Both assim and por isso seems to translate to thus, therefore, so. I wonder whether they are they completely interchangeable, or is there perhaps a subtle difference between them that I just haven’t grasped yet. Is anyone able to help me understand?
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@Tomas, sorry for keeping you waiting! When used in a conclusive sense (as thus/therefore/so), I would consider them interchangeable without any greater subtleties, apart from assim sounding more formal than por isso.
- O mundo mudou. Assim, temos de mudar também. = O mundo mudou. Por isso, temos de mudar também. (The world has changed. Thus, we need to change as well.)
In other uses, they’re not interchangeable. Some examples:
- Está frio, por isso é que tenho um casaco. (It’s cold, that’s why I have a jacket.)
- É assim que fazemos. (That’s how we do it.)
- Um projeto assim é muito ambicioso. (A project like that is very ambitious.)
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I read a previous discussion about assim and por isso, and am still confused, especially since the word então also seems to come up where I expect to hear “so.” Is there a way to distinguish which term I should choose in a given circumstance? A sentence I’m trying to develop now is “Preciso de fazer um ‘ponytail’, então/por isso/assim não demasiado curto.”
Olá, @mstsuzanne 
I moved your post to this topic since it’s in context.
Então and por isso can be considered interchangeable when used in the sense as so/thus/therefore. Assim also means the same in those cases, but sounds more formal, so it’s not our usual preference.
I’m missing some information/context to understand the sentence you used as an example - it sounds incomplete:
- Is the speaker saying something like “I need to wear a ponytail, so please don’t cut my hair too short”? If so, the sentence would sound natural with both então and por isso, which would be used conclusively. For example: Preciso de fazer um rabo de cavalo, então/por isso não corte demasiado curto.
- Is the speaker saying “I need to wear a ponytail that is not too short”, i.e. describing in more detail the style of the ponytail itself? If so, it wouldn’t be a conclusive use and neither por isso nor então would fit. You could eventually use assim in the sense of “like this/that” (explanatory, or comparative): Preciso de fazer um rabo de cavalo assim, não demasiado curto.
Thank you for your response. The sentence I’m working on reflects your first example – I want to be able to make a ponytail with my hair, therefore when it is cut it shouldn’t be too short (because then it would not hold in the elastic.) When I put together sentences like this, entāo and por isso are the terms my mind goes to, but learning about assim had confused me.
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