The History of PKM, the Most Common Machine Gun In the World (Part 1)

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Everyone knows AK-47. It is everywhere: movies, books, crime statistics. Interestingly enough, those who spend some time in the warzone often have stronger feelings towards another Kalashnikov creation – the PK/PKM belt-fed machine gun.

Some say that PK is the best weapon Kalashnikov ever created. While AK was developed at the very beginning of his career, PK was created when Kalashnikov had plenty of experience.

Millions of those machine guns are used all over the world, US special forces requested American companies to produce those guns multiple times, and some experts call it “the best general purpose machine gun”.

However, few people know that it was created almost by accident. There are many great articles on AK history, but there is almost nothing published in English about the PK development, and hopefully, this article can fix that.

One of many PKMs the author inspected and repaired in Afghanistan

How it all started

The summer of 1959 was a busy time for Mihail Kalashnikov. The new family of weapons he designed, which included AKM and RPK light machine guns, was just getting into production. He had to prove for the second time in his career that his rifle was the best.

First, his AK 47 won the competition in 1949, and ten years later his other creation, AKM bested all rivals and now was destined to become the new service rifle of the Soviet Army and most Warsaw Pact countries.

Kalashnikov hadn’t had a vacation in 4 years. That summer there was finally an opportunity to celebrate, and it was all more convenient that his old friend visited him in the city of Izhevsk.

Vladimir Deikin and Mihail Kalashnikov

The old friend was army officer Vladimir Deikin, who was one of the people who made AK happen. The officer of GRAU, the military department responsible for procurement of new weaponry, he supported Kalashnikov all the way through the development of the original AK rifle, ruthlessly crushing bureaucracy and red tape that got in the way of a young weapon design engineer.

As the years went by, a young and shy Kalashnikov became the most respected weapon designer in the Soviet Union, and Vladimir Deikin became a colonel, rising to the top of the career ladder.

That summer two friends who have been through a lot could finally enjoy their life. They took a boat and went fishing, invited friends from the factory, and spent the weekend in a cabin on the lake, talking about guns and cooking fish they caught.

Before leaving, Vladimir Deikin nonchalantly shared some news: “This guy Nikitin at the factory in Tula is developing GPMG (general purpose machine gun). The trials are almost over, it adheres to the requirements… But in GRAU we think it is a little too complicated. The army needs something more simple”.

Prototype of the Nikitin GPMG

He didn’t ask Kalashnikov to get involved. He never asked for help. But he knew his old friend and realized, Kalashnikov won’t just leave it alone. Now, after his friend left, Kalashnikov had a whole bunch of questions.

Why wasn’t I asked to develop this new GPMG? Why don’t they trust me? Am I in trouble? How complicated is too complicated? Will they ask me to redesign this gun once it finishes trials? Or is it the end of my career?

The brainstorming

Kalashnikov decided that he must do something about it. He already had a team of engineers and enough authority to build a machine gun from scratch without asking permission.

There was no money allocated for this project, but he could pull some strings and use money from his other projects to finance the ammo and all the prototype building.

Prototype of the PK. The machine gun is from the collection of the Artillery Museum in Saint Petersburg.

He became obsessed with his new machine gun and completed the first sketches in just ten days. However, drawings alone are no good, you need to make blueprints, which Kalashnikov couldn’t really do – he was never formally educated and always relied on someone else to make blueprints.

In this case, engineer Krupin was tasked with creating proper blueprints, and the entire team got on with the project. The rival machine gun from Tula was already undergoing troop trials, the Ministry of Industry never asked for another contender, but Kalashnikov decided that he would deal with that another day.

The obsession Kalashnikov had was contagious, engineers were staying at work until 5 in the morning, and within weeks they started making the first parts of the prototype.

Milled receiver of the PK prototype. The machine gun is from the collection of the Artillery Museum in Saint Petersburg.

Often, there was no time to make proper blueprints, so engineers just winged it, making parts on the lathe and milling machine relying solely on their imagination and some sketches.

Within a month, the first prototype of PKM was ready. Now Kalashnikov just had to convince the entire Soviet military-industrial complex that his crude prototype was better than a machine gun that already passed all the trials and ticked all the boxes. How did he manage to do that? That is the story for Part 2 of this article.

The Firearm Blog

Understanding MySQL Indexes: Types, Benefits, and Best Practices

https://www.percona.com/blog/wp-content/uploads/2024/06/Understanding-MySQL-Indexes-200×112.jpgWhen it comes to MySQL databases, performance is everything. As more activities move online and data volumes grow exponentially, ensuring efficient data retrieval and query execution becomes crucial. Database indexing plays a significant role in this by providing powerful tools to optimize operations in MySQL. Without an index, MySQL must perform a full table scan, […]Percona Database Performance Blog

These Are My Favorite Google Docs Invoice Templates

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Google Docs templates make it easy to start creating resumes, letters, brochures, reports, and project proposals, but there is no built-in template for making invoices in Google Docs.

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So, what do you do when you need to create an invoice? You could painstakingly create one from scratch for every client or use one of these free, customizable invoice templates available for download.

Square is an end-to-end payment processor that can be used to accept payments from clients as a freelancer. It offers a free, client-ready invoice template that can be downloaded in various formats: Word, Excel, and PDF.

You will need to fill in the details required: your business information (name, location, email address, and phone number), the customer’s information, due date and amount, payment terms, and the job description. Replace the logo placeholder with a suitable image, and delete the Square Invoices footer. List each important line item in the breakdown table. You can duplicate the borderline in the breakdown table and add more items as needed.

The Square invoice template isn’t directly available for Google Docs, but you can download the Word document and open it in Google Docs for editing and customization.

Wave is popular for its invoicing and accounting software, but it also offers a free Google Docs invoice template that any freelancer or small business owner can tailor to send to their clients. There are up to five different invoice templates available in Doc, Sheets, PDF, and Excel. All templates are simple, attractive, and professional. They can be customized to fit your brand image and business clients.

After selecting the template you prefer, you can proceed to insert your business name, project details, and other information. It doesn’t include a logo placeholder, but you can still place one in the header or the background of the document. There is a Notes section at the bottom for additional details such as payment terms, terms of service, and probably, a warm, appreciative message to the client.

Creating an invoice template reduces the work you have to do each time since you can incorporate the logo and other non-changing information in the template itself. Also, it will make it much easier to make templates for more complicated documents. By following our guide to creating an invoice template in Google Docs, you will be able to create simple invoices that you can send to your clients with little editing.

Invoice Simple is a freemium invoicing software available on mobile and web platforms. The company has a collection of free Google Docs and Sheets invoice templates. The spreadsheet versions are recommended for download since they come with built-in formulas and are easier to customize.

You can choose an invoice template from the collection, click Google Docs under the image, and select Make a copy in the next window. You can then proceed to replace the placeholders and enter the requisite information. The Invoice Simple template includes a Ship to section for businesses with a physical product. Make sure to omit this section if you don’t need it.

The GooDocs website features thousands of free templates for Google Docs, Google Slides, and Google Sheets. You can download up to five templates for free without creating an account. On GooDocs, there are several invoice templates to choose from, with categories like consulting, contracting, freelance, medical, wedding, rental, and restaurant. With the myriad choices available, you will be able to find an invoice template that suits your business needs.

Once you find the one you like, you can select Edit in Google Docs from the sidebar options. You should switch the colors, fonts, and other design elements to better match your business’ branding. Your logo should be prominently displayed in the invoice’s header.

With a little bit of editing, you can turn any Google Docs invoice template into a professional, client-ready invoice document that makes a great impression.

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MySql Explain with Tobias Petry

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This week, we welcome Tobias Petry to the Laravel Creator Series show to discuss his journey into database optimization, the development of his MySQL Explain tool, and the acquisition of the domain mysqlexplain.com. Tobias also shares insights about his other projects, including Stack Bricks, a tool for managing different database versions, and his contributions to the Laravel Debug Bar.

➡️ Save 10% on his Indexing Beyond the Basics book and video package with the coupon code LARAVELNEWS

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IMPLEMENTING MULTI-TENANCY IN LARAVEL: A COMPREHENSIVE GUIDE

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Multi-tenancy in web applications refers to the architecture where a single instance of the application serves multiple customers, or ‘tenants.’ Each tenant’s data and, sometimes, specific configurations are kept isolated from others. This setup is essential in SaaS (Software as a Service) platforms where multiple businesses or organizations might use the same application.

In this guide, we’ll walk through setting up a database-per-tenant approach in Laravel, complete with code examples, detailed explanations, and the necessary console commands for creating the database itself with no need or usage of any external package.
Step 1: Setting Up Database Connections
In the config/database.php file, we define two connections:

1. ** Owner Connection**: This connection manages the information about all tenants, such as their domain and database names.
2. **Tenant Connection**: This connection dynamically switches based on the tenant currently being accessed.

Here’s how to set up these connections:

return [
    'default' => env('DB_CONNECTION', 'tenant'),

    'connections' => [
        'tenant' => [
            'driver' => 'mysql',
            'host' => env('DB_HOST', '127.0.0.1'),
            'port' => env('DB_PORT', '3306'),
            'database' => null, // Database will be set dynamically
            'username' => env('DB_USERNAME', 'root'),
            'password' => env('DB_PASSWORD', ''),
            'charset' => 'utf8mb4',
            'collation' => 'utf8mb4_unicode_ci',
            'prefix' => '',
            'strict' => true,
        ],

        ' owner' => [
            'driver' => 'mysql',
            'host' => env(‘OWNER_DB_HOST', '127.0.0.1'),
            'port' => env(,OWNER _DB_PORT', '3306'),
            'database' => env(' OWNER _DB_DATABASE', 'landlord'),
            'username' => env(' OWNER _DB_USERNAME', 'root'),
            'password' => env(' OWNER _DB_PASSWORD', ''),
            'charset' => 'utf8mb4',
            'collation' => 'utf8mb4_unicode_ci',
            'prefix' => '',
            'strict' => true,
        ],
    ],
];

Step 2: Creating the Tenant Model and Migrations
We need to create a Tenant model that uses the landlord connection. This model will manage tenant-related data such as the domain and database name.
Tenant Migration:

In the migration for the tenants table, we’ll include columns for the tenant’s name, domain, and the specific database used:

Schema::create('tenants', function (Blueprint $table) {
    $table->id();
    $table->string('name');
    $table->string('domain')->unique();
    $table->string('database');
    $table->timestamps();
});

Tenant Model:

The Tenant model should be linked to the landlord connection and include methods for configuring and using the tenant:

class Tenant extends Model
{
    use HasFactory;

    protected $fillable = [
        'name',
        'domain',
        'database',
    ];

    protected $connection = 'owner'; // Default connection for the owner database

    /**
     * Configure the tenant's database connection dynamically.
     */
    public function configure(): self
    {
        // Update the configuration for the tenant connection dynamically
        config([
            'database.connections.tenant.database' => $this->database,
        ]);

        // Purge the 'tenant' connection to refresh its settings
        DB::purge('tenant');

        // Clear tenant-specific cache if cache table exists
        if (Schema::hasTable('cache')) {
            $this->clearTenantCache();
        }

        return $this;
    }

    /**
     * Activate the tenant context across the application.
     */
    public function use(): self
    {
        // Set the default database connection to 'tenant'
        DB::setDefaultConnection('tenant');

        return $this;
    }

    /**
     * Clear cache specific to the tenant.
     */
    public function clearTenantCache(): void
    {
        // Get tenant-specific cache keys
        $cacheKeys = Cache::get('tenant_'.$this->id.'_keys', []);

        // Forget each cache key
        foreach ($cacheKeys as $key) {
            Cache::forget($key);
        }

        // Optionally remove the keys tracking itself
        Cache::forget('tenant_'.$this->id.'_keys');
    }

    /**
     * Add a tenant-specific cache key.
     */
    public function addCacheKey(string $key): void
    {
        // Get the current list of cache keys for the tenant
        $cacheKeys = Cache::get('tenant_'.$this->id.'_keys', []);

        // Add the new cache key
        $cacheKeys[] = $key;

        // Update the list in the cache
        Cache::put('tenant_'.$this->id.'_keys', $cacheKeys);
    }
}

Step 3: Custom Console Command for Tenant initialization 

We will create console command to initialize the owner table where all tenant database info will be stored 

class TenantInit extends Command
{
    protected $signature = 'tenants:init';
    protected $description = 'Create owner table where all domains for tenant app live';

    public function handle(): int
    {
        DB::setDefaultConnection('owner');
        $path = database_path('migrations/owner'); // Custom migration path for the owner DB
        $this->info('Running migrations from: ' . $path);

        try {
            $this->call('migrate', ['--path' => $path, '--force' => true]);
            $this->info('Migrations have been executed successfully.');
        } catch (\Exception $e) {
            $this->error('An error occurred: ' . $e->getMessage());
            return 1; // Return non-zero for failure
        }

        return 0; // Return zero for success
    }
}

Step 4: Custom Console Command for Tenant Migrations

Since each tenant has its own database, we need a way to migrate the schema for each one. Laravel’s built-in migrate command only runs migrations on the default connection, so we’ll create a custom Artisan command to handle tenant migrations.
TenantsMigrateCommand:

This command will loop through all tenants, configure the tenant’s database connection, and run migrations on each database:

class TenantsMigrateCommand extends Command

{
    /**
     * The name and signature of the console command.
     *
     * @var string
     */
    protected $signature = 'tenants:migrate {tenant?} {--fresh} {--seed}';

    /**
     * The console command description.
     *
     * @var string
     */
    protected $description = 'Create clean migration and seed for one tenant or for all tenants';

    /**
     * Execute the console command.
     */
    public function handle(): void
    {
        if ($tenantId = $this->argument('tenant')) {
            $tenant = Tenant::find($tenantId);
            if ($tenant) {
                $this->migrate($tenant);
            } else {
                $this->error("Tenant with ID {$tenantId} not found.");
            }
        } else {
            Tenant::all()->each(
                fn ($tenant) => $this->migrate($tenant)
            );
        }
    }

    /**
     * Migrate the given tenant.
     */
    public function migrate(Tenant $tenant): void
    {
        $tenant->configure()->use();
        $this->line('');
        $this->line('-----------------------------------------');
        $this->info("Migrating Tenant #{$tenant->id} ({$tenant->name})");
        $this->line('-----------------------------------------');
        $options = ['--force' => true];
        if ($this->option('seed')) {
            $options['--seed'] = true;
        }
        $this->call(
            $this->option('fresh') ? 'migrate:fresh' : 'migrate',
            $options
        );
    }
}

• {tenant?}: The tenant argument is now optional. If provided, it will run migrations for the specified tenant only.
• {–fresh}: Option to run migrate:fresh, which drops all tables and re-runs all migrations.
• {–seed}: Option to seed the database after running migrations.

Step 5: Middleware for Tenant Resolution

To ensure that the correct tenant is used for each request, we’ll create middleware that identifies the tenant based on the domain and configures the application accordingly.
TenantSessionMiddleware:

class TenantSessionMiddleware
{
    public function handle(Request $request, Closure $next): Response
    {
        if (! $request->session()->has('tenant_id')) {
            $request->session()->put('tenant_id', app('tenant')->id);
            return $next($request);
        }
        if ($request->session()->get('tenant_id') != app('tenant')->id) {
            abort(401);
        }

        return $next($request);
    }}

Step 6: Testing Multi-Tenant Applications
Testing in a multi-tenant environment requires that both the landlord and tenant databases are properly set up before each test. Here’s how you can configure your tests:

public function setUp(): void
{
    parent::setUp();

    // Migrate the owner's database and seed data
    $this->artisan('migrate', ['--database' => 'owner']);
    $this->seed(OwnerSeeder::class);

    // Loop through tenants and migrate their databases
    Tenant::all()->each(function (Tenant $tenant) {
        $tenant->configure();
        $this->artisan('migrate', ['--database' => 'tenant']);
    });
}

Step 7: Setting Up a Service Provider for Tenant Resolution

In a multi-tenant application, it’s crucial to ensure that the correct tenant context is established for each incoming request. This is where a service provider comes into play. The service provider will configure the tenant based on the request’s domain or subdomain, ensuring that the correct tenant’s database and other settings are used throughout the application lifecycle.

Creating the TenancyServiceProvider

<?php

namespace App\Providers;

use App\Models\Tenant;
use Illuminate\Queue\Events\JobProcessing;
use Illuminate\Support\Facades\Event;
use Illuminate\Support\Facades\Queue;
use Illuminate\Support\ServiceProvider;

class TenancyServiceProvider extends ServiceProvider
{
    /**
     * Register services.
     */
    public function register(): void
    {
        //
    }

    /**
     * Bootstrap services.
     */
    public function boot(): void
    {
        $this->configureTenant();
        $this->configureQueue();
    }

    /**
     * Configure tenant based on the domain.
     */
    protected function configureTenant(): void
    {
        if ($this->app->runningInConsole()) {
            return;
        }

        $host = request()->getHost();
        $tenant = Tenant::whereDomain($host)->firstOrFail();
        $tenant->configure()->use();  // Set up and use tenant configuration
    }

    /**
     * Configure the queue system to be aware of tenants.
     */
    protected function configureQueue(): void
    {
        // Add tenant_id to the job payload
        Queue::createPayloadUsing(function () {
            if (app()->bound('tenant')) {
                $tenant = app()->make('tenant');

                return ['tenant_id' => $tenant->id];
            }

            return [];
        });

        // Restore tenant context when job is processing
        Event::listen(JobProcessing::class, function (JobProcessing $event) {
            $tenantId = $event->job->payload()['tenant_id'] ?? null;

            if ($tenantId) {
                $tenant = Tenant::find($tenantId);
                $tenant?->configure()->use();
            }
        });
    }
}

Expanded Explanation of Service Provider Methods
The methods you’ve shared are essential for managing tenant context both during normal HTTP requests and within Laravel’s queue system. These methods ensure that the correct tenant is always in scope, whether you’re handling web requests or processing background jobs.

Method 1: configureTenant

protected function configureTenant(): void
{
    if ($this->app->runningInConsole()) {
        return;
    }

    $host = request()->getHost();
    $tenant = Tenant::whereDomain($host)->firstOrFail();
    $tenant->configure()->use();  // Set up and use tenant configuration
}

Explanation:

Purpose: This method sets up the tenant configuration based on the incoming request’s domain and ensures that the correct tenant is used throughout the request lifecycle.

if ($this->app->runningInConsole())
{ 
   return; 
}:

This check ensures that the tenant configuration logic only runs during HTTP requests. If the application is running in the console (e.g., during migrations or other Artisan commands), the method will exit early. This is because console commands may not be associated with any particular tenant, and running tenant-specific logic could cause unintended behavior.

$host = request()->getHost();:

This retrieves the domain name from the incoming HTTP request. The domain is typically used to determine which tenant the request is for.

$tenant = Tenant::whereDomain($host)->firstOrFail();:
This line queries the tenants table to find the tenant that matches the domain name. The firstOrFail() method will throw a ModelNotFoundException if no tenant is found, which can result in a 404 error being returned to the user.

$tenant->configure()->use();:
Once the tenant is found, the configure() method sets up the database connection and other tenant-specific configurations.
The use() method then registers this tenant in the service container, making it accessible throughout the application for the duration of the request.

Method 2: configureQueue

/**
 * Configure the queue system to be aware of tenants.
 */
protected function configureQueue(): void
    {
        // Add tenant_id to the job payload
        Queue::createPayloadUsing(function () {
            if (app()->bound('tenant')) {
                $tenant = app()->make('tenant');

                return ['tenant_id' => $tenant->id];
            }

            return [];
        });

        // Restore tenant context when job is processing
        Event::listen(JobProcessing::class, function (JobProcessing $event) {
            $tenantId = $event->job->payload()['tenant_id'] ?? null;

            if ($tenantId) {
                $tenant = Tenant::find($tenantId);
                $tenant?->configure()->use();
            }
        });
    }

Explanation:
Purpose: This method ensures that Laravel’s queue system is tenant-aware. By attaching the tenant_id to the job payload, and reconfiguring the tenant context during job processing, we ensure that the job runs in the correct tenant’s context. This is particularly crucial for distributed queue systems like Redis, where workers could be shared across tenants.

Queue::createPayloadUsing():

This method hooks into the queue system to modify the job payload. The payload is essentially the data that is passed along with a job when it is queued.

if ($this->app->bound('tenant')) {:

This checks if the application has a tenant bound to the service container. If a tenant is bound, it means the current request is associated with a specific tenant.

$tenant = $this->app->make('tenant');:

This retrieves the currently bound tenant from the service container.

return ['tenant_id' => $tenant->id];:

This adds the tenant_id to the job payload, ensuring that the tenant context is passed along with the job when it is dispatched.

return [];:

If no tenant is bound, the payload remains unchanged.

Event::listen(JobProcessing::class, ...):

This listens for the JobProcessing event, which is fired just before a queued job starts processing.

$tenantId = $event->job->payload()['tenant_id'] ?? null;:

This retrieves the tenant_id from the job’s payload. If no tenant_id is found, it returns null.

$tenant = Tenant::find($tenantId);:

This finds the tenant by the tenant_id stored in the payload.

$tenant?->configure()->use();:

If a tenant is found, the configure() method sets up the tenant’s database connection, and use() registers this tenant as the current tenant for the job’s processing context.
You can create a service provider that handles the tenant resolution and configuration. This service provider will hook into Laravel’s bootstrapping process and set up the tenant context at the beginning of each request.
Conclusion
Implementing multi-tenancy in Laravel using a database-per-tenant approach offers strong data isolation and scalability. The steps outlined in this guide provide a complete framework for setting up multi-tenancy, handling migrations, and ensuring that your application uses the correct database for each tenant.

Pros:

• Data Isolation: Each tenant’s data is completely separated, ensuring strong data isolation.
• Scalability: This approach allows easy scaling by adding new databases for new tenants.
• Security: By isolating each tenant’s data in separate databases, the risk of data leakage between tenants is minimized.
• Cache Efficiency: The use of tenant-specific cache keys ensures that only tenant-relevant cached data is cleared, improving performance.
• Queue Robustness: Tenant context is preserved in queues, even in distributed environments, preventing cross-tenant data leakage in background tasks.

Cons:

• Complexity: Setting up and managing multiple databases adds complexity to the application architecture.
• Resource Overhead: Maintaining separate databases for each tenant requires more infrastructure resources.
• Backup Complexity: Managing backups across multiple databases can be challenging, especially when scaling to hundreds or thousands of tenants.
• Migration Overhead: Running migrations for each tenant adds additional overhead compared to a single-database architecture.
• By following this approach, you can build robust, scalable multi-tenant applications in Laravel.

the code example can be locale at  :https://github.com/KalimeroMK/multitenant

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A handy guide to the universal language for the mathematically perplexed

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cover of book

Enlarge / Math for English Majors talks about numbers as nouns, verbs as calculations, and algebra as grammar.

Ben Orlin

Galileo once famously described the universe as a great book "written in mathematical language and its characters are triangles, circles, and other geometrical figures." Unfortunately, it’s a language that many people outside of math and science simply do not speak, largely because they are flummoxed and/or intimidated by the sheer density of all that strange symbolic notation.

Math teacher extraordinaire Ben Orlin is here to help with his latest book: Math for English Majors: A Human Take on the Universal Language. And just like Orlin’s previous outings, it’s filled with the author’s trademark bad drawings. Bonus: Orlin created a fun personality quiz, which you can take here to find out your mathematical style.

Orlin’s first book, Math with Bad Drawings, after his blog of the same name, was published in 2018. It included such highlights as placing a discussion of the correlation coefficient and "Anscombe’s Quartet" into the world of Harry Potter and arguing that building the Death Star in the shape of a sphere may not have been the Galactic Empire’s wisest move. We declared it "a great, entertaining read for neophytes and math fans alike, because Orlin excels at finding novel ways to connect the math to real-world problems—or in the case of the Death Star, to problems in fictional worlds."

In 2019, Orlin took on the challenge of conveying the usefulness and beauty of calculus with tall tales, witty asides, and even more bad drawings in Change Is the Only Constant: The Wisdom of Calculus in a Madcap World. That book is a colorful collection of 28 mathematical tales connecting concepts in calculus to art, literature, and all manner of things human beings grapple with on a daily basis.

Orlin’s most recent book was 2022’s Math Games with Bad Drawings—less a book one reads cover to cover and more a chance for readers to browse randomly at their leisure to find the games best suited to their particular tastes and skills, such as Jotto, a logic-oriented word game invented in 1955 that is similar to Wordle. There were five different categories of games: spatial games, number games, combination games, games of risk and reward, and information games. All could be played with just a few common household items: pencil and paper, coins, colored pens, standard dice, Goldfish crackers, paper clips, your hands, and occasionally an Internet connection. (You can try your hand at a game of Quantum Go Fish here.)

Unlike his prior books, where he carefully avoided most mathematical notation, Math for English Majors is designed to teach readers how to read and interpret mathematical symbols, proofs, and mathematical diagrams. His original vision was to write the math-y equivalent to Lynne Truss’ bestselling Eats, Shoots & Leaves. "It’s a very playful book about English punctuation that weaves together fun stories about the common, the semicolon, and the dash," Orlin told Ars. "But I found that math is just a fundamentally different sort of language, and that template didn’t quite work for me."

Some elements of that earlier vision remain: Math for English Majors talks about numbers as nouns, verbs as calculations, and algebra as grammar, highlighting certain idioms ("exponential") and etymologies "squaring") for good measure.

But Orlin’s main objective is to reconcile the expert’s view of math, "where the notation vanishes and you’re just focusing on the ideas that the notation conveys," with the beginner’s experience of math, "where you can’t even access the ideas because there’s this thick wall of symbolism in the way." Math, says Orlin, is both "a collection of beautiful ideas and a language for expressing those ideas." His approach is the opposite of the usual popularizations of math, where ideas are translated into plain English and notation is largely avoided. Here, the notation is the primary focus.

Ars spoke with Orlin to learn more.

Ben Orlin

Ars Technica: People who are not mathematically inclined usually see all those abstract symbols and their eyes glaze over. Let’s talk about the nature of symbols in math and why becoming more familiar with mathematical notation can help non-math people surmount that language barrier.  

Ben Orlin: It’s tricky. When I first became a teacher, I was mostly trying to push against students who’d only learned symbol manipulation procedures and didn’t have any sense of how to read and access the information behind them. It always mystified me: why do we teach that way? You end up with very bright, clever students, and all we’re giving them is hundreds of hours of practice in symbol manipulation. But what is a quadratic? They can’t really tell you.

One of the things I’ve gradually come to accept is that it’s almost baked into the language that mathematical notation has developed specifically for the purpose of manipulating it without thinking hard about it. If you’ve had the right set of experiences leading into that, that’s very convenient, because it means that when you sit down to solve a problem, you don’t have to solve it like Archimedes with lots of brilliant one-off steps where you just have gorgeous geometric intuition about everything. You can just be like, "Okay, I’m going to crank through the symbol manipulation procedures." So there’s a real power in those procedures. They’re really valuable and important.

But if it’s all you have, then you’re doing a dance where you know the moves, but you’ve never heard the music. You can’t troubleshoot. Sometimes I wish as a teacher, you could just say, "Look, the symbol manipulation procedures are worthless. We can just skip those and focus on the ideas." But they’re tangled up in a much more complex way. So somehow you have to climb in there with the students and move back and forth between the things that are happening on the page and the ideas that are unfolding in some kind of higher space.

That’s the place this book eventually gets to. But I go there gradually, because you need a lot of experience with symbols that make sense to you before you can feel comfortable when you do manipulations on a page.

Ars Technica – All content

I Visit Hundreds of Museums Virtually Using This Free App

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Key Takeaways

  • Bloomberg Connects offers guides to partnered museums and cultural institutions across the globe.
  • Besides museums, you’ll find botanical gardens, historic cemeteries, zoos, monuments, theaters, and more in this app.
  • Bloomberg Connects excels in preparing you for real-world visits, while its closest competition, Google Arts & Culture, focuses more on virtual collections.

You probably think that if you want to check out a museum, you actually have to go there. But that’s not the case anymore, thanks to the popularity of smartphones. Today, with apps like Bloomberg Connects, you can see and learn about collections from all over the world.

What Is Bloomberg Connects, and What Can You Use It For?

Bloomberg Connects is an app for iOS and Android that partners with museums and other cultural institutions across the planet to offer guides to their various collections and exhibits. When you open the app, you’ll see a list of nearby locations you can tap on.

Once you open each individual guide, you’ll be presented with a wealth of info about what you can find there, from current exhibits to the permanent collection, organized in various ways that should suit anyone’s preferences.

Curious about who’s buried in a nearby cemetery? Or do you want to see the latest hot exhibition a museum’s putting on? All these things are spotlighted in Bloomberg Connects, with plenty of pictures and essays to feed your desire for knowledge.

The app also includes maps of each location, so you don’t need to pick up a paper guide at the door when you visit. You can zoom in, which is helpful if you have poor eyesight, and the app also marks the highlights of the institution so that you can easily get to them in person.

What Places Can You Visit With Bloomberg Connects?

Like the Bloomberg organization, which serves as its sponsor, the Bloomberg Connects app is available worldwide. You can find over 550 institutions from over 24 countries, including the United States, Canada, the United Kingdom, Mexico, and Italy.

The types of places available include museums, botanical gardens, historic cemeteries, zoos, theaters, historic houses, monuments, galleries, art walks, and even events like the Venice Biennale. Among these locations are heavy hitters like the Metropolitan Museum of Art, the Art Institute of Chicago, and the Guggenheim. You can check out the full list on Bloomberg Connect’s website, where you’ll find dozens of small institutions too.

However, even if your interest doesn’t lie with museums, Bloomberg Connects has a few interesting collections to check out, like MTA Arts and Design. These are artworks you can see inside the New York City subway system if you’re curious. The app covers a lot of street art and other work you may encounter in your everyday life, like the Project Row Houses in Houston, the Street Art Museum in Amsterdam, and the NYC Health + Hospitals Arts in Medicine program.

How Does Bloomberg Connects Compare With Google Arts & Culture?

There are dozens of museum guides available, many of which are bespoke apps limited to a single institution like the Rijksmuseum or Museo del Prado. The one guide you’re most likely to have heard of and used is Google Arts & Culture, which covers over 2,000 institutions across the world and is available on the web or as an app.

Aside from covering far more places, Google Arts & Culture has an extensive collection of images from most of the institutions it covers, and you can easily search for specific keywords. It’s good for doing art research, looking for inspiration for your own work, or just doing virtual visits of collections.

What Google Arts & Culture isn’t great at is preparing you for visits to real-world locations. It’s difficult to find and browse the list of institutions it covers, and both the app and website are extremely cluttered with various experiments like VR experiences and games—although some Google Arts & Culture web games are worth playing.

In contrast, Bloomberg Connects points you to the nearest locations and tells you everything you need to know to visit, from basics like the hours of operation to guides spotlighting the temporary exhibitions on display. During your visit, you can even look up objects via a number or QR code and enjoy text or audio commentary.

There’s no clear "winner" between the two, as they essentially are designed to do different things. For art lovers, both services are worth having in your arsenal. But when it comes to what app you should have on your phone, Bloomberg Connects is definitely worth keeping around for your next trip.

MakeUseOf

How to turn off the gaps in macOS Sequoia’s Window Tiling

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Tiled windows have a gap, or margin, by default, but you can change that.


By default, macOS Sequoia leaves a neat gap between windows when they are tiled — but if you don’t like that, it’s easy to change it.

If you use Apple’s new Window Tiling feature in macOS Sequoia to just tile one window over the side of your screen, you’ll never notice this. But as soon as you tile two next to each other, you’ll see a gap.

It’s the same kind of gap that Apple imposes when you drag widgets onto the Mac screen, the same kind of thing where it’s trying to make things neat. It isn’t a mistake, it’s a conscious choice by Apple — but you can still change it if you like.

For a feature that is meant to help everyone handle all the mess of windows and documents we have open, Apple has rather buried some of the controls in Settings. But if you go there, you’ll find the setting to change.

How to turn off the gaps in Window Tiling

  1. Go to Settings
  2. Choose Desktop & Dock
  3. Scroll down to the Windows section
  4. Turn off Tiled windows have margins

There are two other options in this section that can cause irritation, and both can be switched on or off. One is just whether you have to hold the Option key when you drag a window, if you want it to tile.

Just turn this setting off to get rid of the gaps between tiled windows on macOS Sequoia

That one might actually be useful, once you remember it, because the second option is about what happens when you drag a window to the edge of your screen. Very often, you’re going to find that although you just wanted to reposition a window, you’ve come close enough to the edge that the Mac tiles it.

When that does happen, you can drag the window away again and it will revert to the original size.

You do get used to this, but it never quite goes away. So you could turn on the requirement to use the Option key while you drag — or you could just turn off dragging to the edges.

There isn’t a great deal of functionality in Apple’s Window Tiling, at least not compared to third-party apps such as Moom. But what is there works well — and what is there can be adjusted to suit you.

AppleInsider News

This $10 Walmart Knife Is the Hottest Blade on the Market: Ozark Trail EDC Folding Knife Review

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(Photo/Nick LeFort)

There’s no real way to explain the pricing structure of knives. Brand, materials, function, and country of origin all play a role in retail pricing. But still, the numbers are all over the place.

Perhaps nothing complicates all that more than the $10 Ozark Trail 7.5” EDC folding knife, sold exclusively at Walmart. It’s been on the market for a little while now, but a couple of months ago, it started to get a lot of attention on the internet — so much so that it’s sold out in stores and online.

Dubbed “The Ozark Grail,” the internet stands divided on whether this 7.5-inch pocket knife is actually dependable. Purists note it is strikingly similar in form and function to Benchmade’s Bugout, which starts at $180 and is one of the highest-grossing pocket knives on the market today.

But the Bugout isn’t without its own faults (it’s a medium-duty knife at best), and this $10 Ozark Trail knife addresses that by adding steel liners that beef up the core and eliminate handle flex.

In short: I beat the snot out of this knife, and though it looks like it, it still functions just as well as the day that I took it out of its clamshell packaging in the parking lot at my local Walmart. This $10 Ozark Trail folding knife from Walmart may not have a backstory to brag about. In its place is an underdog knife with the form, function, and materials I expect in knives 10 times its price.


Ozark Trail 7.5-In. Folding Knife

Specs

  • Overall length
    7.5"
  • Blade length
    3.3"
  • Blade steel
    D2
  • Blade shape
    Drop point
  • Grind
    Flat
  • Hardness
    60-62 HRC
  • Lock type
    Crossbar
  • Carry
    Right hand, Tip-up
  • Weight
    2.9 oz.

Pros

  • Hardworking D2 steel

  • Highly reliable crossbar lock

  • Great ergonomics & fast, clean operation

  • Unbeatable price

Cons

  • Extremely high demand and limited stock

Ozark Trail EDC Folding Knife Review

Design & Features

Ozark Trail did its homework with the design and execution of this knife. The Ozark Trail 7.5-inch Slide Lock Folding Knife is a versatile, everyday carry pocket knife aimed at the outdoor crowd.

It sports a 3.3-inch D2 drop-point blade that can be actuated by an ambidextrous thumb stud. Ball bearings around the pivot further aid the opening operation on the knife.

ozark trail 7.5in knife wedged into piece of wood
After hard use and 1,000+ cycles, the blade showed no wobble, wear, or loss of lock strength; (photo/Nick LeFort)

It also boasts a crossbar lock — not only the strongest and most reliable knife lock around, but it also allows for opening and closing the knife with one hand.

There’s no way of avoiding the similarities between this knife and the Benchmade Bugout. Where the Bugout has metal plates that support the pivot and lock, the Ozark Trail carries a full steel frame, from tip to tail. This addresses flexing issues and gives support to both the pivot and lock. Additionally, it does so without adding weight to the knife, which tops out at 2.9 ounces.

Other aspects include a nondescript orange plastic handle scales and a right-hand, tip-up pocket clip. There’s also a black coating on the blade to help stave off rust and corrosion, above and beyond the protective properties of the D2 steel.

First Impressions

Growing up, Ozark Trail always struck me as a value brand. My family bought Ozark Trail tents for a fraction of the price of big-name tents and hoped they’d get us through a season. I’ve found the brand’s products durable and reliable enough for family camping, but not on par with higher quality brands for anything backpacking or trekking related

With that in mind, I walked into this $10 Walmart knife test with low to moderate expectations.

ozark trail 7.5in knife close up on the blade
(Photo/Nick LeFort)

When I first handled this knife, I sat in my truck in the Walmart parking lot looking for build imperfections or a lack of finish work. I found none.

All the layers matched up, and the blade sat perfectly down the center of the handle channel. I saw no marks on the handle scales where they came out of the mold, and felt no wobble in the blade. Then, I spent the next 20 minutes driving back to the house, flicking the knife open and closed.

As someone who’s tested knives that touch the $1,000 mark and all price points up to it, I really can’t make sense of this $10 knife. It seems like the company must take a loss in profits just to upset the industry. D2 steel may now be considered a value steel, but that doesn’t mean it’s any less potent than in the days when it was highly sought after.

The crossbar lock is the strongest, most reliable, and most widely adapted lock mechanism on a folding knife. And from the frame up, this knife is solid and durable. This is easily a $40 knife by today’s standards, if not more.

There had to be a catch.

In the Field

ozark trail 7.5in knife vs. bugout
This knife shares similarities with the Bugout in both form and function, at a fraction of the price; (photo/Nick LeFort)

I found tons of complaints about this knife online, many of which are unsubstantiated. Out of the box, I had no blade wobble nor any issues with the crossbar lock itself. However, you can find some dyed-in-the-wool knife nerds claiming otherwise. This is a common practice when things seem too good to be true. People will go to great lengths to find something negative to say about unicorns.

But I don’t think their findings are genuine.

I spent a month beating the hell out of this knife, but not outside the norm of any other knife I test. I tested it like any other knife, because that’s how it’s going to be treated. In between using it in real-life situations, I cycled the knife as many times as I could when I had some downtime.

It became a habit and I stopped counting at 1,000. There was no blade wobble, no wear on the pivot pin, and the lock worked just as well as it did the day I removed it from the packaging.

One thing that has always bothered me about the Bugout is how the handle flexes. As I stated previously, the inclusion of steel liners on the Ozark Trail eliminated that. Another concern I have had about the Bugout is how well it would stand up to lateral torsion, or side-to-side flexing.

So, I batoned the Ozark Trail into a piece of wood and flexed it left and right, fully expecting it to snap — but it didn’t. After that, there was a little blade wobble, but I easily fixed that by retightening the pivot screw.

(Where) Can You Get One?

I have never seen so much hype around a knife in my life. In the world of knives right now, nothing has more attention focused on it. Suffice it to say, the fan-dubbed “Ozark Grail” is sold out online.

However, there are rumors that you can find them on shelves at random Walmarts throughout the land. If you’re out getting cat food, it might be worth taking the walk a few aisles over to see if you’re in luck.

That said, you can sign up for alerts when this knife comes back in stock online. If you want to get your hands on one now and don’t mind paying a little extra, there are plenty of them on eBay. The markup isn’t terrible — I saw a few for around $30, which is still a good deal for this knife.

Conclusion: Should You Buy?

folded ozark trail 7.5in knife
For just $10, this knife is a standout choice for everyday and outdoor use. Its value is exceptional, proving once again that knife pricing often defies logic; (photo/Nick LeFort)

After a month of real-world use, the “Ozark Grail” has my stamp of approval. The coating on the blade is starting to wear off and the blade could use a rehoning, although it is still fairly sharp. But these things are to be expected. I didn’t notice anything out of the ordinary, aside from the knife being orange and black and giving off some serious Halloween vibes.

In my expert opinion, there is no reason (besides being sold out everywhere) that you shouldn’t buy the Ozark Trail 7.5-in. knife; you could easily trust it to get you through day-to-day life or any outdoor adventures you have planned. For $10, it’s truly an anomaly, but, as I said, knife pricing doesn’t make sense.

The post This $10 Walmart Knife Is the Hottest Blade on the Market: Ozark Trail EDC Folding Knife Review appeared first on GearJunkie.

GearJunkie

T.Rex Arms Is Re-Publishing Useful Military Manuals, And Wants Your In

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You can learn a lot of firearms skills, survival skills, and other useful information from the Internet, but what if the Internet goes down, or you just want a hard copy of all that information because you’re an old-fashioned and practical kind of person? T.Rex Arms is looking to fill that need with a new series of military-issued field manuals that are updated to be more usable.

T.Rex Arms @ TFB:

Re-working the formula

Note that T.Rex Arms isn’t here to change the content of these classic military field manuals. Instead, they want to simply make them easier to read and learn from, instead of offering the shoddily-scanned-and-printed dreck that so many budget-oriented publishers have sold over the years.

Check out the explanation below, from Isaac Botkin of T.Rex Arms:

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It’s a very practical way of looking at the realities of field manuals—yes, doing the typesetting all over again is going to be work, but we’re not talking rocket science here either (as Botkin says, it was not a lot of work, but more than he expected). If the end result is a much more useful book, then it’s well worth paying a bit extra to have that in hand. If you’ve picked up some of these government-issued books at a gun show or army surplus store, you know that they can terrible quality, and T.Rex’s solution sounds like something a lot of customers could use.

Not to mention, they’re still offering links to download these books as PDFs for free in their original and unimproved form. See their entry for the Marine Rifle Squad Handbook here; those links are at the bottom of the page. You can’t accuse them of being out to make a quick buck—they’re only charging for their work of publishing and printing.

Have your say

Botkin says T.Rex Arms doesn’t want to simply reprint the Ranger Handbook or other commonly-published military manuals. Botkin’s X/Twitter post on September 4 said “T.Rex Arms is a publishing company now. We sell books, and we reprint books. It is a small start, but let us know what we should do next!”. So if there’s a field manual you believe deserves a reprint, let them know via comments on YouTube, or social media. Your suggestion could help them get useful, maybe even life-saving, information out there for readers.

The Firearm Blog