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底層邏輯2：帶你升級思考，挖掘數字裡蘊含的商業寶藏: 2 555 2012
作者: 劉潤
看似複雜的商業模式，用幾個簡單的數字便可輕鬆破解！
假如閱讀完《底層邏輯》，你掌握了是非對錯、思考問題、個體進化、理解他人和社會協作五方面的底層邏輯。
那麼現在《底層邏輯2》，將用簡單的數字和思維，讓你看清世界的規則，看透商業的本質，破解商業難題，收穫屬於你的成功！
張旭無限教室線上課程平台創辦人 數學老師張旭（張舜為）――審定
資深企業講師、職場作家、廣播主持人 謝文憲――專文推薦
期待大家都能在被妖魔化的數學裡，找到數學可愛的一面，它會讓你賺大錢，並且實現商業的最高價值：服務人群。――謝文憲
數字不但非常有趣，而且很有用！
如果你覺得數字枯燥、毫無用處，那你就錯過了一門連接現象與本質的語言，錯過了理解商業世界最底層邏輯的終極方法。
持續成功的底層邏輯，只須用一個數學公式即能破解：
提高整體成功率的方法：一是提高基礎成功率，二是增加嘗試次數。
而什麼是「商業世界的加減乘除」？
商業世界的生命體是企業，企業也需要謀求個體的生存繁衍（競爭），以及群體的共生繁榮（合作）。
有時候企業選擇競爭，有時候企業選擇合作，但目的都是永續經營。
合作與競爭可能在同一個維度上，也可能在不同的維度上。
只要理解競爭合作、同維異維，你就能理解什麼是「商業世界的加減乘除」。
本書重點
四則運算：基於數字的加減乘除在商業世界具有獨特價值，掌握這個工具，你就能從數字中開採出「礦藏」。
笛卡兒坐標系：養成「五維思考」的習慣，你就能升維思考、降維執行，從而更好地理解商業世界，在創業道路上所向披靡。
指數和冪：指數和冪以及它們背後的數學規律，幾乎決定了你在商業世界裡能獲得多大的成功。
變異數與標準差：掌握住衡量差異性的重要工具，就能在經營企業、管理團隊、製造產品時正確評估該縮小或擴大，確保企業的良性運轉。
機率與統計：這個世界從來都是不確定的，創業就是管理機率。
博弈論：你在決策時，別人也在決策。這些決策相互影響，甚至相互交織，從而使那些奇妙的決策顯得很愚蠢，使那些莫名其妙的決策產生奇效。
作者
劉潤
南京大學理學學士（數學）、復旦大學工商管理碩士。潤米諮詢創始人，中國著名商業顧問，「5分鐘商學院」主理人，微信公眾號「劉潤」主理人，微軟（中國）有限公司前戰略合作總監，曾任百度、海爾、中遠國際、五源資本、康寶萊等，現任騰訊、恒基、尚景家居、雲漢芯城等多家知名企業的戰略顧問。主理暢銷音頻課程「5分鐘商學院」「商業洞察力」「商業簡史」等，著有暢銷書籍《底層邏輯》《進化的力量》《5分鐘商學院》《商業洞察力》《給孩子的商業啟蒙》《商業簡史》《新零售》《每個人的商學院》《趨勢紅利》《互聯網 ：小米案例版》《傳統企業，互聯網在踢門》《人生，就是一場突如其來的旅行》《2012，買張船票去南極》。
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4.2 ★★★★★
Based on 27 reviews
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Product Reviews
★★★★★ 5
SO MANY BALLS!
I thought id see how my Boston wud react with so many balls to choose from LOL! I love that the squeaker is internal on this toy. On the ones that hv the plug style squeaker my Boston will pull it out then proceeds to pull off the material and a slimy ball is no fun...LOL
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Reviewed in the United States on March 3, 2026
★★★★★ 5
Durable
Size: 10 Pacck, Color: Multicolor
Nice product. These balls have lasted without breaking in half!
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Reviewed in the United States on February 12, 2026
★★★★★ 5
good for puppys young dogs, handle is separate, locking carabiners on both ends
Color: Orange, Size: 30FT
This is a good sturdy leash but probably wouldn't stand up to a conscientious chewer if your dogo has that bad habit. I like this one because the handle is separate so it can be used both as a tie out lead and as a regular lead. I also like the "locking" carabiners that should not open accidentally. I bought the thirty foot version because my new puppy loves to go outside then refuse to come back in or let me catch him when I need him to come inside (not catching me silly Hooman). When he's bigger I won't be so concerned about him being outside alone but since I'm in a sort of rural area, we have the occasional fox and hawk around when the sun goes down. Not too much to worry about in the way of pests but every puppy parent has an obligation to protect their young'un till they gain some wisdom. I have stairs in the back of the house, the way this is made I can attach it to the banister easily so I don't even need one of those tie stakes that bury in the ground. The price wasn't bad, the hardware looks sturdy and should last awhile. I just also bought the fifteen foot version, same quality as the thirty foot product I like that the handle is separate so it can be used as a tie down or a leash easily. My only big wish would perhaps be some more color choices, the orange is nice for visibility a yellow would be nice and then maybe some other colors like red/purple would be good as well. The thickness of the rope means that it doesn't "easily" get tangled into a giant knot. I leave the back door open and puppers can go in and out as he likes but he also sometimes runs around in the living room and thus far haven't had any large tangles to unwrap. He did manage to get the leash caught around a piece of tree branch that was on the ground (and complained loudly) but that was only because the branch was too heavy for him to drag the lead off of by himself. These leads are worth the money, I will likely buy a couple more to keep in the vehicle and other locations besides home.
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Reviewed in the United States on April 29, 2026
★★★★★ 5
My Go-To Leash for Outdoor Fun and Training with My Lab Puppy
Color: Orange, Size: 15FT
The Joytale Long Leash, specifically the 15-foot model, is an exceptional product that has seamlessly integrated into the daily activities of our black lab puppy. Purchasing this leash has proven to be a decision that greatly benefits both our family and our energetic puppy, especially during our adventures in the backyard and while hiking.
The vibrant orange color of the leash stands out, which is not just visually appealing but also significantly enhances safety by ensuring the leash remains highly visible. This feature is particularly useful in varied terrains and during low-light conditions, providing peace of mind that our puppy is always within sight and safe.
The leash's design, featuring a removable padded handle, has been a game-changer for comfort. The padding ensures that our hands are protected from any strain or discomfort, even during those longer hikes or when our puppy gets a bit too excited and pulls. This thoughtful inclusion has made our outdoor adventures much more enjoyable, allowing us to focus on the fun and bonding with our puppy rather than any potential discomfort.
Equally impressive is the double hook mechanism that the Joytale Long Leash boasts. This feature has instilled a great sense of security in us, knowing that the leash is securely attached to our puppy’s collar or harness. It's especially reassuring during hikes in more challenging terrains where a secure leash attachment is crucial for our puppy's safety.
The 15-foot length of the leash has been perfect for our needs. It provides ample space for our black lab puppy to explore and play, whether we're in the backyard or adventuring through hiking trails. This length strikes a perfect balance, offering enough freedom for him to explore while still under our control, facilitating a safe and enjoyable environment for him to learn and grow.
Durability is another aspect where the Joytale Long Leash shines. It has stood up to the rigorous daily activities of our puppy, showing no signs of wear and tear. This durability is not only a testament to the quality of the materials used but also to the thoughtful design that has gone into making this leash a reliable accessory for pet owners.
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Reviewed in the United States on April 7, 2024
★★★★★ 5
Great long leash, would buy again
Color: Blue, Size: 30FT
Well-made leash, perfect for recall training and other situations where the dog needs a bit of space to roam without getting into trouble. Seems to be comfortable for the dog, as it is not inhibiting him from running around and playing.
I bought the 30 foot length 3/8” diameter version. Light weight, good value for the price. Best feature is the locking carabiner, because my rescue pup “moonlights” as an escape artist. 🤣🤣
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Reviewed in the United States on January 22, 2026