Reddit mentions: The best science experiments & measurement books

Just be prepared to be unamazed at the views with this scope or really any scope. What you see in pictures are not what you will see with this scope or really any small aperture scope. With that said though you still can enjoy so much with that scope. This is a fast scope which has some plus and minuses. One is that you can definitely get some high powered lenses without the use of a barlow which will help you all around as the barlow does diminish some of the light gathering capabilities when used. barlows are personal choice I rather use a high power high piece to get where I want rather than a barlow but thats just me. Right now you have a 26 and 75x with your eyepieces so if on a budget a 2x barlow maybe in order with a 450mm focal length. I believe they say 50x per inch of aperture for a useful magnification but that would be pristine conditions. Depending on light pollution it is probably more realistically around 25-30x per inch for your highest useful magnification. A 3mm would give you 150x which is probably going to be on that threshold of usefulness in your scope.

Definitely check eyesonthesky.com. Great site with a ton of great info. It definitely helped me when i jumped back into observing after a 20 or so year hiatus.

The biggest thing though is enjoy it. Remember that you are not going to see the things you see in the magazines or the internet but you can truly enjoy that scope with a little knowledge and perseverance. As good as stellarium I also would suggest getting this book.
http://www.amazon.com/gp/product/1891938193/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

It is really good because it just has stuff that your scope should be able to see. It is great for learning the sky and finding objects that are within the capabilities of your scope for the most part.

Also remember that jupiter and orions nebula are not that far off and those will definitely be in the realm of that scope.

I have not tried the expanse eyepieces but they look nice. Also check out the x-cel eyepieces by celestron they are also nice eyepieces that are moderately priced.

Definitely recommend picking up a book - Turn Left at Orion is excellent, but I also really like David Chandler's Sky Atlas for Small Telescopes and Binoculars since its pretty newbie friendly and light enough that you can take it out in the field with you. Since you're starting off, you'll want to look at the bright stuff anyways.

Another handy field guide is the Sky & Telescope Pocket Field Atlas, which is helpful for even seasoned observers.

Finally, there are two helpful (and free) resources you can use:

1. Skymaps- they publish maps every month for observers you can download via PDF.
   
   
2. Stellarium a free planetarium program from your computer - put in your location, and start exploring the night skies.
   
   
3. Cartes Du Ciel if you want to generate your own star charts. Not as pretty or as user friendly as Stellarium, but helpful for generating custom charts to hunt down objects you're looking for.
   
   Edit: Oh and one more thing, pick up a moon map. Lots of people look at the moon, few people study it - knowing your way around there makes it so much more interesting. Stuff like finding the Apollo landings can give you a sense of connection that a far off galaxy can't.

I’m not sure Khan Academy is the most useful source; most of the assigned exercises I looked at a few years ago seemed pretty much trivial. You just watch someone solve a problem on a video, and then do exactly the same steps but with slightly different details. It’s an exercise in memory and copying, not in thinking for yourself. Basically the same curriculum as standard high school courses, just at your own pace. See Lockhart, “A Mathematician’s Lament” and Toom, “Word Problems in Russia and America”.

If you are self-studying the Gelfand and Kisilev books /u/TheBloodyNine1 mentioned are nice Russian books with some good problems in them, but also some text. If the text exposition is too fast or high level you could try reading the algebra and geometry books by Harold Jacobs. These have easier (standard American style) exercises but gentler exposition. If you are looking for medium to hard (by typical American standards) problems but also a good amount of step-by-step help with solving them, you might enjoy the Art of Problem Solving books, including those about algebra, geometry, basic number theory, “precalculus”.

Or for something a bit more poetic, check out Lockhart’s book Measurement.

The best way to learn the “why” of things in a real way is by doing the work for yourself. If someone just tries to tell you it won’t really sink in – you have to struggle with something for yourself before the explanation even has any relevance. Sometimes a book of nothing but problems can be just as useful as a book full of text.

See if you can work your way through problems such as those in Mathematical Circles (Russian Experience) (designed for ambitious Russian middle school students). Or you can look at the problems used at Exeter (famous private high school): Math 1, Math 2, Math 3–4, Math 4–5, Math 6, Discrete Math.

Or see if you can solve some past contest math problems. E.g. pick up a copy of a past AMC 12 (or AMC 10 or AMC 8 if those are too hard), and see how many problems you can do if you let yourself try to solve each one for 20 minutes without looking up the answer.

If you get through some of those and want less typical fare there are some fun topics in A Decade of the Berkeley Math Circle.

For some more general advice about problem solving methods (alongside problems), the book Thinking Mathematically is nice.

To be honest, the fastest way to improve is to find an expert tutor/mentor/coach to meet with face to face. Self-studying from books or websites or learning from class lectures and completely independent work is much more difficult / less efficient. There might be free tutoring resources available in your area if you hunt around (e.g. sometimes colleges will do free tutoring for nearby high school students).

Finally, if you get stuck on anything (problem, topic, ...) in particular, try /r/learnmath.

>seems to confuse me more, but I’m very interested. Can you please elaborate or provide somewhere I can read a bit more about that?

That's a hard question, but one of my favorite experiment-friendly textbooks is Quantum Optics for Experimentalists by Ou).

To elaborate more, I would say, that using certain parallels between classical physics and quantum physics, people have worked backwards from the classical theory of electromagnetism to develop a quantum theory of electromagnetism (the complete theory is known as quantum electrodynamics, of which quantum optics is a part).

(Seriously abbreviating/oversimplifying here, but...)

For each value of momentum, polarization, and frequency, the quantum electromagnetic field has evenly spaced energy levels, not unlike the different orbitals an electron has in an atom. Each quantum of energy in this mode of the electromagnetic field counts as one photon. The full state of the field would be a superposition of different photon number states for every value of frequency and momentum of the electromagnetic field.

For example, a laser beam would be described as a superposition of many different photon number states over a narrow spread in frequency and momentum, while thermal light from blackbody radiation would instead be a statistical distribution of photon number states. You can also create nonclassical states of light like squeezed light, and beams of entangled photon pairs in spontaneous parametric down-conversion.

Edit: "One Photon" can also be a single-photon state that's a superposition over different values of frequency and momentum. This would be a single-photon wave packet.

Hell yeah!

Like, my brain and special interests all lean towards the Liberal Arts and Humanities.

But math, logic, and programming calm me the hell down.

Do you have any idea how stressful it is that people can't agree on historical interpretations? Or how to best lead a group of people?

Math has answers and makes sense. I'm with Plato. It is this pure and glorious thing. It's why I love Jesus being described as "ὁ λόγος" (which relates to logic and all the rest). To be clear, you don't need to believe Jesus is the logos to appreciate how kickass math is. Plato sure didn't :P

Also, OP! This book by a Mathematician has a really cool take on teaching and learning and understanding math. Since you do it for fun, definitely would be worth checking out.

If you can't afford it, PM me and I'll send you my copy when my wife is done reading it :)

This is incredibly on-topic:

Remember Paul Lockhart of “Lockhart’s Lament” fame? (If not: Let’s just say: IMHO, he hits the nail that is your problem right on its head.)

Well, I mailed him back then, and he promised us a book, to teach one how to think like a mathematician. A “textbook” to finally get rid of that nightmare that you, me, and so many others described, and learn math the right way.

Well, last week he e-mailed me (and many others), that his book is done!

http://www.amazon.com/Measurement-Paul-Lockhart/dp/0674057554/

Here’s the original e-mail:

> Dear Readers of A Mathematician's Lament,

> I wanted to let you know that I have a new book out called Measurement. This is my attempt to explain and illustrate, in an honest and heartfelt way, what it is that mathematicians do and why we do it. On one level, you could say that the book is about geometry and analysis, viewed from a modern mathematical perspective, along with natural and (I hope) engaging problems to work on. But really it's a book about me and the way I think, and what it is that I find so beautiful and compelling about math. I would hate for anyone to call it a textbook (it's way too fun), yet, if you want to really understand the mathematics of measurement in a deep and intuitive, intellectually serious way, then this is the book I would recommend. That's why I wrote it: to see if I could. I'm sure there are ways in which I have failed in the book to get across what I wanted to say, but overall I think I did a pretty good job conveying how I think and feel about mathematics, in what I hope is a refreshing new way---just really being me, and speaking to you person to person. Anyway, the book is out, and I would be very curious to know what you think of it.

> Yours,

> Paul

P.S.: As far as I can tell, he prefers not to be contacted too much, but to be left alone. I want to respect that. So please don’t do as I did. :)

P.P.S.: Don’t get angry at other mathematicians/engineers, who learned math in the color-by-the-number style. They are also just innocent victims. It’s not their intention to annoy or harm you. Maybe suggesting this book to them can make their lives nicer too. ;)

Further reading/research: (Not all of which I've gotten to read yet. Some of which may be quite tangentially relevant to the discussion at hand along with the books and sites I mentioned above. Consider this more a list of books pertaining to the history of technology, machining, metrology, some general science and good engineering texts.)

Dan Gelbart's Youtube Channel

Engineerguy's Youtube Channel

Nick Mueller's Youtube Channel

mrpete222/tubalcain's youtube channel

Tom Lipton (oxtools) Youtube Channel

Suburban Tool's Youtube Channel

NYCNC's Youtube Channel

Computer History Museum's Youtube Channel

History of Machine Tools, 1700-1910 by Steeds

Studies in the History of Machine Tools by Woodbury

A History of Machine Tools by Bradley

Tools for the Job: A History of Machine Tools to 1950 by The Science Museum

A History of Engineering Metrology by Hume

Tools and Machines by Barnard

The Testing of Machine Tools by Burley

Modern machine shop tools, their construction, operation and manipulation, including both hand and machine tools: a book of practical instruction by Humphrey & Dervoort

Machine-Shop Tools and Methods by Leonard

A Measure of All Things: The Story of Man and Measurement by Whitelaw

Handbook of Optical Metrology: Principles and Applications by Yoshizawa

Angle of Attack: Harrison Storms and the Race to the Moon by Gray

Machine Shop Training Course Vol 1 & 2 by Jones

A Century of Electrical Engineering and Computer Science at MIT, 1882-1982

Numerical Control: Making a New Technology by Reintjes

History of Strength of Materials by Timoshenko

Rust: The Longest War by Waldman

The Companion Reference Book on Dial and Test Indicators: Based on our popular website www.longislandindicator.com by Meyer

Optical Shop Testing by Malacara

Lost Moon: The Preilous Voyage of Apollo 13 by Lovell and Kruger

Kelly: More Than My Share of It All by Johnson & Smith

Skunk Works: A Personal Memoir of My Years at Lockheed by Rich & Janos

Unwritten Laws of Engineering by King

Advanced Machine Work by Smith

Accurate Tool Work by Goodrich

Optical Tooling, for Precise Manufacture and Alignment by Kissam

The Martian: A Novel by Weir

Roark's Formulas for Stress and Strain by Young Budynas & Sadegh

Materials Selection in Mechanical Design by Ashby

Slide Rule: The Autobiography of an Engineer by Shute

Cosmos by Sagan

Nuts, Bolts, Fasteners and Plumbing Handbook by Smith Carol Smith wrote a number of other great books such as Engineer to Win.

Tool & Cutter Sharpening by Hall

Handbook of Machine Tool Analysis by Marinescu, Ispas & Boboc

The Intel Trinity by Malone

Manufacturing Processes for Design Professionals by Thompson

A Handbook on Tool Room Grinding

Tolerance Design: A Handbook for Developing Optimal Specifications by Creveling

Inspection and Gaging by Kennedy

Precision Engineering by Evans

Procedures in Experimental Physics by Strong

Dick's Encyclopedia of Practical Receipts and Processes or How They Did it in the 1870's by Dick

Flextures: Elements of Elastic Mechanisms by Smith

Precision Engineering by Venkatesh & Izman

Metal Cutting Theory and Practice by Stephenson & Agapiou

American Lathe Builders, 1810-1910 by Cope As mentioned in the above post, Kennth Cope did a series of books on early machine tool builders. This is one of them.

Shop Theory by Henry Ford Trade Shop

Learning the lost Art of Hand Scraping: From Eight Classic Machine Shop Textbooks A small collection of articles combined in one small book. Lindsay Publications was a smallish company that would collect, reprint or combine public domain source material related to machining and sell them at reasonable prices. They retired a few years ago and sold what rights and materials they had to another company.

How Round Is Your Circle?: Where Engineering and Mathematics Meet by Bryant & Sangwin

Machining & CNC Technology by Fitzpatrick

CNC Programming Handbook by Smid

Machine Shop Practice Vol 1 & 2 by Moltrecht

The Elements of Computing Systems: Building a Modern Computer from First Principles A fantastic book with tons of free online material, labs, and courses built around it. This book could take a 6th grader interested in learning, and teach them the fundamentals from scratch to design a basic computer processor and programming a simple OS etc.

Bosch Automotive Handbook by Bosch

Trajectory Planning for Automatic Machines and Robots by Biagiotti & Melchiorri

The Finite Element Method: Its Basis and Fundamentals by Zhu, Zienkiewicz and Taylor

Practical Treatise on Milling and Milling Machines by Brown & Sharpe

Grinding Technology by Krar & Oswold

Principles of Precision Engineering by Nakazawa & Takeguchi

Foundations of Ultra-Precision Mechanism Design by Smith

I.C.S. Reference Library, Volume 50: Working Chilled Iron, Planer Work, Shaper and Slotter Work, Drilling and Boring, Milling-Machine Work, Gear Calculations, Gear Cutting

I. C. S. Reference Library, Volume 51: Grinding, Bench, Vise, and Floor Work, Erecting, Shop Hints, Toolmaking, Gauges and Gauge Making, Dies and Die Making, Jigs and Jig Making
and many more ICS books on various engineering, technical and non-technical topics.

American Machinists' Handbook and Dictionary of Shop Terms: A Reference Book of Machine-Shop and Drawing-Room Data, Methods and Definitions, Seventh Edition by Colvin & Stanley

Modern Metal Cutting: A Practical Handbook by Sandvik

Mechanical Behavior of Materials by Dowling

Engineering Design by Dieter and Schmidt

[Creative Design of Products and Systems by Saeed]()

English and American Tool Builders by Roe

Machine Design by Norton

Control Systems by Nise

That doesn't include some random books I've found when traveling and visiting used book stores. :)

Oh god, this question is such a can of worms that I will try to answer as best as I can. I'm not a master optician, a master optician will give you a different answer, you ask two master opticians and they'll fight about the answer, ask three and you'll never get a conclusion. I will try to answer this and break it into chunks. For simplicity I will talk about reflector telescopes, or scopes that reflect light back into the eyepiece, and not refractors which would be more like a camera lens.

Telescopes can be broken down into their individual aperture and F ratio, which is nothing like an f ratio in a camera.

Aperture controls the amount of light gathering a telescope can do and in some cases the contrast of a scope. Aperture it is literally the size of the primary mirror or element in the scope. A 10" scope would have a primary mirror 10" across and give light accordingly. The size of the mirror SHOULD have a play on the desired F ratio of the mirror which we'll talk about next.

Your F ratio for a telescope calculates field of view, which is directly related to your magnification. A small F ratio means wider fields of view, a large F ratio has a smaller field of view. F ratio also, to an extent controls brightness of your object, so, the more magnification the dimmer an object becomes, which means you want to make up for the dimness with larger primary mirrors.

Now we're going to get complicated, and I'm going to keep it simple. When you start with ridiculous amounts of magnification (provided by mostly by an eyepiece, but in some parts by a mirror) you end up with very visible defects, the most common is what we call chromatic aberration. It is a prism like shifting of colors in the objects you are looking at. Chromatic aberration comes from small defects in the mirror surface, perhaps an atom or two of silica in height, maybe three or four. (Yes, a good mirror is THAT precise) These color shifts can significantly impact your viewing of things like Alberio, Saturn, and well, just about any other interesting thing you could possibly look at. Other defects we worry about are things like astigmatism, which creates a conical star as opposed to a circular one.

So, simply put what you're getting for 3k+ is a finely figured mirror (that's what we use to describe the process of polishing a mirror to perfection) that has no optical flaws which will produce a smooth and apparition free viewing surface across the entirety of your field of view.

If you have more interest check out the following:
Alberio: http://www.albireovineyards.com/uploads/1/3/0/2/13028271/2582976_orig.jpg
Saturn Through a (pay attention especially to contrast and DETAIL):
Cheap Scope:
http://i1.ytimg.com/vi/9VIhag8tTcs/maxresdefault.jpg
Pricey Scope:
http://astrobob.areavoices.com/astrobob/images/thumbnail/SaturnJimSchaff.jpg
Scope that could have been a car.
http://www.learn.usa.canon.com/app/media/images/articles/60da_astrophoto/08_saturn__hero.jpg

For the hobbyists and clubbers among you:
www.stellafane.org
www.atmob.org

And for the technical readers a nice intro book on building your own:
http://www.amazon.com/about-telescopes-Popular-optics-library/dp/B0006CL970/ref=sr_1_1?ie=UTF8&qid=1404270285&sr=8-1&keywords=sam+brown+telescope

I made them with my uncle when i was a little kid. He was and still is a fun pyro. it does not require all the extras in OPs video, with a little experimentation it's easy enough to do it.

I would recommend this book, it's some nice entry level stuff and most of the builds are super cheap.

Building this stuff with kids imparts ingenuity and creativity while being really fun. Building potato cannons was a highlight on my childhood

Hi, I was surprised to get your reply. I assume you mean you read the Apache Constitution, itself, which is posed online.

Actually, you can express ideas in math non-ambiguously and that lasts for a long time. Most people think math is a science. It's not. Math is a language. And because you can express ideas using math so precisely, it's the preferred language of science.

I wrote the Apache constitution using ideas from Open Source Government2, which is a science (and set of technologies) that explain how to manage societies without the use of centralized coercion. Open Source Gov (OSG) is explained in my book "The End: The Fall of the Political Class by Chas Holloway (that's me).

It's here on Amazon:

https://www.amazon.com/dp/B07B68MJX5/ref=sr_1_1?ie=UTF8&qid=1520004479&sr=8-1&keywords=the+end+the+fall+of+the+political+class

On the other hand, you are right about "non-ambiguous" language not lasting forever. Scientific understanding always evolves. The Newtonian model turned out to be a special case of the Einstein model, which will be shown to be a special case of something even larger. So even though you use math, your ideas don't last forever.

On the third hand, the purpose of science is not to achieve a perfect description of nature. It's to have an intellectual model you can use to build technology to accomplish goals.

Thanks for the reply.

That is a pretty big red flag. Most departments offer a statistics course for non-math majors, I've TA'd that course before, its not good for people who enjoy math. Make sure there is at the very least a calculus pre-req for the course, and you should take a probability course first anyways.

Probability and Statistics in general is such a great field, it would be really unfortunate if a bad class designed for psych majors turned you off from the subject. I would wait until you can take the right classes so you can at least see the material presented in the right way, if your curious what a course sequence should look like:

1. Calculus based probability (undergrad, math major prob)
   
   
2. Calculus based statistics (undergrad, math major stat)
   
   
3. Measure-theoretic probability (grad prob)
   
   
4. Statistical Theory (grad stat - here is where analysis and some really neat math merges with the stats, but undergrad stat does this to some degree as well.
   
   Here are links to textbooks in the same order:
   
   
5. http://www.amazon.com/First-Course-Probability-9th-Edition/dp/032179477X
   
   
6. http://www.amazon.com/Mathematical-Statistics-Analysis-Available-Enhanced/dp/0534399428
   
   
7. http://www.amazon.com/Probability-Measure-Patrick-Billingsley/dp/1118122372
   
   
8. http://www.amazon.com/Mathematical-Statistics-Selected-Topics-Edition/dp/0132306379
   
   You can find most of those in pdf format somewhere online. I'm not saying those are the best textbooks to use, but they should at least provide a guide so that you can be sure you taking the right courses.
   
   Edit: If your school offers a combined prob/stat course (usually offered for engineers) that has a calc 3 pre-req it would probably serve well as a compact introduction to the subject.
   

I understand the techniques proposed by Lockhart, and he has a good book out Measurement that illustrates some of his techniques.

I'm trying to address the same problem in a fundamentally different way. There are elements of discovery in my stuff, but it is more focused on presenting the development in a historical context.

Lockhart's method is great for high school students who have a teacher devoted to the method and who is steeped enough in the mathematics to lead the discovery. I think there is value in both.

Great Experiments in Physics should have a lot of what you are looking for. Firsthand accounts of the most important physical experiments, with side notes to help the reader understand, and with passages giving historical context.

It is quite an undertaking to read through it. But very fascinating.

https://www.amazon.com/Great-Experiments-Physics-Firsthand-Accounts/dp/0486253465

Awesome! As mentioned, Rudin, Folland, and Royden are the gold standards of measure theory, at least from what I have heard from professors and the internet. I'm sure other people have found other good ones! Another few I somewhat enjoy are Capinski and Kopp and Dudley, as those are more based on developing probability theory. Two of my professors also suggested Billingsley, though I have not really had a good chance to look at it yet. They suggested that one to me after I specifically told them I want to learn measure theory for its own right as well as onto developing probability theory. What is your background in terms of analysis/topology? Also, I am teaching myself basic measure theory (measures, integration, L^p spaces), then I think that should be enough to look into advanced probability. Feel free to PM me if you need some help finding some of these books! I prefer approaching this from the pure math side, so mathematical statistics gets a bit too dense for me, but either way, I would look at probability then try to apply it to statistics, especially at a graduate level. But who am I to be doling out advice?!

*Edit: supplied a bit more context.

Those books are definitely geared toward materials science. If you're interested in the operation of TEM, though, it should be helpful. The physics behind the instrument don't really change. In a virology lab, you probably work at lower accelerating voltages, and you might not be doing atomic-resolution work, so those bits wouldn't apply to you.

This book is cheap and discusses biological applications, so it may be a better starting point. Some of the springer publications are nice resources, but they can be quite expensive. You might want to check your school library for any books you may be interested in. Also, some of these things can be found for free in PDF form if you search hard enough online.

Most of the books I've used to learn about TEM are for materials science or specifically STEM and Z-contrast imaging. Those types of resources may not be as relevant to you.

History of science is indeed interesting. I have a little book on the history of modern chemistry that I hope to get to in the near future.

Have you read the Metaphysical Foundations of Modern Science by E. A Burtt? It's a game changer. Burtt, to my knowledge, was neither a Thomist nor a Theist, so you don't have to worry about his bias.

There's more to reading ancient philosophy than looking for prototypes and origins of modern scientific ideas. Philosophy is prior to science. Scientific theories presuppose philosophical theories. Here is one way that natural philosophy is prior to modern physics.

Natural philosophy considers motion as such, at its most universal level. What is common to all types of motion. Modern science looks at one aspect of motion (quantitative) and creates mathematical models of specific types of motion (inertial, gravitational, Brownian).

We must first know that motion exists, and have a general understanding of what it is and how it is possible before we can proceed to look at quantitative aspects of motion, usually considered under experimental conditions.

As for the early Middle Ages, have you read Pierre Duhem's history of physics? His continuity thesis is provocative, but he definitely provides a comprehensive survey.

> Science. Religion has been fighting it for thousands of years.

I'm afraid that to even assume that science and religion existed as distinct concepts or endeavours thousands of years ago is a bit naïve, and this idea that they are eternally opposed is a very simplistic view that reflects the biases of anticlerical 19th Century historians more than the actual facts—it's only really been defended by people with a grudge against religion since a reappraisal of the subject in the 1950s, 60s, and 70s (and especially since the reappraisal by James Moore in The Post-Darwinian Controversies). Here are a few books that could help you develop a richer understanding of the historical relationship between science and religion.

• David C. Lindberg, The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, Prehistory to A.D. 1450 (University of Chicago Press, 2007)
  
• E. A. Burtt, The Metaphysical Foundations of Modern Science (Routledge, 1931)
  
• Gary B. Ferngren, ed., Science and Religion: A Historical Introduction (John Hopkins University Press, 2002)
  
• Ronald L. Numbers, ed., Galileo Goes to Jail and Other Myths About Science and Religion (Harvard University Press, 2009)
  
  These would probably be illuminating reading as well.
  
  
• Thomas S. Kuhn, The Structure of Scientific Revolutions (University of Chicago Press, 1962)
  
• Brian Davies, An Introduction to the Philosophy of Religion (Oxford University Press, 2004)
  
  > Here is just another surrender by a guy at the top of the money chain.
  
  No one interested in the subject should be under the impression that what the Pope has said is anything new. Eminent Catholic theologians like John Henry Newman found Darwin's theory of natural selection consistent with Christianity when it was published, and Pope Pius XII very famously affirmed that there was no intrinsic conflict between them in his 1950 encyclical Humani generis. As for the Big Bang, it is downright foolish to characterise the Church as "surrendering" to a theory that was formulated by a Catholic priest in the first place.

Try to find entry points that interest you personally, and from there the next steps will be natural. Most books that get into the nitty-gritty assume you're in school for it and not directly motivated, at least up to early university level, so this is harder than it should be. But a few suggestions aimed at the self-motivated: Lockhart Measurement, Gelfand Algebra, 3blue1brown's videos, Calculus Made Easy, Courant & Robbins What Is Mathematics?. (I guess the last one's a bit tougher to get into.)

For physics, Thinking Physics seems great, based on the first quarter or so (as far as I've read).

>Maybe recommendations for later would be nice, though.

My current favorite is from the Oxford Masters Series: Atomic Physics, by C. J. FOOT.

But the theory hasn't changed in 80 years. If you're at university, look up any book in the library on atomic physics. If you can, walk back in the stacks. They should all be grouped by subject.

Remember, 4 days in the lab can save you 4 hours in the library.

World in the Balance: The Historic Quest for an Absolute System of Measurement by Robert Crease was published about 2011. The radio interview on National Geographic goes for about three and a half minutes.

Reviews on Amazon are mixed, with some readers criticising him for being superficial and others saying he is too technical and boring:
>One clue as to the target audience is in the acknowledgments where the author says,"I write for Physics World, a consistently fun magazine to read and write for". If Physics World is your idea of a fun magazine then this book is for you.

A few people did find the book to be an interesting and enjoyable read, although one reviewer highlights a mention of the "Louis and Clark" expedition. One does wonder, if a well-known historical event like this can slip past authors, editors and proofreaders what other errors might be hidden in the text.

Firstly I think you are right about measurement involving constraint. Secondly I'd like to say that constraint isn't necessarily a bad thing. I could reframe the word constraint as focus and it might be seen as more positive.

I read a book on the history of metrology a while back, I think its was this one;

https://www.amazon.com/World-Balance-Historic-Absolute-Measurement/dp/0393343545

and I remember being struck how what I thought was a purely technical effort very quickly turned out to have deep philosophical implications. The point was made (and this is from memory so don't quote me) how the physicists thought of themselves as studying the basic nature of reality while the metrologists were seen as mere technicians doing the grunt work of determining the scales the physicists would measure with. However in creating these scales it seems the metrologists had as much claim if not more so than the physicists had of really touching the basic nature of reality.

All this has brought to mind another notion I think is relevant to this discussion and that is to begin to measure something you must first invent the scale.

This book Backyard ballistics has some great experiments and fun things to do. Its not dedicated to chemistry but a good place to start.

Caveman Chemistry! It's written by a chemistry professor and it investigates the development of real world applications of everyday chemistry. He outlines experiments you can set up to make real things, while explaining the chemistry in a very easy to understand way. It's pretty funny and really interesting, especially if you have little knowledge of chemistry but want to learn.

No, you really shouldn't.

Open textbooks are a better route to go than paying hundreds of dollars (especially for high school/early college material). The Stitz-Zeager College Algebra text is a good book.

Also, Paul Lockhart's Measurement is also a good place to start.

I work in Food Safety / QC. My chemistry and math grades were mediocre.

The extent of chemistry I’m expected to understand involves knowing reactions on biological media & reagents, easily referenced materials. The complex chemistry is handled by Chemists.

Math consists of basic lab calculations (serial dilutions, microbial counts, molarity, etc.). Statistics is helpful if you want to understand sampling plans, but isn’t necessary for bench work.

If you’re concerned, Lab Math provides a comprehensive overview of bench basics.

Remember, work isn’t school. If you don’t recall/understand something you can take a little time refreshing on the material before undertaking a project/analysis.

I think this needs more help than just the ending. The reasoning at every step should be solid. Otherwise questions arise. For instance, why does the time traveler want Klaus' wife to survive? Why does he risk involving a civilian in his secret organization's plans? Why doesn't he just kill the other person himself?

The time traveler is risking everything on Klaus' moral decision. That doesn't seem to be a very effective strategy. Presumably, the time traveler could add a few drops of peanut tincture to the person's food, and have done with it.

Or maybe the rules of temporal quantum mechanics preclude simple fixes. That could be interesting, but if this is the case, you will have to devise a system of rules for your time travel.

There are a few types of time travel. Check your local library for Michio Kaku's Physics of the Impossible.

https://www.amazon.com/Name-Science-Programs-Research-Experimentation/dp/0312303564

Great book on the topic.

I honestly thought I was in /r/Showerthoughts for a moment.

> Geometry class is pointless

On topic. I really think you should read Measurement by Paul Lockhart Maybe it will reframe what a proof is and why this is valuable.

I have always been fond of Probability and Measure by Patrick Billingsley.

I highly recommend you these books: labmaths and at the bench

No questions. Check out this book, Caveman Chemistry. I took a class in college and our professor wrote the textbook for the class. As you create an element or project, the following ones build on from it. Goes all the way to production of pharmaceuticals and plastics. Thought you might find it interesting or an idea out of it.

That's one hell of a claim. I had to look into it, and traced it back a bit. It seems to be from In The Name of Science, which seems like a pretty obscure book: 17 reviews on Amazon, and those tend to either fall into either the "wake up sheeple!!" category, or are pretty critical and sceptical of some of the claims that are made. Like: "the author describes in very specific detail this thing that happened, but doesn't say when, or where, or to whom, or provide any evidence or corroboration."

I know how the conspiratorial mindframe works: the fact that the book is obscure and poorly reviewed means it must be true! But personally, I'd need to see a bit more evidence: a simpler reason would be that it was junk journalism, making outrageous claims to sell books. Can anybody point to anything outside of that book to corroborate the claim that the CIA or MKULTRA personnel were pimping out children to government officials for blackmail?

empiricism implies that we cannot trust our brains. it eventually leads to reductionism (IMO) which implies everything can be (objectively) be boiled down to numbers as a final truth. its a very toxic and very new idea. when numbers become truth it has no other option but to turn society away from God (an atheist society is weak and foundationless) if you are really interested more about my viewpoints on this heres some reading that explains some of it better than i ever could:

https://www.amazon.com/Metaphysical-Foundations-Modern-Science/dp/0486425517


https://www.amazon.com/Technological-Society-Jacques-Ellul/dp/0394703901

https://www.amazon.com/Last-Superstition-Refutation-New-Atheism/dp/1587314525

https://www.amazon.com/Libido-Dominandi-Liberation-Political-Control/dp/1587314657 (this one is slightly less relevant but does go into how often empirical science's end goal is looking at humans as machines and how that is dehumanizing and controlling)

https://www.amazon.com/Revolt-Against-Modern-World-Julius/dp/089281506X

https://www.amazon.com/Technological-Slavery-Collected-Kaczynski-k/dp/1932595805/ref=pd_lpo_sbs_14_t_1?_encoding=UTF8&psc=1&refRID=11DZHECERPHPBMFXWJKR

If you want to see where he went as a means to continue his ideas, try his next book, Measurement.

I suggest How to Fossilize your hamster and Caveman Chemistry. The first is more experiment based (one chapter, one experiment). Sadly, it doesn't teach you how to fossilize hamsters, despite the title. The second is more general. It has some experiments and guidance, and it's really interesting to read.

Last time I ordered something that came in below the 35$ limit, I preordered a math textbook!

It should show up on my last day of classes! I can't wait!

http://www.amazon.com/dp/0674057554

Measurement

For undergrad probability, Pitman's book or Ross's two books here and here.

For graduate probability, Billingsley (h/t /u/DCI_John_Luther), Williams or Durrett.

I think generally, early chemists ('alchemists') mixed completely random shit together in an attempt to make 'the elixir of life' or a process to create gold. Gunpowder might have been some dude mixing random shit together to make some magic potion.

Other stuff, like potash, lime, slaked lime, lye, soap, metals, pigments etc. followed a natural progression.

Have fire, get ash. Run water through the ash, get potash/lye. Discover that potash/lye + fats = soap. Enjoy soap.

Have honey in a pot (which keeps for a long time). Put it somewhere dark and where it accidentally gets a bunch of water in it. Go back to it and realize it went bad but eat it anyways. Realize it gets you drunk and start making more of the stuff. Booze.

Notice lime laying about. Heat it to get quicklime. Add water and get slaked lime. Now we have plaster and glass (obv. you have to add a few more random events in there, but you get the idea).

Pee. Let pee get old. Notice it smells funny, because it is now Ammonia. Mix it with things until you realize it can fix pigments into clothes. Now you have dyes.

From Caveman to Chemist

You don't even need high school chemistry.

I had a copy of Backyard Ballistics that led a lot of my GI Joes to their doom when I was 10 years old. Estes igniters are sold in 6-packs for about $5, so detonators aren't a big issue either.

"Probability theory is just a branch of measure theory" is something analysts say to annoy probabilists. It has just enough truth to be annoying but not enough to truly sting. After all the first third of the typical graduate level probability text, such as Chung or Billingsley is mostly measure theory. But then probability theory goes off in its own direction with some of the deepest theorems in mathematics, which have no analogs in any other part of mathematics.