Official Google Cloud Certified Professional Machine Learning Engineer Study Guide Mona Full Chapter PDF
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Professional Official Study Guide Mike Chapple
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Dedication
Acknowledgments
About the Author
About the Technical Editors
About the Technical Proofreader
Google Technical Reviewer
Introduction
Google Cloud Professional Machine Learning Engineer
Certification
Who Should Buy This Book
How This Book Is Organized
Bonus Digital Contents
Conventions Used in This Book
Google Cloud Professional ML Engineer Objective Map
How to Contact the Publisher
Assessment Test
Answers to Assessment Test
Chapter 1: Framing ML Problems
Translating Business Use Cases
Machine Learning Approaches
ML Success Metrics
Responsible AI Practices
Summary
Exam Essentials
Review Questions
Chapter 2: Exploring Data and Building Data Pipelines
Visualization
Statistics Fundamentals
Data Quality and Reliability
Establishing Data Constraints
Running TFDV on Google Cloud Platform
Organizing and Optimizing Training Datasets
Handling Missing Data
Data Leakage
Summary
Exam Essentials
Review Questions
Chapter 3: Feature Engineering
Consistent Data Preprocessing
Encoding Structured Data Types
Class Imbalance
Feature Crosses
TensorFlow Transform
GCP Data and ETL Tools
Summary
Exam Essentials
Review Questions
Chapter 4: Choosing the Right ML Infrastructure
Pretrained vs. AutoML vs. Custom Models
Pretrained Models
AutoML
Custom Training
Provisioning for Predictions
Summary
Exam Essentials
Review Questions
Chapter 5: Architecting ML Solutions
Designing Reliable, Scalable, and Highly Available ML
Solutions
Choosing an Appropriate ML Service
Data Collection and Data Management
Automation and Orchestration
Serving
Summary
Exam Essentials
Review Questions
Chapter 6: Building Secure ML Pipelines
Building Secure ML Systems
Identity and Access Management
Privacy Implications of Data Usage and Collection
Summary
Exam Essentials
Review Questions
Chapter 7: Model Building
Choice of Framework and Model Parallelism
Modeling Techniques
Transfer Learning
Semi‐supervised Learning
Data Augmentation
Model Generalization and Strategies to Handle Overfitting
and Underfitting
Summary
Exam Essentials
Review Questions
Chapter 8: Model Training and Hyperparameter Tuning
Ingestion of Various File Types into Training
Developing Models in Vertex AI Workbench by Using
Common Frameworks
Training a Model as a Job in Different Environments
Hyperparameter Tuning
Tracking Metrics During Training
Retraining/Redeployment Evaluation
Unit Testing for Model Training and Serving
Summary
Exam Essentials
Review Questions
Chapter 9: Model Explainability on Vertex AI
Model Explainability on Vertex AI
Summary
Exam Essentials
Review Questions
Chapter 10: Scaling Models in Production
Scaling Prediction Service
Serving (Online, Batch, and Caching)
Google Cloud Serving Options
Hosting Third‐Party Pipelines (MLflow) on Google Cloud
Testing for Target Performance
Configuring Triggers and Pipeline Schedules
Summary
Exam Essentials
Review Questions
Chapter 11: Designing ML Training Pipelines
Orchestration Frameworks
Identification of Components, Parameters, Triggers, and
Compute Needs
System Design with Kubeflow/TFX
Hybrid or Multicloud Strategies
Summary
Exam Essentials
Review Questions
Chapter 12: Model Monitoring, Tracking, and Auditing Metadata
Model Monitoring
Model Monitoring on Vertex AI
Logging Strategy
Model and Dataset Lineage
Vertex AI Experiments
Vertex AI Debugging
Summary
Exam Essentials
Review Questions
Chapter 13: Maintaining ML Solutions
MLOps Maturity
Retraining and Versioning Models
Feature Store
Vertex AI Permissions Model
Common Training and Serving Errors
Summary
Exam Essentials
Review Questions
Chapter 14: BigQuery ML
BigQuery – Data Access
BigQuery ML Algorithms
Explainability in BigQuery ML
BigQuery ML vs. Vertex AI Tables
Interoperability with Vertex AI
BigQuery Design Patterns
Summary
Exam Essentials
Review Questions
Appendix: Answers to Review Questions
Chapter 1: Framing ML Problems
Chapter 2: Exploring Data and Building Data Pipelines
Chapter 3: Feature Engineering
Chapter 4: Choosing the Right ML Infrastructure
Chapter 5: Architecting ML Solutions
Chapter 6: Building Secure ML Pipelines
Chapter 7: Model Building
Chapter 8: Model Training and Hyperparameter Tuning
Chapter 9: Model Explainability on Vertex AI
Chapter 10: Scaling Models in Production
Chapter 11: Designing ML Training Pipelines
Chapter 12: Model Monitoring, Tracking, and Auditing
Metadata
Chapter 13: Maintaining ML Solutions
Chapter 14: BigQuery ML
Index
End User License Agreement
List of Tables
Chapter 1
TABLE 1.1 ML problem types
TABLE 1.2 Structured data
TABLE 1.3 Time‐Series Data
TABLE 1.4 Confusion matrix for a binary classification
example
TABLE 1.5 Summary of metrics
Chapter 2
TABLE 2.1 Mean, median, and mode for outlier detection
Chapter 3
TABLE 3.1 One‐hot encoding example
TABLE 3.2 Run a TFX pipeline on GCP
Chapter 4
TABLE 4.1 Vertex AI AutoML Tables algorithms
TABLE 4.2 AutoML algorithms
TABLE 4.3 Problems solved using AutoML
TABLE 4.4 Summary of the recommendation types
available in Retail AI
Chapter 5
TABLE 5.1 ML workflow to GCP services mapping
TABLE 5.2 When to use BigQuery ML vs. AutoML vs. a
custom model
TABLE 5.3 Google Cloud tools to read BigQuery data
TABLE 5.4 NoSQL data store options
Chapter 6
TABLE 6.1 Difference between server‐side and client‐side
encryption
TABLE 6.2 Strategies for handling sensitive data
TABLE 6.3 Techniques to handle sensitive fields in data
Chapter 7
TABLE 7.1 Distributed training strategies using TensorFlow
TABLE 7.2 Summary of loss functions based on ML
problems
TABLE 7.3 Differences between L1 and L2 regularization
Chapter 8
TABLE 8.1 Dataproc connectors
TABLE 8.2 Data storage guidance on GCP for machine
learning
TABLE 8.3 Differences between managed and user‐
managed notebooks
TABLE 8.4 Worker pool tasks in distributed training
TABLE 8.5 Search algorithm options for hyperparameter
tuning on GCP
TABLE 8.6 Tools to track metric or profile training metrics
TABLE 8.7 Retraining strategies
Chapter 9
TABLE 9.1 Explainable techniques used by Vertex AI
Chapter 10
TABLE 10.1 Static vs. dynamic features
TABLE 10.2 Input data options for batch training in Vertex
AI
TABLE 10.3 ML orchestration options
Chapter 11
TABLE 11.1 Kubeflow Pipelines vs. Vertex AI Pipelines vs.
Cloud Composer
Chapter 13
TABLE 13.1 Table of baseball batters
Chapter 14
TABLE 14.1 Models available on BigQuery ML
TABLE 14.2 Model types
List of Illustrations
Chapter 1
FIGURE 1.1 Business case to ML problem
FIGURE 1.2 AUC
FIGURE 1.3 AUC PR
Chapter 2
FIGURE 2.1 Box plot showing quartiles
FIGURE 2.2 Line plot
FIGURE 2.3 Bar plot
FIGURE 2.4 Data skew
FIGURE 2.5 TensorFlow Data Validation
FIGURE 2.6 Dataset representation
FIGURE 2.7 Credit card data representation
FIGURE 2.8 Downsampling credit card data
Chapter 3
FIGURE 3.1 Difficult to separate by line or a linear method
FIGURE 3.2 Difficult to separate classes by line
FIGURE 3.3 Summary of feature columnsGoogle Cloud via
Coursera, www.coursera...
FIGURE 3.4 TensorFlow Transform
Chapter 4
FIGURE 4.1 Pretrained, AutoML, and custom models
FIGURE 4.2 Analyzing a photo using Vision AI
FIGURE 4.3 Vertex AI AutoML, providing a “budget”
FIGURE 4.4 Choosing the size of model in Vertex AI
FIGURE 4.5 TPU system architecture
Chapter 5
FIGURE 5.1 Google AI/ML stack
FIGURE 5.2 Kubeflow Pipelines and Google Cloud managed
services
FIGURE 5.3 Google Cloud architecture for performing
offline batch prediction...
FIGURE 5.4 Google Cloud architecture for online prediction
FIGURE 5.5 Push notification architecture for online
prediction
Chapter 6
FIGURE 6.1 Creating a user‐managed Vertex AI Workbench
notebook
FIGURE 6.2 Managed Vertex AI Workbench notebook
FIGURE 6.3 Permissions for a managed Vertex AI
Workbench notebook
FIGURE 6.4 Creating a private endpoint in the Vertex AI
console
FIGURE 6.5 Architecture for de‐identification of PII on
large datasets using...
Chapter 7
FIGURE 7.1 Asynchronous data parallelism
FIGURE 7.2 Model parallelism
FIGURE 7.3 Training strategy with TensorFlow
FIGURE 7.4 Artificial or feedforward neural network
FIGURE 7.5 Deep neural network
Chapter 8
FIGURE 8.1 Google Cloud data and analytics overview
FIGURE 8.2 Cloud Dataflow source and sink
FIGURE 8.3 Summary of processing tools on GCP
FIGURE 8.4 Creating a managed notebook
FIGURE 8.5 Opening the managed notebook
FIGURE 8.6 Exploring frameworks available in a managed
notebook
FIGURE 8.7 Data integration with Google Cloud Storage
within a managed noteb...
FIGURE 8.8 Data Integration with BigQuery within a
managed notebook
FIGURE 8.9 Scaling up the hardware from a managed
notebook
FIGURE 8.10 Git integration within a managed notebook
FIGURE 8.11 Scheduling or executing code in the notebook
FIGURE 8.12 Submitting the notebook for execution
FIGURE 8.13 Scheduling the notebook for execution
FIGURE 8.14 Choosing TensorFlow framework to create a
user‐managed notebook...
FIGURE 8.15 Create a user‐managed TensorFlow notebook
FIGURE 8.16 Exploring the network
FIGURE 8.17 Training in the Vertex AI console
FIGURE 8.18 Vertex AI training architecture for a prebuilt
container
FIGURE 8.19 Vertex AI training console for pre‐built
containersSource: Googl...
FIGURE 8.20 Vertex AI training architecture for custom
containers
FIGURE 8.21 ML model parameter and hyperparameter
FIGURE 8.22 Configure hyperparameter tuning by training
the pipeline UISourc...
FIGURE 8.23 Enabling an interactive shell in the Vertex AI
consoleSource: Go...
FIGURE 8.24 Web terminal to access an interactive
shellSource: Google LLC.
Chapter 9
FIGURE 9.1 SHAP model explainability
FIGURE 9.2 Feature attribution using integrated gradients
for cat image
Chapter 10
FIGURE 10.1 TF model serving options
FIGURE 10.2 Static reference architecture
FIGURE 10.3 Dynamic reference architecture
FIGURE 10.4 Caching architecture
FIGURE 10.5 Deploying to an endpoint
FIGURE 10.6 Sample prediction request
FIGURE 10.7 Batch prediction job in Console
Chapter 11
FIGURE 11.1 Relation between model data and ML code for
MLOps
FIGURE 11.2 End‐to‐end ML development workflow
FIGURE 11.3 Kubeflow architecture
FIGURE 11.4 Kubeflow components and pods
FIGURE 11.5 Vertex AI Pipelines
FIGURE 11.6 Vertex AI Pipelines condition for deployment
FIGURE 11.7 Lineage tracking with Vertex AI Pipelines
FIGURE 11.8 Lineage tracking in Vertex AI Metadata store
FIGURE 11.9 Continuous training and CI/CD
FIGURE 11.10 CI/CD with Kubeflow Pipelines
FIGURE 11.11 Kubeflow Pipelines on GCP
FIGURE 11.12 TFX pipelines, libraries, and components
Chapter 12
FIGURE 12.1 Categorical features
FIGURE 12.2 Numerical values
FIGURE 12.3 Vertex Metadata data model
FIGURE 12.4 Vertex AI Pipelines showing lineage
Chapter 13
FIGURE 13.1 Steps in MLOps level 0
FIGURE 13.2 MLOps Level 1 or strategic phase
FIGURE 13.3 MLOps level 2, the transformational phase
Chapter 14
FIGURE 14.1 Running a SQL query in the web console
FIGURE 14.2 Running the same SQL query through a
Jupyter Notebook on Vertex ...
FIGURE 14.3 SQL options for DNN_CLASSIFIER and
DNN_REGRESSOR
Mona Mona
Pratap Ramamurthy
Copyright © 2024 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada and the United Kingdom.
ISBNs: 9781119944461 (paperback), 9781119981848 (ePDF), 9781119981565 (ePub)
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Trademarks: WILEY and the Wiley logo are trademarks or registered trademarks of John
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not be used without written permission. Google Cloud is a trademark of Google, Inc. All
other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not
associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and authors have
used their best efforts in preparing this book, they make no representations or warranties
with respect to the accuracy or completeness of the contents of this book and specifically
disclaim any implied warranties of merchantability or fitness for a particular purpose. No
warranty may be created or extended by sales representatives or written sales materials. The
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Library of Congress Control Number: 2023931675
Cover image: © Getty Images Inc./Jeremy Woodhouse
Cover design: Wiley
To my late father, grandparents, mom, and husband (Pratyush
Ranjan), mentor (Mark Smith), and friends. Also to anyone trying
to study for this exam. Hope this book helps you pass the exam with
flying colors!
—Mona Mona
Chapter Features
Each chapter begins with a list of the objectives that are covered in
the chapter. The book doesn't cover the objectives in order. Thus,
you shouldn't be alarmed at some of the odd ordering of the
objectives within the book.
At the end of each chapter, you'll find several elements you can use to
prepare for the exam.
To get the most out of this book, you should read each chapter from
start to finish and then check your memory and understanding with
the chapter‐end elements. Even if you're already familiar with a
topic, you should skim the chapter; machine learning is complex
enough that there are often multiple ways to accomplish a task, so
you may learn something even if you're already competent in an
area.
Hyperparameter tuning 8
10
A/B testing different versions of a model
4.2 Scaling online model serving. Considerations include: 4, 5,
6,
10,
13
Assessment Test
1. How would you split the data to predict a user lifetime value
(LTV) over the next 30 days in an online recommendation
system to avoid data and label leakage? (Choose three.)
A. Perform data collection for 30 days.
B. Create a training set for data from day 1 to day 29.
C. Create a validation set for data for day 30.
D. Create random data split into training, validation, and test
sets.
2. You have a highly imbalanced dataset and you want to focus on
the positive class in the classification problem. Which metrics
would you choose?
A. Area under the precision‐recall curve (AUC PR)
B. Area under the curve ROC (AUC ROC)
C. Recall
D. Precision
3. A feature cross is created by ________________ two or more
features.
A. Swapping
B. Multiplying
C. Adding
D. Dividing
4. You can use Cloud Pub/Sub to stream data in GCP and use
Cloud Dataflow to transform the data.
A. True
B. False
5. You have training data, and you are writing the model training
code. You have a team of data engineers who prefer to code in
SQL. Which service would you recommend?
A. BigQuery ML
B. Vertex AI custom training
C. Vertex AI AutoML
D. Vertex AI pretrained APIs
6. What are the benefits of using a Vertex AI managed dataset?
(Choose three.)
A. Integrated data labeling for unlabeled, unstructured data
such as video, text, and images using Vertex data labeling.
B. Track lineage to models for governance and iterative
development.
C. Automatically splitting data into training, test, and
validation sets.
D. Manual splitting of data into training, test, and validation
sets.
7. Masking, encrypting, and bucketing are de‐identification
techniques to obscure PII data using the Cloud Data Loss
Prevention API.
A. True
B. False
8. Which strategy would you choose to handle the sensitive data
that exists within images, videos, audio, and unstructured free‐
form data?
A. Use NLP API, Cloud Speech API, Vision AI, and Video
Intelligence AI to identify sensitive data such as email and
location out of box, and then redact or remove it.
B. Use Cloud DLP to address this type of data.
C. Use Healthcare API to hide sensitive data.
D. Create a view that doesn't provide access to the columns in
question. The data engineers cannot view the data, but at
the same time the data is live and doesn't require human
intervention to de‐identify it for continuous training.
9. You would use __________________ when you are trying to
reduce features while trying to solve an overfitting problem with
large models.
A. L1 regularization
B. L2 regularization
C. Both A and B
D. Vanishing gradient
10. If the weights in a network are very large, then the gradients for
the lower layers involve products of many large terms leading to
exploding gradients that get too large to converge. What are
some of the ways this can be avoided? (Choose two.)
A. Batch normalization
B. Lower learning rate
C. The ReLU activation function
D. Sigmoid activation function
11. You have a Spark and Hadoop environment on‐premises, and
you are planning to move your data to Google Cloud. Your
ingestion pipeline is both real time and batch. Your ML
customer engineer recommended a scalable way to move your
data using Cloud Dataproc to BigQuery. Which of the following
Dataproc connectors would you not recommend?
A. Pub/Sub Lite Spark connector
B. BigQuery Spark connector
C. BigQuery connector
D. Cloud Storage connector
12. You have moved your Spark and Hadoop environment and your
data is in Google Cloud Storage. Your ingestion pipeline is both
real time and batch. Your ML customer engineer recommended
a scalable way to run Apache Hadoop or Apache Spark jobs
directly on data in Google Cloud Storage. Which of the following
Dataproc connector would you recommend?
A. Pub/Sub Lite Spark connector
B. BigQuery Spark connector
C. BigQuery connector
D. Cloud Storage connector
13. Which of the following is not a technique to speed up
hyperparameter optimization?
A. Parallelize the problem across multiple machines by using
distributed training with hyperparameter optimization.
B. Avoid redundant computations by pre‐computing or cache
the results of computations that can be reused for
subsequent model fits.
C. Use grid search rather than random search.
D. If you have a large dataset, use a simple validation set
instead of cross‐validation.
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The Project Gutenberg eBook of The answer
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Language: English
Illustrated by Orban
Hohmann was no fool. The dictator knew that he was bucking the
combined resources of the world, and it worried him somewhat, even
though he put up a brave front and daily told his people that the
United Nations would not act against him.
The espionage that went on reported that little was being done.
Hohmann trebled the external espionage, and multiplied the internal
agencies tenfold. He was taking no chances. Materials shipped into
his country were followed to the addressee, who was then
investigated. Every mail carrier and delivery boy was a member of
Hohmann's Intelligence Group. Shipments of manufactured articles
were stopped or diverted; Hohmann knew that the plating on a cigar
lighter might contain fissionable material.
But there were no moves on the part of the United Nations that
Hohmann's Intelligence Group could detect.
And it was the lack of action—even lack of anything other than
denunciation—that worried him into calling a Security Meeting.
His hall filled to overflowing with higher-ups, Robert Hohmann faced
them and said:
"We are here because of a singular lack of activity on the part of
those who have reason to fear us. Reprisals may come in many
ways, some of them must be new and terrible, even though they are
now undetectable. The problem of the pushbutton war is known to all
—why drop bombs when bombs may be shipped in among the
incoming merchandise, assembled in a tall tower, and touched off by
radio. We, therefore, must locate the manner of the reprisals."
Worried faces nodded.
"This is no war of nerves," thundered Hohmann. "It is possible to
cause mental confusion in someone by merely ignoring his overt act
—he eventually spends more time worrying about what you intend to
do about it than he does in preparation. This will not work. Admittedly
we have multiplied our Intelligence Group in an effort along this
same reasoning. The lack of action on the part of the United Nations
has caused some concern. But we are not an individual, and we can
divert a carefully calculated number of workers to investigate while
the rest of us can prepare for war. The problem, again I must admit,
has achieved a rather overrated proportion, hence this meeting."
Professor Haldrick looked up at Hohmann and said, quietly, "In other
words, Führer Hohmann, even though you state that the so-called
war of nerves cannot succeed, we are meeting to solve that very
problem?"
Hohmann hissed at Haldrick and snarled for the professor to be
quiet.
"Now," said Hohmann, "what has been occurring lately that might
possibly be construed as being out of the line of ordinary
happenings?"
General Friedrice shrugged. "I must admit that the mail has
increased markedly since Hammond's incarceration. Letters pour in
from all over the world to this government bureau and that
government agency. They plead, they cajole, and they call names."
"I can imagine your fear at being called names," laughed Hohmann.
"Indeed, we are cringing abjectly," replied General Friedrice, who
would have had to reduce his figure by at least seventy pounds
before he could possibly cringe without hurting himself. "We find
ourselves in a rather strange circumstance, however. These letters
are, of course, saved. This makes for too much paper work."
"We can take care of that," said Hohmann idly.
"I know. But that is the only thing I know of," said Friedrice.
"Enough," said Hohmann. "This is another example of the confusion-
method. Our enemies hope to worry us by doing nothing—which is
expected to make us fear something ultra-secret. Well, to a certain
extent they have worried us. Not to any dangerous point, however,
for we are too strong to be defeated by a mental condition. This
overbearing arrival of letters is another thing. All letters must be
opened and read, for some of them do contain much valuable
information. They must all be saved and filed, for unless we have
previous letters from some correspondent, we cannot know by
comparison, whether a future letter containing information is false or
true. A letter giving information that comes from a known
correspondent who is helpful in the past will be treated with more
respect than the same information coming from someone who has
written reams of misdirection, falsity, and ranting notes depicting dire
results if we do not release Hammond and behave ourselves."
Hohmann shrugged.
"Even so, we cannot be shunted aside," he added. "We have plenty
of people who can take care of the misdirection, just to see that
something isn't happening to us. The rest of us can continue
preparing. Which brings me to another point."
Hohmann paused dramatically.
"When I press this key," he said, indicating the diamond-studded
telegraph-style key, "the uranium pile will start to go. The key is
connected to the restrainer-rod controls of the pile; when pressed,
the rods leave the pre-set positions of no-reaction and fall under the
automatic controlling circuits. The pile will then start functioning at
approximately ten kilowatts. After checking, it will be advanced to a
more productive power, and we are making the first step toward our
glorious future."
The hours passed. The fires grew. No longer were they merely
hotboxes, but in some important cases open flames broke out and
consumed the paper. The charred ash continued to be too hot to the
touch, and there was panic in the country.
Unger came at last. Dejected and pale with fear.
"Well," stormed Hohmann, "what is it?"
"I'm not certain other than its effect," said Unger shakily. "All paper is
artificially radioactive, and it heats up when the radioelements
approach the critical mass—"
"Get Hammond!" screamed the dictator.
The United Nations representative was brought. He came with a
smile.
"What is this?" stormed Hohmann.
"Your own decision," replied the representative. "You should not
have started the pile."
"Go on," gritted Hohmann.
Greg Hammond smiled. "Plutonium has a characteristics radiation
that we do not quite understand," he explained. "However, this
radiation will cause fission in certain types of medium-long lived
radioelements. The range of the plutonium radiation is unknown, but
it is great enough to bathe the entire country. You will find that most
government offices are bulging with reams and reams of
correspondence, many of which are over the critical mass. Nothing
happens until someone turns on a plutonium-producing uranium pile,
lets it run for a few hours, and the accumulation of plutonium starts.
Right now, Hohmann, you have about four hours before most of your
government offices go sky-high—from their own red tape." Greg
Hammond smiled. "The United Nations only advises," he said. "And
many millions of letters of advice arrived, all written on
radioelemental paper. Had you taken that advice, the paper would
have been innocuous inside of about thirty or forty years. You did
not. Now you have lost completely, Hohmann, for the radiation from
that paper when bombarded with the plutonium radiation, produces a
whole string of secondary radioelements in your offices, in your
desks, in your bodies, and in your air. The ash from burning is still
hot, Hohmann, and the trucks that will carry the deadly paper will be
as deadly. Your very country will be subject to slow fission if you start
another uranium pile for several hundred years. I'd advise you to
stop the one that is now running, Hohmann."
"I'll let the world go up with me," screamed the dictator.
"That it will not do," said Hammond. "You see; if you do not shut it off
by yourself, we'll all be dead in an hour, after which my cohorts can
locate the pile with neither difficulty nor interference. Make your
choice, dictator. And remember, the United Nations only advises,
never demands. Our advice, however, may be said to be written with
letters of fire."
THE END.
*** END OF THE PROJECT GUTENBERG EBOOK THE ANSWER
***
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