Mathematic Mass -- Maximum Results in Minimum Time

Mathematic Mass
by Joe Mullen
Fitness Scientist


This is a just slightly different that it was when my article by the same name appeared in Iron Man magazine many years ago.
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"For whatever deserves to exist deserves also to be known, for knowledge is the image of existence; and things mean and splendid exist alike."

Francis Bacon
(1561- 1626) English essayist, philosopher.

First, let us establish a premise to discuss. Do you agree with the following? In order to stimulate maximum muscle growth or superior strength, a basic prerequisite is producing high levels of muscular contractions. If you agree, continue to read this article and learn a very simple method of quantifying your workouts as either productive or non-productive.

In 1970, I first wrote of how to use the mathematical relationships of proper exercise, to produce maximum results in minimum time. We used the standard Work formula, and transposed it for use in the exercise, bodybuilding, and strength training fields.

The Standard “Work” Formula

The standard “Work” formula is stated: W=Fxd. Meaning, Work equals Force, Multiplied by Distance.

I reworded it to mean, Progress is equal to the Weight (of the object, barbell, high tech machine, etc.) Multiplied by Repetitions performed. Technically, we could measure the “distance” of each movement; however, I feel it is valid to say, “A repetition.”

We re-word the formula and state it as, “Units of Muscular Contraction, or Life Force Index,” depending on the professional with whom we discuss the concept. The Units of Muscular Contraction formula is a most significant insight on the road to assure progress. Everyone interested in building muscle mass or producing greater strength in a time efficient way, will find it extremely beneficial.

To be sure, introducing new concepts into an exercise program is always a battle between previous knowledge, handed down generation to generation without examination, coupled with the common fear among bodybuilder’s that the new suggestion will not work.

Your intellect pulls in two directions at the same time. Our recommendation is to try new ideas. If they do not work out, you will know it soon enough and you can always return to previous patterns of training. However, we believe that there can be no progress without a break with tradition. In this case, I have used this approach for all personal workouts and all workouts of all my personal training client’s for 30 years. It is a major method of proving you are actually progressing and not just satisfying your ego by throwing more weight around.

Units of Muscular Contraction are a mathematical application of long established exercise definitions that include three components: (1) A set (or more) of an exercise; (2) The amount of resistance used; and (3) The total repetitions executed. We are not taking into account the speed-of-movement. We assume a properly supervised program monitors speed-of-movement as a constant.

Technically, speed-of-movement – the time it takes to move from point A to point B -- calculates to measure “Power.” Power is not one of the factors we are interested in for this discussion. More about Power in a future article. Rapid speed-of-movement creates Impact Force within the neuromuscular system and has no definitive value.

The Units of Muscular Contraction states: Units of Muscular Contraction equals, the amount of resistance used, multiplied by the repetitions achieved. Said another way, your improvement will equal the resistance you use, multiplied by the repetitions you perform within a given set of an exercise. Naturally, I am not talking to those who use steroids or human growth hormone. Those folks will improve with little or no scientific exercise. Of course, they may face serious side effects; however, that is their choice.

Let us dissect a typical exercise and analyze what the average trainee believes is a symbol of progress. Characteristically, they increase resistance in a workout in a random manner, believing that the larger the weight increase, workout to workout, the greater the results. This is not necessarily true!

I will use only one exercise as the example, but the concept applies to all exercises, all sets, and all repetitions: therefore the total workout. Assume we are analyzing an exercise done during a Monday workout: The exercise is leg extensions, and 90 lbs. of resistance is used, and say, 10 repetitions are performed (in proper style) before muscular fatigue is reached.

Those two numbers produce a Units of Muscular Contraction factor of 900 units of work. This is established by multiplying 90 by 10. Now, let us move into the workout performed on a following day. You decided to increase the resistance by ten pounds. This decision is arbitrary, not based on valid research, but on a whim, or a guess.

Remember during your previous workout, 10 repetitions were completed using 90 lbs. of resistance. If you could do 10 repetitions with 90, it will not be possible to perform 10 repetitions with 100 pounds. Say, eight repetitions are completed and, it is not possible to perform one more rep in proper style. Eight reps multiplied by 100 lbs. equals, a Units of Muscular Contraction factor of 800 units.

Is the number 800 larger or smaller than the previous 900? Obviously, if one performs 900 units of work on one day and performs 800 units of work on another day, one accomplishes less work. Therefore, we submit the workout is virtually wasted. In the sense that it is not an improved performance and you did not contract more muscle fibers.

Possibly, you might have performed eight reps with l00 during the previous workout, if you decided to try. In effect, your baseline data, the factor from your previous workout, must be improved upon; otherwise nothing of value took place. Usually, this cycle continues with constant weight increases; while at the same time, the repetitions decrease in proportion to the weight increase.

Because we have been brain-washed into thinking that “more weight” guarantees results and because the weight feels heavier – therefore it must be beneficial – we continue the illusion.

How anyone who possesses a rational mind, claim improvements cans took place? It is much like standing in the middle of a room having a goal of reaching the far wall yet proceeding to run in one place. Something does take place. Something is going on but nothing fruitful is taking place, in relationship to your goals.

For improvements to take place, we must strive to improve the units of work (Units of Improvement). It is really quite simple. The measurements can be completed every workout. There is only one wise way of accomplishing this goal. Increase resistance in minimal amounts. This allows you to at least match, or exceed, the previous Units of Muscle Contraction factor.

If in the example we use, say the trainee increases the resistance by 2 1\2 pounds (or less), instead of the 10 lbs. here's what would happen.

Because the increased resistance is minimal, it feels to your mind, as it is almost non-existent weight increase. The mind will accept the new amount without forming any negative thought pattern. Psychologically, a green light is given to perform at a high level.

To the muscles, the increased load will feel like a feather. No negative feelings surface about the weight being too heavy. Another signal is sent to the body that everything is a go. Physiologically and psychologically, everything is giving a green light.
We successfully bridged the gap between mind and body, and eliminated any negative feelings to influence the workout in any negative way. You will not feel like "it's too much" either in the psychological sense, or the physiological sense.

It almost all cases, in almost each exercise, during each visit, improvements take place, which are mathematically correct.

Most importantly, improvements take place workout to workout. As you know, the major problem of increasing the resistance without any guideline is, it will take several workouts or several weeks to match or exceed a previous workload. Time, effort, and energy are wasted.

To prove this to you take a mathematical look at a workout card. You will find many numbers that when rated as we have suggested will amount to wasted workouts. Get the picture? The secret to rapid strength improvements, added muscular size, muscular endurance and cardio-respiratory fitness, and fat loss, lies in applying mathematics to ones' workouts.

Depending on the mass of muscle involved and the origin, insertion and cross-sectional diameter, some muscles can handle slightly larger increases than others can. How much? That depends on factors such as just mentioned plus, neuromuscular innovation, and your present strength level. The stronger you are, the harder it is to get stronger, and resistance increases will come in smaller increments.

Other dependent factors are mental and emotional strength, the ability to keep on keeping on and willingness to follow advice.
If you increases resistance in what seem to be inconsequential amounts, progress will continue in a steady, upward direction. When you use too much resistance, progress WILL plateau and no results will be forthcoming for long periods.

Have you had this experience! Now, if you choose to, you can alter your past.


Joe Mullen
Fitness Scientist
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Sorry Joe, but it seems there is a leap of faith that violates logic in this piece: The weight x reps formula of 90x 10 = 900 units of muscle contraction is ok, but a few lines later you say that this equates to the number of muscle fibers worked ("only 600 muscle fibers..."). That claim needs to be supported as it is not self-evident.

If it really worked that way, then long-term pumping of a very light weight, say 10 pounds, as the spandex-clad aerobics crowd does at the health club, would be as effective as 10 reps of a heavy weight.

But if it takes all my effort to do those six reps with a heavier weight than I could do the 10 with, am I not recruiting as many muscle fibers, possibly at higher intensity? That has been my experience. I am getting better results with 5-6 reps and increasing weight quickly than I was with 8-10 reps and plateauing. I believe that Dave Hudlow in Dr. Darden's experiment in NHIT found that 5 reps SSTF was his ideal routine.

And then there is the time under load factor, as Turpin has shown.

Hello, FiremanBob --

Thanks for responding to the article.

I used the words "muscle fibers" only to illustrate a point. I have no idea how many fiber contract. So, if I'm reading what you mean, I want to rephrase it just to see if I'm on the right track of what you said. Of course, nothing I say is a put down of what you said.

I did mention that 90 X 10 equals 900 units of muscle contraction.

A few lines later, I did mention that "only 600 muscle fibers ....." If I'm reading my own writing correctly, I was talking about increasing the weight by 10 lbs. to 100 lbs. but only bing able to do 6 reps with it (meaning he person reached muscle failure).

So, 100 X 6 equals 600 units of something. I was using the words muscle contraction as a simple example as to what happens during a positive Typically, depending on what I'm talking about, I sometimes, if I'm talking about a negative movement, I use the word "uncontraction" just to keep things simple.

Of course if a person if using a standard workout resistance, the contraction is more effort than the negative movement, since we are much stronger in the negative movement. Typically authors say we are 40% stronger during the negative movement.
Actually, from my point of reference, we are much stronger than 40%, if we are doing a negative movement using multi-joint movements. I think the 40% applies only to single joint movements.

In effect time under load is only effectively true during the positive movement, because depending on how slow you do the negative movement, during a curl (as example) you can do more reps it could prove to be a rest-period for the muscles about to be under the contraction stage.

Although the time under load would be higher, depending on how slow the negative movements were. That can be proven quite simply. If you pick any exercise and have a person go to muscle failure with that resistance using a 2 up and 4 down contraction, they will perform, say 10 reps (make believe).

Pick a rest time and let them rest until you feel he or she, is fully rested. Then have them take the same weight they just used for the curl, but reverse the speed-of-movement.

Have them do a 4 second positive movement, and a 2 second negative movement. My bet is the amount of reps they achieve will be less that the reps they did previously. That proves, at least to me, that doing a slow negative movement during standard training is a rest period. Because it is more important to lift the resistance slower and lower the resistance faster during the standard workout.Because the negative weight is at least 40% too light. Would anyone ever do a set of curls
with a resistance that is 40% below their ability and claim its beneficial?

The rep numbers I used were just to have number as an example. I assumed that HIT folks would know that I am talking to complete muscular failure.

Regarding the number of reps a person benefits from . . . . It will related to the muscle fiber typing of that person and their mental rep number they use. As you know, some muscle fibers are, to use a typical reference point, fast twitch, others are slow twitch, and others are mixed twitch. So, depending on the muscle fiber typing, folks will emotionally like different rep numbers and load up the resistance related to their likes or dislikes.

As I mentioned above, time under load is debatable as a measuring rod. And it is only a test of the muscle endurace of the muscle fibers that are contracting, it does not have meaning for the negative portions of the movement. So, a real time under load would test only the positive movements or the negative movements. At least it seems that way to me.

Again, I appreciate you responding to my articles.

Best Wishes,

Joe Mullen

Joe,

My experience with slow negatives is the opposite. When I resist the downward motion, especially on that last rep when I'm doing all I can to hold the weight up, my rep count goes down but my progress on the next workout improves.

It seems that much of the confusion in strength training research involves the correct measure of intensity, and what kind of intensity stimulates increases muscle strength and size. It also seems, from the large number of conflicting studies, as though this is by no means "settled science".

All I really know about it is what works for me: heavy weight, reps 8 or fewer, slow negatives, all-out effort on every set, every four days.