my daughter loves chemistry and says she wants to be a chemist. she does great ai it at school. so mom and dad helped her find an unpaid spot in an actual lab. so far she loves it but has also learned that it means working all day at 18 degrees c and constantly smelling her colleagues’ lab animal feed. we’ll find out soon if that was too much reality too soon. i hope it will lead her to double-down with the full reality in sight.
> working all day at 18 degrees c and constantly smelling her colleagues’ lab animal feed
That sounds more like biomedical research than chemistry? At the risk of stating the overly obvious to you do keep in mind how great the differences are between subfields. Synthetic organic versus materials science labs will look like entirely different professions from the perspective of a layman glancing in the window (which they are I suppose).
fair point - yes this is a biochemistry lab but her part is specifically to do with analysis of lab data collected from someone’s specific experiment. so she’s learning practical things having to do with actually doing new science in a real environment though she’ll need to generalize a bit in her mind (hopefully correctly but then developing intuition and imagination matters too) to the pure chemistry aspect of it. she’s generally excited to meet actual professionals in their day-to-day work who have specific performance expectations of her and who really care that her part is done correctly and can be thoroughly audited and verified for accuracy. this time she’s not getting her hands on actual lab instruments and things like that (she does that at school and hopefully in next summer’s internship if she can can get one and is still interested by then); but she’s seeing how data comes from each of those physical world manipulations and what is done with it afterwards.
yes first time in a work-like environment. she’s mostly excited about it though we realize in retrospect it might be a bit of a risk to a fledgling interest. fortunately it seems to be a supportive environment (got lucky).
in my opinion this is a high stakes combination with little grey area for outcomes, as in I predict based on the tiny shred of info I have that she'll come out of it knowing whether or not it is something that she wants to pursue. good luck
thanks! yes we sort of saw it as “if it’s not for her better that she know early on”. we don’t want to talk her out of it (quite the contrary), yet we know many others who pursued lab bench science for a decade+ before realizing it was not for them for one of many practical reasons and we thought it best to give her a preview… there are many fields she was happy to rule out after simple conversations but there is a small handful that she finds compelling as stories or narratives but don’t survive the first level of unpacking (math, software, cybersecurity). fortunately the central science has stood up to actual challenges so far…
similarly i wanted to be an entrepreneur until i met the daily grind of it. no questionnaire would have dissuaded me. the highs were high and the lows were low; even in retrospect i’m not sure it was the wrong choice. but it would take abnormally high certainty for me to do it again now that i know the score first hand.
i use one of the largest credit unions in the usa (grown through m&a over the last twenty years). their ability to follow instructions is at best at tech-intern level. their fees are incredibly fat and their people exhibit serious cya and complacency in almost every interaction. my confidence is at an all-time low in their competence.
i still find the original idea of credit unions appealing: ie a small local organization focused on outserving a specific membership who are naturally bound together by meaningful preexisting ties.
the trouble seems to come when the credit union decides it needs to “scale “ sort of defeating the original thing that made it any good. perhaps that comes from just greed (ie the ability to charge fees on a larger customer base) or maybe it’s a requirement of the costs of providing an ever-widening array of newly “expected” services.
I mean i enjoy the idea as well, it doesn't change that our socioeconómico (i'll leave this autocorrect lol) system is controlled by the giant financial institutions, and the moves they're making with regards to crypto are only to ensure their existing positions
recently i made a cash withdrawal from my personal account ahead of a trip abroad (they asked me why) and within days received a FinCEN notice in the mail warning me about “ structured transactions”… having made no other cash transactions days or even check cashing or writing days before or days after.
personally i’ve also seen dev orgs push hard for native apps because they believe it’s better for their skill sets and their future professional prospects snd current comp…
i once wrote a whole data processing library in bash because i didn’t want people at my then workplace to extend and continue developing it. it was needed for a narrow purpose which it served well (details lost). ultimately people ported it to python and kept developing it anyway.
“
A quadratic form over a commutative ring $R$ is a homogeneous polynomial $\operatorname {\textstyle \sum }a_{ij}x_i x_j$ of degree $2$ in $n$ variables $x_1,\ldots , x_n$ with coefficients $a_{ij}$ in $R$. In particular, the sum of squares $x_1^2+x_2^2+\ldots + x_n^2$ is a quadratic form defined over any $R$.
The problem of representing integers as sums of squares dates back to ancient times. The Greeks, especially the Pythagoreans, were interested in the properties of numbers and their geometric interpretations. The concept of sums of squares is closely related to the Pythagorean theorem, conceived in Mesopotamia (1800 BC), first stated precisely in the Shulbha Sutra of Baudhayana (800 BC) and a statement of proof from China.
In the seventh century, the Indian mathematician Brahmagupta considered what is now called Pell’s equation, $x^2-ay^2=1$, and found a method for its solution.
One of the earliest and most significant results in the area of quadratic forms is Fermat’s theorem on sums of two squares. In the seventeenth century, Fermat stated that an odd prime number $p$ can be expressed as a sum of two squares if and only if $p$ is congruent to $1$ modulo $4$.
Another milestone in the study of sums of squares is the four square theorem, proven by Lagrange in 1770. This theorem states that every positive integer can be represented as the sum of four squares.
Euler’s sums of two squares identity
$$\begin{equation} (x_1^2+ x_2^2)(y_1^2+ y_2^2)=(x_1 y_1-x_2 y_2)^2 + (x_1 y_2+x_2 y_1)^2 \end{equation*}$$
shows that the set of sums of two squares in a commutative ring is closed under multiplication; this statement was generalized to the binary quadratic form $x^2+ny^2$ by Brahmagupta. Similar formulas also exist for the sums of four and eight squares.
“
It seems to be taken directly from the article, but it doesn't begin at the beginning or end at the end or shed any light on the part of the title most likely to be puzzling ("beyond arithmetic").
If the intention was to help out readers who don't know what a quadratic form is, I think a more helpful piece of advice would be: if you don't already know what a quadratic form is, then it is very unlikely that you will get anything much out of this article.
i started my comment with a double-quote indicating that the content is directly from the article starting right at the beginning of the introduction section (to your point about starting at the beginning).
i went down to Euler’s sums of two squares identity which i think demonstrates clearly that even middle school algebra suffices to get a sense of depth from this work showing that a product can also be seen as a sum in a more sophisticated context (ie beyond arithmetic structure emerges).
i fail to understand your disapproval on my providing additional context from the page to indicate that this is likely a more interesting post to a wider set of readers than most might assume just from the title. i didn’t feel the need to editorialize further because i thought the quote says it all on its own.
Comments that are just copy/paste from articles almost always gets downvoted and/or flagged. People can always read the article in question to get the same material. If you think something is interesting about the quoted bit, it's more helpful to add your commentary or even just a "Hey, look this section pretty much just requires middle school math." so people can understand why you're copy/pasting from the article.
Without that contextual clue, your comment appears to just be noise.
in retrospect, i can see why you might say that, but as noted in my previous reply i selected those paragraphs deliberately though i understand now it would have maybe helped to say a few words about why i thought those paragraphs would be helpful in particular (see my previous comment about middle school algebra).
it seems to me that a nation determined to control wired network traffic within its borders cannot be circumvented. if they can control the ISPs and observe packet flows then they can just obstruct any connection they cannot conclusively prove is acceptable.
it seems then that store-and-forward ad hoc p2p (ie extremely high unpredictable latency) is the only option for those who can reach some node with a connection to the outside (maybe laser near the border). or perhaps really clever steganography with outside partners assisting.
There is also the travelling salesman hauling in external culture like games and movies via SSD. Wish there was a protocoll to deaddrop large file requests smuggled into a country.
does that mean the authorities can’t locate someone transmitting or receiving to/from starlink? in many places the consequences of detection could be dire…
No. The links between the satellites are lasers, but the user traffic still goes up and down over radio.
You still need the Starlink coverage to be enabled on system level, and the local government to care enough to track down Starlink users at the same time. I can't imagine that there are many countries that meet both criteria.
i believe countries with major firewalls and vpn blocking policies would track down and make examples of a set of users periodically if only to deter others.
