This Document Is A Copy Of The Form 10-Q For The: Fill & Download for Free

Q: “What characterises an excellent PhD thesis?”Novelty characterizes an acceptable (excellent?) PhD thesis. A PhD research must significantly be novel and include new ideas. Most of the PhD candidates claim that their researches subjects are new and novel, while they are actually replicating works of other researchers with some small changes in forms and organization while contents remain almost the same. A PhD research with 90% replication of prior works and only 10% added material is not a novel one.The other character of a good PhD thesis is having good organization.It must be clear and concise. Presenting results of a research clearly in a shorter document is strength of that document. Some PhD theses that I have reviewed clearly show that the author tried to intentionally make it longer with vague organization to mislead and confuse the reviewer, actually to trick.The writing of the thesis must be clear and correct.Excellent? Who knows. These are characters required by a PhD thesis, as I observe. The influence of a research on the related field of science and arts determines its quality. It is almost impossible to evaluate the real significance of a PhD thesis at the time of publication, but it is not hard to examine its novelty. It may take years or decades till it reveals its values and influence that can be evaluated in a typical ranking.Canadian physicist Donna Strickland | Physics and Astronomy presented her PhD thesis with Gérard Mourou as mentor in the University of Rochester in 1988. At that time who knew how influential would be this research and thesis, while its novelty was obvious, at least to PI and researchers in that field of physics. After 20 years, Prof. Strickland was awarded the most prestige medal in physics (Nobel Prize) for her work and thesis she had conducted and written in 1988 as a PhD candidate. That is a typical excellent PhD thesis. Full copy available at this site:http://www.lle.rochester.edu/media/publications/documents/theses/Strickland.pdf.

Much Simpler & Faster Online Process (Updated February 2017)My experience was with KR puram RTO without using any broker or agent. Now that the process is centralized, I believe this procedure can be applied across all RTOs.Step I: Online Application (20 mins)The home page for license application is https://parivahan.gov.in/sarathiservice/sarathiHomePublic.do. This is a user friendly website and has all necessary links for the required steps as given below.1.LL Application:Clicking on “Apply online – New Learner’s license” should take you to New LL Stage Details. Select new driving learning license and fill the form in the next page. (If you need license for car & 2 wheeler, you need to select both LMV and MCWG in the “Class of vehicles”) Make sure all personal details match with the document proofs.Once the form is submitted, you will get an acknowledgement and receive a sms on your mobile with the application number. You can take a print out of the completed form (Captioned as Form 2).Paste your photograph and fill in any missing details including CMV Form 1 and sign where required. You need to scan or take a picture of filled-in CMV Form 1 (along with annexures, if applicable) for uploading later.Tip : If you are 40 years or older (and / or) require a commercial yellow board license, then you may need to undergo a medical test and submit a fitness certificate as a part of Form 1 above. (Depending upon your RTO, you can also get a medical certificate near RTO office for about Rs 50 to 100)2. Uploading documents:The next page will have options to upload the required documents. Online form dropdown menu in that page shall give you the list of eligible documents. You basically need to upload scanned copies of three types documents (in pdf or jpeg format and size less than 1 MB).(i) Age Proof – Common documents include any one of PAN Card, Passport, School Certificate or Birth Certificate(ii) Address Proof – Common documents include any one of Passport, Voter id card, Electricity Bill, BSNL/MTNL Bill, Rental agreement. If you are staying at a temporary address, please upload the rental agreement with your name on it and the latest electricity bill with the name of the owner (merged into a single pdf document). You won’t get an option to upload your permanent address proof and it is recommended that you carry it while you visit the RTO.(iii) Form 1 (self-declaration) – This is the scanned copy of the CMV Form 1 as mentioned above.Tip : You can get the entire list of documents or procedure by visiting the official link https://sarathi.nic.in:8443/nrportal/sarathi/HowTo/howtoLL.pdf.3.Uploading photo & signatureYou need to upload your latest passport size photo and signature. The tricky thing is both of these should be less than 20 kb each. Use websites like Resize Images online or Smallpdf.com - A Free Solution to all your PDF Problems to reduce the size and they should be good to go.4. Booking LL Slot:The next step is to book a slot to visit your chosen RO. As many mentioned here, chose weekdays if possible and preferably the earliest slot in the morning.5. Fee paymentThis is an option for online payment but this may not work depending upon the RTO chosen. If your RTO does not have this option, the website shall give you a message to visit the RTO to make the payment.This marks the end of your online application process. If you wish to view or modify the details of application or appointment time later, you can do so by selecting the required option in the home page https://parivahan.gov.in/sarathiservice/sarathiHomePublic.do and entering your application number and date of birthOnce you are satisfied with the application, you should take printouts of the acknowledgement form, appointment receipt and application form (as already done in Step 1)Step II: Preparation for the LL Test (20 mins)You have to prepare for an online test (at RTO) to test your knowledge on signs and driving rules. Preparation is a short but very important process and if not done properly, you may have to visit the RTO one or more time again. You can refer the following sectionsTypes of traffic signshttp://transport.karnataka.gov.in/index.php/information/details/mandatory_signshttp://transport.karnataka.gov.in/index.php/information/details/coutionary_signshttp://transport.karnataka.gov.in/index.php/information/details/informatory_signTraffic questions Q&A bank is available here http://licencetest.in/question-bank/category/en/Step III: Visit the RTO (20-30 mins)It is preferred that you visit the RTO on the allotted date and time, but generally you can visit any time after you complete your application process in Step 1 (RTO systems have improved so you need not wait for 4 hours as many have mentioned)Things to carry(i) Original Age Proof(ii) Original Address Proof(iii) Printout of Application form (Photo pasted and signed)(iv) Printouts of acknowledgement form and appointment receiptIn most cases documents (i) and (ii) are enough and is only to be shown. Since they have all the details online, your application number is enough to fetch them the details of your application. RTO officials won’t ask you for (iii) and (iv) above, but it is good to carry them just in case.At this stage, your photograph or copies of documents are not required to be taken either (no need for a brown paper folder). You can carry them if you want to be super prepared (But nobody would ask you)Fee PaymentYou need to visit the cash counter to pay the fee for your application first. (In case of KR Puram RTO, this is Counter 3 located on the left corner as soon you enter the ground floor).There should be a separate counter for LL fees payment. Mention your application number (from the sms message) or show the application form if you have taken the printout.Fee may vary depending upon the vehicle you have chosen. For ex. If you need both LMV and MCWG, then you may be asked to pay Rs 350 and they will give you a system generated receipt for this amount (Keep this safe)Document Scrutiny & LL TestTip: The RTO office is typically filled with many people applying through driving schools and also those who require commercial license (yellow board). Please don’t get baffled by seeing long queues or seek advice from them. If you are unsure, better to ask the RTO staff by mentioning you applied online. They will guide you.The next step is to visit the room for verifying your documents and the online test. (In KR puram RTO, this is counter 4). Normally the queues for online applications are shorter so you can directly ask the RTO staff regarding whom to approach.The verifying officer will check your online details and online uploaded documents along with your originals. (In very rare cases if he finds any discrepancy, he may ask you to edit information or upload documents. It would be good to carry a mobile phone with good internet connection and camera).Once documents are verified, the assessing officer will ask you to note down a pin number for your test and will allot you a computer to take the test. You can login to the test using the application number, DoB, password (you will receive this as a message on your mobile before the test) and pin number (as given above).The test will consist of 15 questions related to signs and road rules. Test duration is 15 mins (Each question will have one minute to answer with timer running). You have to score 10 marks to pass (Should be a cake walk if you have prepared from the links above).If you have failed, you may have to come back the next working day to repeat the test.If you have passed, then inform the officer and he will collect your receipt and confirm that your process is complete.After 2 days, you will receive a message that your learning license is approved. You can collect your learning license by either (i) Visiting the RTO in the evening time or (ii) Downloading it from the home page by logging in to your application page.Hope this helps. I will update the details of obtaining the driving license after one month.

In the history of mathematics, it can be difficult to match the sheer audacity of the great minds of Ancient Greece. At a time before the invention of notebook paper—even before the invention of zero—several visionary Greeks managed to calculate aspects of the natural world that remain staggering to this day.I will focus on two such audacious calculations from two of the greatest minds ever to grace this Earth with their consideration. Both lived in the 3rd Century BCE, and though neither one lived in modern-day Greece (one was born in Libya and worked in Egypt, the other was from Sicily), they both fall squarely under the umbrella of Greek thought and study. Both had the audacity to reach for the impossible, and both used unparalleled brilliance to reach their conclusions.So let me address each in turn.Eratosthenes of CyreneImage Credit[1]Eratosthenes may not have been the most attractive dude on the block, but boy was he ever smart. In fact, smart doesn’t really cover what Eratosthenes was. Born in Cyrene, on the northern coast of Africa, Eratosthenes’ education brought him eventually to Athens, where he studied philosophy first under the Stoic Zeno of Citium[2] and then under the Stoic/Cynic Aristo of Chios.[3] During this time, he began to write mathematical analysis of Plato’s postulates and even began writing poetry on the side.His poetry was so good that it began to get him some recognition, and in time even crossed the sea to reach the halls of the Pharaohs in Egypt. Ptolemy III Euergetes invited him to be the head Librarian of the Great Library at Alexandria. As head Librarian, he did a great deal to expand the library’s already-unparalleled collection of knowledge. He also invented an early cataloguing system, so that scrolls could more easily be found within the library’s extensive archives.It is clear that, throughout his tenure as librarian, he did more than simply copy and tag texts. Finding himself with access to more knowledge than perhaps any other man on Earth at the time, Eratosthenes seems to have recognized his privilege, and at the same time allowed his curiosity to run wild as he sought to amass as much knowledge and understanding as could be fit within a human mind.His studies led to some answers but, like any great scholar, he always found himself with a surplus of questions that surpassed even his his knowledge to address. One question in particular would lead him to a calculative effort that is truly exquisite in its audacity. It is a question that would likely tax even you—dear reader—living in the modern world of calculators, textbooks, and mathematical concepts that would not be devised until centuries after his death:How large is the Earth?Take a moment to consider how you might try to answer that question if you were deprived of the access to any authority that could simply hand the answer to you on a platter. If you had to calculate the size of the Earth without looking it up, how confident do you feel that you could do so, even with modern technology? How would you prove it?Now imagine that you are living in a world without the internet, without calculators, without pens and paper, without zero, and without anyone who has ever even tried to make this calculation before, and you can perhaps begin to understand the conditions which were met by Eratosthenes. Would you even begin to know where or how to start?Before I begin on his calculation, I should take a moment to dispel a myth. It is often taught in America that back in Columbus’s day, everyone thought that the world was flat. That is, for lack of a better word, a lie. People had understood that the Earth was a sphere since well before Eratosthenes, and by his day every educated Greek was well aware of the globular Earth. That is remarkably important if we are to sensibly examine his calculation of its circumference.It is hard to say how exactly the process began, but Eratosthenes set out to make this unfathomably audacious calculation for himself. There was a single piece of information that passed through his grasp as he studied in his library, and he had the presence of mind to recognize it as the pivotal fact that it was in his pursuit.At some point, Eratosthanes read the account of someone who had travelled through the city of Syene, in southern Egypt (a short way south of the modern city of Aswan, the location of Syene is now under the waters of Lake Nasser, which was created by the Aswan Dam in order to bring hydroelectric power to Egypt). The account said that there was a deep well in Syene in which, at noon on the Summer Solstice, the sun shone all the way to the bottom without casting any shadow.That might not sound like much to you, dear reader, but Eratosthenes recognized it for the exquisite datum that it was. That meant that on the Summer Solstice, the sun stood directly above the city of Syene at noon, meaning that Syene must lie exactly on the Tropic of Cancer.[4] From there, all it would take to calculate the circumference of the Earth was patience and mathematics.Those unfamiliar with Greek often spend their lives blissfully unaware of the fact that the word “geometry” literally means “earth-measuring,” and it was Eratosthenes who first exemplified its capability to accomplish that end. He commissioned a long wooden pole to be crafted, perfectly straight and with a length that was measured exactly. This pole he had erected in Alexandria as close to perfectly vertical as the tools of his day would allow. Now he only had to wait.On the Summer Solstice, he had the greatest masters of measurement in the land wait for the sun to reach its apex. At exactly noon, measurements were taken of the shadow cast by the pole. More mathematically-minded readers will likely have worked out the rest of the calculation for themselves, but I am more than happy to explain it for the rest of us.The length of the pole (which he knew) and the length of the shadow (which had just been measured) provided two sides of a right triangle. From there, the trigonometric principles established by Pythagoras and embellished upon by those who came after him allowed Eratosthenes to calculate the angle at which the same sun that sat vertically above Syene cast its rays upon Alexandria, and thereby to determine the angular degrees that divided the two cities in the greater sphere of the Earth.Image Credit[5]Once he had calculated the angular distance between Alexandria and Syene from the perspective of the Earth’s core, all Eratosthenes needed was the distance between the two to extrapolate the total circumference of the Earth. In this regard, he had a great deal of luck on his side. For all its twists, turns, and cataracts, the Nile River, on which both cities were situated, runs a remarkably longitudinal course throughout all of Egypt. Taken as a whole, its adherence to a perfectly south-to-north course is almost uncanny. Furthermore, as the most trafficked river of trade in the world (at the time) there were already extensive and continually-updated documents measuring the distances between all of its major ports of trade.And Eratosthenes was the overseer of the greatest compilation of knowledge on Earth, and in Egypt most particularly.So it was that Eratosthenes, using only the facts he had read, his own grasp of the principles of mathematics, and a bit of on-the-fly thinking, calculated the circumference of the entire planet more than seventeen centuries before Columbus would drastically underestimate that same calculation and believe that he had found India when he was actually in the Dominican Republic.By modern calculations, Eratosthenes’ calculation was only off by about 41 miles,[6] roughly the distance from San Jose to San Francisco.(The circle above has a diameter of 41 miles) Also, not sure if I need to source a screenshot, but here is the site I used.[7]Now if you ask me, that is pretty effing audacious. To stare down a calculation that had never even been attempted and to work it out so perfectly with means so limited is truly a testament to the ambitious ingenuity of the human mind.But Eratosthenes was not alone, and my next entry might even outdo him on sheer audacity, so let’s keep going.Archimedes of SyracuseImage Source[8]Now when it comes to ultra-badass scientists/mathematicians, there really may be no parallel to Archimedes. His brilliance—matched only by his ultra-badassery—is so intense that there is still some skepticism regarding the assertion that anyone could ever have truly been as much of a baller as Archimedes appears to have been every single day.Among his myriad* accomplishments not to be examined in this answer, you will find:An efficient water-pump that still bears his name (and which, for the record, was apparently invented to pump water from the hull of a warship he had invented, which just so happened to be the largest in the history of the Ancient World).[9]The use of mirrors to literally set enemy ships on fire, which still—twenty-three centuries later—continues to bear the unbelievably sci-fi name of the “Archimedes Heat Ray.”A Renaissance Painting of the Heat Ray from Wikimedia Commons, still inspiring fear and awe 1800 years later.Devising a way to calculate the density of an object by combining the measurement of its displacement in a measured quantity of water with its mass, now known as Archimedes' principle (the discovery of which was apparently made while he was in the bath, leading him to famously shout “Eureka!” (or, more properly, “εὕρηκα,” meaning, “I’ve found it,”) while running naked around the building which contained the bath that no longer contained the ecstatic Archimedes).But, worthy as all those discoveries were, they are subjects for another day. Now we are looking at something that somehow manages to be more audacious than sprinting naked through the halls of academia, pumping water from the bellies of gargantuan warships, or even—somehow, bafflingly—setting enemy fleets on fire with nothing but a mirror and the Sun.As I have already mentioned, the mathematicians of the Hellenistic period, for all their brilliance and far-sightedness, were working with a vastly inferior set of tools than those with which I empower my Second-Graders every day in math class. Indeed, every day I teach place value to a group of seven-and-eight year olds who already seem to think that it is kids stuff. The concept of zero, and the magical way that it allows a mere ten digits (itself included) to express an infinite spectrum of numerical value is so ingrained on us these days that it seems quite basic, even to children.That’s why I always love to tell them about Archimedes.See, in Archimedes’ day, the numbers didn’t go on forever like they do now. Of course, people recognized that there was no “highest number,” but even within the culture of mathematics that had the likes of Euclid and Pythagoras for inspiration, it was widely accepted that some numbers were just too high to be discussed in any kind of a constructive manner. Greek Numerals were drastically different than the numbers we know and love today. The concept of zero and the place-value it empowered would not even be invented in India until about six centuries after Archimedes’ death, and the Arabs wouldn’t bring it to prominence in Europe until centuries thereafter.The Ancient Greeks did math with letters. While they used the Greek alphabet, their system can be transferred to our own Latin alphabet without much effort for the ease of explanation. To put it in our own letters, the Greek system would use the first nine letters (a, b, c, d, e, f, g, h, and i) to represent the numbers 1–9. Then the following letters could be used to represent the next order of magnitude, so that j, k, l, m, n, o, p, q, and r would represent 10–90 respectively. As numbers got higher, it was decided that not every one of the nine non-zero numerals requires representation. But still, the problem of simply running out of letters remained.As such, Greek Numerals had an upper bound, above which the numerals had yet to be invented to express such a quantity. For the Greeks, as for a remarkable number of other contemporary cultures, the greatest expressible number was 10,000, which they called “μυριάς” (myrias). Anything above 10,000 was considered an uncountable multitude, which is why we still use the term “myriad” to mean “innumerable” in modern English.[10](Note: I discuss this a bit in another answer on a very different subject, but one well worth a read.)One of the common analogies in Archimedes’ day was that the number of grains of sand on a beach was something that could never be mathematically expressed with any degree of exactitude. It was simply, “a lot,” and everyone should be content to leave it at that.As it happens, Archimedes didn’t like other people telling him what was beyond the bounds of his ability to calculate or express. Not only did he scoff at the idea of the grains of sand on a beach defying his calculative abilities, but he decided to take the proposed impossibility about ten-trillion steps further.“The grains of sand on a beach are too numerous to be calculated, you say?” Archimedes quipped. “Hold my fermented grape mash. I’m gonna calculate how many grains of sand it would take to fill the universe!”Of course, those weren’t his exact words, nor even any kind of close translation, but I nonetheless feel that the sheer audacity of Archimedes’ mathematical cojones are accurately conveyed in the lines above. Not only did he reject the innumerable quantity of sand on a beach, he jumped straight to the whole damn universe (as he understood it, of course).But to do that, he first had to invent his own number system.Without spending too much time going into the details of his invention, Archimedes saw that the numerical systems of his day could be extrapolated out exponentially to the point that they could encompass numbers on a scale that we still haven’t come up with specific names for.(Note: as much of a Greek purist as I tend to be, I will transition all of the terms in the following section into English for you, dear reader. You’re welcome.)Archimedes figured that if myriad was the highest number, then he could start working from there. Myriad—which is to say 10,000—became his “number of the first order.” You could have one myriad, two myriad, three… I’m just playing. You could go all the way up to a myriad myriad, also known as [math]10^8[/math], which could then be used as a new substitute for myriad. He named this new quantity as his “number of the second order.” And then the pattern continued.This system allowed Archimedes to succinctly write numbers ranging up to [math]((10^8)^{(10^8)})^{10^8}[/math] . As someone with very little experience with LaTeX math coding, I hope that comes out coherently, but in case it doesn’t, that is a one with eighty-quadrillion (80,000,000,000,000,000) zeroes.That’s a pretty effing huge number, and the fact that Archimedes took the Greek Numeral system all the way from 10,000 to [math]10^{79,999,999,999,999,996}[/math] times as much is pretty hardcore if you ask me.But that is not all.Now that he had invented super-huge numbers, Archimedes had to calculate the size of the universe, and even in that small step, he was so far ahead of his time that it is difficult to even fathom just how insanely right he was.But first, let’s take a moment to examine what a word like “universe” would mean to an ancient Greek. To Archimedes, the “universe” was generally confined to what we would now call the solar system. The universe had a single sphere at its center, and a whole host of planets circulating around it. Beyond that was a spherical edge painted with stars. The very concept of foreign galaxies was yet to be devised.Indeed, for the greater part of the next two millennia, it would be held as an indisputable fact that the Earth was the center of the universe, and even 1800 years after the death of Archimedes, the assertion that it might be otherwise would remain so revolutionary as to merit oppression against those who spoke it. When Copernicus’ heliocentric theories were first printed—more than eighteen centuries after the death of Archimedes—they were enormously controversial.Not to Archimedes.Indeed, the works of the first great heliocentric astronomer, Aristarchus of Samos, who I discuss in this remarkably popular answer, were lost to history entirely, and it is entirely through the work of Archimedes that we know of his brilliance at all. Were it not for his incredible work, even educated people would still blithely assert that Copernicus was the first to posit that the Earth orbited the Sun, and the depth of Greek insight into the matter would lie in the darkened vaults of unrecorded history.While I may not be able to solidly attribute Archimedes’ reason for believing that the Earth revolved around the Sun, it is undoubtedly true that he accepted the heliocentric model of Aristarchus as the one by which he ought to make his calculations.Armed with his new form of advanced large-number mathematics and his unbelievably-prescient Aristarchan Heliocentric model, Archimedes determined that the number of grains of sand that it would take to fill the universe (a.k.a. the Solar System) was approximately [math]10^{64}[/math].I would comment on the accuracy of that calculation if I was anywhere near brilliant enough to do so. As it stands, all I can really say is, “damn, that Archimedes dude was smart as hell!”ConclusionI have always thought that there was something staggeringly audacious about the very premise of mathematics. Terms like infinity, which are beyond the scale of the human mind to comprehend, get thrown around in school classrooms like Halloween candy. Every so often, I have a student ask me the remarkable question, “how high can you count?” The truth of the answer, that I could keep counting not only for the rest of my life, but for the length of time that the universe has existed without even nearly exhausting the list of numbers whose names I have already learned in my infinitesimal time on Earth almost moves me to tears.Numbers are a different dimension. We can write them, but after a certain point, we lose our ability to even conceptualize their scale or scope. I can talk about 7.5ish Billion people on Earth, but that number means literally nothing more to me than μυριάς did to the Greeks. At that point, it’s all just “a friggin lot.”I would therefore posit that a huge percentage of the mathematical calculations that a high school calculus student makes over the course of a single standard class exist on a level of audacity that they will never fully realize.This is why I like to teach children about the history of mathematics. Algebra is so much more beautiful when you see it through the eyes of Muhammad ibn Musa al-Khwarizmi, and when you know the words from which its name was taken: “calculation through the completion and balance of broken things.” I am sure that my translation is less-than-perfectly accurate, but it bears a portion of the beauty that is lost on algebra students.If I am honest, I don’t think that the most audacious mathematical calculations are confined to the Ancient World. Truly I believe that mankind’s most audacious calculations are still ahead. I am so confident as to be pretty-well positive that what we have yet to learn will dwarf the whole monumental mass of what we have learned so far.So I say we keep our eyes on the horizon. I say we keep our minds to the Aristarchuses of our time, and dare to believe in their monumental hypotheses. I say we take the word “incalculable” out of our personal lexicons, and set ourselves to the task of continuing the path of brilliance that has carried us this far.After all, we are humanity. We may be small, but look what we’ve done so far!Just imagine what we can do next.Thank’s for reading.Now it’s your turn.*See what I did there?Note: Somehow, bafflingly, I managed to get through this whole answer without mentioning that the name of Archimedes’ revolutionary text, originally called Ψαμμίτης (Psammites) is usually translated into English as the incredibly awesome-sounding title: The Sand Reckoner.Here is an annotated translation: Archimedes, Sand-Reckoner, Intro.Update: So this answer seems to have rather inexplicably gotten some traction, and I have several comments questioning how reasonable Archimedes’ calculation of the number of grains of sand that could fit into the Solar System/Universe (which had a radius of around one lightyear, by his estimation) was, and several comments have claimed that he was off by many orders of magnitude.Rather than arguing Archimedes’ rigor or accuracy, I would rather like to point out that a “grain of sand” has no officially established size, and that the grains with which Archimedes performed his calculations were likely quite a bit smaller than those being perceived by dissenters.Indeed, given that Archimedes was conducting his work well after that of Democritus and Epicurus, I am not entirely convinced that the “grains of sand” to which Archimedes refers were not essentially synonymous to atoms in his mind.Of course, that only makes him more incorrect, but if we take into account the sort of limited perception the Ancient Greeks had about atoms, I think it makes the whole calculation a great deal more sensible. The word “atom” comes from the Greek for “unbreakable.” The prefix a- (as in atheist) is negatory, and the root “-tom” (as in lobotomy) means “to cut.”The root of Greek Atomic Theory was that microscopic infinity just didn’t make sense. If everything could be broken, then everything would be insubstantial. Democritus and Epicurus held that there must be a smallest form of matter, beyond which it could no longer be broken down.I think that Archimedes’ calculation played upon this theory by using the smallest possible grain of sand as its calculative unit rather than the average grain. Indeed, Archimedes posited that a myriad (ten-thousand) grains of sand could fit into a single poppy-seed. If you know how small a poppy-seed is, then you can hopefully conceptualize just how small Archimedes’ grains of sand are, and hopefully understand my assertion that they may have been a filler-term for atoms.Here it is in the annotated translation of his own words:With some of these supposed and others demonstrated, the proposed claim will be proved. For since it is supposed that the diameter of the poppy-seed is not less than a fortieth-part of an inch, it is clear that the sphere having an inch diameter is not larger than can contain six-ten-thousand and four-thousand poppy-seeds. For they are multiples of the sphere having its diameter a fortieth-part of an inch by the stated number. For it has been proved that spheres have the triplicate ratio to one another of their diameters. It is clear that if a sphere having an inch diameter is filled with sand, the number of the sand would not be larger than ten-thousand-times six-ten-thousand and four-thousand.[11]I hope this clears some things up. I doubt it, but I hope…Footnotes[1] Biography of Eratosthenes, Greek Mathematician and Geographer[2] Zeno of Citium - Wikipedia[3] Aristo of Chios - Wikipedia[4] Tropic of Cancer - Wikipedia[5] Eratosthenes | Biography, Discoveries, & Facts[6] Eratosthenes - Wikipedia[7] Draw a circle with a radius on a map[8] Archimedes | Facts & Biography[9] Archimedes' screw - Wikipedia[10] myriad - Wiktionary[11] Archimedes, Sand-Reckoner, ch. 4