In the blink of an eye, it takes off and dashes away, sprinting on top of the water.

眨眼間，它就飛了起來，在水面上衝刺。

Meet the basilisk lizard, the water-walking dragon that seems to defy gravity and challenge a lot of what we know about movement and locomotion.

巴斯里斯克蜥蜴是一種在水中行走的巨龍，它似乎無視地心引力，挑戰著我們對運動和移動的認知。

Unlike its mythical counterpart, basilisk lizards aren't in the business of causing death with a single glance.

與神話中的同類不同，巴斯里斯克蜥蜴並不是看一眼就能致人於死地。

In fact, real-life basilisks are not very formidable, and are quite vulnerable to death at the hands of other forest dwellers such as large birds, snakes, and fish.

事實上，現實生活中的巴斯里斯克並不可怕，它們很容易死在其他森林居民（如大型鳥類、蛇類和魚類）的手中。

They generally lay motionless, and their cryptic coloration allows them to blend in with the brown hues of branches or dead leaves on the forest floor, or the deep greens of foliage higher up in the trees.

它們通常一動不動地躺在地上，其隱蔽的顏色使它們能與森林地面上的棕色樹枝或枯葉，或樹上的深綠色樹葉融為一體。

When threatened, however, basilisks employ one of the most creative escape strategies known in the animal kingdom.

然而，當受到威脅時，巴西利斯克會採用動物界已知的最有創意的逃學生策略。

When jolted from their statue-like state, a basilisk lizard's hind limbs whir into action, bicycling across the surface of the water and propelling the tiny lizard up to 15 feet, covering more than 10 times its own body length in a single second.

當它們從雕像般的狀態中驚醒時，巴斯里斯克蜥蜴的後肢就會開始行動，在水面上騎自行車，並將這隻小蜥蜴推高至 15 英尺，在一秒鐘內就能覆蓋超過自身體長 10 倍的面積。

Once this aquatic roadrunner has sprinted as far as it can, it sinks down into the water, far from whatever threat caused it to move in the first place.

一旦這隻水生跑路鳥盡力衝刺，它就會沉入水中，遠離一開始導致它移動的任何威脅。

This seemingly miraculous escape tactic has earned the basilisk the nickname the Jesus Christ Lizard in its homeland of Central and South America, and has captured the attention of not only reptile enthusiasts, but of biomechanical engineers looking to recreate this water-walking ability using adaptive robotics.

這種看似神奇的逃學生戰術為玄武蜥在中美洲和南美洲的故鄉贏得了 "耶穌基督蜥蜴 "的綽號，不僅吸引了爬行動物愛好者的注意，也吸引了生物力學工程師的注意，他們希望利用自適應機器人技術重現這種水中行走的能力。

What is it about these seemingly physics-defying lizards that allow them to possess such a biblical ability?

究竟是什麼讓這些看似物理定律的蜥蜴擁有如此聖經般的能力？

And what might these skittish creatures teach us about being able to walk on water ourselves?

這些膽小的生物會告訴我們怎樣才能在水上行走呢？

Basilisk lizards belong to the Cascade lizard family, in reference to the round crests atop their heads.

巴斯里斯克蜥蜴屬於級聯蜥蜴科，因為它們頭頂上有圓形的嵴。

This might have earned them their scientific name, Basilicus, which translates to Little King.

這可能是它們學名 Basilicus 的由來，翻譯過來就是 "小國王"。

These little, helmeted kings belong to a much grander lineage of super-powered lizards, the iguanians.

這些頭戴頭盔的 "小皇帝 "隸屬於一個更為龐大的超能力蜥蜴家族--鬣蜥。

This suborder includes some 2,000 lizards, from the fearsome, frilled, and spiky lizards in Australia, to the flying acrobats of Southeast Asia gliding across canopies, to a colorful array of hue-shifting chameleons across different continents.

該亞目包括約 2000 種蜥蜴，從澳洲的可怕、長滿褶皺和尖刺的蜥蜴，到東南亞在樹冠上滑翔的飛行雜技演員，再到各大洲色彩斑斕的變色龍。

But only the basilisk lizard can walk on water, a unique and extreme adaptation that may have come from an ancient ancestor.

但只有玄武蜥能在水上行走，這種獨特而極端的適應能力可能來自遠古的祖先。

The babby basilicus, a 48 million year old lizard skull fossil, is a close relative of the basilisk lizard.

巴斯比蜥蜴是距今 4800 萬年前的蜥蜴頭骨化石，是巴斯比蜥蜴的近親。

While there isn't exactly a way to prove that this ancient relative was also able to walk on water, researchers do know that this ancestral species lived during a time where it would have been very useful to do so.

雖然沒有確切的方法證明這個遠古親戚也能在水上行走，但研究人員確實知道，這個祖先物種生活的時代，水上行走是非常有用的。

The environment was full of the early ancestors of carnivorous mammals, raptors, and even crocodiles, and you can be sure that being able to run on water would have definitely improved chances of survival amidst these predators.

環境中到處都是食肉哺乳動物、猛禽甚至鱷魚的早期祖先，可以肯定的是，能夠在水上奔跑肯定會提高在這些掠食者中生存的機會。

So it's entirely possible that the incredible ability to walk on water has been around for an extremely long time.

是以，在水上行走這種不可思議的能力完全有可能已經存在了很長時間。

And this survival strategy is still necessary in the modern world, with snakes, predatory birds, and big mammals who would happily snack on a little lizard.

在現代社會，這種生存策略仍然是必要的，因為蛇、掠食性鳥類和大型哺乳動物會很樂意吃掉一隻小蜥蜴。

They do their best to camouflage, but even the best camouflage can sometimes be discovered by the keen eyes of larger birds, the supercharged smell of snakes, and the prowling of mammals that can even see in the dark of the night.

它們會盡力偽裝，但即使偽裝得再好，有時也會被大型鳥類敏銳的眼睛、蛇類超強的嗅覺以及甚至能在黑夜中看到的哺乳動物的徘徊發現。

And that's when running on water comes in handy.

這時候，水就派上用場了。

To fully appreciate the miracle of the basilisk lizard being able to walk on water, consider how most legged animals walk on land.

要想充分了解玄武蜥能在水上行走的奇蹟，就要想想大多數有腿的動物是如何在陸地上行走的。

To describe the gait of terrestrial organisms, biokinematic researchers typically refer to the classic spring mass model.

為了描述陸生生物的步態，生物運動學研究人員通常會參考經典的彈簧品質模型。

Imagine what it's like when you take a step to walk.

想象一下，當你邁開步子走路時是什麼感覺。

After you plant your foot firmly into the ground, notice how your leg flexes ever so slightly before you push off, raise your leg, and prepare to take that next step.

當你將腳穩穩地踩在地上後，注意在你推開、抬起腿並準備邁出下一步之前，你的腿是如何微微彎曲的。

This slight flexion can be compared to compressing a spring, priming it for expansion as you bounce off your one leg to propel yourself forward.

這種輕微的屈曲可以比作壓縮彈簧，當你單腿彈起推動自己前進時，彈簧就開始膨脹。

This bouncing gait is common in many forms of terrestrial locomotion, from the galloping of horses to the hopping of rabbits, and it's a particularly efficient way of moving on land.

這種彈跳步態在許多陸地運動形式中都很常見，從馬的奔跑到兔子的跳躍都是如此。

For the basilisk lizard sprinting across a pond, it's easy to see that this model wouldn't be a good fit.

對於在池塘中衝刺的玄武蜥來說，很容易發現這種模型並不適合。

For such a spring system to work, the ground you're walking on needs to provide enough resistance for the spring to push against and be primed.

要使彈簧系統正常工作，您行走的地面需要提供足夠的阻力，使彈簧能夠頂住並啟動。

But water is, well, water.

但水就是水。

Unlike solid ground, it's weak, yielding, and gives to most any kind of pressure that's applied to it.

與堅固的地面不同，它軟弱無力，容易屈服，可以承受任何壓力。

Most limbs that attempt to take a step in the water sink, and those that don't, as is the case for the other water walkers of the animal kingdom, typically have to rely on other mechanisms to stay afloat.

大多數試圖在水中邁步的肢體都會下沉，而那些沒有在水中邁步的肢體，就像動物界的其他水上步行者一樣，通常必須依靠其他機制才能浮在水面上。

The water strider, for example, floats atop the surface with the help of its multiple, extremely long, widespread legs with waterproof hairs.

例如，水黽藉助多條極長、長滿防水毛的腿漂浮在水面上。

The buoyancy created by these legs can support up to 15 times the insect's weight, a useful adaptation for when it's raining and water drops add considerably to their body weight.

這些腿產生的浮力可以支撐昆蟲體重的 15 倍，在下雨天，水滴會大大增加昆蟲的體重，這種適應性非常有用。

Waterfowl, like ducks and geese, can also occasionally be seen to be running on the water, but are usually assisted by flight that allows them to just barely skim the water's surface.

鴨和鵝等水禽偶爾也能看到它們在水面上奔跑，但它們通常是藉助飛行才勉強掠過水麵。

The basilisk lizard doesn't have any long, buoyant limbs, and unlike some gliding lizards, the basilisk isn't able to glide or fly.

玄武蜥沒有長長的、有浮力的四肢，與一些滑翔蜥蜴不同，玄武蜥不能滑翔或飛行。

So how does this reptile manage such an incredible task?

那麼，這種爬行動物是如何完成如此艱鉅的任務的呢？

Using high-speed cameras, researchers have discovered just how the basilisk lizard does it.

通過使用高速攝影機，研究人員發現了巴斯里斯克蜥蜴是如何做到這一點的。

Instead of the classical bouncing spring model, basilisk lizard hind limbs move in a more bicycling, piston-like fashion, a totally unique form of movement.

與傳統的彈跳彈簧模式不同，玄武蜥後肢的運動方式更像自行車的活塞運動，這是一種完全獨特的運動形式。

The piston-like movement of the basilisk can be sequenced into three distinct phases known as the slap, the stroke, and the recovery phase.

玄武的活塞式運動可分為三個不同的階段，即拍打階段、衝程階段和恢復階段。

As the name of the first phase suggests, the basilisk lizard first slaps the surface of the water, which creates a pocket of air that keeps the lizard from sinking.

正如第一階段的名稱所示，玄武蜥首先拍打水面，形成一個氣囊，使蜥蜴不至於沉入水底。

It's this same kind of air cavity forming phase that allows us to skip tiny pebbles across the surface of a lake.

正是這種氣穴形成階段，讓我們能夠跳過湖面上的小石子。

In the stroke phase, the lizard starts to propel itself forward, its leg very quickly digging into the air pocket and kicking back as it pushes off the cavity formed in the slap phase.

在划動階段，蜥蜴開始向前推進，它的腿迅速鑽入氣囊，並在推開拍打階段形成的空腔時向後踢腿。

Then, just before the air pocket collapses and water rushes in to sink the basilisk's leg, the basilisk curls its toes and swiftly pulls its leg out of the air pocket before it breaks, transitioning into the next slap-stroke recovery cycle on the other leg.

然後，就在氣囊坍塌、水流湧入並使玄武腿下沉之前，玄武蜷起腳趾，在氣囊破裂之前迅速將腿從氣囊中拉出，並過渡到另一條腿的下一個拍擊恢復循環。

In this sense, basilisk lizards aren't so much water walkers as they are airbenders, forcing bubbles of air beneath their feet at each step they take.

從這個意義上說，玄武蜥與其說是水上行走者，不如說是空氣傳播者，它們每走一步都會在腳下產生氣泡。

With movements so quick on a surface so fragile, the basilisk also employs some tactics to maintain its center of gravity.

在如此脆弱的表面上進行如此快速的運動，玄武岩還採用了一些戰術來保持重心。

On the slap phase, the lizard's leg is slightly pushing off towards the midline, while on the stroke phase, the lizard's leg shifts slightly laterally as it tries to right itself.

在拍打階段，蜥蜴的腿稍稍向中線推開，而在划動階段，蜥蜴的腿稍稍向側面移動，試圖擺正自己的位置。

This kind of wobbly, transverse movement, coupled with its flailing upper limbs and a long, rudder-like tail, helps the basilisk to stay balanced as it dashes across the water and gives it its characteristic goofy, almost clumsy-looking way of running.

這種搖擺不定的橫向運動，再加上它甩動的上肢和像船舵一樣的長尾巴，有助於巴斯里斯克在水面上衝刺時保持平衡，並使它的奔跑方式顯得呆頭呆腦，近乎笨拙。

But is this something that all basilisk lizards can do, from the tiniest ones to the absolutely huge ones?

但是，從最小的玄武蜥到體型巨大的玄武蜥，是不是所有的玄武蜥都能做到這一點呢？

Is there a point at which its size prevents it from running on water?

它的體積是否會阻礙它在水上運行？

A group of researchers found that smaller, juvenile lizards were much more successful at running on water than larger adults, so size clearly plays some role.

一組研究人員發現，與體型較大的成年蜥蜴相比，體型較小的幼年蜥蜴在水上奔跑的成功率要高得多，是以體型顯然起到了一定的作用。

When they analyzed the gait mechanics required for lizards weighing between 2 grams and 200 grams, they found something interesting.

當他們分析體重在 2 克到 200 克之間的蜥蜴所需的步態力學時，他們發現了一些有趣的現象。

All of them generate more than enough force to stay on the surface of the water, but how they move changes.

它們都能產生足夠的力量停留在水面上，但移動方式卻發生了變化。

Small lizards can be pretty sloppy with how they move, because at 2 grams, they can generate 225% of the force needed to maintain their center of mass at a constant position.

小蜥蜴在移動過程中可能會非常馬虎，因為 2 克的重量就能產生 225% 的力來將質心保持在恆定位置。

In fact, the researchers say that a 2 gram lizard could carry another lizard of the same size on its back and still easily run across the water.

事實上，研究人員說，一隻 2 克重的蜥蜴可以揹著另一隻同樣大小的蜥蜴在水面上輕鬆奔跑。

Lizards that weigh 200 grams, on the other hand, only produce just over the amount of force needed to support their body weight.

而體重為 200 克的蜥蜴所產生的力僅剛剛超過支撐其體重所需的力。

They have to avoid, drag, and yank their feet out of the water as quickly as possible, because they're much more likely to sink.

它們必須躲避、拖拽，並儘快把腳從水中拽出來，因為它們更有可能沉入水底。

No chance of them carrying a hitchhiker on their backs.

他們不可能揹著一個搭便車的人。

And this brings us to the next question.

這就引出了下一個問題。

Could humans ever do this?

人類能做到這一點嗎？

If we wore the world's biggest flippers and never skipped leg day at the gym, could we generate the force necessary to walk on water?

如果我們穿上世界上最大的腳蹼，並且每天在健身房不間斷鍛鍊，我們能產生在水上行走所需的力量嗎？

Unfortunately, not on this planet.

遺憾的是，在這個星球上沒有。

Researchers calculated that humans would have to run at 30 meters per second, or 67 miles per hour, on one square meter fins to generate the necessary force.

研究人員計算出，人類必須以每秒 30 米或每小時 67 英里的速度在一平方米的鰭上奔跑，才能產生必要的力量。

Not even Usain Bolt could manage it.

就連尤塞恩-博爾特也做不到。

But if we reduced the gravity to only 20% of Earth's gravity, basically getting it to the moon's gravity, we'd have a chance.

但是，如果我們把重力降低到只有地球重力的 20%，基本上達到月球的重力，我們就有機會了。

You'd still have to wear small fins and weigh no more than 73 kilograms, but then it would actually be possible to walk on water.

你仍然必須佩戴小鰭，體重不超過 73 千克，但這樣就可以真正在水上行走了。

But considering there's no water on the moon, this isn't the most useful information, but who knows what future humans might get up to.

但考慮到月球上沒有水，這並不是最有用的資訊，但誰知道未來的人類會做出什麼呢？

Until then, we're more likely to use the Basilisk Lizard for inspiration with our machines.

在此之前，我們更傾向於用 Basilisk Lizard 來啟發我們的機器。

This simultaneously funny-looking and incredible adaptive strategy of the Basilisk Lizard has captivated the attention of researchers in the field of biomimetic robotics.

巴斯里斯克蜥蜴的這種既滑稽可笑又令人難以置信的適應策略吸引了生物仿生機器人領域研究人員的注意。

That is, scientists and engineers who take inspiration from movements in nature and emulate it with machinery.

也就是說，科學家和工程師從自然界的運動中汲取靈感，並用機械加以模仿。

In the context of the Basilisk Lizard, that means amphibious robots, which are designed to navigate between terrestrial and aquatic environments.

就巴斯里斯克蜥蜴而言，這意味著水陸兩棲機器人，可以在陸地和水生環境之間航行。

While there are already a number of species of amphibious robots coming in all shapes and sizes, many of these rely on wheeled or leg mechanisms that sink into the water, while others inspired by the water strider rely more on buoyancy and thus move across the water considerably slower.

雖然現在已經有了許多形形色色的水陸兩棲機器人，但其中許多都依靠沉入水中的輪式或腿式裝置，而其他受水黽啟發的機器人則更多地依靠浮力，是以在水中的移動速度要慢得多。

While useful, these robotic designs don't quite fill in the niche of function that a water-running robot could provide.

這些機器人設計雖然有用，但並不能完全滿足水上機器人的功能需求。

A fast and highly reliable robot that could transition almost instantly from land to water and back could be incredibly useful for unmanned rescue missions, research into dangerous terrain, more efficient ocean explorations, and maybe eventually the exploration of alien environments.

一個快速且高度可靠的機器人，幾乎可以瞬間從陸地轉換到水中，這對於無人救援任務、危險地形研究、更高效的海洋探索，甚至最終的外星環境探索，都會非常有用。

Consider some of the prototype robots inspired by the water-walking Basilisk.

考慮一下從水上行走機器人 Basilisk 中獲得靈感的一些機器人原型。

This blade-type crawler, developed by Yamada and Nakamura, has blade-like legs attached to a conveyor belt-like mechanism around the robot's body.

這種刀片式爬行器由山田和中村開發，機器人身體周圍有一個類似傳送帶的裝置，連接著刀片一樣的腿。

Compared to other approaches to rough terrain, this mechanism allows for a good balance between the high velocity that a wheeled vehicle provides and the adaptability that a legged robot could provide.

與其他應對崎嶇地形的方法相比，這種機制在輪式車輛提供的高速度和腿式機器人提供的適應性之間實現了良好的平衡。

And unlike its reptile counterpart, this blade crawler wasn't designed for running away.

與爬行動物不同的是，這種刀片爬行動物並不是為了逃跑而設計的。

This tiny robot headed straight towards danger as it was field-tested to explore volcanic areas of Mount Mihara in Japan.

在對日本三原山火山區進行實地探測時，這個小機器人直奔危險而去。

The Basilisk-inspired robot didn't disappoint as it waded seamlessly through small ponds and puddles and demonstrated the potential for unmanned observation of otherwise dangerous sites such as active eruptions.

這個受巴西里斯克啟發的機器人並沒有讓人失望，它在小池塘和水坑中穿行自如，並展示了對活躍噴發等危險地點進行無人觀測的潛力。

Other projects take the inspiration from nature to the extremes, like this lizard-spider-octopus- jellyfish-rolling robot.

其他項目則將大自然的靈感發揮到極致，比如這個蜥蜴-蜘蛛-章魚-水母滾動機器人。

You heard that right.

你沒聽錯。

This robot is envisioned not only to be able to walk on water like the Basilisk lizard, but also roll and fold up on top of the water like the golden wheel spider and propel itself underwater just as we see octopus and jellyfish do.

根據設想，這種機器人不僅能像巴斯里斯克蜥蜴一樣在水上行走，還能像金輪蜘蛛一樣在水面上滾動和摺疊，並能像我們看到的章魚和水母一樣在水下推進。

And if this wasn't impressive enough, researchers also hoped to have this robot release a swarm of other baby robots, also engineered to mimic some of nature's best water travelers.

如果這還不夠令人印象深刻的話，研究人員還希望讓這個機器人釋放出一群其他的機器人寶寶，這些機器人寶寶也是模仿大自然中一些最好的水上旅行者設計的。

While this mind-boggling robot was initially designed for the purpose of deep-sea research and ocean object identification, the authors mention that such an alien-looking robot may potentially be suited for out-of-this-world explorations in unpredictable environments beyond Earth.

雖然這個令人匪夷所思的機器人最初是為深海研究和海洋物體識別而設計的，但作者提到，這種外形酷似外星人的機器人有可能適合在地球以外不可預知的環境中進行超自然探索。

The Basilisk lizard is a prime example of how seemingly small scientific curiosities can be transformed into real-world practical applications that have the potential to save lives and provide us with a better understanding of worlds we've never been to before.

巴斯里斯克蜥蜴是一個很好的例子，它說明了看似微小的科學好奇心是如何轉化為現實世界中的實際應用，從而有可能拯救生命，並讓我們更好地瞭解我們從未去過的世界。

Our growing understanding of the Basilisk's funky movements has allowed a more analytical approach to recreating this biblical ability, with researchers experimenting with dynamic folding feet and different kinds of rigid and active tails to slowly, hopefully, reach a point where walking on water will be nothing out of the ordinary.

我們對 Basilisk 有趣動作的理解不斷加深，這使得我們能夠採用更多的分析方法來重現這種聖經中的能力，研究人員試驗了動態摺疊腳以及不同種類的剛性和活動尾巴，希望能夠慢慢達到在水上行走的境界。

But as researchers are starting to realize, manually programming robots to deal with tons of different situations, such as highly variable terrain, from ice to gravel to water to rocks, is time-consuming and also just doesn't work that well.

但是，正如研究人員開始意識到的那樣，手動為機器人編程以應對大量不同的情況，例如從冰到礫石、從水到岩石等千變萬化的地形，不僅費時費力，而且效果也不盡如人意。

To really unlock the true potential of robots like the Basilisk bot, researchers are starting to use neural networks that allow the robot to learn on its own how to deal with obstacles it faces.

為了真正釋放像 Basilisk 機器人這樣的機器人的潛能，研究人員開始使用神經網絡，讓機器人自己學習如何應對所面臨的障礙。

This is, without a doubt, the next huge leap in robotics, and it's one that I don't really understand that well.

毫無疑問，這是機器人技術的下一個巨大飛躍，而我對它的理解還不是很透徹。

The papers on the subject are dense, and I can only barely wrap my head around what they're saying.

這方面的論文密密麻麻，我只能勉強理解他們的意思。

But in this line of work, and just as a human in this modern world, I really need to understand how neural networks work.

但在這一行，作為現代社會中的人類，我真的需要了解神經網絡是如何工作的。

So to learn about this from the ground up, I use Brilliant.

是以，為了從基礎開始學習，我使用了 Brilliant。

Brilliant is a free and easy way to learn math, data science, and computer science interactively.

Brilliant 是一種以互動方式學習數學、數據科學和計算機科學的免費而簡單的方法。

And their Introduction to Neural Networks course has allowed me to dive into the inner machinery of neural networks to discover how these flexible learning tools actually work.

他們的《神經網絡入門》課程讓我深入瞭解了神經網絡的內部機制，發現了這些靈活的學習工具究竟是如何工作的。

They start you off by showing you some simple neural networks to first just show you how they work, and then you get to explore a much bigger neural network to appreciate all that they can do.

首先，他們會向你展示一些簡單的神經網絡，讓你瞭解它們是如何工作的，然後，你將探索一個更大的神經網絡，領略它們的所有功能。

So if you've also been hearing about neural networks all over the place, and are a little lost on how they actually work, this is the course for you.

是以，如果你也經常聽說神經網絡，但又對其實際工作原理有些迷茫，那麼這門課程就是為你準備的。

Brilliant is fun and interactive, with thousands of lessons from basics to advanced topics, and new lessons are added every month.

Brilliant 具有趣味性和互動性，提供從基礎到高級主題的數千節課程，並且每月都會增加新課程。

For me, the best part of Brilliant is the interactivity.

對我來說，Brilliant 的最大亮點在於互動性。

I don't learn best by simply reading documents, I need to engage with the material.

僅僅閱讀文件並不是我學習的最佳方式，我需要參與到材料中去。

And Brilliant lets you do this with levers, sliders, buttons, and questions all along the way to ensure you are really absorbing the lesson.

Brilliant 可以通過槓桿、滑塊、按鈕和問題讓你做到這一點，以確保你真正吸收課程內容。

Whatever your skill level, Brilliant customizes content to fit your needs, and lets you solve at your own pace.

無論您的技能水準如何，Brilliant 都能根據您的需求定製內容，讓您按照自己的節奏解決問題。

So to learn more about this new age of neural networks, and to try everything Brilliant has to offer free for a full 30 days, visit brilliant.org slash real science, or click on the link in the description.

是以，要了解有關神經網絡新時代的更多資訊，並免費試用 Brilliant 所提供的一切，請訪問 brilliant.org slash real science，或點擊描述中的鏈接。

The first 200 people will get 20% off Brilliant's annual premium subscription, and every sign up helps this channel.

前 200 名註冊者可享受 Brilliant 年度高級訂閱八折優惠，每一位註冊者都將對本頻道有所幫助。