الفعل بطّل (شدة على الطاء ) و الأسم منه بطالة (بدون شدة على الطاء ) . ز unemployment مثال : بطَّلَ الرجل:، تعطّل عن العمل الفعل بَطُلَ (بدون شدة على الطاء ) و الأسم منه بُطُولَةً (بدون شدة على الطاء ) . ز heroism مثال: بَطُلَ الرجل : شَجُع واستبسل

البطل هو الشخص الذي يبيّن بين البطولة والبطالة To translate: A بطل is a person who distinguishes between بطولة (heroism) and بطالة (acts done in vain). Someone who manages to distinguish between such deeds exposes himself/herself to a lot of bad deeds from others, and as such s/he is a hero. This is a really dense read, but it's very informative nonetheless: http://bit.ly/2CEYg6J You can scroll down to where it says مقاييس اللغة. I hope this helps!

Well, first, as infinitives; joblessness means بطالة while heroism means بطولة Secondly, you're right they have the same root بطل (by letters only) but not by pronunciation. You know already that movements on individual letters mark how a letter is pronounced because there is no vowels in Arabic. So for بطالة joblessness the root (and the past tense verb) is بَطَلَ (ba ta la), while for بطولة heroism the root is بَطُلَ (ba to la). Think of it as "mode" and "mood" in English; only vowels change but the same consonants used. Thirdly, Why linguistics use these closely related roots for two words that are not related (apparently) to each other? Because - as mentioned earlier in the wonderful answers here - the meaning of the word "hero" in Arabic was intended to be derived from the meaning of the original word بَطَلَ (batala) which means to be lost, or gone before achieving what was intended, or stopped working. So a hero بطل (batal) is someone who knows that probably his work or fight will not achieve the intended outcome, yet, he continues doing it, and may be die for it, because of his principles or what he believes is the right thing to do and he knows that his blood - if killed - will not be revenged, and in Arabic it means بَطَلَ دمه (batala damohu), so they derived the root بَطُلَ (batola) from the original to describe this specific case of courage.

I totally edited my answer after seeing Abdullah link. Thanks to him. That link has many good sources. I read them all. As I understand باطل is something doesn't have any value, nor effect. Saying in English went in vain is like saying ذهب باطلاً in Arabic. In same time, باطل is the opposite word of rightness so this word always has negative meaning. In Arabic, ذهب دمه باطلاً means their is no weight for his death. In old days, دية definition was killer's tribe pays for the died person's tribe. If their isn't دية the died person's tribe will revenge by killing any member of the other tribe. Which might case a war. This was before Islam. Actually, today, in some place that still the norm with a stupid saying "الدم يغطي العيب". As I understand, بطل sacrifices has life without a toll. That's my conclusion.

If you really want to dig deep, I looked this up in Lisan Al-Arab. This is what I found (goto page 56 in the Lam chapter): http://ia800209.us.archive.org/28/items/waq10576/11_10586.pdf Here is a brief translation of what it has to say on the root ب ط ل: the root بطل means to for something to be gone or be lost, the thing is therefore باطل , and باطل is the opposite of truth, or something that's worthless, and أبطل is to commit باطل (that is, to lie), and البطلة means witches, and a man who is بطال is a man of باطل. And البطالة is being ignorant and wasteful. And البطل is a brave man (hero) a man who distinguishes between heroism البطولة and being wasteful البطالة، and it was said that he is called بطل because the tough men يبطلون (lose their worth) at encountering him, and it was said that it is he at whom the blood of relatives تيطل (become obsolete), that is you are unable to obtain blood vengeance from him, and to some it's a noun that has no verb.