-Daddy who died before I was born was an accountant. All these digital tools lately - I think they have "dumbed down" a generation or two....I think that is fixing to change course.
I also think, I need to "repost" aspects of this "Proof" I have so much fun presenting - I'll do it in an easy to follow way as I pursue the solution to the hexagon puzzle I proposed well over a year ago!
December 10 is not far away....."lots" of excitement in SA these days - but I heard they kicked out the whole Israeli staff diplomatically - good on SA on that. I mean SA knows about apartheid better than anywhere else I reckon and better to be there than in the floundering island of england.....(ha, ha). The UK is toast.
All so very true my good friend - we are on the same page of the hymn book! I look forward to your proof repost. Yes SA is a fine country in spite of the negative press - their potential is enormous and I hope to contribute.
I'll share one of my techniques when dealing with various numbers and computations.....sometimes there is just an itty bitty error when the numbers don't balance as expected.....one could often choose to ignore that, but sometimes upon further evaluation the "itty-bitty" error points out even larger mistakes in calculation....so even when an error is small, if it is unexpected and time permits, I give it heed and try to get to the bottom of it....
Another technique simple is to have ways to "check" the work done for internal consistency - ways that may point out flaws in thinking....I do this all the time....it is sort of part of my nature cause I know how easy it is to make mistakes in computation and best to check before submitting any "final answer".
I am going to create a new post focusing on my "hexagon" puzzle.....but I'm fairly confident with 5 perfect hexagon "tiles" connected, there are 23 discrete shapes that can be created independent of orientation and I suppose I should go back and look closely at the shapes I've presented above in this regard and I will before I post the new article that will have better "logical flow" in thought and presentation. I can't deny, I was sort of "winging" it yesterday....but this was based on considerable effort already made.
Thing is, the ability to present ideas contemplated here at Substack with images and all really makes it easier to discuss this puzzle - so, if you go back to the very original link at sott.net - I discuss some aspects of this effort in great detail and there are also some other posters there and articles shared from fine mathematical minds.
I might as well go on record with the post above linked - I'll link it below cause it was here I posed this on 101822 1430:
~~~
OK, so I did a search using the term "geometry" and this was the top article so this is where I'm gonna try in my mind to take the hexagonal puzzle in imagination mostly out to the 4th tile. Wish me luck because this is all a mind game just now mainly, but later if I'm still alive, I'll take the hexagon tiles I have and put it to a real-world test. Probably just moments after posting this.
~~~~here goes~~~~~~
1. First tile is placed - there is one shape only distinct.
~
2. Second tile is placed - there is still only one shape distinct, because two tile edges connecting on hexagons have no differentiation without consideration for orientation. Basically, the two of them together will be the same regardless of which two sides initially connect no matter perspective 2-dimensionally - the shape is singular even with two pieces. Can you visualize this? I'm not talking trash - really.
~
3. As explained elsewhere, and per the logic expressed already, there are 3 possible shapes without consideration for orientation and in a 2-dimensional plane or field when 3 hexagonal shapes are connected - side by side. One of the three is three in a row so that they form a line (***). The second of the three is three combined so that they form the beginnings of a circle so-to-speak - they are all matched together in nice symmetry with each other (*$*). The third is when one of the many options to place the 3rd tile after two already been placed off to the side of either starting tile not being either the straight line option (#1) nor the all packed in there option (#2), but at the end of the day, there is only one discrete shape and it doesn't matter really which side gets connected even if there are 4 options for this on the two previous played tiles having 2 each....by the way, for the 3rd tile placement into a discrete shape there are two options for #1 above and two options for #2 above as well, but for the 3rd shape there are 4 options and so likely its occurrence might be higher all other things being equal.
~
4. Herein lies the formula already I suspect, but it wouldn't be difficult to extend this out to the fourth hexagonal tile placements, just walk through it per each of the 3 options indicated above. For each of the 3 there will then be several options I suspect when the 4th tile is added. This is where doing it physically is helpful because when unbiased a mind sometimes has a hard time coming to conclusion with respect to redundance without orientation - it helps to get the senses involved.
~
5. If you can do it for 4, you can do the same thing for 5. I think the solution beckons and I'll figure it out myself if need be.
~
Peace and I hope all are doing well and how about them damn Buffalo Bills?
Nobody wants to play them and now they get a week off to relish, but I hope they don't relish too much.
The season is young.
Peace, Poem of the Day, 101822 1430
BK
~~~
If you got the solution - please don't tell me - I want to figure it out on my own.
Phew - well above my pay-grade Ken but I do know Stonehenge and drive past it often. It is indeed an enigma and contains secrets we know not of. The ancients keep their secrets close it seems.
Three years later Chubb gave the monument to the nation, to be cared for by the then Ministry of Works. A series of major restorations and excavations took place from 1919 to 1929, and another major programme between 1958 – 1964.
Oh my, I just started reading that link closely - I got down to the 6th or 7th thing and I'll read the rest. One thing I remember were some of the mounds nearby in the area....those mounds are all over the place in England. That place has been inhabited for a long time no doubt.
OK P&S - this is what I did. I ordered some hexagon shapes like the ones used is so many games from the 1970's and afterwards - if you have never heard of it the game Magic Realm sort of inspired this - https://boardgamegeek.com/boardgame/22/magic-realm
Well, I won't deny I also created some hexagonal images in a PowerPoint file - (I wonder if there is an easy way to share this file???).....
But, the point is you can take these hexagons and connect them 2-dimensionally and then the question is how many discrete shapes are there.
So, I think it has been determined that with 4 hexagons there are 7 discrete shapes that can be made independent of orientation, and with 5 hexagons there are 23 discrete shapes. Both 7 and 23 are prime numbers and I know I should have done this by now, but I haven't gotten around to figuring it for sure with 6 hexagons, but my guess is the final number will also be prime.
Somehow all these number relations seem to matter to me and that is independent of any ideology - tis just a matter of figuring numbers in Base10.
So, while "angels" watching over is something I basically think is true, even the angels tread "lightly" around the law of numbers in Base10. In the world of numbers - a law is a law - tis inviolate.
Anyhow - I think you have convinced me to figure out the number of shapes with 6 hexagons and when I do this, assuming I do, I'll take pictures of each shape (as I've already done for 5 hexagons connected), and then that will be the proof - but it might be a long post...still, for the sake of math I'll do it and I'll post it here or possibly in a special article that references back to this initial "Proof".
I hope you are feeling better - I'll never forget this conversation. I remember.
It must suck to suffer when the temperature is cold - did I ever tell ya bout the mean ass ground hog I met once P&S? Holy moly - you can't make it to Fries, VA in July '26 then I guess you never gonna hear bout it pal.....plus - you will miss out on the porter - got your name on it.
OK - I clicked the link, and I've seen that before...in fact, I think I may have saved some of the info there....but now...most of the other links are dead ends P&S....just like sometimes on the sea, the storm is so ferocious...you just have to hope there is a Bermuda somewhere....
So, I haven't included the 2nd and 3rd parts of this post where I think I can prove that out of the remaining numbers - those being 3, 7, and 9 that could end a possible prime number - used for so many things - that out of those digits 9 is the least likely to be prime followed by 3 in a close runup with 7. And will I prove it so simple as I prove the digit of #1 above? Most unlikely, but that is my intuition presently and frankly I'm more than exhausted with all the dying babies in Gaza and something has got to give - if not soon - then all humanity I reckon is destined to die with the zionist ideology.....oh well, sometimes when you play to win it just means you don't play to lose.
Sad when one thinks about it with conviction - how much better it could be.
But if the zionist ideology is the one that captures the day - then so be it.
Let us all die together than give in to an ideology obviously flawed - just like calculus is - at the edges.....
Still - I'll kill so many of them before they even lay a hand upon me.
I think you are confusing data and number P&S. Data are what they are (datum is just one piece). Numbers have connections no doubt - within those connections lies logic and geometry. Shapes, numbers, and language - go hand-n-hand-n-hand.
Philosophically there must be some truisms in the geometry of numbers - don't you think P&S - this is more than just angels....it is more than faith in a way....it is law. Regardless, angels are out there, but so are demons - sometimes it ain't easy to tell the difference.
Save travels and I'll keep studying and learning as long as I'm breathing.
"I'll keep studying and learning as long as I'm breathing" - me too Ken! You may be very right for I am no mathematician just a simple accountant - I count beans Ha Ha.
But perhaps the magic squares will give you pause for thought?
Nature trumps all with math - the golden ratio is but one example. Now then, consider the number 153. It was the number of fishes that Jesus caused the fishers to net.
"When they came ashore, they saw there a charcoal fire with fish lying on it and bread. Jesus said to them: “Bring some of the fish you just now caught.” So Simon Peter went on board and hauled the net ashore full of big fish, 153 of them. And though there were so many, the net did not burst. Jesus said to them: “Come, have your breakfast.” [John 21:9-12]
You know sometimes there is nothing better then getting on your hands and knees on the ground and putting tiles together over thinset placed proper - and so, the edit above today - during the month of gusto on the 11th speaks to that.
You know what the funny thing is - I know I could just do some searching using the current mathematical tools easy and ask the question - what digit is most likely to end a prime number?
Or, better yet, I could take the computers they have nowadays and run the numbers up as high as they could go and then look at the data evident....of course there will be trends there as well....
and then - wa-la -
the code is broken once again but other codes remain and anybody understands a triangle or a 2-dimensional image, must realize there is endless code.....
still, in this season, can't deny - seems time for some code to be broken.
I got ideas on primes and hexagon shapes - I like to share...
you got a problem with that?
If so, it ain't my problem - tis yours!
I don't have a problem Ken - I just don't have the brain-system to comprehend math beyond grade X! As you say, if/when we can get to meet we can talk it over. Unlike engineering, accountancy & finance is not certain - more an art-form where we 'take a view' and create BS!
I'm pleased to hear "you don't have a problem" cause of course the statement in my comment above was not directed at anybody personally, but rather a statement that I consider my effort to explore these hexagon shape combinations "harmless".....so why could ANYBODY have a problem with that? If they do, as I indicated - tis their "problem" and not mine - my efforts are harmless in regard to this hexagon shape exploration endeavor.
As I got into this effort, I made a commitment to be definitive with respect to six shape possibilities - and that is what I'm doing - keeping my commitment.
Warmly to you P&S,
Ken
Gratefully accepted Ken - I am at sea on all this!
This is what is on my mind…..
* ??? *
Well, here is the proof why any whole number ending in digit #9 is less likely to be prime versus whole numbers ending in digit #3 or digit #7 in base10. Assuming you have read the article, R U Ready?
1. 3*7=7*3=21. 3*9=9*3=27. 7*9=9*7=63. So, giving these each a “count of 1” versus counting them both ways, gives one ending in #1, one ending in #7, and one ending in #3, respectively.
2. The other possibilities are 3 * 3 = 9, 7*7 = 49, and 9*9=81. This gives 2 ending in #9 and one ending in #1.
3. Therefore, per the approach of not “double-counting” forwards and backwards, the totals are two ending in #1 and two ending in #9 versus just one ending in #7 and #3, respectively.
4. Therefore, whole numbers ending in #9 are less likely to be prime versus those ending in either #7 or #3, respectively.
~~
BK
* If somebody wants to prove that incorrect, please do.
Ha Ha - excellent work Ken you are well ahead of me - my math is somewhat basic.. But when I was training as a company secretary in the 1960s we didn't have calculators and had to do all the math in our heads. When trying to balance our ledgers and finding a differnce my mentor said: "if the difference is divisible by 9 you will have a transpositon event."
So figure that out my good friend?
Blessings
AP
You realize - all my suppositions above could be made without computers much less calculators. So, there is something to that kind of proof resolute and "analog" in a way versus easy digital proofs vulnerable to error. I mean I could do a search on likelihood of prime numbers per last digit ---- I could do it digitally, but ain't it better to prove it beforehand!
It's always better to deduce the proof Ken. I am a slow learner and therefore have difficulty in remembering formulae so I always go back to first principles
Well, begs the question - what are your first principles?
I mean, I'm not trying to be facetious, cause I think I have a sense of them and that is why I enjoy our discourse, but being you mentioned it, why not elaborate please.
Ken
(smile)
Hey P&S - I'm putting "Notes" to the test...
ha, ha...
Well anything divisible by 9 is divisible by 3 two times - and any digits that added up are divisible by 3 give a number divisible by 3 itself no matter how many digits - ergo - 1/3 of all numbers are not prime by definition and then when you add a 2 divisor as well as a 5 one, then the number of primes diminishes as numbers get bigger - and that is part of what I'm getting at and maybe it has something to do with transposition and maybe it don't, but let me go check first...oh goodness, transpose means so many things - can you please narrow it down P&S - https://www.merriam-webster.com/dictionary/transposing
OK, if the "difference" is divisible by 9, it depends on the origin of the "difference", but assuming in simple "long math" if I remember my terms, you try to divide one number by another and you have a "remainder" - I'm not sure this difference really matters - it sort of is random, but maybe not?
My guess is a "transposing event" is one where things may not be as they seem.
(plus, if you add the digits up in any whole number and they are divisible by 9, then so is the number - prove that! I mean it is true, so the proof is already in the pudding and I'm sure somebody has demonstrated why it is a truism)
When I began doing manual accounts in early 1960s as an apprentice Company Secretary (purchase ledger in my case), I would post individual Journal entries to the customer's ledger (1,000s). Then - the acid test - I had to total all the new ledger balances (red underline) and using the control account, the total of the journal invoices minus the payments received (per the bank account) must balance.
When it didn't balance and the difference was divisible by 9 then I would look for a transposition error which narrows down the search. NB We didn't actually total all these numbers ourselves but sent them down to the 'Comp-room' where highly trained girls would use their Sumlock Comptometers to add thousands of numbers - (£s, shillings and pence! - L,S,D - Latin) we were never allowed to question their results as they were ALWAYS right! https://americanhistory.si.edu/collections/nmah_690486
No adding machines in those days Ken!
That is awesome P&S - that is good stuff......in a way one learns so much when most of the effort is done in the brain......
You know - as a chemical engineer, I remember some of the tests we had and one thing learned over time, was how to avoid making errors in computation....I have many techniques for doing this - sometimes there is a balance twixt expediency and accuracy, but usually accuracy matters more!
I got lots of bean counters in my family - My Grand-Daddy who died before I was born was an accountant. All these digital tools lately - I think they have "dumbed down" a generation or two....I think that is fixing to change course.
I also think, I need to "repost" aspects of this "Proof" I have so much fun presenting - I'll do it in an easy to follow way as I pursue the solution to the hexagon puzzle I proposed well over a year ago!
December 10 is not far away....."lots" of excitement in SA these days - but I heard they kicked out the whole Israeli staff diplomatically - good on SA on that. I mean SA knows about apartheid better than anywhere else I reckon and better to be there than in the floundering island of england.....(ha, ha). The UK is toast.
Ken
All so very true my good friend - we are on the same page of the hymn book! I look forward to your proof repost. Yes SA is a fine country in spite of the negative press - their potential is enormous and I hope to contribute.
I'll share one of my techniques when dealing with various numbers and computations.....sometimes there is just an itty bitty error when the numbers don't balance as expected.....one could often choose to ignore that, but sometimes upon further evaluation the "itty-bitty" error points out even larger mistakes in calculation....so even when an error is small, if it is unexpected and time permits, I give it heed and try to get to the bottom of it....
Another technique simple is to have ways to "check" the work done for internal consistency - ways that may point out flaws in thinking....I do this all the time....it is sort of part of my nature cause I know how easy it is to make mistakes in computation and best to check before submitting any "final answer".
I am going to create a new post focusing on my "hexagon" puzzle.....but I'm fairly confident with 5 perfect hexagon "tiles" connected, there are 23 discrete shapes that can be created independent of orientation and I suppose I should go back and look closely at the shapes I've presented above in this regard and I will before I post the new article that will have better "logical flow" in thought and presentation. I can't deny, I was sort of "winging" it yesterday....but this was based on considerable effort already made.
Thing is, the ability to present ideas contemplated here at Substack with images and all really makes it easier to discuss this puzzle - so, if you go back to the very original link at sott.net - I discuss some aspects of this effort in great detail and there are also some other posters there and articles shared from fine mathematical minds.
Happy Sunday!
Ken
I might as well go on record with the post above linked - I'll link it below cause it was here I posed this on 101822 1430:
~~~
OK, so I did a search using the term "geometry" and this was the top article so this is where I'm gonna try in my mind to take the hexagonal puzzle in imagination mostly out to the 4th tile. Wish me luck because this is all a mind game just now mainly, but later if I'm still alive, I'll take the hexagon tiles I have and put it to a real-world test. Probably just moments after posting this.
~~~~here goes~~~~~~
1. First tile is placed - there is one shape only distinct.
~
2. Second tile is placed - there is still only one shape distinct, because two tile edges connecting on hexagons have no differentiation without consideration for orientation. Basically, the two of them together will be the same regardless of which two sides initially connect no matter perspective 2-dimensionally - the shape is singular even with two pieces. Can you visualize this? I'm not talking trash - really.
~
3. As explained elsewhere, and per the logic expressed already, there are 3 possible shapes without consideration for orientation and in a 2-dimensional plane or field when 3 hexagonal shapes are connected - side by side. One of the three is three in a row so that they form a line (***). The second of the three is three combined so that they form the beginnings of a circle so-to-speak - they are all matched together in nice symmetry with each other (*$*). The third is when one of the many options to place the 3rd tile after two already been placed off to the side of either starting tile not being either the straight line option (#1) nor the all packed in there option (#2), but at the end of the day, there is only one discrete shape and it doesn't matter really which side gets connected even if there are 4 options for this on the two previous played tiles having 2 each....by the way, for the 3rd tile placement into a discrete shape there are two options for #1 above and two options for #2 above as well, but for the 3rd shape there are 4 options and so likely its occurrence might be higher all other things being equal.
~
4. Herein lies the formula already I suspect, but it wouldn't be difficult to extend this out to the fourth hexagonal tile placements, just walk through it per each of the 3 options indicated above. For each of the 3 there will then be several options I suspect when the 4th tile is added. This is where doing it physically is helpful because when unbiased a mind sometimes has a hard time coming to conclusion with respect to redundance without orientation - it helps to get the senses involved.
~
5. If you can do it for 4, you can do the same thing for 5. I think the solution beckons and I'll figure it out myself if need be.
~
Peace and I hope all are doing well and how about them damn Buffalo Bills?
Nobody wants to play them and now they get a week off to relish, but I hope they don't relish too much.
The season is young.
Peace, Poem of the Day, 101822 1430
BK
~~~
If you got the solution - please don't tell me - I want to figure it out on my own.
Oh yeah - here is the link:
https://www.sott.net/article/157471-Stonehenge-builders-had-geometry-skills-to-rival-Pythagoras
Phew - well above my pay-grade Ken but I do know Stonehenge and drive past it often. It is indeed an enigma and contains secrets we know not of. The ancients keep their secrets close it seems.
https://www.english-heritage.org.uk/visit/inspire-me/blog/blog-posts/30-things-you-might-not-know-about-stonehenge/
I'm not piling on I hope you know P&S, but the link you provided has scarves for sale - here is one I am fond of....
https://www.english-heritageshop.org.uk/mosaic-scarf-viscose-65-x-180cm
The one I have is no longer for sale apparently!
(I'm going to post an image of it...)
~
Oh to be in the sea....
Ken
LOL I had no idea! And indeed to be at sea! I don't want to be in it Ken!
OK - this one is great - the image won't show, but the text should - let me paste it...
10. Stonehenge was bought at an auction in 1915
It was purchased for £6,600 by local business man Cecil Chubb, who (reportedly) came to the auction to buy some dining chairs.
al0913_017_02-General-view-looking-south-west-showing-stones-of-the-outer-circle-propped-with-timbers-1919.jpg
General view of Stonehenge looking south west, showing stones of the outer circle propped with timbers. May 1919. © Historic England Archive
Three years later Chubb gave the monument to the nation, to be cared for by the then Ministry of Works. A series of major restorations and excavations took place from 1919 to 1929, and another major programme between 1958 – 1964.
What a weird history but well found my friend
What you mean - you didn't even read the link you sent me!
(ha, ha...
Come on P&S - get to the destination safely please....we need you!
Ken
Love doesn't express how I feel about you! I need you too my good friend - wisdom is rare these days.
Oh my, I just started reading that link closely - I got down to the 6th or 7th thing and I'll read the rest. One thing I remember were some of the mounds nearby in the area....those mounds are all over the place in England. That place has been inhabited for a long time no doubt.
Best to you P&S - safe travels friend.
Ken
Many thanks Ken - yes I fly on my mother's birthday, Dec 10, so that must be a portent!
OK P&S - this is what I did. I ordered some hexagon shapes like the ones used is so many games from the 1970's and afterwards - if you have never heard of it the game Magic Realm sort of inspired this - https://boardgamegeek.com/boardgame/22/magic-realm
So what I did was I ordered these cardboard pieces - https://www.amazon.com/gp/product/B07MTV99HB/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1
Well, I won't deny I also created some hexagonal images in a PowerPoint file - (I wonder if there is an easy way to share this file???).....
But, the point is you can take these hexagons and connect them 2-dimensionally and then the question is how many discrete shapes are there.
So, I think it has been determined that with 4 hexagons there are 7 discrete shapes that can be made independent of orientation, and with 5 hexagons there are 23 discrete shapes. Both 7 and 23 are prime numbers and I know I should have done this by now, but I haven't gotten around to figuring it for sure with 6 hexagons, but my guess is the final number will also be prime.
Somehow all these number relations seem to matter to me and that is independent of any ideology - tis just a matter of figuring numbers in Base10.
So, while "angels" watching over is something I basically think is true, even the angels tread "lightly" around the law of numbers in Base10. In the world of numbers - a law is a law - tis inviolate.
Anyhow - I think you have convinced me to figure out the number of shapes with 6 hexagons and when I do this, assuming I do, I'll take pictures of each shape (as I've already done for 5 hexagons connected), and then that will be the proof - but it might be a long post...still, for the sake of math I'll do it and I'll post it here or possibly in a special article that references back to this initial "Proof".
Yours truly,
Ken
Ken
Thank you so much Ken - you are special person with indepth intitution because of course primes reign supreme. I think what you have discovered is magic squares but I might be wrong which is what investigation is all about, eh? https://www.math.wichita.edu/~richardson/mathematics/magic%20squares/magicsquares-intro.html
I hope you are feeling better - I'll never forget this conversation. I remember.
It must suck to suffer when the temperature is cold - did I ever tell ya bout the mean ass ground hog I met once P&S? Holy moly - you can't make it to Fries, VA in July '26 then I guess you never gonna hear bout it pal.....plus - you will miss out on the porter - got your name on it.
Here - is a song in memory:
https://youtu.be/W4ga_M5Zdn4
OK - I clicked the link, and I've seen that before...in fact, I think I may have saved some of the info there....but now...most of the other links are dead ends P&S....just like sometimes on the sea, the storm is so ferocious...you just have to hope there is a Bermuda somewhere....
I say "YES" before even clicking the link...
Ken
So, I haven't included the 2nd and 3rd parts of this post where I think I can prove that out of the remaining numbers - those being 3, 7, and 9 that could end a possible prime number - used for so many things - that out of those digits 9 is the least likely to be prime followed by 3 in a close runup with 7. And will I prove it so simple as I prove the digit of #1 above? Most unlikely, but that is my intuition presently and frankly I'm more than exhausted with all the dying babies in Gaza and something has got to give - if not soon - then all humanity I reckon is destined to die with the zionist ideology.....oh well, sometimes when you play to win it just means you don't play to lose.
Sad when one thinks about it with conviction - how much better it could be.
But if the zionist ideology is the one that captures the day - then so be it.
Let us all die together than give in to an ideology obviously flawed - just like calculus is - at the edges.....
Still - I'll kill so many of them before they even lay a hand upon me.
I understand Ken - but if death is not the end what does it matter anyway?
The thing is P&S - nobody really wants to keep wisdom secret, so I think let it be known.
But knowledge is power Ken, so keeping the secrets is a lever? As a knowledge engineer and a systems analyst I understand the power of knowledge:
(1) Data are merely indiscriminate digits/letters
(2) Organised data are information
(3) Information, understood, is knowledge
(4) Knowledge applied efficaciously on human activity is wisdom which accumulates over time - thus the elderly are revered in ancient society.
We seem to have lost something of profound understanding in our pursuit of 'The Science' https://www.amazon.co.uk/Gods-Undertaker-Has-Science-Buried/dp/0745953719
QED
Blessings
AP
I think you are confusing data and number P&S. Data are what they are (datum is just one piece). Numbers have connections no doubt - within those connections lies logic and geometry. Shapes, numbers, and language - go hand-n-hand-n-hand.
Philosophically there must be some truisms in the geometry of numbers - don't you think P&S - this is more than just angels....it is more than faith in a way....it is law. Regardless, angels are out there, but so are demons - sometimes it ain't easy to tell the difference.
Save travels and I'll keep studying and learning as long as I'm breathing.
Ken
"I'll keep studying and learning as long as I'm breathing" - me too Ken! You may be very right for I am no mathematician just a simple accountant - I count beans Ha Ha.
But perhaps the magic squares will give you pause for thought?
Blessings
AP
I'm into hexagons P&S!
(smile)
So are bees Ken!
Nature trumps all with math - the golden ratio is but one example. Now then, consider the number 153. It was the number of fishes that Jesus caused the fishers to net.
"When they came ashore, they saw there a charcoal fire with fish lying on it and bread. Jesus said to them: “Bring some of the fish you just now caught.” So Simon Peter went on board and hauled the net ashore full of big fish, 153 of them. And though there were so many, the net did not burst. Jesus said to them: “Come, have your breakfast.” [John 21:9-12]
So Ken, why 153? It is in fact a magic square and an intregral part of the Universe. https://www.math-salamanders.com/magic-square-worksheets.html
Is God and eternal mathematician? Read on:
https://www.amazon.co.uk/Gods-Undertaker-Has-Science-Buried/dp/0745953719