Guess Who

Undergrad: This proof is so hard!

Grad student: My proof is 17 pages long, involves six lemmas, and the author just ‘leaves the rest to the reader.

“ok is this math really useful though what’s the point of it existing does it matter or is there no practical application” alright. if you write a poem does it matter? Is there an application? What if I killed you

”Are you an introvert or an extrovert? Do people energize you or drain you? Would you rather be at a party or a library?” Stop subscribing me to binaries. Social interaction is invigorating and makes my life better and I’m exhausted the whole time.

there should be a tax that youtubers pay where 1.5% of all of their revenue goes back to Kevin Macleod for basically supplying YouTube with it’s own soundtrack.

Isomorphism

everything IS like everything else

Ooohhhh that's quite something.

Fun scary fact: Let g: ℝ→ℝ be given by g(x)=x if x∈ℚ and g(x)=0 if x∉ℚ. Then the function f: ℝ->ℝ given by f(x)=g(x)tan(x) is differentiable at x=0. In fact it is only differentiable at x=0

Just elementary topology will give you a good enough idea. The empty set is both open and closed and the universal set is both open and closed in a topology for instance.

Sometimes open balls are closed :)

where can I read more about this?

Tamil Linguistics thread (bc nobody cares but me)

but really, if you are interested in linguistics at all, give this post a read, because this shit really blew my mind ...

have been reading the following paper: https://ccat.sas.upenn.edu/~haroldfs/public/h_sch_9a.pdf

"The Tamil Case System" (2003) written by Harold F. Schiffman, Professor Emeritus of Dravidian Linguistics and Culture, University of Pennsylvania

Tamil is one of the oldest continuously-spoken languages in the world, dating back to at least 500 BCE, with nearly 80 million native speakers in South India and elsewhere, and possessed of several interesting characteristics:

a non-Indo-European language family (the Dravidian languages, which include other languages in South India - Malayalam being the most closely related major language - and one in Pakistan)

through the above, speculative ties to the Indus Valley Civilization, one of the first major human civilizations (you can read more about that here)

an agglutinative language, similar to German and others (so while German has Unabhängigkeitserklärungen, and Finnish has istahtaisinkohankaan, in Tamil you can say pōkamuṭiyātavarkaḷukkāka - "for the sake of those who cannot go")

an exclusively head-final language, like Japanese - the main element of a sentence always coming at the end.

a high degree of diglossia between its spoken variant (ST) and formal/literary variant (LT)

cool retroflex consonants (including the retroflex plosives ʈ and ɖ) and a variety of liquid consonants (three L's, two R's)

and a complex case system, similar to Latin, Finnish, or Russian. German has 4 cases, Russian has at least 6, Latin has 6-7, Finnish has 15, and Tamil has... well, that's the focus of Dr. Schiffman's paper.

per most scholars, Tamil has 7-8 cases - coincidentally the same number as Sanskrit. The French wikipedia page for "Tamoul" has 7:

Dr. Schiffman quotes another scholar (Arden 1942) giving 8 cases for modern LT, as in common in "native and missionary grammars", i.e. those written by native Tamil speakers or Christian missionaries. It's the list from above, plus the Vocative case (which is used to address people, think of the KJV Bible's O ye of little faith! for an English vocative)

... but hold on, the English wiki for "Tamil grammar" has 10 cases:

OK, so each page adds a few more. But hold on, why are there multiple suffix entries for each case? Why would you use -otu vs. -utan, or -il vs -ininru vs -ilirintu? How many cases are there actually?

Dr. Schiffman explains why it isn't that easy:

The problem with such a rigid classification is that it fails in a number of important ways ... it is neither an accurate description of the number and shape of the morphemes involved in the system, nor of the syntactic behavior of those morphemes ... It is based on an assumption that there is a clear and unerring way to distinguish between case and postpositional morphemes in the language, when in fact there is no clear distinction.

In other words, Tamil being an agglutinative language, you can stick a bunch of different sounds onto the end of a word, each shifting the meaning, and there is no clear way to call some of those sounds "cases" and other sounds "postpositions".

Schiffman asserts that this system of 7-8 cases was originally developed for Sanskrit (the literary language of North Indian civilizations, of similar antiquity to Tamil, and the liturgical language of Vedic Hinduism) but then tacked onto Tamil post-facto, despite the languages being from completely different families with different grammars.

Schiffman goes through a variety of examples of the incoherence of this model, one of my favorites quoted from Arden 1942 again:

There is no rule as to which ending should be used ... Westerners are apt to use the wrong one. There are no rules but you can still break the rules. Make it make sense!!

Instead of sticking to this system of 7-8 cases which fails the slightest scrutiny, Dr. Schiffman instead proposes that we throw out the whole system and consider every single postposition in the language as a potential case ending:

Having made the claim that there is no clear cut distinction between case and postpositions in Tamil except for the criterion of bound vs. unbound morphology, we are forced to examine all the postpositions as possible candidates for membership in the system. Actually this is probably going too far in the other direction ... since then almost any verb in the language can be advanced to candidacy as a postposition. [!!]

What Schiffman does next is really cool, from a language nerd point of view. He sorts through the various postpositions of the language, and for each area of divergence, uses his understanding of LT and ST to attempt to describe what shades of meaning are being connoted by each suffix. I wouldn't blame you for skipping through this but it is pretty interesting to see him try to figure out the rules behind something that (eg. per Arden 1942) has "no rule".

On the "extended dative", which connotates something like "on the behalf of" or "for the sake of":

I especially find his analysis of the suffix -kitte fascinating, because Schiffman uncovers a potential case ending in Spoken Tamil that connotes something about the directness or indirectness of an action, separate from the politeness with which the person is speaking to their interlocutor.

Not to blather on but here's a direct comparison with Finnish, which as stated earlier has 15 cases and not the 7-8 commonly stated of Tamil:

What Schiffman seems to have discovered is that ST, and LT too for that matter, has used existing case endings and in some cases seemingly invented new ones to connote shades of meaning that are lost by the conventional scholar's understanding of Tamil cases. And rather than land on a specific number of cases, he instead says the following, which I find a fascinating concept:

The Tamil Case System is a kind of continuum or polarity, with the “true” case-like morphemes found at one end of the continuum, with less case-like but still bound morphemes next, followed by the commonly recognized postpositions, then finally nominal and verbal expressions that are synonymous with postpositions but not usually recognized as such at the other extreme. This results in a kind of “dendritic” system, with most, but not all, 8 of the basic case nodes capable of being extended in various directions, sometimes overlapping with others, to produce a thicket of branches. The overlap, of course, results from the fact that some postpositions can occur after more than one case, usually with a slight difference in meaning, so that an either-or taxonomy simply does not capture the whole picture.

How many cases does Tamil have? As many as its speakers want, I guess.

Love math textbooks so much <333

having depression makes your friends seem like the coolest most put together people on earth like wow... you got out of bed, had breakfast, went to work, AND spent some time on a hobby when you got home....? that's so impressive you're like superman or something. can i borrow your power.