#why is that able to be explained using mathematical principles?

[khaanahbadoshiyaan]

the more you know, the less you can claim to know

[hotheadedhero]

hellooo!! I’ve never done this before. So I’m hoping I did it right.

can you please write a one shot rise Donnie x mystical user (preferably yokai) reader? Where Donnie feels like he’s constantly competing against the reader, and is always down playing mystic. To the point where reader confronts him :>.

AN: Hello there! I'm so glad you trusted me with your first request. It was really fun to write 😋 I hope it does the job <3

Science vs Mystic

Donatello x Reader

Warnings: angst, arguing, I didn't proof read, kinda made Donnie an ass in this I'm sorry

Donatello’s disdain for the mystic arts and magic alike has always been well known. Ever since he and his family came across the strange world hidden beneath New York, this distaste has only grown. It continues to grow with every adventure involving such, which is becoming a more regular occurrence than he’s comfortable with. 

Then, you came along. You with your inexplicably, aggravating abilities. He had hoped that after the day was saved and the trouble was dealt with, that would be the last of your affiliation. Quite the opposite, it turned out. A permanent friend was made out of you that day, which meant frequent team-ups and visits by yours truly. In his mind, he’s tried to put aside the differences, he’s attempted to let bygones be bygones, but you always manage to steal the spotlight with your ostensibly fantastical displays.

Perhaps it's jealousy. His brothers are always so enamoured by your mystical mastery, showering you with compliments after each fight you assist. They just won't shut up about how cool you are. What's "cool" is how he has been able to make his inventions in a sewer, how he’s turned a bunch of scraps into the glorious creations they are now. Sure, he may need to commandeer the odd chemical from time to time but what he does is leaps and bounds more impressive than your flashy little magic shows. Illusions are based on principles of physics and mathematics. There is objective evidence for it all. The charms that your kind uses to blend in with humanity? Simple. Like how military operations will cater technology to make their vehicles appear invisible, it’s a matter of deflecting light around an object. This same premise can be applied. Rather than deflecting the light, your charms can refract it and make a person appear to be someone they’re not. Mere cloaking devices. In fact, he’s been working on something similar for himself and his brothers.

If not that, chemistry plays a fundamental role, at least. So what if you can shoot sparks of light from your sleeves? Fireworks. That’s all it is and those are just ignited gunpowder with various metal compounds to create different colours. You can make plants grow from the ground at inhuman rates? Poppycock, he says. Ever heard of auxin? Cytokinin? These are just a couple of the plant growth regulators that are so ordinarily used by modern man. Even then, you probably dabble in the use of mutagen to make it seem more impressive.

Scratch the jealousy. There’s nothing to be envious of. He knows that science is superior. It always has been and always will be. He can hardly say he's surprised by his family's fascination. They aren't as intellectually adept as he is. Unfortunately, that commentary doesn't provide him with the closure he needs to feel that much better about it, which is why he resorts to jabbing at your abilities with passing comments, whether they be snide, sarcastic or just downright mean.

You aren't an idiot. You can feel his malice towards you before he even has a chance to open his mouth. At first, you merely thought it was a feature of his persona - that it’s in his nature to berate what can’t be explained by science. That was a misstep in your thinking. His entire deal is that everything can be explained with science. Try you may to convince him otherwise but it’s always the same song and dance: you curate something with your magic and he shuts it down with a zealous drone that is starting to grate on you. 

If you were to ever meet someone outside of your home, you were always taught that there would be an indifference to your powers. People often either shun what they don’t understand or change the scriptures to what they’re familiar with so they can understand it, even if it means they’re wrong. You have always sworn to be the bigger person and not stoop to such levels of belittling pettiness but it’s getting harder. There’s only so many times you can bite your tongue before you start bleeding from the mouth. As waining as it may be on your patience, there are civil ways of going about this. You have been practising the conversation in your head for days now. Everything to want to make peace with has been rehearsed over and over and over again. With your head held high, you march right over to the garage and there he is, tinkering away at one of his many inventions.

“Donatello,” you declare, making your presence known. “Can we talk?”

Without looking, he hums and flails a dismissive hand in your direction. He doesn’t even bother to wave his real hand, opting for the use of a bionic limb so that he may keep his focus on his work. You bite your tongue like you have so many times before and tread closer. You had hoped that your irregular hardiness would be enough for him to realise you mean business but nothing. He fails to turn his music down even, so you take the liberty of doing it yourself. His lack of respect is already urging a rise out of you but you keep your mantra in mind: remain peaceful, aggression leads you nowhere. 

You breathe deeply to settle yourself and start your case, “Why do you always make such a point of overruling my abilities with science?”

“It’s not an overruling,” he retorts blandly. “I’m merely giving you the facts.”

“What you think are the facts,” you correct him.

"Please. Science is unquestionable.” Still, his eyes are glued to his device rather than paying attention to the situation at hand. “Atoms make the very backbone of everything that exists, etcetera, etcetera. Need I go on?” There’s that grating tone in his voice again; snobbish and agonisingly vain. “You can't seriously tell me that ‘magic’ has a constructive place in the world nearly as much as science does."

"I can if it's what I grew up believing," you object, more stern but remaining the peacekeeper where you can. “How would you feel if I tried to pick apart everything you believe and tell you it means nothing?”

He scoffs, “As if you could.” 

“Excuse me?” you ask through your teeth.

The tips of your fingers dig into your palms. By now, your blood is boiling. It’s one thing to throw out the odd comment but now it feels as though he’s making a straight mockery out of you. Keep a steady pace. You can do this. It’s becoming increasingly difficult but you know you can see this through without a violent fit. 

“Science is everything and that is the objective truth. Magic is just-”

“Donatello,” you attempt to gently interrupt him lest he anger you further but he takes no notice.

“- a childish way-”

“Stop.”

“- to view the world in fairy-like wonder.”

“Oh my stars, just shut up,” you cry out, "you arrogant, condescending, self-bloated ignoramus!” 

You throw your fists down at your sides and the very ground beneath you shakes. Where he was so absorbed in his creation, he failed to realise how worked up you were getting. You undeniably have his full attention now. If your outburst alone wasn’t enough to shut his mouth, the large cracks around your feet certainly are. There’s a wide, unfocused glow in your eyes and you’re heaving for air. He sits up, prepares to say something but his lips lock back down when yours open again.

“I am not just talking about stories or fairy tales or made-up fantasies from a child’s daydream! This is my life!”

Another loud shriek erupts from your chest, seizing the fragile floor and destroying it further. Luckily, it isn’t enough to permanently harm the infrastructure but it makes for a harrowing sight: your crumbling emotions devastating that which surrounds you. Silence follows, though not completely. Stray pieces of broken brick clammer around you two. 

In the short seconds that you try to regain your breath, Donnie stares up at you. Once shadowed over his hunched frame, your body is now slumped and weary. Your eyes point up at the ceiling in an attempt to stop crying but to no avail. In the end, you decide to just cover them with your hand.

“All you're doing is trying to convince me that my life is a lie,” you shakily whisper, “and if that’s how it’s going to be then I… I just can’t.”

You walk out before he has a chance to consider a response, leaving him in his stupefied state. His gaze follows the largest crack from the floor to the ceiling until it falls back on the doorway. By no means had he ever intended to make you doubt your livelihood. He was just… he was… he doesn’t know what he was doing, actually. Have his unappetising quips really led you to such turmoil? His face slowly morphs into a frown and he finds himself lying back on his shell. Then, his lips scrunch together and his throat groans in frustration. He shouldn’t feel bad for handing out the realities. He shouldn’t harbour guilt when you’ve been stealing his brothers’ attention all this time. 

Oh. 

The back of his head taps back into the ground. Gosh darn it. Jealousy. That’s the kicker. It has been this whole time. He’d like to leave it at that and continue with his previous task but he knows his family would start asking questions. His heart doth protest against his logical brain too much. With another long lament into the open air, he pries himself onto his feet and readies his venture to retrieve you. Such fun. Not only does he have to help a mystic user but now he has to traverse the very land from which you came. 

It doesn’t pan out the way he initially thought it would, however. The time he has to himself whilst he scavenges - the time he has to think - is time enough for him to go over your words. More so, the look on your face. He hates to admit it but his short-sightedness led him astray and hurt you. Whilst he doesn’t put much thought towards mystics, you are still a valued friend of his family. You’ve aided them so many times in their missions. You’re a person of great power even if that power comes from something he disagrees with. His brows furrow and he grimaces. Okay. He’ll admit he was out of line. That can wait, however. He still needs to find you first.

Donatello searches high and low across every surface of the mystic lands as he prowls further, faster. He always forgets how big it is. New York is an impressive feat but this realm could be worthy of putting it to shame on size alone. His efforts almost seem fruitless but, finally, he spots you atop a hillside, sitting with your legs pressed into your chest. The sight of your dimmed spirit tips him further into shame. He hates that fact but he supposes it’s the least he deserves. 

Before he knows it, he’s standing beside you. He didn’t realise he had gotten here so quickly upon finding you but here he is. You just about look up at him but your eyes quickly fall back onto the luscious landscape. There’s no telling what he plans to say or even why he’s followed you this far. You can’t say you have the energy to argue further, nor can you find it in yourself to tell him to leave. You can only hope he chooses his words carefully whilst he’s in the centre of your home.

“I don’t really know how to go about this,” he admits. “I…”

He blows out a breath and sits down beside you. For all the time he took to find you, he thought he would have at least thought about what he wanted to say. It isn’t that he lacks the capacity to apologise but admitting he’s wrong is a whole other kettle of fish he struggles to reach into. The whole crux of this is that he couldn’t admit to being wrong, he couldn’t allow your very being to defy what he believes to be the sole truth and the only truth. If there’s ever a time for trying, it’s now.

“I’m sorry. This has all been blown wildly out of proportion.” Donatello holds his hands together and his mouth curls uncomfortably. Part of this may involve revealing what he wishes to keep a secret but if it stands any chance of helping the situation, it may be his only resort. “I suppose it just seems unfair that you can make all of these things happen with the wave of your hand whilst I work so hard to accomplish the same.”

His head falls between his legs and yours lifts to properly look at him. Had he tried to illustrate this earlier, the whole ordeal may have been avoidable. Better late than never, you suppose. You never meant to feed into whatever inferiority complex he’s dealing with but that still doesn’t excuse the way he’s acted towards you. You want to get mad again and tell him just that but his shrunken stature speaks for you. Guilt is the moral emotion of a man who realises that they have compromised or has violated universal moral standards and bears significant responsibility for that violation - he who knows he has done wrong. That alone is a start to pave the way for what you had longed for. It’s a shame it came to this to begin with but beggars can’t be choosers.

“It was never my intent to upset you,” he continues when you stay silent. “Would you please come back to the lair? My brothers enjoy your company, so…”

“I’ll come back on one condition.” You turn back to the view but an invisible string tugs at your mouth. “You don’t have to agree with everything I stand for but can we at least put our differences behind us and be friends?” you ask and the upward lilt in your voice gives him a hope he hadn’t anticipated to be so easy. “Who’s to say science and mystics can’t co-exist?”

You outstretch your hand with a coy, friendly smile. He wouldn’t have blamed you if you were to give him an earful about his behaviour but this is far better. It’ll be a good chance to at least try and make up for all the awful things he’s said. If not for his own gratification then for the sake of his family in keeping an ally around.

One of his robotic limbs goes for the shake only to stop. If he’s going to do this, he’s going to do it properly. His fingers sequentially tap against his palm before he reaches out and clasps your hand. Your smile brightens and, in turn, his cheeks rise above an apologetic grin. Even if he has his quarrels with your powers, what you stand for, he doesn’t need to hold issue with you as a person. Who knows? This could be the start of a wonderful friendship. Jeez, though, remind him to never get on your bad side. He still needs to repair those damages to the garage.

[spacetimewithstuartgary]

Oceans of water found on Mars

Using seismic activity to probe the interior of Mars, geophysicists have found evidence for a large underground reservoir of liquid water — enough to fill oceans on the planet's surface.

The data from NASA's Insight lander allowed the scientists to estimate that the amount of groundwater could cover the entire planet to a depth of between 1 and 2 kilometers, or about a mile.

While that’s good news for those tracking the fate of water on the planet after its oceans disappeared more than 3 billion years ago, the reservoir won't be of much use to anyone trying to tap into it to supply a future Mars colony. It's located in tiny cracks and pores in rock in the middle of the Martian crust, between 11.5 and 20 kilometers below the surface. Even on Earth, drilling a hole a kilometer deep is a challenge.

The finding does pinpoint another promising place to look for life on Mars, however, if the reservoir can be accessed. For the moment, it helps answer questions about the geological history of the planet.

“Understanding the Martian water cycle is critical for understanding the evolution of the climate, surface and interior,” said Vashan Wright, a former UC Berkeley postdoctoral fellow who is now an assistant professor at UC San Diego’s Scripps Institution of Oceanography. “A useful starting point is to identify where water is and how much is there.”

Wright, alongside colleagues Michael Manga of UC Berkeley and Matthias Morzfeld of Scripps Oceanography, detailed their analysis in a paper that will appear this week in the journal Proceedings of the National Academy of Sciences.

The scientists employed a mathematical model of rock physics, identical to models used on Earth to map underground aquifers and oil fields, to conclude that the seismic data from Insight are best explained by a deep layer of fractured igneous rock saturated with liquid water. Igneous rocks are cooled hot magma, like the granite of the Sierra Nevada.

"Establishing that there is a big reservoir of liquid water provides some window into what the climate was like or could be like," said Manga, a UC Berkeley professor of earth and planetary science. "And water is necessary for life as we know it. I don't see why [the underground reservoir] is not a habitable environment. It's certainly true on Earth — deep, deep mines host life, the bottom of the ocean hosts life. We haven't found any evidence for life on Mars, but at least we have identified a place that should, in principle, be able to sustain life."

Manga was Wright's postdoctoral adviser. Morzfeld was a former postdoctoral fellow in UC Berkeley’s mathematics department and is now an associate professor of geophysics at Scripps Oceanography.

Manga noted that lots of evidence — river channels, deltas and lake deposits, as well as water-altered rock — supports the hypothesis that water once flowed on the planet's surface. But that wet period ended more than 3 billion years ago, after Mars lost its atmosphere. Planetary scientists on Earth have sent many probes and landers to the planet to find out what happened to that water — the water frozen in Mars' polar ice caps can't account for it all — as well as when it happened, and whether life exists or used to exist on the planet.

The new findings are an indication that much of the water did not escape into space but filtered down into the crust.

The Insight lander was sent by NASA to Mars in 2018 to investigate the crust, mantle, core and atmosphere, and it recorded invaluable information about Mars' interior before the mission ended in 2022.

"The mission greatly exceeded my expectations," Manga said. "From looking at all the seismic data that Insight collected, they've figured out the thickness of the crust, the depth of the core, the composition of the core, even a little bit about the temperature within the mantle."

Insight detected Mars quakes up to about a magnitude of 5, meteor impacts and rumblings from volcanic areas, all of which produced seismic waves that allowed geophysicists to probe the interior.

An earlier paper reported that above a depth of about 5 kilometers, the upper crust did not contain water ice, as Manga and others suspected. That may mean that there's little accessible frozen groundwater outside the polar regions.

The new paper analyzed the deeper crust and concluded that the "available data are best explained by a water-saturated mid-crust" below Insight’s location. Assuming the crust is similar throughout the planet, the team argued, there should be more water in this mid-crust zone than the "volumes proposed to have filled hypothesized ancient Martian oceans."

IMAGE: A cutout of the Martian interior beneath NASA's Insight lander. The top 5 kilometers of the crust appear to be dry, but a new study provides evidence for a zone of fractured rock 11.5-20 km below the surface that is full of liquid water — more than the volume proposed to have filled hypothesized ancient Martian oceans. Credit James Tuttle Keane and Aaron Rodriquez, courtesy of Scripps Institute of Oceanography

[ghelgheli]

I think a significant blunder of math education is the failure to explain where the fuck numbers come from. they are, from the beginning, presented as an inventory of symbols conjured ex nihilo with little purpose other than being the objects of (often torturous) rote memorization. but I think one of the most interesting things about math is the fact that it originated from and has almost always developed through material circumstances. and this is rather straightforward in principle:

somewhere along the way, perhaps in between early homo and contemporary humans, people independently developed linguistic symbols to indicate cardinals - to allow them to count one, two, three, four, maybe a little more. but this doesn’t come free. cognition is expensive, language is expensive, and counting blades of grass would never have been a preferred leisure activity. why bother?

humans tend to have the ability to approximate magnitudes without symbolic representation. if I show you two piles of figs, you’ll be able to tell if there’s more in one than the other as long as the difference is big enough. you don’t need to know how many there are in each. you don’t need numbers. you don’t need to know what the symbols “ten” or “fifty” or “a hundred” is to be able to tell that a mound of a hundred figs is a lot more than a mound of fifty. you can just tell

humans can also, in general, represent smaller numbers (up to four, maybe a little more more) precisely without symbolic representation. if you have two siblings, you don’t need a symbol for “two” to know it. you don’t need any representation of numbers to put four figs against four figs and know that they’re equal in quantity. so again, why bother?

somewhere along the way, accounting became important for some people (some. it’s not clear that every language even has an extensive number system). it became important to keep track of how many cows, or horses, or chickens, you had - precisely. it was no longer good enough to have an approximate sense of the size of your herd, or the volume of goods in your possession. for reasons of trade, tracking, etc. it became important to know exactly how many of something you had, so you could be sure none went missing, or so that you could barter precisely. the mathematical realists will not like me for putting it this way, but as far as our linguistic representations go, numbers were invented because it became useful to us to know how many of something there was

but, critically: not all numbers were invented at once, because they weren’t all needed at once. maybe you needed to know how many heads of grain you had. so you needed to count one, two, three, up to a few hundred. maybe more! but those are just positive, whole numbers (the “natural numbers” without zero). you didn’t need to know how many heads of grain you didn’t have. if you had none, you didn’t really need a number for that either. that’s why negative numbers and “zero” did not have symbolic existence until more recently: it was only when concepts like debts became widespread that the notion of a negative quantity of something was accepted as intelligible. otherwise, what the fuck could “-4 apples” mean? again - accounting.

as for rational numbers, defined as one integer divided by another (like 3/4, or 11/3): the name gives away that they’re about ratios between numbers. the building should be thrice as wide as it is long. that’s a ratio of 1/3. we need four units of water for every three units of flour. 4/3. these numbers only exist because they’re needed for myriad tasks through architecture, engineering, accounting...

irrational numbers, of course, came from the trouble of trying to figure out what the length of the diagonal of a unit square is: suppose you have a square that’s one long on each side (could be one meter, one foot, whatever). how long is the line from corner to opposite corner? surely, ancient mathematicians thought, it should be a nice number like 5/3 or something. it should have a pleasant representation. but, surprise! it doesn’t (the proof that the square root of two is irrational is one of the elementary exercises in number theory and I recommend trying it out or just reading it. it’s incredibly accessible). pi makes its appearance here, too. these quantities matter because, if you’re trying to figure out what length of timber you need for diagonal struts in your building, you need to be able to measure it out! if you want to know how much fencing you need for a circle that’s a particular width, you need to have a guess at what pi is! these numbers aren’t gratuitous trivialities; they’re materially significant

concepts of constructible numbers, algebraic numbers, infamous complex numbers, and so on, all came to be studied because material circumstances made it useful to do so. the shit you can do with complex numbers is OFF THE RAILS. it is 100% jaw dropping at times. I think this is abysmally communicated despite how important it is to understand why we bother with numbers.

[kurokoisbae]

Stop Introducing Science to the Wizarding World

Science is detrimental to magic.

I've read a lot of fanfictions criticizing Hogwarts for not offering muggle subjects, but in my opinion, offering muggle subjects wouldn't really help much. The main subjects taught to kids are science, math, and language.

Witches and wizards could probably benefit from having a class that teaches them new vocabulary and sentence structures, but the amount of essays assigned to the students probably does a well enough job ensuring that the students at least know how to present information by the time they graduate, through sheer trial and error when the teacher returns the essays marked full of red due to grammatical errors, at least. They could offer Latin classes or something similar to help students understand the language they use in spellwork, but that's not really a class regularly offered to children and teenagers in the normal world so it can't really be called a 'muggle' class.

Mathematics is already offered, for those who wants to learn, in arithmancy. It's most likely a required OWL or NEWT for jobs that require a lot of calculations and the little math that is required in normal day to day life are already already taught to muggleborns in their primary classes, and to kids growing up in the magical world by their parents as part of their home schooling.

Science, I believe, is not only unnecessary but detrimental to the magical education process. Magic is something that has a lot to do with belief. Science imposes a lot of rules, laws, and principles that outlines what is possible, impossible, what's supposed to happen in a specific situation, etc. It is rigid. Magic defies the laws of reality. Teaching the students those laws would make them subconsciously believe in them, making them think that even with Magic, it is impossible. More over, they may even try to apply the laws of reality to Magic. I've read a few fanfictions where they applied chemistry to transfiguration. Where they must understand the chemical composition of both the object they are turning and the object they are turning it to. Eleven year olds were able to transfiguration a wooden match to a needle. Wood is an organic substance with carbon and hydrogen atoms while a needle is usually made of steel, which is an alloy of multiple metal atoms. Do you really think children know enough chemistry to be able to manipulate the protons, electrons, and neutrons withing an atom to turn carbon and hydrogen atoms to different metal atoms like iron and nickel? Of course not. But they were all able to do it as a first year, why? Because their teacher said they could and it's the first day of class, so many probably assumed that it's the simplest and easiest thing to do with magic. It's belief that makes it happen. Knowing the actual process that's happening would just overcomplicate things in their mind and make it difficult for them to visualize the bigger picture of what they want to happen. Instead of focusing on the match turning into a needle, they would instead think about the atoms turning into another atom and arranging those atoms so they form the desired shape. That may be somewhat doable with the match to needle transformation, but what about the later classes where they would be asked to change something made with different materials to another object also filled with different materials? Don't even get started with animate to inanimate transfiguration. How would you even explain cells turning into atoms? They don't have the same constituents of protons, electrons, and neutrons like changing between atoms do.

I really don't like that these fanfictions try to make the Wizarding world more like the muggle world. It's a different world with their own abilities. You can't expect them to do things like the muggles would. You can show them what the muggles do, and they can find inspiration to make a Wizarding version of it. Someone has probably already invented a spell that does the same thing a calculator would, a graphing calculator even, with the graph showing in 3D as a hologram. Some of the magical spells we see in the books are more advanced than even the present stage of technological advancement where AIs and robots are becoming more advanced. Especially household spells. They have a spells that makes the dishes wash themselves! A spell that makes a broom clean by itself! Those are imbueing objects with artificial intelligence all with one spell! The objects don't even have to be specially made to do these things, magicals can just buy a regular old broom from a store and wave a wand over it and boom! No more cleaning chores. Magical sensors are also way more advanced than technological sensors. They can detect intent, spells, forgotten thoughts (the remembrall), and likely more.

In conclusion, adding muggle subjects is not only redundant, but would hamper the progress of magical advancement. Similarly, converting muggle technology and following its progression instead of finding a way to make something like it with Magic would make innovating within the Wizarding world hard. Not to mention, while phones and computers are something that doesn't exist in that Wizarding world, the later technological advancements like AI and robots can already be done using spells, which everyone can do, so following the muggle technology progression can't really be sustainable for long anyway.

Besides, magicals have different needs than muggles. While the muggles' current primary focus is electricity and food, magicals power everything with magic, and while food can't be made out of thin air, it can be doubled from existing food. There's probably even magic that causes plants to grow quicker, and if there isn't, magicals don't have the same problem muggles do with space for their food crops. They can expand a space, plant a lot of crops, cast some spells that would provide all the nutrients and water needed for healthy plants, and they can have food right at their backyard. I've always thought magicals are very independent creatures. With the magic and classes taught at Hogwarts, they can conjure or transfigure everything they need, use charms to make their life easier, defend themselves with magic, brew their own medical potions, and grow their own crops with herbology.

What do we learn in school? How to do math we'll likely never use and science laws most don't even care about.

[yamuna2345]

Navigating a Career in Data Science: Is It Worth It?

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The answer is clear: a career in data science offers immense potential for growth, job satisfaction, and societal impact. Let’s explore why data science is a great career choice and how you can prepare yourself for a successful journey in this dynamic domain.

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Explore Machine Learning Concepts A solid understanding of machine learning principles and algorithms is crucial for many roles in data science. Online courses and certifications can help you build this expertise and stay updated with industry trends.

Hone Your Soft Skills Communication is key in data science. You should be able to explain complex data insights to diverse audiences effectively. Additionally, strong problem-solving abilities and teamwork skills are essential in collaborative work environments.

Network with Industry Professionals Join data science communities, attend conferences, and engage in online forums. Networking can provide valuable insights and uncover job opportunities while allowing you to learn from others in the field.

Create a Strong Portfolio Showcase your skills by building a portfolio that highlights your projects, analyses, and data visualizations. A well-crafted portfolio can significantly enhance your appeal to potential employers.

Conclusion

In summary, a career in data science offers a wealth of opportunities and the chance to make a meaningful impact. By building your skill set, gaining relevant experience, and actively networking, you can position yourself for success in this exciting field. If you have a passion for data and a desire to drive innovation, embarking on a data science career may be one of the best decisions you ever make. The future is bright for data science professionals—now is the time to take the leap!

[gigglystudent]

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[jonathankatwhatever]

It’s about 1AM 22 August 2024. My anniversary. I found an honest card. It says I love loving you and I wrote that I’ve learned loving requires better versions of myself and that I actively choose those versions, and that this comes from you. I didn’t specify what that last part means.

I was walking along thinking about partisan political perspectives, and it hit me: Triangular. Not moderate in positions but Triangular to the Ends. As I’m seeing it, make a bT and rotate it around one side and that generates a number line. That number line is uncountable and thus contains countable. An fD is that representation, so any point relates to any other point on the number line to and over the 0Space segment. Is that the notation? The relationship between political poles is a 0Space segment? It’s a little long, isn’t it? I’ll use the idea but think about the notation.

I can then say the typical sheet projective plane models the match, fit and thus choice which relates across that gs sheet. As I was typing that, I was seeing images of a rotating mirror. That says the ‘meaning’ of the reduction from ideal 1Space to 0Space is the reduction in causality necessary to fit the fD, to get the cards lined up properly so stuff appears in the wrong place. It’s necessary to enforce consistency, coherence nad persistence. These are the base forms of continuing existence. One is that the existence is continuous in its own existence, which means it obeys standard mathematical rules, like being differential, like having a Taylor Series which relates that existence to higher dimensions. That is consistency. Another is that the existence makes sense relative to other existences. This is consistency at a larger scale and thus involves the processes by which that consistency occurs. That is why the usage of coherence; the existence coheres at scale.

The third is persistence. This is also related to consistency; it means no binary existence with visible 0. If you disappear for a while, it’s because a series of events occurred, not that you went poof and rematerialized like Jeanie. That would be a visible 0.

I’ve never been able to explain those that clearly. So let’s have a few minutes of playtime before I turn off the typing. Why 207,542? The 200k appears to be a count of 2, meaning a Triangular segment forming against which there’s an injection point. This came to me when I was thinking about political perspectives because partisan shifts the Triangular so the person and the party, so the person and the principles is the 0Space segment which relates to the opposition End, which is a characterization, etc. It draws as an HG, meaning the fD above flips the other way, around the End instead of around the 1-0Segment. Think about the orientation.

As you move on the sheet, which we’re doing, we draw a line across whatever appears to fit the drawings, so look at a step. At the fD, we enter at an End and can see the center 1-0Segment would rotate. This idealizes to the K-forms, and the grid squares drawings. So then we step to the next End and we see the square we’re leaving behind has actually been rotating along the axis of your travel across on the szK, and that scales. What about the HG? What does that look like?

On a sheet, the rotation around an End requires rotating 2 Ends of a bT. These rotations are hard to see until they’re seen. So there are 2 base ones, with one being rotation in yK, which takes it out of the sheet, and one with rotation in xK, and thus within the sheet. This then adds another to rotating the fD, right? Can rotate by ripping it apart, so counter rotation to the one described. And it can be like a pinwheel, which is yK. I’m tired so that was probably a bad list.

The idea of a 2:1 is into 1 and out of 1. That’s the communicative process. We’ve been doing that math. So 100,000 of those, which is 10 to the 5th, which is a hand in exponential form, which is SBE3+1, which means you start or end with 1 and Between is SBE3, which the 1-0-1 which makes the 0-1-0. That’s why base10 works. It counts to 1 plus this relationship, on either End of the relation, larger or smaller, connecting the existence within, that 1-0-1 which makes the 0-1-0, within the larger context.

Fit and misfit. Hero and villain.

Then it’s 18 times 419, which Attaches to 420, which connects in the same manner, and which represents the Hexagonal which appears when we rotate the pinwheel because the pinwheel or plural becomes a hexagon. The last stop before circle is Hexagon. Then the existences need to overlap because you can’t fit 7 or more in while maintaining the 1Space bT’s.

This is of course what sets up the counter threading in 0Space. The 18 is 2*9, which is f&b, which is SBE2 as well. It can also be a hand: just don’t count the turn around along the zK. It’s a cube with sides of six gs and thus faces of 36. It’s SBE of Hexagonal. I don’t have anything more compelling.

The 419 to 420 is a bit clearer because this is class counting in 1Space and 0Space. It’s the object created to Attach at either End. I would love to get deeper but I’ll settle for this for now.

[cosmoshiden]

Math troubles

In my recent experience with taking university math, I was informed to take principles of math, pre-calculus, or foundations of mathematics. My institution insisted that I needed one of these courses in order to continue on with my degree as a bachelor of arts. However, what I was not told at the time is that principles of math was long gone. I will elaborate on this later, but for now I will focus on what happened when I made my choice.

Basically, I took on pre-calculus, but found myself unable to grasp the math. From there I fell behind within several weeks. This caused me to withdraw from the course. About 3 months later, I was about to sign up for a course in logic, but I was informed to take either of the three as mentioned above. In my blindness I took pre-calculus again, and tried my luck by finding a tutor. The course ended in failure for me, as I wasn't able to once again grasp the content, even with a tutor's help and recieved an "F". It also didn't help that I have a learning impairment that hinders my understanding of math. As such, I tried again with a tutor and received a "C-", yet that wasn't enough for the administrators, so I was given a "hardblock" on my attendance. My institution's standards at the time were either a 60% or a 70% in math.

At this point, I was given a choice of signing a contract to take pre-calculus again, taking a placement test or going back to my old high school to take Math 11 or 12. I went with the third option and spent over a year retaking pre-calculus, while failing miserably. My math teacher grew worried about my poor performance, so I told her my situation, and she later informed me that principles of math was discontinued, that the information I was given by my university was misleading, and that as a student in the humanities, I should have been taking Foundations of Math. Meanwhile, I was informed that Pre-Calculus was in fact for students going into the Sciences, Technology, Engeneering and Mathematics (STEM). With this revelation, I came to realize that my university didn't explain this to me when advertised, nor is this explained on their website.

Now I did take foundations of math, and passed with a 62% or a "C", and that should have been enough right? Nope. Once I returned to my university to show to my academic advisor, they later informed me that I needed to score a 70% in math. This came to me as another door slammed in my face. My university had moved the goalpost over, especially as they demand that I take pre-calculus yet again! I find this no only absurd, but that it begs the question, why the heck does a humanities student need to take a math course that's designated for the STEM fields? Even the placement test solely covers pre-calculus.

This changing of the rules also entails that by raising the standards higher, it prevents humanities students such as myself from completing their degrees and graduating. Not to mention that earlier I was informed that the 60% grade in math was reserved for persons with cognitive disabilities. This in turn makes it difficult for neuro-divergent students to continue attending the university, while also being ableist. Also, without making a clear distinction of which math course is designated for which field or degree, it creates confusion for students and is detrimental to humanities students insofar as it would cause them to drop out, waste their time, and money. This has me pondering is my own institution leans more towards the STEM fields rather than the Humanities.

Favoring the STEM fields and showing a disregard for the Humanities is no different from science worship, which is akin to phallic worship. This is especially in the case of hyper-rationality and scientism, where the former is in favor of reason rather than intuition is the primary source of knowledge, while the latter assumes that only science can give us knowledge. In feminist epistemology, the sciences are seen as masculine, as they favor reason.

When trying to explain this to my academic advisor, they told me the conditions and tried to suggest the same hoops I shoot through. However, I wanted none of it, and threatened to move to back to my previous university. My advisor tried to sweet talk me from taking this suggestion, but I would not relent or buy into the same offerings and solutions that didn't work for me beforehand. Even when I tried to explain the differences between the two math courses, they just brushed it off. Hence, I just walked out angrily while never looking back.

So here I am as neuro-divergent person, embittered, humiliated, and feeling hoodwinked. I had my degree in my grasp, only to have it taken away from me. My advice is for students in the humanities is to make sure you ask which is relevant to their fields.

[jcmarchi]

How Do Neural Networks Learn? A Mathematical Formula Explains How They Detect Relevant Patterns - Technology Org

New Post has been published on https://thedigitalinsider.com/how-do-neural-networks-learn-a-mathematical-formula-explains-how-they-detect-relevant-patterns-technology-org/

How Do Neural Networks Learn? A Mathematical Formula Explains How They Detect Relevant Patterns - Technology Org

Neural networks have been powering breakthroughs in artificial intelligence, including the large language models that are now being used in a wide range of applications, from finance to human resources to healthcare. However, these networks remain a black box whose inner workings engineers and scientists struggle to understand. A team led by data and computer scientists at the University of California San Diego has given neural networks the equivalent of an X-ray to uncover how they actually learn. 

The researchers found that a formula used in statistical analysis provides a streamlined mathematical description of how neural networks, such as GPT-2, a precursor to ChatGPT, learn relevant patterns in data, known as features. This formula also explains how neural networks use these relevant patterns to make predictions. 

“We are trying to understand neural networks from first principles,” said Daniel Beaglehole, a Ph.D. student in the UC San Diego Department of Computer Science and Engineering and co-first author of the study. “With our formula, one can simply interpret which features the network uses to make predictions.”  

The team presented their findings in the Science journal. 

Why does this matter? AI-powered tools are now pervasive in everyday life. Banks use them to approve loans. Hospitals use them to analyze medical data, such as X-rays and MRIs. Companies use them to screen job applicants. But it’s currently difficult to understand the mechanism neural networks use to make decisions and the biases in the training data that might impact this. 

“If you don’t understand how neural networks learn, it’s very hard to establish whether neural networks produce reliable, accurate, and appropriate responses,” said Mikhail Belkin, the paper’s corresponding author and a professor at the UC San Diego Halicioglu Data Science Institute. “This is particularly significant given the rapid recent growth of machine learning and neural net technology.”

The study is part of a larger effort in Belkin’s research group to develop a mathematical theory that explains how neural networks work. “Technology has outpaced theory by a huge amount,” he said. “We need to catch up.” 

The team also showed that the statistical formula they used to understand how neural networks learn, known as Average Gradient Outer Product (AGOP), could be applied to improve performance and efficiency in other types of machine learning architectures that do not include neural networks.

“If we understand the underlying mechanisms that drive neural networks, we should be able to build machine learning models that are simpler, more efficient and more interpretable,” Belkin said. “We hope this will help democratize AI.”

The machine learning systems that Belkin envisions would need less computational power and, therefore, less power from the grid to function. These systems would also be less complex and so easier to understand. 

Illustrating the new findings with an example

(Artificial) neural networks are computational tools to learn relationships between data characteristics (i.e. identifying specific objects or faces in an image). One example of a task is determining whether in a new image a person is wearing glasses or not. Machine learning approaches this problem by providing the neural network many example (training) images labeled as images of “a person wearing glasses” or ”a person not wearing glasses.” The neural network learns the relationship between images and their labels, and extracts data patterns, or features, that it needs to focus on to decide. One of the reasons AI systems are considered a black box is because it is often difficult to describe mathematically what criteria the systems are actually using to make their predictions, including potential biases. The new work provides a simple mathematical explanation for how the systems are learning these features.

Features are relevant patterns in the data. In the example above, there are a wide range of features that the neural networks learns, and then uses, to determine if in fact a person in a photograph is wearing glasses or not. One feature it would need to pay attention to for this task is the upper part of the face. Other features could be the eye or the nose area where glasses often rest. The network selectively pays attention to the features that it learns are relevant and then discards the other parts of the image, such as the lower part of the face, the hair and so on.  

Feature learning is the ability to recognize relevant patterns in data and then use those patterns to make predictions. In the glasses example, the network learns to pay attention to the upper part of the face. In the new Science paper, the researchers identified a statistical formula that describes how the neural networks are learning features. 

Alternative neural network architectures: The researchers went on to show that inserting this formula into computing systems that do not rely on neural networks allowed these systems to learn faster and more efficiently.  

“How do I ignore what’s not necessary? Humans are good at this,” said Belkin. “Machines are doing the same thing. Large Language Models, for example, are implementing this ‘selective paying attention’ and we haven’t known how they do it. In our Science paper, we present a mechanism explaining at least some of how the neural nets are ‘selectively paying attention.’” 

Source: UCSD

You can offer your link to a page which is relevant to the topic of this post.

[lpuengineering]

Scope and Career Prospects of Aeronautical Engineering in India

Have you ever been fascinated by the airplanes or the fighter jets that fly above us? Have you ever wondered how they’re built or able to fly that high? Aeronautical engineering doesn’t just deal with airplanes and jets but much more including space shuttles. Each one of us has a different idea on what aeronautical engineering is and what scope it has in India. To make things clear, read below:

What is Aeronautical Engineering?

It’s a discipline of engineering which deals with designing, testing and maintaining aircraft related technologies that stay and fly within the earth’s atmosphere and can be used for surveillance, defense, transportation, and research. It’s a complex yet interesting branch of engineering.

List of Courses in Aeronautical Engineering

Aircraft engine repairs and maintenance:

This is a course in which students will learn the working of aircraft engines and ways to repair and maintain them.

Aircraft reliability and safety engineering:

Students will be taught about different types of hydraulic machines and fluid mechanical principles.

Aircraft engineer

Aircraft maintenance technician

Professor of aircraft engineering

Aero-thermal engineer

Aircraft performance engineer

Repair design engineer

Stress engineer

Eligibility criteria:

Any student who has passed 10+2 with 60% aggregate marks and physics, chemistry and mathematics as their subjects are eligible to join aeronautical engineering.

Scope of aeronautical engineering in the government sector: India is rapidly growing and giving tough competition to other countries in the field of aeronautics. Government provides numerous opportunities in various companies such as Indian Space Research Organization (ISRO), Hindustan Aeronautics Limited (HAL), Bharat Electronics Limited (BEL), Defense Research Development Organization (DRDO), Bharat Earth Movers Limited (BEML Limited),Bharat Dynamics Limited reasons why it’s better to pursue a degree in aeronautical engineering in LPU. The scope of aeronautical engineering in India is rapidly on the rise with the governments of various countries and the billionaires in the race to space.

Aircraft system and maintenance:

This course provides practical exposure toaircraft systems and their maintenance.

Airport planning and design:

Explains the principles of patents, trademarks, industrial designs, and copyright.

Aeroacoustics:

Focusses onthe study ofnoise production using turbulent fluid motion or aerodynamic forces.

Introduction to cryogenics:

Students will study about production and behavior of materials at very low temperatures.

Rockets and missiles:

This course will inculcate the knowledge of various materials and tools used in building rockets and missiles.

Satellite technology:

Provides knowledge of the tools involved in the manufacturing and production of satellites.

Careers in aeronautical engineering:

There is a huge scope for aeronautical engineers in India and because of the number of people opting this branch is very low, the job opportunities are very high in India as well as abroad. Some of the careers are as follows:

(BDL),BrahMos Aerospace, Mishra Dhatu Nigam Limited (MIDHANI), Ordnance Factory Board (OFB).

Scope of aeronautical engineering in the private sector:

Various research, transport and aviation companies operating in the private sector provide jobs in India. In private sector, at the start of one’s career, one may be recruited as a junior engineerand then will be promoted along with being given a lucrative package based on one’s experience and expertise.

Scholarships in aeronautical engineering:

Students can avail up to 50% scholarship at Lovely Professional University in aeronautical engineering courses by appearing for LPUNEST.

[skillslash]

Mathematical Foundations for the Data Scientists

In recent years, data science has become one of the most sought-after and promising fields in the digital era. It has the potential to gain valuable insights from large data sets, which can be used to inform decision-making in various industries. However, in order to make the most of this opportunity, data scientists need to have a good grasp of mathematics. Mathematics is the basis on which data science is developed. 

In this article, we will look at the most important math concepts every data scientist needs to know. 

Why Math Matters in Data Science ? 

Mathematics is a fundamental component of data science, providing the essential tools and methods for modeling and analyzing data, making predictions, and extracting pertinent information. Here are some of the reasons why mathematics is essential for data science: 

Data Modeling: Mathematical models are used by data scientists to explain what's actually happening in the real world. They can be used to predict stock prices, categorize images, or even make product recommendations. Basically, they act as a link between the data and what we can actually do.

Data Analysis: Mathematics provides data scientists with the tools to analyze, summarize, and visualize data using statistical techniques. It is essential for data scientists to have a thorough understanding of probability distributions and hypothesis testing, as well as regression analysis, in order to draw meaningful inferences from data.

Machine Learning: Machine learning algorithms are a fundamental part of data science, as they are based on mathematical principles such as linear algebras, calculus and optimization. They are capable of learning from data and making predictions or decisions based on them.

Data Visualization: Charts, graphs and visualizations are the tools used by data scientists to convey information. Geometrical knowledge and linear transformations are key to producing impressive data visualizations

The Essential Math Concepts for Data Science

Let's now explore the fundamental mathematical principles that underlie data science:

Linear Algebra 

Linear Algebra is the foundation of a variety of data science methods. It is commonly used in machine learning to reduce dimensionality, process images, and make predictions. Matrices, vectors, and matrix-based operations are some of the most commonly used concepts in machine learning.

Calculus 

Calculus is really important when it comes to machine learning, especially when it comes to optimization. We need to be able to understand derivatives and how they relate to each other in order to make the best optimization algorithms for training neural networks and more.

Probability and Statistics

Utilizing probability theory, data scientists are able to accurately measure uncertainty and inform their decisions. Statistical techniques such as average, variance, and probability distributions, as well as hypothesis testing, are essential components of data analysis.

Differential Equations

Differential equations play a fundamental role in the modeling of dynamic systems. These equations are utilized in a variety of disciplines, such as physical science, biological science, and finance, to illustrate the transformation of variables over time.

Information Theory

Information theory is a field of study that focuses on measuring the amount of information contained in data. It plays an important role in data compression, feature selection, and other areas where it is essential to understand the content of variables.

Optimization

Optimization is all about finding the best way to solve a problem from a bunch of different options. Gradient descent is one of the most popular optimization algorithms used to train machine learning models.

Graph Theory

Graph theory plays a fundamental role in the analysis of network data, including social networks and transportation systems. Graph-based algorithms, such as PageRank, which are used by Google to power its search engine, are based on graph theory.

Linear Programming

Linear programming, also known as linear programming, is a programming technique used to solve optimization problems that involve linear objective functions and constraints. It can be applied to a variety of applications, such as resource allocation and supply chain management. 

Time Series Analysis

Time series analysis is all about modeling and predicting data points that have been collected over time. This is really important for things like predicting stock prices or looking at weather patterns in finance or climate science.

Learning Resources for Math in Data Science 

If you are interested in becoming a data scientist and would like to enhance your mathematical skills, there are a number of resources available to you, including: 

Online Courses: Platforms like Coursera, edX and institutes offer courses on various math topics, often tailored for data science and machine learning. 

Textbooks: Consider classic textbooks such as “Introduction to Linear Algebra” by Gilbert Strang, “Pattern Recognition and Machine Learning” by Christopher Bishop, or “Introduction to Probability” by Joseph K Blitzstein and Jessica Hwang. 

MOOCs(Massive Open Online Courses): Platforms like Coursera and edX offer comprehensive data science and machine learning specializations, which include math prerequisites. 

Interactive Learning: Websites like Khan Academy and Wolfram Alpha offer interactive lessons and exercises to practice mathematical concepts. 

Community and Forums: Engage with the data science community on platforms like Stack Overflow, Reddit’s r/datascience, and Linkedin groups to seek advice and guidance. 

In Conclusion, mathematics is not only a theoretical foundation for data science, but also a practical set of tools that can be used to gain knowledge and understanding from data. Although the complexity and intricacy of mathematics may appear to be a lot, it is important to remember that these concepts can be learned and applied over time. As you progress in your data science career, it is recommended to dedicate time to mastering these fundamental mathematical concepts. By doing so, you will be able to build predictive models, analyze data, and create algorithms, all of which will benefit from a solid mathematical foundation.

[ailtrahq]

After the collapse of FTX, crypto traders have been looking for decentralized, non-custodial and safer ways to execute orders and store their Assets. This explains why some decentralized crypto exchanges (DEXs) like Brine Fi are getting investor Interest even as VCs across the board continue to keep off the digital asset industry. Brine is announcing a $16.5 million Series A at a post-money valuation of $100 million as investors appear Bullish about the new orderbook-based decentralized exchange. The DEX, of which “mainnet”, or its fully operational network, launched merely months weeks ago and has already accumulated $500 million in Trading volumes, according to stats from Starkware, the Ethereum scaling solution that powers Brine. DEXs, as the name implies, carry out transactions purely on blockchains, a contrast to centralized exchanges (CEXs) that include consumer household names like FTX, Binance and Coinbase, which Brine sees as its closest competitors. Traders might choose DEX not just for full custody over their Assets but for Privacy – CEXs are normally required to undergo know-your-customer or KYC with local regulators, whereas regulations around DEXs are still largely undefined due to the lack of a central party. “While they are the safest way to trade, many traders opted for a CEX to counter higher Trading fees on DEXs, Price slippage, transaction fees ($5-$25 per transaction), liquidity issues, the absence of an orderbook, transaction delays and an inability to provide Privacy on orders causing front-running attacks. All things that can impact profit margins and substantially increase the uncertainty of specific trades,” said Shaaran Lakshminarayanan, Brine Fi cofounder, in a written response to TechCrunch. “Keeping all these points in mind, we’ve built Brine Fi to let traders experience the best of both worlds, get access to the merits of a DEX and a CEX at the same place. Moreover, high volume traders and institutions don’t need to worry about front-running attacks anymore as we provide complete Privacy on orders by using zkP (Zero Knowledge Proofs) technology which is backed by Starkware.” Orderbook and zero knowledge That’s a mouthful of crypto jargon – the takeaway is that Brine has found a way to provide the benefits of CEX that aren’t normally available in DEX. One of these is an orderbook. An orderbook, as in a traditional Stock market, matches Buyers and sellers based on Price and quantity. It allows for types of orders not possible on a DEX which are ideal for institutional traders because it lets them better manage their positions under different Market conditions and minimize slippage, the different trade execution Price than intended. DEXs such as Uniswap, on the other hand, operate on a completely different principle. Instead of matching Buyers and sellers, DEXs allow traders to exchange one type of asset for another by interacting with a pool of liquidity. So rather than having prices be determined by other traders, prices are set by a mathematical formula used to maintain the overall value of the Assets deposited by liquidity providers. Brine says it’s also able to prevent “frontrunning” for traders by leveraging zero-knowledge proof (ZKP), a cryptographic method that has been picking up steam recently as users look for more transactional Privacy. The technique, which is a way of authenticating a statement without revealing the statement itself, allows a transaction to be verified on a DEX without revealing details of one’s Trading position. The round was led by US-based crypto investor Pantera Capital, with participation of Elevation Capital, Starkware Ltd, Spartan Capital, Goodwater Capital, Upsparks Ventures, Protofund Ventures and a number of angel investors. Lakshminarayanan said Brine Fi is building for both retail and institutional traders. For the former, it’s introduced a beginner mode and inked a deal with liquidity aggregation platforms like 0x to enable people to easily start Trading.

The DEX is going after institutions like crypto hedge funds looking to transition away from centralized exchanges, which are currently driving a big chunk of its transactions. During its testing phase between February and June this year, Brine claims to have processed 4 million transactions and surpassed a Trading volume of over $1.6 billion. “Over the past month, Brine has been able to execute orders in milliseconds while remaining fully non-custodial. It has helped us onboard some of the largest hedge-funds, exchanges and high-frequency traders in the world by helping them diversify their asset allocation and mitigate counterparty Risks,” said Lakshminarayanan, who co-founded Brine with the firm’s CTO Bhavesh Praveen (CTO) and CDO Ritumbhara Bhatnagar. Regulation As centralized exchanges like Binance continue to face regulatory scrutiny over their operations in the U.S. and claims of canvassing breaches and money laundering in France, DEXs also face a risk of misuse as they are not required to abide by any Know Your Customer (KYC) and AML (Anti-Money Laundering) regulations. The founder suggested that regulations would require DEXs to forfeit user anonymity, which is one of the appeals for users who prefer decentralized exchanges in the first place. “DEXs present an opportunity for unscrupulous bad actors to take advantage of the industry for money laundering purposes as well as other financial crimes. Because individual users don’t need to verify their identity or the source of their funds when they create an account with a decentralized exchange, it’s much easier for them to slip under the radar compared to traditional financial institutions. For this reason, many industry experts believe that it’s only a matter of time before decentralized exchanges find themselves subject to such regulations,” said Lakshminarayanan. “With this in mind, it would be prudent for decentralized exchanges to recognize the potential for regulation and begin generating a framework for KYC and AML compliance in the event that it becomes required. At Brine we are already using providers such as Chainalysis and Merkle Science to ensure that we are taking the best measures to protect ourselves from such bad vectors,” he added.

[singaporeeconomicstutor]

JC Economics Tuition: The best means to secure good grades in Economics!

A branch of social science, economics is a study of the production, distribution, exchange and consumption of goods and services. It provides you with an in-depth understanding of real-world issues like inflation, international trade and unemployment alongside other areas like government policies and current economic trends. However, complex theories and intricate mathematical calculations often lead students to perceive economics as a challenging and tough subject. The Economics tuition in Singapore can be a game-changer in this endeavor.

Besides, if you opt for the GCE-A level examination, you must secure good scores to win entry tickets to the top universities. But the schools often fail to complete the vast syllabus due to limited time, impacting the student's knowledge and understanding of the subject adversely. Worry not! The best Economics tutor in Singapore provides thorough knowledge about the subject. Also, they follow a unique programme that aims to improve the student's performance remarkably. Here is how joining the economics tuition in Singapore can prove beneficial:

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· Experienced Teacher: The top-ranking economics tuition in Singapore has the best JC economics tutor. With profound knowledge of economics and more than ten years of experience, they will provide the best guidance and hand-hold you until you become proficient in the subject. Also, the efficient teaching professional is the author of several economics guidebooks and ten-year series that are a popular choice amongst JC students and GCE-A level aspirants. Rest assured! Joining their classes will enable you to grasp the concepts and prepare better for your A-level exams.

·  Up-to-date Syllabus: The A-level economics tuition in Singapore has designed a comprehensive curriculum based on the current MOE syllabus. They explain the fundamental concepts and tough topics through effective and engaging teaching methods. This makes the subject interesting for the student. Hence, they can overcome fear and become more confident.

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A well-formulated pedagogy assists in skill development and boosts the student's confidence. Here is the secret formula that widely-acknowledged

JC economics tuition in Singapore use to drive you towards success:

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[tuitionnz]

How Does The Subjects Complexity Lessen with Maths Tutor?

Maths is one of the most important subjects in the world. It is a subject that has been taught since ancient times and continues to be an essential part of today's curriculum.

The reason why it is so crucial to hire Maths Tutor, despite being quite straightforward, is because mathematics can be used in almost every aspect of life. For example, you can use maths in business or finance as well as engineering and construction industries.

Considering Subjects Complexity

The Subject's Complexity is based on the level of difficulty.

The Subject's Complexity is based on the subject's importance.

The Subject's Complexity is based on the subject's relevance.

The Subject's Complexity is based on the subject's application.

The Subject's Complexity is based on the subject's utility.

Subjects Complexity Lessens With Maths Tutor

You know the basics, but you need help understanding the concepts. You need someone who can explain why and how. Someone who can show you where to apply them in real life situations.

A math tutor will help you understand the formulas, but they also teach the applications of those formulas so that they make sense when applied to real-life situations in your career or personal life.

The Tutors Are Invaluable

With the tutor, you will learn to use your brain and problem-solving skills. The maths tuition will help you with math problems, which means that you can go back to school and focus on other subjects.

The tutors are great teachers because they can explain things in ways that kids understand or at their level of understanding. They also help students figure out how to solve a problem based on what they already know about math, so it's not like they're supposed to teach everything from scratch!

 Once you've learned how to solve one type of problem, your tutor will show you how other types of problems are solved too - so if one formula doesn't work for solving a particular issue (which can definitely happen), then learning more tricks might be helpful!

The Tutors Have Experience

One of the reasons why tutors are helpful is because they have experience with the subject. This means that they know what to teach you, and how to teach it.

If you're having trouble in a particular area, the tutor can determine which concepts need more attention, then help break down those concepts into smaller chunks so you can grasp them more easily. They'll also know when it's time for a break or if you should keep going without any breaks at all.

For instance, let's say your student wants to learn about circles and angles but isn't getting it after reading through some textbooks and doing practice problems on their own. The tutor will be able to figure out where the student has been going wrong and help them understand why certain mathematical principles work together (or not).

Conclusion

All in all, maths is an important subject and should be taken seriously by students. Students must understand that maths is not a difficult subject, but it requires patience and time.

The good thing about math tutors is that they have experience in teaching mathematics to students. The maths tutor can guide you on how to solve problems easily and quickly without wasting much time on it. They will also guide you on the best way of tackling tough questions or even how to approach them so that students don't get frustrated when solving them

Source: https://123tuitionnz.wordpress.com/2022/12/19/how-does-the-subjects-complexity-lessen-with-maths-tutor/

[art-of-mathematics]

What field are you in and how do I get there? ( I dont understand shit from your posts but they're the coolest things I've ever read)

Hi their, thanks for coming along my ask box - unfortunately I am not really able to offer a plain answer - as I am currently doing it all in isolation (autodidactic) - working on all that stuff since ten years - and I am also working on writing about my principles of research/learning - most I do is interdisciplinary - I recommend Vijay Balasubramanian's work - polymath in mathematics, theoretical physics, theoretical cognitive science - he researches about statistical inference, quantum field Theory, quantum gravity, string theory and I can't summarize the broad spectrum of his research more clearly now. My work is merely similar/related - yet, it is a mess to explain - Although math, physics and cognitive science might be my main sevtors of focus - my knowledge is 'heterogeneous", say, I lack much of the rigourously studies topics one learns along the formal education path.

Currently I do some merely low-level stuff, basic calculus/analysis so to speak - but the approach of how I understand is... is merely odd. You see how I synthesize multiple perpectives/modes of perception. I find the notation of integral and differential calculus confusing - somehow, my journey into analysis started with fourier transform, superposed waves and multiple parallel thought ramblings - In retrospect, the mathemetics is the actual and concrete form of how I have perceived my own reasoning and perception.

And I understand why people think it might just be psychotic nonsense. Yet, the methods are highly advanced. I try to put them in a comprehensible language/mathematical model/algorithm currently.

To further investigate career options, I think about seeking entry into the academic world through the IT sector - most certainly quantum developer - I want to write assmbler code for non-lineary working quantum computers, so to speak. Good thing: I could apply much of my own research directly and advance/develop them better [especially the non-linear axiomatic system/quantum information flows topics] and say, start research without having a degree - but that might open some options to attend university programs, or get a degree in the future, and especially: I could do what I love, and could finally learn to master my stuff in a way that is functional and applyable in that world - and not just rotting in my filecases...

Yet, my health, being neurodivergent, having no support socially/in health issues/financially, and german buerocracy are really hindering factors in that constellation of situation - especially if they are combined.

Yet I have a rough plan. In the recent weeks I could finally leave a many-year long traumatic situation - one that involved my father keeping my mind tiny - supressing and abusing my neurodivergent self - whatever, I do not want to burden with details nor do I want to be pitied. It gets better and I can finally unravel my potential and start my academic life - tough, in a very odd and statistically unprobable way - but that's it: In some sense I use(d) game theory to free myself from that trap of situation: An almost zero percent probability to have a fullfilling life becomes gradually more probable - as for now, it's me showing initiative and dedicated autodidactism that has secured me a hope to a career in my special interests. (I am sorry for the much bla bla)

Alongside that way I also try to make mathematics more accessible and enjoyable for curios and/or neurodivergent people. As I believe, hope is something people need more than ever. And a new way to see can be exactly that for some people. Especially neurodivergent people have to suffer tremendously under that worldwide defective education system - alongside other systematic deficits including basic human dignity and respect. In some sense, I want to write books, create content and art on mathematics and other inspiring branches, to inspire, to give someone the hope and enthusiasm I wish I would have received as kid, to ignite a flame of wonder and awe - and in some sense, yes, I am becoming sentimental, but honest, somehow, ten years ago, I have received that hope of inspiration on that platform - by fellow (most certainly also neurodivergent) blog owners/content creators. And if I look back, I am extremely thankful for the kindhearted and honest community here, the hilarious puns and posts, the insightful debates, the silly memes, the common appreciation for infodumping on special interests, and the very humane and heart-wearming and welcoming social interaction.

I could link some users here, but I would feel bad if I forgot some - so, in some sense, for whoever is reading that - I am thankful for our encounter!

(Ahh completely lost track of my thoughts...) I really appreciate your appreciation! Yet, I can't really give you info in how you could get iny my field - as I do not know it myself unfortunately. But I let you know once I know more. (I can only recommend Vijay Balasubramanian's work. As he is already in that career path, maybe research about him might be helpful... interestingly he also entered via the CS sector...)