Because the people in Seneca's life are off enjoying the games and boxing, Seneca has time to himself, uninterrupted. He then observes:
my thoughts may march safely on, – and that is all the more necessary for one who goes independently and follows out his own path. Do I then follow no predecessors? Yes, but I allow myself to discover something new, to alter, to reject. I am not a slave to them, although I give them my approval.
Said differently, he indeed follows predecessors, but he also reflects on what has been discussed and he feels the freedom to agree, reject or alter it. He simply asserts his independent thought. I admit I've suffered from a "going-along mindset" for much of my life. It feels that I spend most of my time reviewing what has been discussed, said or thought, and then I agree, reject or add a nuance. I don't think I'll ever come up with some novel philosophical idea. And even if I do, the chances are likely that it's simply a matter of having not yet discovered who has previously thought it!
He next ponders the amount of time and effort people spend on their bodies, but don't dedicate as much time and effort on the mind. The premise is that humans' unique nature is the rational. We share the physical with beasts, but they do not share the rational with us. Therefore, if we are to live according to our unique nature, we ought to spend our time in the rational area of our lives. Seneca writes:
How many men, I say to myself, train their bodies, and how few train their minds! What crowds flock to the games, – spurious as they are and arranged merely for pastime, – and what a solitude reigns where the good arts are taught! How feather-brained are the athletes whose muscles and shoulders we admire!
Epictetus notes in Enchiridion 41,
It is the mark of a crude disposition to spend most of one's time on bodily functions such as exercise, eating, drinking, defecating, and copulating. These are things to be done just incidentally. All your attention should be on your mind.
How many people are willing to train and torture the body for a few minutes of fame in the arena. Ought we not to spend more time training our minds to withstand the "blows of Fortune"?
if this can be done, how much more easily might the mind be toughened so that it could receive the blows of Fortune and not be conquered, so that it might struggle to its feet again after it has been laid low, after it has been trampled under foot? ... Yonder athletes must have copious food, copious drink, copious quantities of oil, and long training besides; but you can acquire virtue without equipment and without expense. All that goes to make you a good man lies within yourself.
All that is needed to make progress is to wish for freedom from Fortune. And the first areas to overcome are freedom from death, and poverty.
shall you not be eager to attain liberty at any price, seeing that you claim it as your birthright? ... freedom is possessed neither by those who have bought it, nor by those who have sold it. You must give this good to yourself, and seek it from yourself. ... First of all, free yourself from the fear of death, for death puts the yoke about our necks; then free yourself from the fear of poverty.
You may look on those who have much wealth and think them happy. But you do not know if they truly have freedom or not. Don't be so hasty to fall for the trap in thinking wealth brings happiness and freedom.
in every case their happiness is put on like the actor's mask. Tear it off, and you will scorn them. ... if you judge a man, do you judge him when he is wrapped in a disguise? ... If you wish to see what he amounts to, and to know his full worth, take off his diadem; much evil lurks beneath it. But why do I speak of others? If you wish to set a value on yourself, put away your money, your estates, your honours, and look into your own soul.
The only thing that is up to you, is your soul. You cannot accurately judge yourself by using the standard of health, wealth, status or fame. Your lucid judgement and discerning assessment of events, things, people and circumstances and how you react to these is what is up to you. This is never so simple, and can only be ascertained through much thought and objectivity - seeing things from the perspective of Nature. Do not let such worldly deceptions deceive you. Always look to wisdom to guide you.