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Enrique Dans

Enrique Dans

3 years ago

You may not know about The Merge, yet it could change society

More on Technology

CyberPunkMetalHead

CyberPunkMetalHead

3 years ago

I made ChatGPT copy itself.

OpenAI's ChatGPT is an amazing AI-powered chatbot. It can write poetry, stories, and marketing campaigns, and it's also adept at coding. ChatGPT's coding is so amazing that it replicated itself. What happened:

Me: Hi

Hello! Can I help? I'll answer any inquiries you have.

Me: Build a python and flask AI chatbot that responds to user messages on the frontend.

CGPT:

from flask import Flask, request, jsonify

import openai
openai.api_key = "YOUR_API_KEY"

@app.route('/chatbot', methods=['POST'])
def chatbot():
    user_message = request.get_json()['message']
    response = chatbot_response(user_message)
    return jsonify({'response': response})


def chatbot_response(user_message):
    response = openai.Completion.create(
        engine="text-davinci-002",
        prompt=user_message,
        max_tokens=1024,
        n = 1,
        temperature=0.5
    )
    return response['choices'][0]['text']

if __name__ == '__main__':
    app.run()

To integrate a chatbot with a frontend, use Flask to serve an HTML page with a form for user messages and the chatbot's answer. AJAX can submit the form to the /chatbot route, and JavaScript can show the chatbot's response.

I imported code snippets at the top of the file.

Let's add a frontend interface, I said.

CGPT:

<!DOCTYPE html>
<html>
<head>
    <title>AI Chatbot</title>
</head>
<body>
    <h1>AI Chatbot</h1>
    <form id="chatbot-form">
        <label for="message">Message:</label><br>
        <input type="text" id="message" name="message"><br>
        <input type="submit" value="Submit">
    </form> 
    <div id="chatbot-response"></div>

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
    <script>
        $(document).ready(function() {
            $("#chatbot-form").submit(function(e) {
                e.preventDefault();
                var userMessage = $("#message").val();
                $.ajax({
                    type: "POST",
                    url: "/chatbot",
                    data: JSON.stringify({message: userMessage}),
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function(response) {
                        $("#chatbot-response").text(response.response);
                    }
                });
            });
        });
    </script>
</body>
</html>

To serve this HTML page using Flask, build a new route that returns the page as a GET response.

So far, so good.

Looked quite basic so I got chatGPT to add some tailwind to the project.

Me: Tailwind the chatbot.html page, please. Give it a futuristic style with purple and neon

After a few more prompts, Talk GPT aligned the form to the center, changed some colors, and added padding.

CGPT:

<!DOCTYPE html>
<html>
<head>
    <title>AI Chatbot</title>
    <link href="https://unpkg.com/tailwindcss@^1.0/dist/tailwind.min.css" rel="stylesheet">
</head>
<body class="bg-black flex flex-col justify-center items-center">
    <h1 class="sm:text-center text-purple-500">AI Chatbot</h1>
    <form id="chatbot-form" class="border-purple-500 bg-purple-800 rounded">
        <label for="message">Message:</label><br>
        <input type="text" id="message" name="message" class="min-w-30 rounded"><br>
        <input type="submit" value="Submit" class="bg-purple-500 border-red-500 transform hover:scale-110 rounded">
    </form> 
    <div class="flex justify-center">
        <div id="chatbot-response" class="text-white rounded"></div>
    </div>

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
    <script>
        var colors = ['red', 'orange', 'yellow', 'green', 'blue', 'indigo', 'violet'];
        var colorIndex = 0;
        
        $(document).ready(function() {
            setInterval(function() {
                $("#chatbot-form").css('border-color', colors[colorIndex]);
                colorIndex = (colorIndex + 1) % colors.length;
            }, 1000);

            $("#chatbot-form").submit(function(e) {
                e.preventDefault();
                var userMessage = $("#message").val();
                $.ajax({
                    type: "POST",
                    url: "/chatbot",
                    data: JSON.stringify({message: userMessage}),
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function(response) {
                        $("#chatbot-response").text(response.response);
                    }
                });
            });
        });
    </script>
</body>
</html>

Improved:

A few more prompts like “Add more vertical and horizontal padding to the submit button and vertical margin, and vertically align this file's body.”

The result:

Is it effective? Now, I'll chat with ChatGPT's AI Chatbot. I intervened minimally throughout construction. Chat GPT created numerous files, connected and interacted with its own API, and presented the user request response on the front end by itself.

Me to AI Chatbot: Hey, can you give me 6 name suggestions for a black horse?

Me to AI Chatbot: Write a poem in the style of Jim Morrison. Make sure to mention cacti and black holes

ChatGPTs Chatbot:

In the desert night, I am confronted by cacti, 
Their arms reaching out, As if to grab me and take me away. 
The stars in the sky, Beckon me to come, 
To a world of black holes, Where I can be free. 
I am in a trance, My body and mind, 
In a state of limbo, As I wander the night. 
I hear a voice, Calling me to the unknown, 
I cannot resist, The lure of the black hole. 
The cacti watch, As I take my leave, 
To a place of mystery, Where I can find peace.

Of course, the next question I gave it was to build a chatbot!

Me: Build a python and flask AI chatbot that responds to user messages on the frontend.

ChatbotGPTs:

import os from flask 
import Flask, request, jsonify 
from chatterbot 
import ChatBot 
from chatterbot.trainers 
import ListTrainer 

# Create a new chatbot 
bot = ChatBot( 
  "My Bot", 
  storage_adapter="chatterbot.storage.SQLStorageAdapter", 
  logic_adapters=[ 
    "chatterbot.logic.BestMatch", 
    { "import_path": "chatterbot.logic.BestMatch", 
      "statement_comparison_function": "chatterbot.comparisons.levenshtein_distance", 
       "response_selection_method": "chatterbot.response_selection.get_first_response" } 
    ], 
    database_uri="sqlite:///database.sqlite3" ) 

# Train the chatbot with a few sample conversations 
conversation = [ "Hello", "Hi there!", "How are you doing?", "I'm doing great.", "That is good to hear", "Thank you.", "You're welcome." ] 
trainer = ListTrainer(bot) trainer.train(conversation) 

# Create a Flask app 
app = Flask(__name__) 

# Define a route for the default URL 
@app.route("/") def index(): return "<h1>Chatbot</h1>" 

# Define a route for the /get_response URL 
@app.route("/get_response", methods=["POST"]) 

def get_response(): 
# Get the user's message 
user_message = request.form["user_message"] 
# Get the bot's response 
bot_response = bot.get_response(user_message) 
# Return the bot's response 
return str(bot_response) 
# Run the Flask 
app if __name__ == "__main__": app.run()

No matter how many times I tried, the second generation always used chatterbot instead of the ChatGPT API. Even when I told it to use the ChatGPT API, it didn't.

ChatGTP's ability to reproduce or construct other machine learning algorithms is interesting and possibly terrifying. Nothing prevents ChatGPT from replicating itself ad infinitum throughout the Internet other than a lack of desire. This may be the first time a machine repeats itself, so I've preserved the project as a reference. Adding a requirements.txt file and python env for easier deployment is the only change to the code.

I hope you enjoyed this.

Shawn Mordecai

Shawn Mordecai

3 years ago

The Apple iPhone 14 Pill is Easier to Swallow

Is iPhone's Dynamic Island invention or a marketing ploy?

First of all, why the notch?

When Apple debuted the iPhone X with the notch, some were surprised, confused, and amused by the goof. Let the Brits keep the new meaning of top-notch.

Apple removed the bottom home button to enhance screen space. The tides couldn't overtake part of the top. This section contained sensors, a speaker, a microphone, and cameras for facial recognition. A town resisted Apple's new iPhone design.

iPhone X with a notch cutout housing cameras, sensors, speaker, and a microphone / Photo from Apple

From iPhone X to 13, the notch has gotten smaller. We expected this as technology and engineering progressed, but we hated the notch. Apple approved. They attached it to their other gadgets.

Apple accepted, owned, and ran with the iPhone notch, it has become iconic (or infamous); and that’s intentional.

The Island Where Apple Is

Apple needs to separate itself, but they know how to do it well. The iPhone 14 Pro finally has us oohing and aahing. Life-changing, not just higher pixel density or longer battery.

Dynamic Island turned a visual differentiation into great usefulness, which may not be life-changing. Apple always welcomes the controversy, whether it's $700 for iMac wheels, no charging block with a new phone, or removing the headphone jack.

Apple knows its customers will be loyal, even if they're irritated. Their odd design choices often cause controversy. It's calculated that people blog, review, and criticize Apple's products. We accept what works for them.

While the competition zigs, Apple zags. Sometimes they zag too hard and smash into a wall, but we talk about it anyways, and that’s great publicity for them.

Getting Dependent on the drug

The notch became a crop. Dynamic Island's design is helpful, intuitive, elegant, and useful. It increases iPhone usability, productivity (slightly), and joy. No longer unsightly.

The medication helps with multitasking. It's a compact version of the iPhone's Live Activities lock screen function. Dynamic Island enhances apps and activities with visual effects and animations whether you engage with it or not. As you use the pill, its usefulness lessens. It lowers user notifications and consolidates them with live and permanent feeds, delivering quick app statuses. It uses the black pixels on the iPhone 14's display, which looked like a poor haircut.

iPhone 14 Pro’s ‘Dynamic Island’ animations and effects / GIF from Tenor

The pill may be a gimmick to entice customers to use more Apple products and services. Apps may promote to their users like a live billboard.

Be prepared to get a huge dose of Dynamic Island’s “pill” like you never had before with the notch. It might become so satisfying and addicting to use, that every interaction with it will become habit-forming, and you’re going to forget that it ever existed.

WARNING: A Few Potential Side Effects

Vision blurred Dynamic Island's proximity to the front-facing camera may leave behind grease that blurs photos. Before taking a selfie, wipe the camera clean.

Strained thumb To fully use Dynamic Island, extend your thumb's reach 6.7 inches beyond your typical, comfortable range.

Happiness, contentment The Dynamic Island may enhance Endorphins and Dopamine. Multitasking, interactions, animations, and haptic feedback make you want to use this function again and again.

Motion-sickness Dynamic Island's motions and effects may make some people dizzy. If you can disable animations, you can avoid motion sickness.

I'm not a doctor, therefore they aren't established adverse effects.

Does Dynamic Island Include Multiple Tasks?

Dynamic Islands is a placebo for multitasking. Apple might have compromised on iPhone multitasking. It won't make you super productive, but it's a step up.

iPad’s Split View Multitasking / Photo from WinBuzzer

iPhone is primarily for personal use, like watching videos, messaging friends, sending money to friends, calling friends about the money you were supposed to send them, taking 50 photos of the same leaf, investing in crypto, driving for Uber because you lost all your money investing in crypto, listening to music and hailing an Uber from a deserted crop field because while you were driving for Uber your passenger stole your car and left you stranded, so you used Apple’s new SOS satellite feature to message your friend, who still didn’t receive their money, to hail you an Uber; now you owe them more money… karma?

We won't be watching videos on iPhones while perusing 10,000-row spreadsheets anytime soon. True multitasking and productivity aren't priorities for Apple's iPhone. Apple doesn't to preserve the iPhone's experience. Like why there's no iPad calculator. Apple doesn't want iPad users to do math, but isn't essential for productivity?

Digressing.

Apple will block certain functions so you must buy and use their gadgets and services, immersing yourself in their ecosystem and dictating how to use their goods.

Dynamic Island is a poor man’s multi-task for iPhone, and that’s fine it works for most iPhone users. For substantial productivity Apple prefers you to get an iPad or a MacBook. That’s part of the reason for restrictive features on certain Apple devices, but sometimes it’s based on principles to preserve the integrity of the product, according to Apple’s definition.

Is Apple using deception?

Dynamic Island may be distracting you from a design decision. The answer is kind of. Elegant distraction

When you pull down a smartphone webpage to refresh it or minimize an app, you get seamless animations. It's not simply because it appears better; it's due to iPhone and smartphone processing speeds. Such limits reduce the system's response to your activity, slowing the experience. Designers and developers use animations and effects to distract us from the time lag (most of the time) and sometimes because it looks cooler and smoother.

Dynamic Island makes apps more useable and interactive. It shows system states visually. Turn signal audio and visual cues, voice assistance, physical and digital haptic feedbacks, heads-up displays, fuel and battery level gauges, and gear shift indicators helped us overcome vehicle design problems.

Dynamic Island is a wonderfully delightful (and temporary) solution to a design “problem” until Apple or other companies can figure out a way to sink the cameras under the smartphone screen.

Tim Cook at an Apple Event in 2014 / Photo from The Verge

Apple Has Returned to Being an Innovative & Exciting Company

Now Apple's products are exciting. Next, bring back real Apple events, not pre-recorded demos.

Dynamic Island integrates hardware and software. What will this new tech do? How would this affect device use? Or is it just hype?

Dynamic Island may be an insignificant improvement to the iPhone, but it sure is promising for the future of bridging the human and computer interaction gap.

Nikhil Vemu

Nikhil Vemu

2 years ago

7 Mac Apps That Are Exorbitantly Priced But Totally Worth It

Photo by Jack Carter on Unsplash

Wish you more bang for your buck

By ‘Cost a Bomb’ I didn’t mean to exaggerate. It’s an idiom that means ‘To be very expensive’. In fact, no app on the planet costs a bomb lol.

So, to the point.

Chronicle

(Freemium. For Pro, $24.99 | Available on Setapp)

Credit: LittleFin LLC

You probably have trouble keeping track of dozens of bills and subscriptions each month.

Try Chronicle.

Easy-to-use app

  • Add payment due dates and receive reminders,

  • Save payment documentation,

  • Analyze your spending by season, year, and month.

  • Observe expenditure trends and create new budgets.

Best of all, Chronicle features an integrated browser for fast payment and logging.

iOS and macOS sync.

SoundSource

($39 for lifetime)

Background Music, a free macOS program, was featured in #6 of this post last month.

It controls per-app volume, stereo balance, and audio over its max level.

Credit: Rogue Amoeba Software Inc.

Background Music is fully supported. Additionally,

  • Connect various speakers to various apps (Wow! ),

  • change the audio sample rate for each app,

  • To facilitate access, add a floating SoundSource window.

  • Use its blocks in Shortcuts app,

  • On the menu bar, include meters for output/input devices and running programs.

PixelSnap

($39 for lifetime | Available on Setapp)

Credit: MTW

This software is heaven for UI designers.

It aids you.

  • quickly calculate screen distances (in pixels) ,

Credit: MTW
  • Drag an area around an object to determine its borders,

Credit: MTW
  • Measure the distances between the additional guides,

Credit: MTW
  • screenshots should be pixel-perfect.

What’s more.

You can

  • Adapt your tolerance for items with poor contrast and shadows.

  • Use your Touch Bar to perform important tasks, if you have one.

Mate Translation

($3.99 a month / $29.99 a year | Available on Setapp)

Credit: Gikken

Mate Translate resembles a roided-up version of BarTranslate, which I wrote about in #1 of this piece last month.

If you translate often, utilize Mate Translate on macOS and Safari.

I'm really vocal about it.

It stays on the menu bar, and is accessible with a click or ⌥+shift+T hotkey.

It lets you

  • Translate in 103 different languages,

  • To translate text, double-click or right-click on it.

  • Totally translate websites. Additionally, Netflix subtitles,

  • Listen to their pronunciation to see how close it is to human.

iPhone and Mac sync Mate-ing history.

Swish

($16 for lifetime | Available on Setapp)

Swish is awesome!

Swipe, squeeze, tap, and hold movements organize chaotic desktop windows. Swish operates with mouse and trackpad.

Some gestures:

• Pinch Once: Close an app
• Pinch Twice: Quit an app
• Swipe down once: Minimise an app
• Pinch Out: Enter fullscreen mode
• Tap, Hold, & Swipe: Arrange apps in grids
and many more...

Credit: Christian Renninger

After getting acquainted to the movements, your multitasking will improve.

Unite

($24.99 for lifetime | Available on Setapp)

It turns webapps into macOS apps. The end.

Unite's functionality is a million times better.

Credit: BZG Apps LLC & Binyamin Goldman
  • Provide extensive customization (incl. its icon, light and dark modes)

  • make menu bar applications,

  • Get badges for web notifications and automatically refresh websites,

  • Replace any dock icon in the window with it (Wow!) by selecting that portion of the window.

This will help know weather or stock prices easily. (Credit: BZG Apps LLC & Binyamin Goldman)
  • Use PiP (Picture-in-Picture) on video sites that support it.

  • Delete advertising,

  • Throughout macOS, use floating windows

and many more…

I feel $24.99 one-off for this tool is a great deal, considering all these features. What do you think?

https://www.bzgapps.com/unite

CleanShot X

(Basic: $29 one-off. Pro: $8/month | Available on Setapp)

Credit: MTW

CleanShot X can achieve things the macOS screenshot tool cannot. Complete screenshot toolkit.

CleanShot X, like Pixel Snap 2 (#3), is fantastic.

Allows

  • Scroll to capture a long page,

  • screen recording,

    With webcam on,
    • With mic and system audio,
    • Highlighting mouse clicks and hotkeys.

  • Maintain floating screenshots for reference

  • While capturing, conceal desktop icons and notifications.

  • Recognize text in screenshots (OCR),

  • You may upload and share screenshots using the built-in cloud.

These are just 6 in 50+ features, and you’re already saying Wow!

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Rachel Greenberg

Rachel Greenberg

3 years ago

The Unsettling Fact VC-Backed Entrepreneurs Don't Want You to Know

What they'll do is scarier.

Photo by DESIGNECOLOGIST on Unsplash

My acquaintance recently joined a VC-funded startup. Money, equity, and upside possibilities were nice, but he had a nagging dread.

They just secured a $40M round and are hiring like crazy to prepare for their IPO in two years. All signals pointed to this startup's (a B2B IT business in a stable industry) success, and its equity-holding workers wouldn't pass that up.

Five months after starting the work, my friend struggled with leaving. We might overlook the awful culture and long hours at the proper price. This price plus the company's fate and survival abilities sent my friend departing in an unpleasant unplanned resignation before jumping on yet another sinking ship.

This affects founders. This affects VC-backed companies (and all businesses). This affects anyone starting, buying, or running a business.

Here's the under-the-table approach that's draining VC capital, leaving staff terrified (or jobless), founders rattled, and investors upset. How to recognize, solve, and avoid it

The unsettling reality behind door #1

You can't raise money off just your looks, right? If "looks" means your founding team's expertise, then maybe. In my friend's case, the founding team's strong qualifications and track records won over investors before talking figures.

They're hardly the only startup to raise money without a profitable customer acquisition strategy. Another firm raised money for an expensive sleep product because it's eco-friendly. They were off to the races with a few keywords and key players.

Both companies, along with numerous others, elected to invest on product development first. Company A employed all the tech, then courted half their market (they’re a tech marketplace that connects two parties). Company B spent millions on R&D to create a palatable product, then flooded the world with marketing.

My friend is on Company B's financial team, and he's seen where they've gone wrong. It's terrible.

Company A (tech market): Growing? Not quite. To achieve the ambitious expansion they (and their investors) demand, they've poured much of their little capital into salespeople: Cold-calling commission and salary salesmen. Is it working? Considering attrition and companies' dwindling capital, I don't think so.

Company B (green sleep) has been hiring, digital marketing, and opening new stores like crazy. Growing expenses should result in growing revenues and a favorable return on investment; if you grow too rapidly, you may neglect to check that ROI.

Once Company A cut headcount and Company B declared “going concerned”, my friend realized both startups had the same ailment and didn't recognize it.

I shouldn't have to ask a friend to verify a company's cash reserves and profitability to spot a financial problem. It happened anyhow.

The frightening part isn't that investors were willing to invest millions without product-market fit, CAC, or LTV estimates. That's alarming, but not as scary as the fact that startups aren't understanding the problem until VC rounds have dried up.

When they question consultants if their company will be around in 6 months. It’s a red flag. How will they stretch $20M through a 2-year recession with a $3M/month burn rate and no profitability? Alarms go off.

Who's in danger?

In a word, everyone who raised money without a profitable client acquisition strategy or enough resources to ride out dry spells.

Money mismanagement and poor priorities affect every industry (like sinking all your capital into your product, team, or tech, at the expense of probing what customer acquisition really takes and looks like).

This isn't about tech, real estate, or recession-proof luxury products. Fast, cheap, easy money flows into flashy-looking teams with buzzwords, trending industries, and attractive credentials.

If these companies can't show progress or get a profitable CAC, they can't raise more money. They die if they can't raise more money (or slash headcount and find shoestring budget solutions until they solve the real problem).

The kiss of death (and how to avoid it)

If you're running a startup and think raising VC is the answer, pause and evaluate. Do you need the money now?

I'm not saying VC is terrible or has no role. Founders have used it as a Band-Aid for larger, pervasive problems. Venture cash isn't a crutch for recruiting consumers profitably; it's rocket fuel to get you what and who you need.

Pay-to-play isn't a way to throw money at the wall and hope for a return. Pay-to-play works until you run out of money, and if you haven't mastered client acquisition, your cash will diminish quickly.

How can you avoid this bottomless pit? Tips:

  • Understand your burn rate

  • Keep an eye on your growth or profitability.

  • Analyze each and every marketing channel and initiative.

  • Make lucrative customer acquisition strategies and satisfied customers your top two priorities. not brand-new products. not stellar hires. avoid the fundraising rollercoaster to save time. If you succeed in these two tasks, investors will approach you with their thirsty offers rather than the other way around, and your cash reserves won't diminish as a result.

Not as much as your grandfather

My family friend always justified expensive, impractical expenditures by saying it was only monopoly money. In business, startups, and especially with money from investors expecting a return, that's not true.

More founders could understand that there isn't always another round if they viewed VC money as their own limited pool. When the well runs dry, you must refill it or save the day.

Venture financing isn't your grandpa's money. A discerning investor has entrusted you with dry powder in the hope that you'll use it wisely, strategically, and thoughtfully. Use it well.

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

  • x+5
  • x^4
  • x^3+3x^2+3x+1
  • 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

  • A(0)+B(0)=C(0)
  • A(1)+B(1)=C(1)
  • A(2)+B(2)=C(2)
  • A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

  • 12+1=13
  • 10+8=18
  • 15+8=23
  • 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

  • A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
  • B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
  • C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

see part 3

Faisal Khan

Faisal Khan

2 years ago

4 typical methods of crypto market manipulation

Credit: Getty Images/Cemile Bingol

Market fraud

Due to its decentralized and fragmented character, the crypto market has integrity difficulties.

Cryptocurrencies are an immature sector, therefore market manipulation becomes a bigger issue. Many research have attempted to uncover these abuses. CryptoCompare's newest one highlights some of the industry's most typical scams.

Why are these concerns so common in the crypto market? First, even the largest centralized exchanges remain unregulated due to industry immaturity. A low-liquidity market segment makes an attack more harmful. Finally, market surveillance solutions not implemented reduce transparency.

In CryptoCompare's latest exchange benchmark, 62.4% of assessed exchanges had a market surveillance system, although only 18.1% utilised an external solution. To address market integrity, this measure must improve dramatically. Before discussing the report's malpractices, note that this is not a full list of attacks and hacks.

Clean Trading

An investor buys and sells concurrently to increase the asset's price. Centralized and decentralized exchanges show this misconduct. 23 exchanges have a volume-volatility correlation < 0.1 during the previous 100 days, according to CryptoCompares. In August 2022, Exchange A reported $2.5 trillion in artificial and/or erroneous volume, up from $33.8 billion the month before.

Spoofing

Criminals create and cancel fake orders before they can be filled. Since manipulators can hide in larger trading volumes, larger exchanges have more spoofing. A trader placed a 20.8 BTC ask order at $19,036 when BTC was trading at $19,043. BTC declined 0.13% to $19,018 in a minute. At 18:48, the trader canceled the ask order without filling it.

Front-Running

Most cryptocurrency front-running involves inside trading. Traditional stock markets forbid this. Since most digital asset information is public, this is harder. Retailers could utilize bots to front-run.

CryptoCompare found digital wallets of people who traded like insiders on exchange listings. The figure below shows excess cumulative anomalous returns (CAR) before a coin listing on an exchange.

Finally, LAYERING is a sequence of spoofs in which successive orders are put along a ladder of greater (layering offers) or lower (layering bids) values. The paper concludes with recommendations to mitigate market manipulation. Exchange data transparency, market surveillance, and regulatory oversight could reduce manipulative tactics.