Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 10th 2019

    for the moment just to make links work

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 1st 2021

    added pointer to this article, from a few days back:

    • Susan Gardner, Samuel D. McDermott, Brian Yanny, The Milky Way, Coming into Focus: Precision Astrometry Probes its Evolution, and its Dark Matter (arXiv:2106.13284)

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021

    added this quote:

    The Milky Way, is made up of a very large number of small, tightly-clustered stars, which, on account of their concentration and smallness, seem to be cloudy patches. Because of this, it was likened to milk in color.

    (Naṣīr al-Dīn al-Ṭūsī in Tadhkira 1261 AD, as translated in Ragep 1993, p. 128)

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021
    • (edited Aug 22nd 2021)

    What’s a good primary source on the common claim that Democritus already held this same view on the Milky Way?

    Here it says that Democritus’ claim is related by Plutarch in “De Placitis Philosophorum”. What exactly does the one line of (untranslated) Greek there say?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021

    added also the quote from (Pseudo-)Plutarch (thanks to David C. for digging it out!):

    Democritus, [[holds]] that it is the splendor which ariseth from the coalition of many small asterons, which, being firmly united amongst themselves, do mutually enlighten one another.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorGuest
    • CommentTimeAug 22nd 2021

    The relevant page of Plutarch’s work is translated here. The ’milk’ analogy seems to be attributed to Parmenides.

  1. The above was me!

    • CommentRowNumber8.
    • CommentAuthorRodMcGuire
    • CommentTimeAug 22nd 2021

    splendor which ariseth from the coalition of many small asterons,

    Why are you using “asterons” (ἀστέρων) which is just the genitive plural of “aster” (ἀστήρ) = star?

    The Greek is: Δημόκριτος πολλῶν καὶ μικρῶν καὶ συνεχῶν ἀστέρων συμφωτιζομένων ἀλλήλοις συναυγασμὸν διὰ τὴν πύκνωσιν.

    Then again there is the question of why in some translations “small stars” becomes “small bodies”.

    This Quora brings up the translation issue. https://www.quora.com/How-did-Democritus-recognize-that-the-Milky-Way-consists-of-a-number-of-stars

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021
    • (edited Aug 22nd 2021)

    Re #7. Thanks, yes, that’s the pointer that David C. had given! Had recorded it here, should have said so.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021

    Re #8:

    Why are you using…

    As you probably suspected, the reason is that I am ignorant. But from that Quora comment it looks like we may just put “stars” instead of “bodies” and have the translation improved thereby. Am making that edit now.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021

    Now that we went this far in this entertaining distraction, we ought to add a quote from Galilei where he first reports seeing the MW stars resolved. I am out of time for this now. But if anyone has a good pointer to an ~original source/quote, let’s add it.

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 22nd 2021

    Added this quotation from Galileo

    the Galaxy [Milky Way] is nothing else than a congeries of innumerable stars distributed in clusters. To whatever region of it you direct your spyglass, an immense number of stars immediately offer themselves to view, of which very many appear rather large and very conspicuous but the multitude of small ones is truly unfathomable.

    diff, v6, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021

    Thanks!! I have added a pointer to a pdf.

    diff, v7, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeAug 22nd 2021
    • (edited Aug 22nd 2021)

    Galileo clearly has a point with his:

    all the disputes that for so many generations have vexed philosophers are destroyed by visible certainty, and we are liberated from wordy arguments.

    For how good was Democritus’ claim really, given that it, apparently, came with no more substantiation than all the others that Plutarch lists.

    Reminds one of the long list of predictions of the Higgs mass. A couple of which were right, but nobody is sure if these were right for the right reasons…

    • CommentRowNumber15.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 22nd 2021

    Mind you, in case one imagines observation is straightforward, take a look at his Moon on p. 19. That large circular crater on the diameter isn’t really there.

    • CommentRowNumber16.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 22nd 2021
    • (edited Aug 22nd 2021)

    Not to mention the Martian canali.

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2021

    Footnote 36 is concerned with this point:

    It was not Galileo’s purpose to make an accurate map of the Moon, but rather to illustrate its Earth-like nature. It is therefore often difficult to identify features on his drawings.

    In view of this scientific shortcoming it is interesting to see from the introduction how the true genius behind all this was his figuring out how to construct a good “spyglass” from the hints he received of that “certain Dutchman” (old tradition of not citing sources properly!) given that, as footnote 24 claims, available mathematical

    theory could not, however, give him much guidance in duplicating the invention.

    Because, as footnote 31 knows, the idea of pointing telescopes to the moon was not that new, it just needed better instruments:

    In fact, in August 1609 Thomas Harriot in England had turned a six-powered spyglass on the Moon—not much better that what could be seen with the naked eye.

    Besides the engineering skill, the lead-in shows a remarkable energy for fund-raising.

    • CommentRowNumber18.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 23rd 2021

    Hans Lippershey was the Dutchman.

    It helped in this case that the instrument had a separate commercial use, allowing merchants to see their ships approaching port sooner.

    It’s an intriguing era. Lots of discussion of what it means to see something. Had we lost Adam’s sensory abilities in the Fall? Etc.

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2021

    Hans Lippershey was the Dutchman.

    Makes sense that a Galileo I wouldn’t reference a mere Hans or Thomas.

    It helped in this case

    But did he have a prototype to inspect, or did he manage to go by verbal hints?

    • CommentRowNumber20.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 23rd 2021

    According to Wikipedia

    Lippershey’s application for a patent was mentioned at the end of a diplomatic report on an embassy to Holland from the Kingdom of Siam sent by the Siamese king Ekathotsarot: Ambassades du Roy de Siam envoyé à l’Excellence du Prince Maurice, arrivé à La Haye le 10 Septemb. 1608 (Embassy of the King of Siam sent to his Excellency Prince Maurice, arrived at The Hague on 10 September 1608). This report was issued in October 1608 and distributed across Europe, leading to experiments by other scientists, such as the Italian Paolo Sarpi, who received the report in November, and the English mathematician and astronomer Thomas Harriot, who used a six-powered telescope by the summer of 1609 to observe features on the moon.[36]

    The Italian polymath Galileo Galilei was in Venice in June 1609[37] and there heard of the “Dutch perspective glass”, a military spyglass,[38] by means of which distant objects appeared nearer and larger. Galileo states that he solved the problem of the construction of a telescope the first night after his return to Padua from Venice and made his first telescope the next day by using a convex objective lens in one extremity of a leaden tube and a concave eyepiece lens in the other end, an arrangement that came to be called a Galilean telescope.[39] A few days afterwards, having succeeded in making a better telescope than the first, he took it to Venice where he communicated the details of his invention to the public and presented the instrument itself to the doge Leonardo Donato, who was sitting in full council. The senate in return settled him for life in his lectureship at Padua and doubled his salary.

    I wonder why the Siamese distributed an embassy report across Europe.

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2021

    Curious, didn’t know that story. It still leaves open whether Galileo just heard verbal hints or saw technical details in print.(?) But it sounds a little like there was grand-scale breach of the patenting process once the impact of Lippershey’s application transpired. Maybe Lippershey applied for patent in a far-away country like Siam to prevent exactly that? Would be interesting to read-up on, but I fear I am occupied elsewhere now.

    • CommentRowNumber22.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 23rd 2021
    • (edited Aug 23rd 2021)

    Of course, it wasn’t the Siamese doing this, just a report from someone in the Dutch United Provinces about their visit. You can catch a glimpse from around p. 17 of this.

    So much going on in this period - Dutch-Spanish politics, etc.

    • CommentRowNumber23.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2021

    Thanks again for the pointer. That’s an interesting read. On p. 19 it suggests that the concept wasn’t actually new, and that Lipperhey’s contribution was mainly to bring it to the attention of the elite – who promtly saw the potential military application and (as far as the visible text takes me before it breaks off on p. 20) nothing but the military application.

    But where were we? Ah right, the Milky Way.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)