Math, like language was created by man. There have always been things that could be counted and sorted, but we have not always counted and sorted them. There are cultures like the Piraha that have concepts like one and many, but no system of counting a group of things. Systems of counting and math began as a way to keep track of stuff, particularly stuff that belonged to the ruler of a culture large enough to have a lot of stuff to organize. In a larger and more complex society it was practical and useful. These days we count and measure all the time. It seems as obvious to us to measure a half cup of water into our instant oatmeal as to someone younger to google something about which we want to know. When I open my copy of Cook's Illustrated and my metal teaspoon and quarter teaspoon it is easy to forget that it was something like 120 years ago that Fannie Farmer published a system for more accurate measurements, leaving behind things like 'an egg sized lump of butter'.
I think it is really interesting to look at how we use tests and measurements not just about our stuff, but about ourselves: our bodies, our health, our intellectual and physical progress toward certain goals. At your annual physical you will likely have blood work, weight and height, and often questionnaires on lifestyle and safety. At school there are entrance tests, progress tests, and regional (in New England we have the NECAP) or national tests (like the SAT). There are IQ tests and tests to measure emotional satisfaction or stress levels or depression. If you have ever joined a gym odds are you have you have filled out a sheet asking about your health history, and possibly your exercise history as well. You might also have had someone test you on the number of push ups you can do, or use a set of calipers to measure percentage of body fat. And anyone who has watched their weight is at least familiar with tools to measure calorie and nutritional intake.
The benefits of these sorts of tests and tools for data collection are many. They can help discover underlying weaknesses or other problems. For example if your doctor gives you a blood test and measures total cholesterol above 240 they are going to have a conversation with you as this is a risk factor for heart disease. And if you are a fifth grader who measures at a second grade reading level on a standardized test your teachers are (hopefully) going to be recommending you for extra help to bring this score up.
Data collection goes on through our lives, and by having what is called 'baseline' data, or how things were at the beginning (of a program, of our lives, or of a specific chunk of time) we can keep track of trends and see where there is progress or loss.If you can do 10 push ups and every 4 months you add another 5 that is a good trend, whereas if you do less every month that is not.
The types of tests we do, or data we collect is predicated on what we have done before. You wouldn't do that push up test until you did a health history (you really do not want to do a sit up test with someone with a history of osteoporosis), and then did some postural assessment to make sure the spine and hips are working as they should. Before a teacher gives a test on Shakespearean vocabulary they would want to know the person's reading level.
Baseline tests and measures and data collection can help create strategies for change based on how things are, what needs to be addressed, and what needs to be modified. We might have a general idea that we need to loose some weight, or want to add some shoulder muscle to complete our daily activities more efficiently, or that there is a family history of borderline hyperlipidemia. These pieces of information can help us set goals that are more specific: not “I want to loose some weight”, but “I see I am about 30 pounds into the obese range, and would like to loose that 30 pounds”. They can help us see patterns: “Gee, my blood pressure is really high since the year started, and this test indicates high stress level, and my workout log shows I have not been at the gym in 4 months.” Testing and data collection is like putting lights and sign posts on the path... They can make it much easier to follow.
Quantified information can help motivate us to change, as well as set strategies to do so, “Gosh, the pretest shows I am weak on polynomials, I had better spend some extra time studying that.”
More broadly they foster self understanding. In The Yoga Sutras Patanjali talks about svadhyaya, or self study as one of the niyamas or ethical/philosophical/spiritual underpinnings of yoga. This study can be done in an unstructured or intuitive way, but because the tool of understanding is malleable based on its own understanding when it studies itself such rational data points can help to hone the course of that intuition. It is like practicing trikonasana against a wall.... it lets us compare how we feel we are standing with how we are actually standing.
This does not mean that it is good to do as many tests as there are available. That is like taking every vitamin you hear might be good for you in the highest possible dose. You can spend so much time writing things down and taking tests that you don't get to live. You can also spend time and money taking tests that have no value to your health or individual interests and goals. I personally do not feel the need at this point in my life to spend time taking the Taylor Manifest Anxiety Scale. Like everyone else I have things that I worry about, but they tend to be transient and do not cause me to be unable to focus on or do pretty much anything. Blood work might be a good idea though, it has been a while since I have had that done. It really is a question of time management and appropriate selection. Remember that path we are lighting? We don't want to trip, or take a wrong turn, but we do want to end up standing in the same place dithering.
What are some specific tests or tools to capture data I would recommend? I think it is highly variable. It will depend on the person's health status, age, weight, goals, emotional state, intellectual interests, personality type, and so on. It is also important to stress that not all useful information is quantifiable or countable, or might be countable, but does not need to be counted to be helpful. To help understand one's interests and goals better simple journaling is a great data tool. It is not going to give you a mathematically precise answer, but will provide much insight into your interests, goals, concerns, weaknesses, etc. Knowing those things can help you decide what things you either want to watch to make sure they do not become a problem (like a yearly weigh in), or want to set goals for as a way to track and organize progress (like measuring hamstring flexibility with the sit and reach test).
Generally speaking a yearly trip to the doctor for a health screen is a good starting point. Resting heart rate, blood pressure, some simple blood screens, weight, height, and so on can help almost any one by providing basic health information and a history to track changes for the better or worse. It also allows the physician to make a judgement on whether other medical tests are useful, such as tests for bone density, or tests for cardiovascular fitness.
Can you administer basic fitness tests for yourself? Sometimes yes. However the results will never be as accurate as when they are administered by an experienced trainer. Moreover, with some tests there are health risks if done in the wrong way, or if done by someone with certain kinds of underlying health issues. That is one reason why a trainer will generally have a student fill out something like the 'PAR-Q' health history before testing or training someone. Plus a well trained trainer can help figure out which tests are likely to help you reach your goals best. There are dozens of possible tests, sometimes measuring slightly different things, and sometimes using different tools. For example, to test cardiovascular fitness there are protocols for the treadmill, the stationary bike, the step, walking, etc.... and some are ok to do in a gym, some are best done in a hospital setting. It all depends. And of course there are tons of fitness tests you can do. You can test your flexibility at various joints, strength, endurance, cardiovascular ability (one of the differences between a medical test and a fitness one is that the trainer will generally use a test designed to measure what they call 'submaximal' and the doctor will be equiped to measure 'maximal' effort. The submaximal tests are pretty accurate, and unless there is a medical reason to do so the trainer will not usually refer you to do a maximal test. They are both designed to see how hard your heart can work to provide oxygen to the working muscles. There are tests that can be done on bikes, treadmills, steps, even walking. The Rockport walking test is a really easy one to take). You can also test sport specific skills, like speed, power, or agility. What you choose to do should relate to what your goals are, and whether there are some limitations you perceive in your everyday activities. If you are having trouble with a stiff low back, or can't reach down easily to tie your shoes you might want to do flexibility testing and create a stretching program to increase the flexibility in the areas where your flexibility is significantly less than normal. If you are having trouble picking up your child or your backpack you might want strength or endurance testing.
By the same token though there are inventories to measure stress, overload, personality, anxiety, if there are interpersonal, or emotional weaknesses or areas you would like to improve on it is absolutely helpful to work with a well trained professional therapist. There may be things for which you would go to a psychiatrist, or a therapist, just as there may be things you go to a general practitioner before starting a fitness regimen. The same is true with nutrition. It is straightforward enough to do a 3 day diet log, and to get a general idea ('gee, do I really eat that much bread?), and just journaling for yourself may give you enough information. But you may find working with a trained certified nutritionist can give you more accurate data. How accurate you want/need will depend on goals, needs and interests.
To take time to collect data or not? To write down or not? Well, we are back with Aristotle. Some is helpful. Too much can be a burden rather than a help. So we try to choose our data collection intelligently. The golden mean is our yellow brick path lit with self exploration and understanding, on which we are accompanied by and pointed forward as needed by trained professionals.