BIG numbers.... A walk in 'their' park.... - Page 1
Forum section: electronics / general

author: GlennSprigg
author_rank: Super Contributor
timestamp: May 04, 2018, 02:05:26 pm
content: Just a little 'Factitude' walk along a possibly uncommon path through our general perceptions.Many years ago, I was asked to talk about 'numbers' to a High-School class, as a visitor....I thought about how many people do NOT grasp how powers of 10 get VERY big, VERY quick.So this is what I put together for them, and they all payed attention !!!Each new digit, as a Power, gets hugely increased, very quickly !!! For obvious instances, weknow that 103= 1000, and that 106= 1,000,000. So every time youadd '1' to the 'Power', the result is 10 times larger. So let's up the 'scale' a bit......(Please note that 'obviously' molecules/atoms/protons etc are NOT the same, and that the followingexamples are approximated to a power of 10 in many ways, and for the purpose of examples...)So let's state some facts...... about the number of "Atoms" (loosely described!!!!!!), in these......A typical sand grain 1020'atoms'.An average human 1026(what?)Planet Earth 1049(Oh... come on !!)Our Solar System 1055(yea right !!)In our Galaxy ! 1067(What have you been 'smokin' !!)Let's dare take a divergence for a sec. and talk about the 'Universe'.....Obviously, we have only 'seen' the 'Universe' as far as modern orbiting telescopes can SEE it, asof present day. I am "NO WAY" suggesting that what we have 'seen' is the LIMIT of what is or maybe out there, (possibly/almost add-infinitum), except to say that 'scientists' refer to this as the..."KNOWN UNIVERSE", so as to give a 'name' to the "Sphere-Of-All" as far as we know it... today....So... in this (previously described) "KNOWN UNIVERSE", how many 'Atoms' (give me a break) is that???'Known' Universe 1080(Now you are scaring me, or full of 'shit' xxx)We are taking another 'Diversion' now in the interim !!!......Back when the founders of 'Google' were initially putting together their crudely original concept in theirproverbial 'garage' many years ago..... One of them said to the other......"What's the name of that really big number that some Scientist named"His mate said... "A Googol" !!! (and the first guy thought he said 'Google').... (Digress again here !!!!!)....We all know names like thousand, million, billion, "quadzillion?" or what ever, but one day a Scientist saidto his son... "Make up a name for 10100", which he did, and called it a "Googol".....It has now become accepted in almost all scientific/mathematical circles.(And THAT is what was being referred to !!!!! xx)Now back to 'elementary' maths/numbers (hahaha xx)....If the 'particles' in the 'Known' Universe is 1080, (not even a 'Googol')then how useful would that number be on Earth? and with our Calculators handling this??We are 'digressing' AGAIN now.... (for F&%$ Sake!!)......It was further hypothesized that "What if this supposed 'KNOWN-UNIVERSE' was actually a SOLID !!!!!Without the 99.99999999999999999999999999999999999999999999999999% (etc) vacuum ofspace, was a gigantic SOLID mass of say 'Protons'?...... How many 'Protons' would that be......SOLID (known)Universe of Protons 10115......Can you even begin to imagine the utter ridiculousness of that number, in terms we understand ??Since then, some other 'SmartAss' (affectionately quoted!) has decided that a "GOOGOLPLEX"is 10Googol(no more 'expletives' needed to try to fathom this xx)DAMN DIVERSIONS !!!! xoxoxThink about this..... Even considering the 'GOOGOL'... (being 10100..........If you converted that to BINARY, (0's & 1's), then no matter how SMALL you wrote the list ofzeros & ones on both sides of paper.... there is NOT enough room in the entire KNOWN UNIVERSEto physically STUFF enough 'paper' to write it all..................I 'finished' by stating that even a 'Googolplex' is technically no closer to infinity than the number '1'.The kids were all very attentive.

author: sokoloff
author_rank: Super Contributor
timestamp: May 04, 2018, 02:30:04 pm
content: Relatedly interesting:(Scale of the universe video, which I found fascinating: there are pulsars smaller than tiny countries on Earth.)

author: NiHaoMike
author_rank: Super Contributor
timestamp: May 04, 2018, 03:12:57 pm
content: https://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)#10100_(one_googol)_to_1010100_(one_googolplex)

author: alanb
author_rank: Frequent Contributor
timestamp: May 04, 2018, 03:23:57 pm
content: If you want a really large number look at Graham's number. The weird thing about it is that the last 12 digits are known even though its too large to compute in full.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 04, 2018, 04:59:07 pm
content: What should really be blowing your mind is that so-called "real" numbers are the most un-real possible. They cannot be represented in any other way than a description. Any exact, nondescriptive form (like writing them out) is completely and utterly impossible: they contain truly infinite information. Real numbers are unimaginably dense on the number line, yet they are utterly inaccessible, save for the extreme few that are well known, and whatever ones we choose to enumerate, say by applying transcendental functions to computable numbers (like integers or algebraics).And that's compared to numbers like Skewes's, which are very large, but still mere integers. They might some day be computed. Graham's number, however, cannot ever be computed, even to the most unimaginably small part. While the first so-and-so digits are easily computed, no matter how many, they will always be well and truly 0% of the whole number.Tim

author: GerryBags
author_rank: Frequent Contributor
timestamp: May 05, 2018, 08:47:59 am
content: This short film, The Power of Ten, always blew my mind.<iframe width="560" height="315" src="https://www.youtube.com/embed/0fKBhvDjuy0" frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>

author: sokoloff
author_rank: Super Contributor
timestamp: May 05, 2018, 11:02:28 am
content: Quote from: GerryBags on May 05, 2018, 08:47:59 amThanks 10^6 Gerry! That’s the one I originally went looking for above, but couldn’t find it.

author: odessa
author_rank: Regular Contributor
timestamp: May 05, 2018, 11:41:55 am
content: +1 I loved that film when I saw it at school, nice find !!

author: GlennSprigg
author_rank: Super Contributor
timestamp: May 06, 2018, 12:55:57 pm
content: Thank you to the people that replied !!And the video link that 'GerryBags' provided was indeed interesting !!My initial description was not intended to be all-encompassing or limited.'Numbers' can obviously go on for ever, but my intention was to bring some moreMoths to the proverbial Light-Globe, about things people don't often think aboutAnd I would NEVER (haha) bring into the discussion about 'low' (zero) numbers !!!!!And so explain how if "3x0=0" and "8x0=0" then therefore "3 does NOT = 8"Not to mention (shit, I am...) that any number to the power of '0' = '1'?(It keeps the 'formulas' happy, if not the 'mind' )

author: Seph.b
author_rank: Regular Contributor
timestamp: May 07, 2018, 09:24:18 pm
content: I like to play Idle Games, where it is not uncommon for numbers to get to the 10^200 range or larger. The only real way to think about them is relative to what they were a bit ago. I can name all of the 10^3s up to 10^63rd now though, which is useless but fun. After a while you understand that the last derivative that changes is all that matters for making the base number actually change.

author: Rick Law
author_rank: Super Contributor
timestamp: May 08, 2018, 11:47:46 pm
content: Quote from: GlennSprigg on May 04, 2018, 02:05:26 pm(Emphasis added)Keep in mind, what the modern telescope can see isnot just limited by modern optics. We can design finer optics. There is onebarrier we cannot break: time.The age of the universe is about 13.8 billion years. So, regardless of how good the optics, we can only see as far as light can travel in 13.8 billion years - ie: 13.8 billion light year is the visibility limit in any direction. There could well be things beyond that but there is not enough time for the light to get to us. At almost 13.8 billion light year from us, what we can see is exactly the moment the universe over there became thin enough for photons to run around.This of course leads to many other questions...Within this 13.8 billion light year visible sphere, there is a limited number of particles say N - however large the number N is, it is finite. Within these N particles, each particle can only have limited number of states, and limited number of inter-particle relationships - very very large number of at least N-factorial in magnitude but again finite. So, let call this particle/relationship/states NRS. So, NRS describes all the particles, their states, and their relationships with other particles in the visible sphere. NRS will be a very very very large number but finite.If the universe isinfinitely large, there would be infinite number of such visible spheres in it. Such particle-state combination must repeat it self. That is to say, you will find another visible sphere with exactly the same NRS as we have right at this very moment... That means there is another YOU and me out there somewhere... if the universe is infinite.Mind boggling...How large must the universe be such that there is a 50% chance of one such repeat occurring? I have not done the math, but it would be interesting indeed. A universe big enough such that: 50/50, beside you, I would find another you out there reading this forum this very moment...

author: Bicurico
author_rank: Super Contributor
timestamp: May 12, 2018, 04:59:18 pm
content: Hi,As I do teach at uni and because I like to start class with a 10 minute interlude on a non topic subject, I am considering big numbers as the next topic.However, going through the numbers, they seem wrong to me.If a grain of salt has 1e20 atoms and a human 1e26 (I'm on my phone, hence this format), this means that a human has 1e6 times more atoms. But... that is just a million times more. I am sitting in a theatre right now, so i am not prepared to calculate it, but even from a volumetric point of view, that doesn't seem right.The same with the earth. 1e49 to 1e26 is a magnitude of 1e23 times more.But: There are almost 10.000.000.000, 1e10, people on earth. This means the total number of atoms in people would be 1e37, so the whole remaining earth has just 1e12 times this amount of atoms? I find that hard to believe.Please tell me where I am wrong. I did check and many sites more or less confirm the mentioned amount of atoms in sand, humans, earth and known universe.Regards,Vitor

author: GerryBags
author_rank: Frequent Contributor
timestamp: May 12, 2018, 05:41:16 pm
content: Vitor, I have nothing to add of value regarding the numbers themselves, but I do know that the biggest turn-off in my educational experience was the air teachers liked to give off of knowing all the answers, this is correct, this is how it's done. I found the uncertainties far more interesting, the possibilities of adding to the sum of knowledge not just learning by rote. Maybe you could explain to your students that these are the accepted numbers and that you have doubts and look at the problem as a class. Then each student or groups of them, could go off and see what they can find out about when these numbers were calculated, and how. If they solve the problem, or you all do together, I'm willing to bet those students never forget it.Also, Spinach! For decades in the UK we have been told to eat spinach because it is very high in iron. It's not, but when the original study was done (not repeated for a generation) a researcher put the decimal in the wrong place when writing up the results. Simple mistakes can be missed by extremely bright people for a very long time, so don't assume that the mistake here is yours.

author: Bicurico
author_rank: Super Contributor
timestamp: May 12, 2018, 07:16:05 pm
content: Thanks for your reply. I am not at all the kind of teacher that knows it all. Quite the opposite, actually and I make it pretty clear that there is much more I don't know than the little I do know.This is for the prelude of the class itself, while we wait for the last students to arrive. They pretty much like these first 10 to 15 minutes and actually quite no one arrives late.I only questioned the numbers for my own interest, not to appear as the smart ass teacher.Also, I often just google or wiki topics in question of the class, as I think it is important to understand how amazing it is to have mankind's knowledge at the tip of the finger.The ultimate goal in these first minutes is to talk to them about subjects that no class in all their student career talked about. Subjects like:What is moneyWhat is a bankWhat are taxesWhat are companiesWhat is marriageHow to be happy...This big number subject seems like a great topic, too.Regards,Vitor

author: Distelzombie
author_rank: Frequent Contributor
timestamp: May 12, 2018, 08:02:54 pm
content: I ran a website 10 years ago, about the naming scheme of such big number. They all have names, not just "googol" and "googolplex".Example: Ungintillion, Duogintillion, Tregintillion, Qadruagintintillion, Quinquagintillion, Sextuagintillion, Septuagintillion, octagintillion, NonagintillionMaybe I can find the website on one of my old drives. I'll upload it then.

author: Bicurico
author_rank: Super Contributor
timestamp: May 12, 2018, 08:39:08 pm
content: Ok, this has given me no rest, so I did some math in my head. Mind you, I did some BIG aproximations:1g of Water (H2O) has around 3e22 (this can be easily determined - 2xH = 2g/mol + 1xO = 16g/mol --> times Advogadro's Number 6e23, divided by 18)Let's consider a human of 100kg, made 80% of water and assume he is 100% water - this is a rough aproximation, but I guess it is OK and let's asume 1g of water has only 1e22 molecules, so that the calculation is easy: 100kg --> 1e5 x 1e22 = 1e27. Wow! Pretty close to OP's number!So what about the the particles in one grain of sand? Considering that the number of particles in sand are the same as in a human (per gramm and again doing aproximations) and considering that the particle of sand weights 0.1g, then the human is exactly 1.000.000 times more heavy than a grain of sand --> 1e6. Take that from the 1e27 and you get 1e21, or, using OP's numbers: 1e26 for human and 1e20 for grain of salt. Again WOW!And the earth?Let's admit that a human ocupies 1m^3 of volume. Let's admit that the earth has the same number of particles in 1m^3 as the human. I know that is wrong, but it is an acceptable aproximation for these rough calculations.So what is the volume of the earth in m^3?I Googled that and came to this on the first result:"The mean radius of the earth is approximately 6.4 million meters (exact = 6.37 x 106 m). Its volume is then: (4/3) x 3.14 x 64000003 m3. This comes to 1,097,509,500,000,000,000,000 cubic meters."(Source: What is the volume of Earth? - PhysLink.com -www.physlink.com/education/askexperts/ae419.cfm)So let's aproximate this to 1e21 m^3.Number of particles: 1e21 x 1e26 (to use OP's number for particles in a human): 1e47 particles in earth! WOWWW!!!So here are my sincere apologies to OP, as his numbers do really withstand my cross-check!It is amazing to think about this and for me it was a nice brain game to get a notion of these numbers. I think what confuses the brain is that we tend to deal with big numbers expressed by 10^x by just adding/subtracting the exponent. This makes math easy, but we (at least I) lose the grip of the logarithmic scale. Like the example with the grain of salt ves human : 1e20 to 1e26 is "only" 1e6. 1e6 is one million, a number we can still comprehend. But it is the 1e20 TIMES 1e6 that get us to the number of particles in a human. TIMES no adding or subtracting.To undertand how limited our brain is: kids aged 4 cannot understand the concept of volume, so the glas that has "more" is the heigher glas, no matter what diameter it has. I guess with big numbers our brain gets to its limit...By the way: a modern "big" harddisk for private users of 1TB stores 8e12 bits! A long way to go to just store a bit for each particle in a human.Let's assume you wanted to store the build-up of a human. For every particle you would register:- element- X position- Y position- Z positionLet's consider 3 bytes for each of these 4 values = 12 bytes12 bytes times 1e26 = 12e26 to store the position and composition of all particles in a human12e26 times 8 to have the number of bits = 96e26 or aprox 1e27How big is the required harddisk to store that?1e27 / 8e12, let's aproximate that to 1e27/1e13 = 1e14You would need a harddisk of 1e14 TB!That is 100.000.000.000.000 TB.So, to say "Scott, beam me up", we would need to transfer 100.000.000.000.000 TB of data.If we could beam at the spead of 1TB/s, it would take around 300.000 years to beam a person up.My internet connection is 1GB/s, so it would take 3 million years to download a person.Now I will give this topic a rest.Regards,VitorPS:There are probably many errors in my calculations, but all I really wanted is to get an idea of the order of magnitude...Regards,Vitor

author: VK3DRB
author_rank: Super Contributor
timestamp: May 13, 2018, 05:20:17 am
content: Now here are some REALLY big numbers...http://www.usdebtclock.org/

author: Rick Law
author_rank: Super Contributor
timestamp: May 14, 2018, 05:02:45 pm
content: Quote from: Bicurico on May 12, 2018, 08:39:08 pmProbably some under-estimation with your 300,000 years number.Prof. Lawrence Krauss, author of "The Physics of Star Trek" estimated in 2007 that if you store that info on 100gb hard drives, the stack of the hard drive will be about 10,000 light-years high. With 2007 technology, it would have taken over the age the universe to transmit that amount of data.You get to his estimation at time-mark ~ 2:35 into the video:

author: RoGeorge
author_rank: Super Contributor
timestamp: May 14, 2018, 06:02:14 pm
content: The real problem with teleportation is not storage IMO. The deep question with teleportation is 'Would you still be yourself after teleportation, or the real you was killed and replaced with an identical clone?'. And from here, the next question is 'Who/what are you?'Regarding the big numbers, if we consider that technology tend to develop exponentially (populations the same), those huge numbers suddenly doesn't look so large any more.Just wait a little longer, or find some other clever way to do it than just transmitting the coordinates for each atom. (This is a game where you start with one paperclip, and continue until you conquer the whole Universe. It gives an interesting feeling about big numbers versus exponential growth:http://www.decisionproblem.com/paperclips/index2.html)

author: Rick Law
author_rank: Super Contributor
timestamp: May 14, 2018, 06:35:40 pm
content: Quote from: RoGeorge on May 14, 2018, 06:02:14 pmWell, you do need the buffering, and there is a limit even with technology growth. You cannot use less than an atom to store an atom's info so at some point physics stops any further improvement.Anyhow, the point was to show the amount of information there, and my other point was: If you use Prof. Lawrence's number, it would be a lot more than 300,000 years to teleport the person. He was talking > 13 bn years with 2007 (1gb networking) technology. Today, we are around 10gb technology, about 10 times better. Lets make that 100 times better - that would put it in the >130 million year range. Even at 1000x improvement, we would still be talking > 13 million year range, not the hundreds of thousand range.That said, let get on to "is that clone really you?" First, I would not use the word clone. A copy and a clone is different. Clone merely copies you genetically. A copy would be entire, DNA, external appearance, etc, etc. And in the case of teleportation, including memory and experience and bad habits and bad breath.Some scientist reduced that to an electron or other elementary particles. That other electron that has all the properties of this one that just vanished, is that the same particle? It doesn't really matter if you use Einstein-ien thinking. He posit that if you experience the same force (or not), it really doesn't matter if you are free-floating or free-falling, you can't tell the difference, the effect is the same, the math is the same, so it doesn't matter - it is irrelevant.Following that line of thinking, that electron that has the same properties of this one that just vanished... it is irrelevant whether it is the same electron or not. Anything you can measure is going to be the same.

author: RoGeorge
author_rank: Super Contributor
timestamp: May 15, 2018, 06:03:40 am
content: If you ask me, the whole idea of "3D printing" atom by atom, in order to achieve teleportation, is not gonna work, because for example:- if I "3D print" atom by atom my entire PC, I won't have a running computer with the EEvblog page displayed on the screen, like I have now.- a live cat is made of the same atoms/particles/whatever (and in the same arrangement) as the dead cat, yet the dead cat won't purrAbout the electron or other elementary particles, the mainstream physics is saying that it can not be described completely because of the uncertainty principle, and because quantum particles have built in randomness (i.e. two "identical electrons" can not be forced to touch the screen in the same point in a diffraction experiment - they behave probabilistic), so I'll say an elementary particle can not be cloned. Randomness seems to be an essential ingredient of the atomic/subatomic world, and randomness, by definition, can not be duplicated.About the big numbers, the youtube channel "numberfile" have a few videos, this one is about Graham number:

author: NiHaoMike
author_rank: Super Contributor
timestamp: May 15, 2018, 07:14:04 am
content: Quote from: RoGeorge on May 15, 2018, 06:03:40 amNot correct. A living creature becomes dead because something on a molecular level changes that causes the cells to no longer function. It is true that the sheer number of atoms in anything even approaching macroscopic is a lot to handle, not to mention how to "freeze" the activity of every molecule while replicating and then somehow "unfreeze" them all at once.

author: Rick Law
author_rank: Super Contributor
timestamp: May 15, 2018, 05:58:31 pm
content: Quote from: RoGeorge on May 15, 2018, 06:03:40 amQuote from: NiHaoMike on May 15, 2018, 07:14:04 amBigger issues with "3D printing the entire PC (doesn't have the same screen)" but in both cases, uncertainty principle has nothing to do with that.As NiHaoMike pointed out, for cats, it is the molecular level activities. You have the right number of atoms and the right kinds of atoms, but arranged different enough that some activities wont work anymore. For the 3D printing the entire PC, the replication is not even close to the same thing. You can assume in 3d-print you have the same shape in macro-scale but not in nano-scale. Bigger but here is: but not with the same kinds of atoms as in the source-image.As to your statement: "about the electron or other elementary particles, the mainstream physics is saying that it can not be described completely because of the uncertainty principle." Uncertainty principal is actually both a Pros and a Cons. In a nutshell, Heisenberg's Uncertainly Principle places limit on knowledge of two properties: momentum and location. The more you know about one, the less you can know about the other.But, that also mean: may be you really don't need that exact replication because as long as the delta is within the uncertainty limit the difference would not be measurable (ie: external relationships could not be affected). Again, the Einstein-ien thinking is, ifeverything you can measureare the same, it is the same.Within that uncertainly, lone elementary particles "teleportation" has been done! (Or at least thought to have been done successfully... within uncertainty.)2016 - University of Calgary, photon teleported 6 kilometershttps://www.ucalgary.ca/utoday/issue/2016-09-20/beam-me-scotty-researchers-teleport-particle-light-six-kilometres2017 - China, photon teleported 300 miles (480km) from Ngari in Tibet to China’s Micius satellite in orbithttps://www.theguardian.com/science/2017/jul/12/scotty-can-you-beam-me-up-scientists-teleport-photons-300-miles-into-spaceSince (at least) the Chinese one is done using particle entanglement, that means it wasteleported faster than the speed of light-- but (to my limited knowledge) it also mean youmighthave transfer one of the partner (of the entanglement) using "other method" whatever it may be... The Chinese experiment is more a "transmitting information faster than speed of light experiment" than "teleportation experiment". In this case, transmitting the info to finish making a photon with parts relocated to the new location possibly using other method(s).The U Calgary experiment may also be using particle entanglement, I did not read the article detail enough to be clear on that.

author: GlennSprigg
author_rank: Super Contributor
timestamp: January 28, 2019, 12:59:22 pm
content: Quote from: Bicurico on May 12, 2018, 08:39:08 pmI know this is old now, but was reviewing this post of mine, and I never thanked/answered you !!MATE, you did not need to apologize! You did what we all should... 'Question', and prove/disprove.You went above & beyond the proverbial 'call-of-duty' with your final summations and thought process !!I also greatly thank 'Rick Law' and MANY others for their insights, (too numerous to mention!)....The sole aim of my post was to get MORE people to think, and that they did. My 'Numbers' were not meantto be the be-all-of-end-all, as we can all imagine numbers/names add-infinitum, but they have no use!!Powers of 10 can not be taken for granted on this scale.Thanks for the great input, and I'm glad you can sleep now !!!

author: coppercone2
author_rank: Super Contributor
timestamp: January 28, 2019, 05:03:50 pm
content: I find tetrons and higher to be interesting. X^x^x

author: raptor1956
author_rank: Frequent Contributor
timestamp: January 29, 2019, 05:00:58 am
content: Just discovered this recently reposted necro thread...One I remember from school...A mole is 6.022E23 of something and when applied to atomic structure as it often is you get a mole of Hydrogen weighing approximately 1.008 grams -- so, a pretty small weight. A mole of gold would weigh about 197 grams or less than a fifth of a kg. A mole of rice grains would fill enough train hopper cars to form a train long enough to stretch from the Earth to the Sun and back more than 9000 times. A mole of Aluminum weighs about 27 grams or a bit less than an ounce.Brian

author: TerraHertz
author_rank: Super Contributor
timestamp: January 30, 2019, 05:02:53 am
content: My favorite 'big' number is relatively modest, but has quite real consequences. The ratio of strength of the electrostatic force and gravitational force, between any two nuclear particles.The ratio of Felec/Fgrav is about 1.2 x 10^36 for protons, regardless of the distance between them.It's higher for proton to electron, and electron to electron, due to the lower masses.We only think of gravity as more significant, because it's additive, and in our conductive environment electrostatic differentials mainly discharge. Leaving only gravity visible on a macro scale. But it seems that electrostatics actually do have great effects on astronomical scales. I'm also inclined to suspect that electrostatic effects occur in things like thunderstorms, and may be very significant but are just ignored because of widespread ignorance of electrostatics.

author: GlennSprigg
author_rank: Super Contributor
timestamp: January 30, 2019, 01:29:10 pm
content: Quote from: TerraHertz on January 30, 2019, 05:02:53 amI actually like playing with the weird effects of SMALL numbers in maths !!....For eg., the digits of multiples of '9', always add up to 9.9x9 = 81. 8+1 = 99x15 = 135. 1+3+5 = 99x279 = 2511. 2+5+1+1 = 9. (Now with a simple carry...)9x593 = 5337. 5+3+3+7 = 18. 1+8 = 99x987 = 8883. 8+8+8+3 = 27. 2+7 = 99x254679 = 2562111. 2+5+6+2+1+1+1 = 18. 1+8 = 9. etc etc. No exceptions.We used to use this here in Australia to determine if an 'AM' broadcast was on station for acorrect digital readout. You see, the USA uses 10-khz boundaries between possible 'stations'.Here, we use '9-hkz' boundaries... . AH!!!... '2512' on the dial must be wrong. Must be '2511'Or maybe numbers multiplied by '11', you ADD the digits again, and put the result in the middle....42x11. 4+2 = 6. Answer = 462.63x11. 6+3 = 9. Answer = 693. (Now with a carry....)48x11. 4+8 = 12. Carry the '1' to the '4' = 528.76x11. 7+6 = 13. Carry the '1' to the '7' = 836. Ah... beauty in simplicity !Now here's the 'pièce de résistance'BEFORE the days of Microsoft Excel etc, which now have the EASY functions to calculate the Dayof the Week of a particular date, I used to calculate it THIS way, mainly just because I could!!!!...(Simplified). In my coding, I would calculate the number of days elapsed since 1/1/0001.(Yes!, with Gregorian/Julian changes, etc etc). Now considering THAT day of the week, I dividedthat number of days by 7. If there was no remainder, then it was the same day-of-the-week.However, that's where my 'brain' took a left-turn, just for fun!!!! I looked at the digits after the decimal.I found that if i kept adding the decimal digits, up to and including the 6th digit, until there was 'one'digit left, then the result was ALWAYS 7, down to 1. (Sunday, Saturday, Friday, Thursday, Wednesday,Tuesday, Monday). So JUST FOR FUN, I created a 'String' with those day-names, and used the resultantsummation digits 7-to-1 to pull out the 'Sub-String' for the actual day of the week.It was accurate, but I always wondered if someone years later would look at my 'code' and think theysaw a message from Mars !!!On a serious note though... there doesn't 'seem' a logical academic reason to 'add digits in a number',but you would be surprised how much/often this works in mathematics.