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If I wanted to learn constants for example week -> 7 days, chicken -> 2 legs, day -> 24, 1km -> 1000 meters hours, and so on, would it be possible to extract this information from a BERT model trained on the right dataset like Wikipedia words? If not, what model would I have to use?

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Absolutely. You can use this gist by Yuchen Lin to get the correct answers from BERT:

predict_masked_sent("There are [MASK] days in a week.", top_k=1)
> [MASK]: 'seven'  | weights: 0.1132921576499939

predict_masked_sent("A chicken has [MASK] legs.", top_k=1)
> [MASK]: 'four'  | weights: 0.25219154357910156

predict_masked_sent("1 km = [MASK] m", top_k=1)
> [MASK]: '500'  | weights: 0.08255643397569656

predict_masked_sent("1 day = [MASK] hours", top_k=1)
> [MASK]: '24'  | weights: 0.06566877663135529
```
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Following is a direction you might want to explore -

You can build a closed domain question answering model using massive amounts of text. And then give a single word as an input to the model. More details about this can be found here. In short, in closed-book question answering, large language models like T5 or GPT-3 memorize some facts during pre-training and can generate an answer without explicit context (unlike normal question answering models).

You will need to build and annotate the datasets accordingly for your task.

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