This means something like "A ladybug is coming, it doesn't have a place to sleep. It's looking for a little bed. Tickly-tickly-tickle".

But Emerik would always say "Gigili gigili gić" at the end, intead of "Gili gili gić".

@robjohn There, I think I fixed it. Here.

That's great. I should admit that we say the same thing in the same situation now that I think more carefully about it, to make a baby laugh: "gili gili".

With a hard G, not a J-sound, right?

But I'm not sure about the last part, gić.

Yes, with a hard G sound.

In English, this would probably be spelt "geetch" or something similar. With a hard G.

It's completely unnecessary, if the baby would laugh, would do it with Gili gili. Geetch doesn't play an important role there.

But it makes it rhyme with krevetić.

and who are you and I to argue with generations of Yugoslav mothers tickling their babies?

Well known in your own home.

Umm, I think I'm just under the illusion.

Okay, they're allowed to use the last word.

I'll let them all know.

Yes please.

Anyway, it fits the rhythm better with gić - it makes it |QQQQCC|QQQQCC|QQQQM|QQQQM|| - where Q = 1/8, C = 1/4, M = 1/2.

hello

'Ello.

hi

what is the Euclidean measure?

That just means the normal measure for Euclidean spaces.

@DavidWallace What it means? Is it just the Hausdorff measure in R^n for example?

Would you like to post it in context, and I'll translate it for you?

@DavidWallace Have you read any of Euclid's Elements David?

Not in the original Greek.

How about the English translation?

Yeah, I've read most of it.

cool

The front inside dustjacket of my edition says "Euclid's Elements is the greatest textbook of elementary mathematics that there has ever been or is likely to be ..."

@DavidWallace I look for definition of the Radon transform in Helgison's book

@DavidWallace Would you agree with "Euclid's Elements is the greatest textbook of elementary mathematics that there has ever been or is likely to be ..."

I don't have Helgison's book. But "Euclidean measure" is usually just used as a synonym for "Euclidean metric" or "Euclidean distance"; so that's most likely what it means in your context. If it actually means some kind of measure (not a metric), then, yeah, I guess it would have to mean the Hausdorff measure; if that makes sense in your context.

@N3buchadnezzar Yo "bro" whatz "up"?

@Skullpatrol The ceiling

@DavidWallace It may be Hausdorff measure or the measure corresponding to the Gelfand-Leray form (because generalised Radon transform is defined using the last one). So I don't know what the Euclidean measure is (from these two)

@Skullpatrol Actually, no.

@Nimza - you've just soared beyond the level of stuff that I know about. I can't help you with this. Sorry.

@DavidWallace thanks for trying to help :)

@DavidWallace I think it depends on what they mean by "greatest," here it is not a synonym for best, but means "most influential."

@JonasTeuwen Is $W^{1,1}$ closed?

@robjohn In what space? In $BV$?

Ah, yes.

I believe so.

But I might be wrong 8-).

I'm going to go out on a limb, and claim that Whitehead and Russell's Principia Mathematica seems more influential to me than Euclid's Elements. This may be a controversial view.

influential in what quarters??

or in general?

@DavidWallace Have you read Whitehead and Russell's Principia Mathematica ?

it seems to me that PM was an inevitability, a very natural thing to do in that time. Euclid's elements not so much, and it seems to me clearly more inspirational and pioneering

@EricGregor Good question. I'm analysing the claim in my copy of Euclid's Elements about it being the "greatest textbook", with respect to Skullpatrol's definition of "greatest".

@EricGregor I didn't know you are that old!

@Asaf it's not polite to inquire about age, you know

True

"Euclid alone has looked on Beauty bare."

@EricGregor I am about as furtherest as possible from polite, so it's fine for me.

the millennia have been good to me

@EricGregor Right, I agree. Whitehead and Russell were, to some extent "standing on the shoulders of giants".

What is the furthest possible from polite?

We have no way of knowing whether or not Euclid merely summed up the work of his teachers.

@Asaf that seems unlikely.

It's unlikely that there was more than one person, of that level of genius, alive at that time.

@Asaf, in any case the question is influence

So whereas Euclid may have been committing to paper the work of just ONE teacher, it still seems that there's just one brain behind the Elements.

I find that statement to be equivalent "It seems unlikely that several people wrote the bible... it is obviously a divine textbook." - that is purely dogmatic and subjective.

I thought long messages got automatically shortened?

Euclid's book was much more influential, but I completely disagree that it wasn't coming naturally like PM.

@AsafKaragila what do you mean by "a divide textbook"?

divine

divine?

@DavidWallace But you didn't answer my question: Have you read Whitehead and Russell's Principia Mathematica ? (for comparison purposes)

No, I haven't. There's a lot more of it.

I am thinking about reading Euclid

We have absolutely no way of judging how and who did mathematics at that time.

multiple people of Euclid's supposed level are not necessary to have produced Elements; only multiple people with the combined genius required to produce such work

When you say "Oh man, Cohen really 1UP'd set theory with forcing" it's true, but that idea grew out of the mathematics that was around him.

Not sure if I want to read an english translation of the first 1-3 books, or if I want to read an interpretion.

the Elements seems to be vastly more influential to Western (post Greco-Roman) mathematics than PM, questions of the respective geneses of these texts aside

@EricGregor With that I agree.

Asaf - the Bible has a wide diversity of styles; it's obviously the product of several authors. The Elements has a much more consistent style; it seems to have been written by just one person. Also, my point was that it's unlikely that there was more than one person of sufficient genius alive in Euclid's day; whereas the Bible was written over many centuries.

the Elements has probably inspired more people to become mathematicians, surely

@DavidWallace Oh look, all the books by Serge Lang have the same style!! He must have invented everything in mathematics!!

@Asaf have you read the Elements?

However the direct influence of Euclid's writing has diminished in the past century or so.

@DavidWallace Parts of its English translation. Have you read what I said about the Elements?

@anon Yeah, good one. :-D

@DavidWallace Do you bother to read things I say, or do you just skim and point out the things you disagree with - out of context?

I never said that there were several authors.

I said that the mathematics might not have been his.

It is perfectly reasonable that many of the theorems presented in the book and attributed to Euclid came from his teachers or colleagues.

@Asaf I have read all your comments above. I still consider PM to be a more influential work than the Elements. The fact that one was written several centuries before the other makes it more revolutionary; and means that over the centuries it has inspired more people. But what about this century? What about the inspirational value of these two books today?

Any claim otherwise is nothing more than a wild speculation.

What???

@AsafKaragila Pardon me for not being completely awake. Disregarding who wrote Elements, what do you think of the contents. (From what you read)

I have serious doubts about that claim of yours that you read what I said.

Let me switch the capslock on, so it would seem as if I am raising my voice. Maybe then you'll get it...

@DavidWallace, would you explain your understanding of PM's influence?

@Asaf - you said he might have "merely summed up the work of his teachers". In the plural.

ONE WRITER, MANY TEACHERS.

I have never written anywhere above that Euclid was not the sole writer.

I have never written above that those are his theorems and his alone.

@Asaf is not claiming there was another writer in the grassy knoll, but that there was still a conspiracy

I have never written above that he invented and developed the rigorous proof.

ALL I SAID WAS THAT THE BOOK IS ATTRIBUTED TO EUCLID, WHEREAS THE MATHEMATICAL CONTENT MAY HAVE COME FROM OTHER PEOPLE.

@AsafKaragila WHO CARES??

@Asaf - please calm down. I'm not sure what I have said that has caused you such offence. I'm only claiming that it's unlikely that more than one mind contributed to Elements.

Night.

L`hoptial merely summed up the works of others, even though the influence of the first book on calculus can not be disputed.

We build on the shoulders of giants, even Leibniz and Newton did this. I would say "of course" Euclid did this aswell. And frankly I dont give a **** about it.

@DavidWallace From this day forward I am going to start claiming that everything written in any Lang book and is not directly attributed to someone else in person is actually Serge Lang's work. In a millennium or three everyone will think he was the greatest mathematician of the 20th century. While his work is surely appreciated I would not endow him with this title (if anything, Shelah would be my pick as the greatest mathematician of the 20th century).

@Asaf OK.

this argument is irrelevant to the original discussion, Asaf is just demanding that David admit his imprecision, because Asaf is prickly and all imprecisions demand ritual disavowals. let's get back to the discussion.

@EricGregor I feel that modern logic and computer science were both built on PM.

I'm sorry I asked ;-)

take it easy you all :D

Please forgive me.

@David, did PM influence, say, Turing?

what's PM?

i'm trying to separate your feelings from your claims

@Mariano Principia Mathematica

of course, then

Turing must have studied it

as everyone did at the time

@EricGregor I can't prove it, of course, but I feel strongly that it did.

@David i would be interested in reading an extended argument on it, even if only to understand the history of computer science better

@user49523 Do you also sell viagra?

lol

Spam spam spam spam spam spam wonderful spaaaam wonderful spaaaam!

LOL

we needed that distraction

PM always seemed supremely boring to me, though this is more a judgment of me than the book

@EricGregor OK, my experiences of the last several minutes here have left me a little wary of an "extended argument" as you put it. I also feel that my expertise in this area may not be quite up to it.

very anti-Babylonian it seems to me, to use a phrase of Feynman's!

Really, all I did was express an opinion about the relative greatness of two great works. I'm starting to wish I hadn't.

@DavidWallace, i understand, i didn't mean here. but if you ever wrote something up. i was just expressing a passing wish

Wow, that spamming user got a 4 hours suspension. This means like 8 messages were flagged as spam.

I think some of the questions he's asked are also spam...

@EricGregor Yeah, umm, I'm actually currently working on writing something completely unrelated to this. I'm unlikely to find either the time or the inclination to write anything about the history of computer science and the influence thereon of PM.

@tb PS: It was only hard work for you, I was enjoying myself.

one gets automatically suspended by being flagged as spammer?

some flags on the main site are quite fun to read :P

@MarianoSuárezAlvarez The flag itself or the questions/answers?

the combination

@tb Hi Teddy check out the link I posted above, if you're interested.

@MattN wasn't hard work. Definitely more fun than endomorphisms of $S^1$ :)

A few corrections:

In 2.2: "then $g$ is a bijection $g: X \to g(X)$ hence has a continuous inverse $g^{-1}$ because $X$ is compact and $g(X)$ is Hausdorff.

@hhh: does my answer not make sense?

@robjohn: when you do the cross-product, do you use Sarrus or some other rule?

@MattN: still 2.2: from a subset -> from the subset $g(X)$.

@hhh I take the cross product. What do you mean the Sarrus rule?

@robjohn I have learnt cross-product with Sarrus-rule, more here, but it is slow...

@hhh Since left handed or right handed cross product has not been specified, I chose the one I mentioned.

@MattN: in 3.2: This is also necessary -> Surjectivity is also neccessary

@hhh cross product: $(x,y,z)\times(u,v,w)=(yw-zv,zu-xw,xv-yu)$

@MattN: In 4.1: a) it suffices to show $\|T(f)\| = \|f\|$ by linearity of $T$. b) if $g(X)$ is dense in $Y$ then $g(X) = Y$ because $X$ is compact (hence $g(X)$ is closed).

@hhh but the order of the vectors is not specified, so the sign can be + or -

@MattN: In 4.2 you could write $f(x) = \max{\{ \frac{ \cdots}{\cdots}, 0\}}$

...and finally "if and only if $g(X) = Y$" at the very end.

@robjohn Yes that is right, verified with Sarrus (did a matrix and then calculated it), always wondered whether there is some easier way to compute that (I always need to verify the formula with matrix...slow).

@MattN: one last thing: put punctuation inside double dollar signs to avoid that the period is moved to the beginning of the next line.

Hi robjohn, hhh

@tb Hello t.b.!

@hhh for the basis vectors, $i\times j=k$, $j\times k=i$, and $k\times i=j$ and for any vectors, $a\times b=-b\times a$

@Skullpatrol thanks, I knew about that. Here's the relevant proposition in it's full glory:

Hi, Ben

@hhh it's a cyclic permutation of $i,j,k$

@tb What is that?

@DylanMoreland $1+1=2$

@robjohn Yes I was coming to that, some chains. Have to develop some calculation tricks to do them fast (easy to mess up with minuses...).

Oh, I remember this now. Who wrote that, again?

@DylanMoreland I believe they are discussing Whitehead and Russell

@DylanMoreland The proof of $1+1 = 2$ in Principia Mathematica by Whitehead and Russell. For context see here.

@tb See, I do pay attention ;-)

I'm impressed :)

@robjohn Could one do a chain diagram of this? To visually see it...perhaps mathematically called "lattice diagram", dunno?

I'm still puzzled by the remark afterwards... Especially when they mention only two results where they use it.

@hhh I don't know if I know what you mean.